Experimental classification of divertor detachment

Experimental classification of divertor detachment Von der Universit¨at Bayreuth zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung von Steffen Potzel aus Kulmbach 1. Gutachter: Prof. Dr. Michael Kaufmann 2. Gutachter: Prof. Dr. Arthur Peeters Tag der Einreichung: 15. Mai 2012 Tag des Kolloquiums: 10. Juli 2012 Abstract Avoiding damage of the divertor material by keeping the power load below a certain threshold is a major challenge for the operation of future fusion devices such as ITER. For Tungsten, the foreseen ITER divertor target material, the power load must be kept below 5 MW/m2in continuous operation. This can in ITER only be achieved with the plasma being detached or partially detached from the divertor. Divertor detachment is characterized by a strong reduction of the ion flux to the target. With a reduction of the temperature, achieved by increasing the main plasma density or by seeding additional impurities, volumetric processes such as charge exchange collisions and recombination become dominant. These processes lead to a strong reduction of the ion flux and plasma pressure in front of the divertor target. Although the single physical mechanisms leading to detachment seem to be understood, it was not yet possible to theoretically simulate detachment correctly with respect to experimental observations. This means that some understanding of this process is still missing. In the detached regime, the region of high electron density is retracted from the target and a knowledge of the electron density distribution in the divertor volume is necessary to understand the detachment process. In this context, a diagnostic determining the electron density in the divertor volume, based on the spectroscopic measurement of the Stark broadening of the Balmer lines, has been installed at ASDEX Upgrade. Initial problems with reflected stray-radiation have been solved and first measurements were successfully compared for consistency with other diagnostics. The detachment process was then investigated with an extensive set of density ramp discharges with different heating powers, fuelling species and magnetic field directions. The density measurements in the divertor volume were combined with all other available divertor diagnostics and a consistent picture of the detachment process was obtained. It was found that detachment is not a continuous evolution but undergoes three different states. During one of these states radiative fluctuations close to the X-point and high densities far away from the separatrix occur. This is a situation which is not described by present day theoretical models. Furthermore, it was shown that the conditions of both the inner and outer divertor are strongly coupled and that the inner divertor even influences the outer divertor. This effect was not shown yet, neither experimentally nor by theoretical simulations. It was further discovered how additional puffing of nitrogen into the divertor, which removes power via radiation, changes the detached divertor conditions and may even change the confined plasma conditions. The effect of an additional magnetic perturbation field on the detachment process has also been investigated. Finally, an unstable situation was found, during which the divertor plasma oscillates between two detachment states back and forth. I II Zusammenfassung Eine große Herausforderung f¨ur den Betrieb zuk¨unftiger Fusionsreaktoren wie ITER ist eine Besch¨adigung des Divertors zu verhindern. Dies kann nur gew¨ahrleistet werden, indem der Leistungsfluss auf das Wandmaterial auf einen tolerierbaren Wert reduziert wird. Im Falle des f¨ur ITER vorgesehenen Divertormaterials Wolfram betr¨agt der Grenzwert des Leistungsflusses bei kontinuierlichem Betrieb 5 MW/m2. In ITER kann dies nur erreicht werden wenn das Plasma von den Aufprallplatten des Divertors losgel¨ost, detached, ist. Divertor Detachment ist durch eine starke Reduktion des Ionenflusses auf die Divertorplatten charakterisiert. In dem, durch Erh¨ohung der Plasmadichte oder Zufuhr von Verunreinigungen, die Temperatur reduziert wird, gewinnen volumetrische Prozesse, wie Ladungsaustauschst¨oße oder Rekombination, an Bedeutung. Diese Prozesse f¨uhren vor der Divertorwand zu einer starken Reduktion des Ionenflusses und des Plasmadrucks. Obwohl die einzelnen physikalischen Mechanismen, die zu Divertor Detachment f¨uhren, verstanden zu sein scheinen, war es bis jetzt noch nicht m¨oglich, experimentell beobachtete Vorg¨ange des Detachments mit Hilfe theoretischer Simulationen zu reproduzieren. Das l¨asst darauf schließen, dass die physikalischen Vorg¨ange beim ¨ Ubergang zum Detachment noch immer nicht vollst¨andig verstanden sind. Die Region hoher Elektronendichte ist beim Detachment nicht mehr direkt vor der Divertorwand. Um den Vorgang des Detachments zu verstehen, ist die Kenntnis ¨uber die Verteilung der Elektronendichte im Divertor unabdingbar. Deshalb wurde an ASDEX Upgrade eine Diagnostik installiert, mit der man die Elektronendichte im Divertor mit Hilfe der spektroskopischen Messung der Stark Verbreiterung der Balmer Linien bestimmen kann. Anf¨angliche Probleme durch reflektierte Streustrahlung wurden behoben und die Konsistenz erster Messungen mit anderen Divertor Diagnostiken wurde erfolgreich best¨atigt. Der Vorgang des Detachments wurde dann mittels einer umfangreichen Serie von Entladungen mit Dichterampen untersucht, bei der die Heizleistung, die Ionen Spezies und die magnetische Feldrichtung variiert wurden. Die Dichtemessungen wurden dabei mit allen, zu Verf¨ugung stehenden, Divertor Diagnostiken kombiniert und ein konsistentes Bild des Detachment Vorgangs wurde gewonnen. Dabei konnte festgestellt werden, dass der Vorgang des Detachments nicht kontinuierlich verl¨auft, sondern in drei verschiedene Phasen unterteilt werden kann. W¨ahrend einer dieser Phasen treten nahe des X-Punktes hoch-frequente Fluktuationen der Strahlung und hohe Elektronendichten weit entfernt von der Separatrix auf. Diese Situation kann mit gegenw¨artigen theoretischen Modellen nicht erkl¨art werden. Es wurde außerdem gezeigt, dass die Bedingungen im inneren und ¨außeren Divertor stark gekoppelt sind. Dieser Effekt wurde bisher weder experimentell noch mittels theoretischer Simulationen gezeigt. III Weiterhin wurde gezeigt, wie die Zufuhr von Stickstoff, wodurch Leistung im Divertor abgestrahlt wird, die Eigenschaften des detachten Divertorplasmas und eventuell auch des eingeschlossenen Haupt-Plasmas ver¨andert. Ferner wurde der Einfluss eines zus¨atzlichen magnetischen St¨orfeldes auf den Vorgang des Detachments untersucht. Schließlich wurde eine instabile Situation entdeckt, w¨ahrend der das Divertor Plasma zwischen zwei Detachment Phasen oszilliert. IV Contents 1 Introduction 1 1.1 Nuclearfusion................................. 1 1.2 Magnetic confinement fusion - the tokamak . . . . . . . . . . . . . . . . . 2 1.3 Divertor configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Aimofthiswork ............................... 7 2 Divertor physics 9 2.1 Plasma-wall transition, the sheath ...................... 9 2.1.1 Particle outflux from the plasma to the surface . . . . . . . . . . . 9 2.1.2 Power deposited on the surface . . . . . . . . . . . . . . . . . . . 11 2.2 Divertor operating regimes . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.1 The low recycling regime . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.2 The high recycling regime - the Two-Point-Model . . . . . . . . . 15 2.2.3 The detached regime . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 Additional processes in the SOL . . . . . . . . . . . . . . . . . . . . . . . 20 2.3.1 Radial transport in the SOL . . . . . . . . . . . . . . . . . . . . . 21 2.3.2 Drift flows in the SOL . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4 Current understanding of detachment . . . . . . . . . . . . . . . . . . . . 26 3 Atomic processes 28 3.1 Atomic processes and equilibrium . . . . . . . . . . . . . . . . . . . . . . 28 3.2 The Collisional Radiative Model . . . . . . . . . . . . . . . . . . . . . . . 29 3.3 Electron temperature determination from line ratios . . . . . . . . . . . . 33 3.4 Spectroscopic determination of hydrogen flux densities . . . . . . . . . . 34 3.4.1 Ionizingplasma............................ 34 3.4.2 Recombining plasma . . . . . . . . . . . . . . . . . . . . . . . . . 35 4 Diagnostic 38 V CONTENTS 4.1 Theory of Stark broadening in a plasma . . . . . . . . . . . . . . . . . . 38 4.1.1 Validity of the collision damping and statistical theory . . . . . . 39 4.1.2 The unified theory . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1.3 Statistical theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.1.4 Model Microfield Method . . . . . . . . . . . . . . . . . . . . . . 44 4.2 Influence of other broadening mechanism . . . . . . . . . . . . . . . . . . 45 4.2.1 Zeeman splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.2.2 Doppler broadening . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.3 Diagnostic Setup and data evaluation . . . . . . . . . . . . . . . . . . . . 49 4.3.1 Diagnostic setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.3.2 Data evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.3.3 Reflection issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.4 Consistencycheck............................... 52 4.4.1 Comparison with Langmuir probes . . . . . . . . . . . . . . . . . 53 4.4.2 Comparison with pressure gauges . . . . . . . . . . . . . . . . . . 55 5 Experimental investigations on divertor detachment 57 5.1 Experiment and diagnostic Setup . . . . . . . . . . . . . . . . . . . . . . 57 5.1.1 Discharge setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1.2 Diagnostic setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.1.3 The degree of detachment . . . . . . . . . . . . . . . . . . . . . . 60 5.2 Evolution of divertor detachment - the three detachment states . . . . . . 62 5.2.1 The three detachment states in forward field . . . . . . . . . . . . 63 5.2.2 Detachment in hydrogen . . . . . . . . . . . . . . . . . . . . . . . 71 5.2.3 The three detachment states in reversed field . . . . . . . . . . . . 72 5.3 Additionaleffects............................... 78 5.3.1 Effect of impurity seeding during the fluctuating state . . . . . . . 78 5.3.2 Effect of magnetic perturbation coils . . . . . . . . . . . . . . . . 82 5.3.3 Divertor plasma oscillations . . . . . . . . . . . . . . . . . . . . . 85 6 Summary and discussion of the experimental results 89 6.1 Summary ................................... 89 6.2 Discussion................................... 92 7 Conclusions and outlook 97 Bibliography 100 VI Chapter 1 Introduction 1.1 Nuclear fusion The combination of two light atoms into a heavier one is called nuclear fusion. As the mass of the final atom is smaller than the sum of the masses of the two initial atoms, energy is released by this process according to Einsteins formula E=mc2. Nuclear fusion is the process which produces the energy in stars. Here, in a so-called protonproton chain reaction four protons fuse into one He nucleus. The net equation of this reaction is: 4p →4 2He + 2e++ 2νe+ 26.7 MeV (1.1) In addition to the helium nucleus, two positrons, two neutrinos νeand an energy of 26.7 MeV are produced. This reaction is limited by the weak force combination of p-p, for which rate coefficients are small (hσvi ≈ 10−45 m3s). This makes the fusion process very slow. Figure 1.1: Rate coefficients for various fusion reactions versus ion temperature. In order to realize a fusion power plant on earth, a different fusion reaction must be 1 1 Introduction outer divertor regions simultaneously. The density measurements in the divertor volume were compared to several other parameters, such as e.g. the ion flux to the target and the total radiation distribution in the divertor. With this, a consistent picture of divertor detachment in ASDEX Upgrade was obtained. This thesis is structured as follows. In chapter 2, an introduction to divertor physics is given. The atomic processes valid in a plasma, which for example determine the radiance of a spectral line, are discussed chapter 3. Also in this chapter, a method is derived which enables the determination of hydrogen flux densities in attached and detached conditions by measuring the radiance of a Balmer line. Thereafter, in chapter 4, the theory of Stark broadening in a plasma is reviewed, the setup of the new diagnostic is presented, and initial measurements are compared with other diagnostics for consistency. The experimental results concerning divertor detachment are presented in chapter 5. These results are summarized and discussed in chapter 6 and, finally, conclusions are given in chapter 7. 8 Chapter 2 Divertor physics In this chapter an introduction to the physics of divertor plasmas is given which is based on extensive reviews given by [9, 10, 11]. In section 2.1 the interaction of the plasma with the facing surfaces1is discussed. After this, in section 2.2 the different divertor operating regimes are described in a simplified picture. Extensions to this simple picture will be given in section 2.3. Finally, in section 2.4 the current understanding of the detached divertor regime, which is the main focus of this work, will be summarized. 2.1 Plasma-wall transition, the sheath Plasma particles and energy, diffusing out of the confined plasma, will be transported along the open magnetic field lines in the SOL until they finally hit the divertor targets. In section 2.1.1 the effects of the particle flux on the target will be introduced. An expression for the heat, which is deposited on the target, will be derived in section 2.1.2. 2.1.1 Particle outflux from the plasma to the surface In a simplified picture, the plasma away from the surface is quasineutral (ne=ni) and the plasma potential is Vp= 0. Assuming thermal equilibrium, the thermal velocity of the electrons is much higher compared to the ions, since ve=pmi/mevi. Therefore, the surface will receive a higher flux of electrons and become negatively charged, thus lowering the potential on the surface. As a consequence, the surface will attract the ions and repel the electrons. Within a narrow region close to the surface, called the sheath, quasineutrality is broken and ni> ne. The width of the sheath is of the order of one Debye length, λD=pǫ0kBTe/e2ne, which, for typical AUG parameters is of the order of 10−5m. The potential distribution is described by the Poisson equation: 1If not explicitly mentioned, surface is in the following referred to as the surface of the plasma facing wall. 9 2 Divertor physics d2V dx2=−e ǫ0 (ni−ne) (2.1) The velocity of the ions which are accelerated by the potential drop is: vi=−p2eV/mi(2.2) With the continuity equation ji=nivi= const, the ion density can be written as: ni=ni,srVs V(2.3) where ni,s and Vsare the ion density and the potential at the sheath entrance (at a distance of ≈λDfrom the surface), respectively. The potential at the sheath entrance is, contrary to the upstream region (at a distance of ≫λDfrom the surface), not zero anymore. The electrons, in contrast, are reflected by the potential in the sheath. The electron density is given by the Boltzmann relation: ne=ne,s exp e(V−Vs) kBTe(2.4) At the sheath entrance quasineutrality still holds and ni,s =ne,s =ns. Inserting equations 2.3 and 2.4 into equation 2.1 and making a Taylor expansion at x=xsyields: d2(Vs−V) dx2≈ens ǫ0e kBTe−1 2Vs(Vs−V) (2.5) To get a non oscillatory physical solution for V, the expression in the brackets must be negative: Vs≥ −(kBTe)/(2e). Combined with equation 2.2 this gives a constraint on the ion velocity at the sheath entrance: vi,s ≥rkBTe mi (2.6) For Ti= 0 this is the ion sound speed cs, which is defined as: cs=rZkBTe+αkBTi mi (2.7) where Zis the ion charge and α= 1 for isothermal flow, α= 5/3 for adiabatic flow with isotropic pressure and α= 3 for one dimensional adiabatic flow [12]. Hence, the ions are accelerated to at least sound speed at the sheath entrance. This constraint is called the Bohm criterion [13] which was also derived earlier by Langmuir [14]. Another consequence of equation 2.6 is, as mentioned above, that the potential at the sheath entrance is not zero, meaning that there is already a potential drop in the SOL upstream 10 2.1. Plasma-wall transition, the sheath of the sheath. Assuming no ion-neutral collisions, the so-called pre-sheath potential is, for isothermal flow, approximately: Vs≈ −0.7kBTe e(2.8) This potential forces the ions to flow from upstream (V= 0) towards the divertor surfaces, the so-called divertor sink action. The pre-sheath potential Vsis small compared to the potential at the surface (Vsurf ≈ −3kBTe/e for typical divertor conditions) which is caused by the potential drop in the sheath. However, the particle and power outflow rate to the surface is determined entirely by Vs, thus by the forces in the plasma and not in the sheath. Finally the particle flux density on the surface is introduced: Γs=ne,sve,s =ne,scs(2.9) As it is assumed that there is no particle source or sink in the sheath, the flux density is equal at the surface and the sheath entrance, Γs= Γsurf . It should be noted here that, due to the magnetic field present in a tokamak, a so-called magnetic pre-sheath exists in front of the sheath. This magnetic pre-sheath is formed due to the gyration of the charged plasma particles around the magnetic field lines together with non perpendicular incident angles of the field lines on the target. However, the above derived basic properties of the sheath are not changed by the presence of the magnetic pre-sheath [15]. 2.1.2 Power deposited on the surface Here, the power deposited on the surface by the plasma particles will be discussed. As the electron distribution function is Maxwellian, the electron power flux density at the surface can be calculated by integration over the velocity space: qe surf = −∞ Z0mev2 x 2vxfe(vx)dvx+kBTe= 2kBTeΓs(2.10) The ions, however, are accelerated by the potential and therefore do not follow a Maxwellian distribution. With the assumption that the ion distribution is a Maxwellian distribution shifted by cs, the ion power flux density can be calculated similarly: qi surf =5 2kBTi+mic2 s 2Γs=7 2kBTeΓs here and in the following Te=Tiis assumed. In addition, the sheath and the presheath transfer energy from the electrons to the ions by an amount of |eVsurf |and |eVs|, 11 2 Divertor physics respectively. The power density deposited on the plasma surface by electrons and ions can thus be written as: qsurf =qe surf +qi surf =2kBTe+7 2kBTe+|eVsurf |+|eVs|Γs =γkBTeΓs(2.11) with the sheath heat transmission coefficient γ≈2 + 3.5 + 3 + 0.7≈9.2. It should be noted that this is just a simplified derivation. If one includes other effects, such as e.g. secondary electron emission [15], there is a strong variation of γ. In ASDEX Upgrade, values of γbetween 3 and 8 were found [16]. In a multi machine comparison, γeven varies between 2 and 11 [17]. The power density in equation 2.11 can be referred to as the kinetic energy deposited on the surface. In addition, incoming ions recombine on the surface with electrons to form neutral atoms and incoming neutrals will recombine on the surface with other neutrals to form molecules. These processes release the potential energy, or at least a significant fraction of it, as heat to the surface. For deuterium, the ionization energy is Eion pot = 13.6 eV and the molecular dissociation energy is Ediss pot = 4.5 eV. The total power density, including the kinetic and potential energy, Epot =Eion pot +Ediss pot = 18.1 eV, deposited on the surface is then given by: qtot = (γkBTe+Epot)Γs(2.12) From equation 2.12 it can be seen that a reduction of the temperature results in a decrease of the deposited power. In present experiments this is usually sufficient for safe operation in terms of melting or damaging the wall material. In larger scale devices such as ITER, however, the particle fluxes to the surface are predicted to be so high that the potential power deposited on the surface becomes important. Thus, for a safe operation not only the temperature but also the particle fluxes to the surface must be reduced. The question how a reduction of both parameters at given input power can be achieved, resulting in different divertor operating regimes, will be addressed in the following section. 2.2 Divertor operating regimes The divertor plasma is usually described by a fluid approach. The use of a fluid approach is appropriate if the collisional mean-free-paths of electron and ion self-collisions, λee,ii ≈ 1016T2 e,i/ne,i, are small compared to the characteristic scale length in the SOL, Lc. For typical AUG parameters (ne≈1·1019 m−3,Te≈50 eV), λee ≈2.5 m ≪Lc≈40 m and 12 2.2. Divertor operating regimes the fluid approach is valid. Here, the plasma parameters such as density and temperature are described by the Fokker-Planck kinetic equation: ∂f ∂t +~v ·∇f+q m(~ E+~v ×~ B)·∇~v =S(f) (2.13) where S(f) describes particle sources and sinks due to ionization, recombination or interaction of plasma particles with impurities and f(~r,~v, t) is the particle distribution function in position-velocity-time space. The fluid equations of the various plasma parameters, the so-called Braginskii equations [18], are derived by taking the velocity moments of equation 2.13 up to the third order. These result in a set of coupled, non linear differential equations which only can be consistently solved with sophisticated computer codes. One of the most important processes in the SOL is the heat transport parallel to the field lines to the target. This transport is a combination of a conductive and a convective heat transport. The parallel electron heat flux density qke, derived from the Braginskii equations, is given by: qke=5 2kBTeneve−κ0eT5/2 e dTe dx(2.14) where the first term on the right hand side describes the convective part and the second one the conductive part. The corresponding ion heat flux density is: qki=1 2miv2 i+5 2kBTinivi−κ0iT5/2 i dTi dx(2.15) The electron and ion heat conductivity coefficients, κ0eand κ0irespectively, were derived by Spitzer and H¨arm [19] and are given in [20] to be: κ0e,i =kB √me,i ln Λ e4Z(2.16) It can be seen that κ0i∝pme/miκ0e. Thus, the ion heat conduction can be neglected compared to the electron heat conduction, i.e. the power is conducted mainly by the electrons. Assuming Te≈Tiand ne≈ni, one can combine equations 2.14 and 2.15 and obtain the total heat flux density: qk=1 2miv2+ 5kBTnev−κ0eT5/2 e dTe dx(2.17) Another important process is that of plasma particle production and flow in the SOL. Plasma ions impacting the surface will release neutrals from the wall. These neutrals will be ionized in the plasma, providing a source of plasma particles. The resulting ions will flow back to the surface and release new neutrals. This particle cycle is called 13 2 Divertor physics recycling. The degree of recycling and the region where the ionization of the recycled neutrals occurs strongly affect the divertor plasma conditions. In the following section, simplified relations between upstream and target parameters will be derived with respect to the degree and location of the recycling. From now on, the focus is on the values at the sheath entrance, see section 2.1. These values are called the target parameters. 2.2.1 The low recycling regime If the upstream density at a given heating power is sufficiently low, the divertor is in the low recycling regime and a model can be developed, linking upstream and target parameters, under the following simplified assumptions. The recycling level is low and the particle source due to the ionization of recycled neutrals is assumed to be negligible with respect to the main plasma particle source, i.e. it is assumed that the main plasma is the only particle source. It is further assumed, that the main plasma is the only power source, thus all power and particles enter the SOL at the upstream position sup. Furthermore no cross field transport between different flux tubes is considered. The electrons and ions will flow from upstream due to the divertor sink action (the presheath potential drop Vs, section 2.1.1) towards the target within a flux tube, reaching sound speed, cs, at the target (see eq. 2.6 and eq. 2.7) and the heat is then convected to the targets. The heat transport to the target is limited only by the heat, which can be transmitted by the sheath. Therefore, this regime is also called the sheath limited regime. As a consequence of the heat being convected, the temperature along the field line is approximately constant (assuming Te=Ti=Tand ne=ni=n): Tu≈Tt=T(2.18) Throughout this thesis, the indices uand trefer to as the values at the upstream position and target, respectively. With the assumption of no cross-field transport the total pressure ptot =pstat +pdyn is conserved along a field line, with the static pressure pstat =nkBT and the dynamic pressure pdyn =nmev2/2. The plasma is static at the upstream position and is accelerated to sound speed, cs, at the target (see eq. 2.6 and 2.7). With α= 1 for cs, this yields a relation between upstream and target pressure: nukBT=ntkBT+2ntmekBT 2me ⇒nt=1 2nu(2.19) Now, with equations 2.19, 2.11 and 2.7 the temperature along the field line can be approximated as: 14 2.2. Divertor operating regimes T≈me (2kB)31/3qk γnu2/3 (2.20) The particle flux density at the target, equations 2.7 and 2.20, finally results in: Γt=ntcs=1 16m2 e1/6qkn2 u γ1/3 (2.21) The target parameters depend now only on the external control parameters nuand qk which relate to the main plasma density and the plasma heating power, respectively. 2.2.2 The high recycling regime - the Two-Point-Model If the upstream density is increased while keeping the heating power constant, the level of recycling increases. It is assumed here, that the particle source due to recycling is much stronger than the main plasma particle source. For simplicity it is assumed that all the recycled neutrals ionize in a very thin layer close to the target and in the same flux tube of the originally impacting ion. As in section 2.2.1 it is further assumed that there is no cross field transport of either particles or heat. The main plasma is the only heat source and all the heat will enter the SOL at the upstream position. In contrast to the low recycling regime, the only particle source is now the region in front of the target where the recycled neutrals ionize, called the recycling zone. This is a valid assumption, as the mean free path for electron impact ionization is short enough (sec. 4.4.1) such that the recycling cycle occurs near the target. Thus the plasma in the SOL between upstream and the entrance of the recycling zone is assumed to be stagnant, i.e. there is no particle flux, Γ = 0. Within the recycling zone the plasma is then accelerated to sound speed at the target, equation 2.6. Hence, the heat between upstream and the recycling zone is now conducted, giving this divertor regime also the name conduction limited regime. In order to carry the heat via conduction, temperature gradients have to arise in the SOL which result in lower temperatures at the target relative to the upstream position. In reality, the plasma in the SOL is not completely stagnant and convection still plays a role. In order to account for this, a convection factor (0 < fconv <1) which determines the heat fraction carried by convection, qkcond = (1 −fconv)qkis introduced. Integration of the conduction part in equation 2.17 from x= 0 to x=Lc(Lcis the connection length between upstream and the target, defined in section 1.3) yields: T7/2 u=T7/2 t+7 2 (1 −fconv)qkLc κ0,e (2.22) Strictly, it should be integrated from upstream to the entrance of the ionization zone as the heat in this zone is then convected. However, as convection is a very effective process and the ionization zone is taken to be very thin, it is assumed that the temperature at 15 2 Divertor physics the entrance of the zone is equal to the target temperature (see eq. 2.18). Due to the large exponent for Tin equation 2.22, the term T7/2 tcan be neglected as soon as Tt becomes even slightly smaller than Tu. Equation 2.22 thus simplifies to: T7/2 u≈7 2 (1 −fconv)qkLc κ0,e (2.23) In order to account for frictional collisions between ions and neutrals, viscous forces and volume recombination, a momentum loss factor (0 < fmom <1) is introduced. With this, the pressure conservation (eq. 2.19) modifies to: 2ntTt= (1 −fmom)nuTu(2.24) Line radiation in the SOL, either by impurities or recycled neutrals, and charge exchange collisions provide an energy sink for the electrons. These processes can be included by introducing a power loss factor (0 < fpow <1), yielding qSOL rad +qSOL cx = (1 −fpow)qk. The parallel heat flux density at the target, equation 2.11 (in which the potential energy can still be neglected with respect to the kinetic energy), can then be written as: (1 −fpow)qk=qt=γkBTtΓt(2.25) The three equations 2.23, 2.24 and 2.25 in the three parameters of interest, nt,Ttand Γtcombine to give: Tt=q2 k n2 u7qkLc 2κ0e−4/72mi γ2e2 (1 −fpow)2 (1 −fmom)2(1 −fconv)4/7(2.26) nt=n3 u q2 k7qkLc 2κ0e6/7γ2e3 4mi (1 −fmom)3(1 −fconv)6/7 (1 −fpow)2(2.27) Γt=n2 u qk7qkLc 2κ0e4/7γe2 2mi (1 −fmom)2(1 −fconv)4/7 (1 −fpow)(2.28) The simplest case neglecting all loss factors (fconv =fmom =fpow = 0) is called the simple Two-Point-Model [21]. At moderate upstream densities, which are sufficient to enter the high recycling regime, the target conditions can be fairly well described by the TPM. In this regime the target temperature is now very sensitive on the upstream density (∝1/n2 u) and low values can be achieved by increasing the density. In the simple Two-Point-Model all power entering the SOL is deposited on the surface. As the upstream density is increased, however, the hydrogen recycling is also increased due to the increased particle flux. This high recycling will, via line radiation, remove power from the SOL. Thus the power loss factor fpow is no longer negligible which directly results in a reduction of the target heat flux (eq. 2.25). Another commonly used method 16 2.2. Divertor operating regimes to increase the radiated power in the SOL is the injection of so-called seeded impurities such as N2, He, Ne or Ar. A further effect of the radiation losses is to decrease the target temperature and to increase the target density and particle flux. In order to reduce the target flux, the ratio of conducted to convected heat flux must change, fconv >0, or momentum must be removed from the divertor plasma, fmom >0. 2.2.3 The detached regime The necessary characteristics of the detached regime are, amongst the reduction of the surface heat load, that the particle flux to the target, Γt, decreases and that there is a pressure drop along the field line. It was shown in section 2.2.2, equation 2.24, that this can be achieved when momentum is removed in the SOL, fmom >0. Changing the ratio of conducted to convected heat transport, fconv >0, also reduces the particle flux at the target. The pressure, however, would still be conserved along a flux tube (eq. 2.24). The main mechanisms which remove momentum are elastic ion-neutral collisions (CX-collisions) and recombination. These processes dominate with respect to the ionization at temperatures below ≈5 eV and ≈1.5 eV, respectively (see Fig. 3.1). These low temperatures can be achieved by a further increase of the main plasma density, as Tt∝n−2 u. At these temperatures, however, the simplification that the potential energy can be neglected with respect to the kinetic energy in equation 2.12 is no longer valid. Equation 2.25 is now written as: (1 −fpow)qk=qt= (2γkBTt+Epot)Γt(2.29) with Epot = 18.1 eV, section 2.1.2. Combining this equation with equation 2.24 yields an expression for the target temperature: √mkBTt (2γkBTt+Epot)= 1.01 nu q5/7 kκ0e Lc−2/7(1 −fmom) (1 −fpow)(2.30) This equation can not directly be solved for Tt, but it can be seen that there is a competition between the power loss, necessary to remove the heat flux on the target, and the momentum loss which is needed to reduce the particle flux at the target. In the following, the two basic processes which remove momentum in the SOL are described. Ion-neutral collisions - the gas target Assume that in an elastic collision zone in front of the target the temperature is low enough for CX-collisions to occur. Recycled neutral hydrogen atoms or molecules will travel through this so-called gas target [22] and undergo several elastic collisions with hydrogen ions which flow to the target. As the masses of the neutral atom or molecule 17 2 Divertor physics Γθ Er BtBt Γr Eθ R0 a α (a) (b) Figure 2.2: Sketch of the ~ E×~ Bdrifts in the SOL. Blue arrows denote the electric fields and red arrows show the drift direction for forward field (Btis pointing out of the paper). See text for explanation. can be neglected, yielding Ek≈ −(kBTe)/(2eLc). In the conduction limited regime the temperature gradient can become large (sec. 2.2.2). Assuming that the temperature gradient expands through the entire length of the SOL, Lc, gives Ek≈ −(kBTu e)/(eLc). The associated radial drift flux density is larger in the high recycling regime than in the low recycling regime, and is given by: Γdr r≈nekBTu e BΘeLc (2.52) ~ E×~ Bdrift fluxes vs. basic SOL fluxes Drift induced fluxes will alter the overall flux distribution in the SOL, but particles will still flow towards the targets due to the basic divertor sink action. It is possible to approximate the strength of the drift fluxes relative to the basic SOL fluxes. The basic parallel SOL flux projected onto the poloidal plane is ΓΘ≈(B/BΘ)ntcs. With the ion poloidal gyro frequency ωiΘ=eBΘ/miand ρsΘ=csωiΘ, the relation of the poloidal drift flux (eq. 2.50) to the basic poloidal flux is: Γdr Θ/ΓΘ≈ρsΘ/λTe(2.53) With the basic cross-field flux (eq. 2.43) one can derive the associated ratio for the radial fluxes: Γdr r/Γr≈ρsΘ/λne(2.54) 24 2.3. Additional processes in the SOL Drift fluxes become less important with higher density (and therefore lower temperature) as ρsΘ/λTe,ne∝T3/4qDeff ⊥. Finally it should be pointed out that although the ~ E×~ B drifts are charge independent they change direction when the toroidal magnetic field is reversed. Changing ~ BΦin the experiment therefore allows to untangle to some extent the effects of these drifts. The diamagnetic drift Another drift naturally arising in the SOL is the diamagnetic drift caused by the pressure gradient: ~v =~ B×∇p eneB2(2.55) This drift is the fluid analogue to the particle ∇Bdrift (eq. 2.48) and, in contrast to the ~ E×~ Bdrifts, is charge dependent. This charge separation results in parallel currents in the SOL, known as Pfirsch-Schl¨uter (PS) currents, and, in parallel (or poloidal) particle flows. The focus is now on the ion flow, because the ions are less mobile and the density in the divertor is mainly determined by their transport. In forward field, this flow is directed towards the divertor. Therefore, the density in both the inner and outer divertor will be higher in forward field compared to reversed field. It is common to define the PS flows as a combination of this flow and the poloidal ~ E×~ Bflow (section 2.3.2). Assuming a cylindrical plasma geometry, the parallel PS velocity is given as [34]: ~vP S ki= 2 cos αaB R0BΘEr B−∇rp eneB(2.56) where α,aand R0are indicated in Figure 2.2b. It can bee seen that ~vP S kiis zero at the top and bottom of the machine and maximum at the midplane. A detailed investigation of the effect of PS flows on the SOL plasma and comparison of measurements with code calculations can be found in [34] and references therein. Ionization driven flow reversal Another effect inducing an additional flow in the SOL is the so-called ionization driven flow reversal [35, 36]. The origin of this flow is independent of electric or magnetic fields in the SOL. Consider the divertor as being in the high recycling regime with the ionization zone close to the targets. Both density and temperature profiles decay radially along the target (sec. 2.3.1) being highest close to the separatrix. Neutrals, which are released from the surface, will ionize preferentially in the region of higher temperature and density close to the separatrix. The ionization source in this region can exceed the ion loss to the divertor target and a water-shed is formed at some distance from the 25 2 Divertor physics target. Above this water-shed, the ions then flow upstream in a thin region close to the separatrix. Such flow reversal has been measured e.g. in the outer divertor of Alcator C-Mod [37]. Here, it occured only in forward field where the outer divertor was hotter than the inner. This led to the suggestion that flow reversal results in a plasma flow from the hotter to the colder divertor. A recent modelling approach [38] showed that flow reversal can occur at both the inner and outer divertor, being stronger at the hotter outer divertor. It must be noted that flow reversal and all drifts discussed above will appear, in the worst case, simultaneously. Hence, they will affect each other to some extent. A correct treatment of the drift effects on the SOL plasma is therefore only possible with the use of sophisticated two dimensional computer models. 2.4 Current understanding of detachment Plasma detachment has been experimentally investigated in all present day tokamaks and the qualitative mechanisms leading to detachment seem to be understood [10, 11]. As detachment is a 2D strongly coupled nonlinear process a quantitative description is only possible with extensive code simulations. In particular to predict the ITER divertor performance a correct simulation of divertor detachment is indispensable. But even with the most sophisticated codes, divertor detachment of present day machines has not yet been successfully reproduced [8]. Several experimental observations are still not fully understood. For example, the onset of detachment, defined as when the ion flux to the target starts to decrease as the plasma density is further increased (the so-called roll over), happens in most tokamaks much earlier at the inner divertor in forward field configuration. Moreover, the inner divertor receives a higher ion flux and a lower power load before the onset of detachment compared to the outer divertor. Several reasons for this so-called divertor asymmetry have been discussed [37, 39, 40, 41, 42]. At present it is thought that they are primarily caused by drift flows [43, 44]. The effect of the drift flows on the SOL flow has been tried to model (e.g. [45, 46]). Although the qualitative trend of the drift effects was reproduced by the models, absolute values of the flow velocity in the SOL were underestimated by at least a factor of 2-10. Furthermore, the radial transport of plasma particles in the SOL is not experimentally well known. In the codes it is usually assumed to be of diffusive nature [47] including a radial dependence, D⊥(r) (equation 2.43). However, it was shown for medium to high densities that intermittent transport (equation 2.44) can be dominant [48] and increases with increasing density [49]. In recent modelling of experimental observations, a collisionality, and hence density dependent diffusion coefficient, was used [50]. This 26 2.4. Current understanding of detachment yields better agreement with the experimental density necessary to achieve the roll over. Detachment is typically studied by comparing target and upstream values, as no information on plasma parameters in the divertor volume (aside from the bolometric measured radiation distribution) is available. The DIII-D tokamak is an exception, as it has a divertor Thomson scattering system at the outer divertor. As the mechanisms leading to detachment are volumetric processes, however, knowledge of the distribution of the plasma parameters, such as the electron density, in the divertor volume is necessary to understand the detachment process. In addition, the evaluation of the target density and temperature from Langmuir probe measurements is difficult in strongly detached conditions (which are earlier achieved in the inner divertor), as the particle fluxes are usually to low for a correct data evaluation. Moreover, the outer target is more critical in terms of the received heat flux due to the divertor asymmetry. Therefore, studies on detachment are normally concentrated on the outer divertor. Thus it is not known if the inner and outer divertor evolve independently of each other or not. 27 Chapter 3 Atomic processes In this chapter the basic atomic processes appearing in a plasma will be introduced. Based on this, the emissivity of a certain spectral line with respect to the density and temperature of the surrounding plasma will be derived. Finally, a method is presented which allows the determination of the particle flux of a certain species based on the measurement of the radiance of a spectral line emitted by that species. 3.1 Atomic processes and equilibrium The basic atomic processes in a plasma due to their interaction are derived. Consider an atom or ion being in the charge state z, named Az. An excited atom or ion is denoted with Az∗. Each of the following equations describe processes which can happen in both directions, thus they have two names: impact excitation ↔impact de-excitation Az+e↔Az∗+e′(3.1) spontaneous emission ↔photon absorption Az∗↔Az+hν (3.2) impact ionization ↔three body recombination Az+e↔Az+1 +e′+e′′ (3.3) radiative recombination ↔photon ionization Az+1 +e↔Az+hν (3.4) These processes tend to bring the population densities of the various species into equilibrium. If the relaxation time is short compared to the transport time scale in the plasma, then these processes are in a local equilibrium which depends on the local plasma density and temperature. For very high densities, like in the centre of stars, the mean free 28 3.2. The Collisional Radiative Model path of a photon is short compared to the gradient length. The usual situation in fusion plasmas is that the photonic reactions (equations 3.2 and 3.4) are not in equilibrium and the plasma is optically thin. For high densities, the collisional processes are in equilibrium and it holds the Boltzmann relation and the Saha equation, which is called the local thermodynamical equilibrium. In the opposite case, at low densities almost all ions are in the ground state. The only excitation process is the impact excitation which is completely balanced by spontaneous emission. This is called the corona model. The typical densities in divertors, however, are above the area of validity of the corona model (ne<1·1018 m−3). In this density range, models have to be used which also take into account collisions and radiative processes, i.e. collisional radiative models. 3.2 The Collisional Radiative Model Extensions to the Corona model have been made by Bates [51], which became known as the Collisional Radiative Model, and was further improved by McWhirter and Summers [52]. In this approach, a detailed review of which can be found in [53], all atomic processes (eq. 3.1-3.4) are taken into account. The excitation levels of a specific charge state are divided into metastable states indexed by a Greek character, Az ρ, and excited states index by a Roman character, Az i. The main mechanisms leading to the population of Az i are excitation from the metastable level Az ρand recombination from the ground level of the next higher charge state, denoted by Az+1 1. The ratio of their population densities, nρand n+ 1respectively, which are called the dominant populations, are assumed to be known. The populations of the excited levels, nican be assumed to be in a quasi static equilibrium with respect to the dominant populations since the equilibration time scale is of the order of the radiative decay time of the excited levels which is typically of the order of 10−9s. The collisional radiative model evaluates the dependence of the excited populations on the the dominant populations. The solution for the population density of a certain excited state is given by: nj=− O X i=1 C−1 ji M X σ=1 Ciσnσ+ O X i=1 C−1 ji rinen+ 1+ O X i=1 C−1 ji qCX inHn+ 1 = M X σ=1 Fexc jσ nenσ+Frec j1nen+ 1+FCX j1nHn+ 1(3.5) with Oand Mthe number of excited and metastable levels, respectively, riis the free electron recombination coefficient directly to the level iand qCX iis the charge exchange recombination coefficient from neutral hydrogen with density nHto the level i. As the usual plasma species is hydrogen or a hydrogen isotope, see section 1.3, this element is taken as charge exchange partner. The Care elements of the collisional radiative matrix: 29 3 Atomic processes Cji =−Ai→j−neqe i→j−npqp i→j(3.6) with the rate coefficients for spontaneous transition, Ai→j, electron induced collisional transition, qe i→jand ion induced collisional transition, qp i→j. Usually, the ion induced collisions can be neglected compared to the electron induced collisions. Their rate coefficients depend only on Teas ve≫vi. The Fs in equation 3.5 are the effective contributions to the population of the excited level jby excitation from metastables, free electron recombination and charge exchange recombination from neutral hydrogen, respectively. Multiplying these Fs with the appropriate Einstein coefficients for a transition from the excited level jto k,Aj→k, gives the so-called Photon Emissivity Coefficients, PEC. The emissivity of a spectral line with charge zcan finally be derived by: ǫz j→k=nenzPECexc(neTe) + nenz+1PECrec(neTe) + nHnz+1PECCX (neTeTiTH) (3.7) These PECs depend on the local density and temperature and have been calculated for various elements and transitions by the ADAS1project [54]. From this, total rate coefficients for ionization, recombination and charge exchange can be obtained for a specific element. These rate coefficients for deuterium are shown in Figure 3.1 for two different densities. 0.1 1 10 100 Te (eV) 10-20 10-19 10-18 10-17 10-16 10-15 10-14 10-13 <σv> (m3 s-1) Ionization Recombination Charge Exchange ne = 1021 m-3 ne = 1021 m-3 ne = 1019 m-3 ne = 1019 m-3 Figure 3.1: Ionization, recombination and charge exchange rate coefficients for two different densities and Te=Ti=TH. 1Atomic Data and Analysis Structure 30 3.2. The Collisional Radiative Model It can be seen that the charge exchange process dominates with respect to the ionization process when Te<5 eV. Furthermore, recombination becomes stronger than ionization when Te<1.5 eV. This was discussed in section 2.2.3, where a strong temperature reduction in the divertor is needed in order to remove momentum via CX and recombination processes. In this work, the radiating element of interest is the hydrogen isotope deuterium. As the CX partner is also hydrogen, these are elastic collisions which do not cause photon emissions. For this specific case, the charge exchange contribution has not to be taken into account in equation 3.7 for the line emissivity. For the Balmer Dδline, n= 6 → n= 2, equation 3.7 is then written as: ǫ+0 6→2=nen+0 HPECexc(neTe) + nen+1 HPECrec(neTe) =nenHf+0PECexc(neTe) + f+1PECrec(neTe) |{z } TEC (3.8) with n+0 Hand n+1 Hthe neutral hydrogen and ionized hydrogen density, respectively. The fractional abundance, f, is the ratio of the neutral or ionized hydrogen density to the total hydrogen density nH:f+0,+1 =n+0,+1/ntot. The expression in the brackets is in this work called the total line emission coefficient, TEC. 0.1 1 10 100 Te (eV) 10-21 10-20 10-19 10-18 10-17 PEC (Ph m3/s) ne = 1021 m-3 ne = 1019 m-3 ne = 1021 m-3 ne = 1019 m-3 excitation recombination Figure 3.2: Balmer Dδphoton emission coefficients (PEC) for excitation (red) and recombination (blue) derived from ADAS for two different densities. Figure 3.2 shows the photon emission coefficients for excitation and recombination for the Balmer Dδline. It can be seen that at Te≈1.5−2 eV there is a sharp transition from recombination dominated radiation to excitation dominated radiation. Furthermore, the PECrec is relatively insensitive to the electron density, in contrast to the PECexc. 31 3 Atomic processes 0.1 1 10 100 Te (eV) 10-8 10-4 10-2 Fractional Abundance 100 f+1 f0 ne = 1019 m-3 (colored) = 1021 m-3 (black) 10-6 Figure 3.3: Fractional abundance for neutral (red) and ionized (blue) deuterium derived from ADAS for two different densities. In Figure 3.3 the fractional abundance for neutral and ionized deuterium, which is almost insensitive to the electron density, is shown. For this plot, the transport effects are neglected and only the balance of ionization and recombination rates is taken into account. Below Te≈1.5 eV almost all deuterium atoms are in the neutral state as the rate coefficient for ionization is low in this temperature range (Fig. 3.1). Above Te≈1.5 eV almost all deuterium atoms are in the ionized state as then ionization dominates with respect to recombination, see Figure 3.1. The neglected transport effects will lead to a modification of the curves, but the transition from neutral to ionized hydrogen is always around ≈1.5 eV. 0 1 10 100 Te (eV) 10-24 10-23 10-22 10-21 10-20 TEC (Ph m3/s) ne = 1021 m-3 ne = 1019 m-3 Figure 3.4: Balmer Dδtotal emission coefficient for two different densities. 32 3.3. Electron temperature determination from line ratios With the PECs for excitation and recombination, Figure 3.2, and the fractional abundance, Figure 3.3, one can calculate the total emission coefficient for the Balmer Dδline, equation 3.8, which is shown in Figure 3.4. The TEC peaks at Te≈1.5 eV and drops rapidly when the temperature decreases. This is due to the strong decrease of the ionized deuterium density when the temperature decreases, which is stronger than the increase of the PECrec. Moreover, the TEC does almost not depend on the electron density. 3.3 Electron temperature determination from line ratios By measuring the line emission ratio of two different transitions of the same atom it is in principle possible to determine the electron temperature. Therefore it is necessary that the line emission of both transitions, the TEC, does weakly depend on the electron density. For example, this is routinely done at TEXTOR by measuring helium line ratios [55]. The determination of the electron temperature is also possible by measuring deuterium line ratios. With the spectrometers used for this work, it was possible to measure the Balmer Dδand Dǫlines simultaneously, see section 4.3.1. The line emission ratio is the ratio of the corresponding TECs and given by equation 3.8: ǫ6→2 ǫ7→2 =TECDδ TECDǫ (3.9) where the electron and total hydrogen densities cancel out. The line ratio of Dδ/Dǫis calculated for two different densities and shown in Figure 3.5. 0.1 1 10 100 Te (eV) 1.0 1.5 2.0 2.5 3.0 Dδ/Dε ne = 1021 m-3 ne = 1019 m-3 Figure 3.5: Line emission ratio of Dδand Dǫfor two different densities. 33 4 Diagnostic Table 4.1: Critical wavelength shift ∆λcfor different Balmer lines and temperatures. Temperature: 5 eV 10 eV 20 eV Electrons 73.23 nm 146.4 nm 292.9 nm DβIons 0.040 nm 0.060 nm 0.100 nm Electrons 21.94 nm 43.88 nm 87.75 nm DγIons 0.012 nm 0.018 nm 0.030 nm Electrons 9.90 nm 19.79 nm 39.58 nm DδIons 0.005 nm 0.008 nm 0.013 nm Electrons 6.88 nm 13.76 nm 27.52 nm DǫIons 0.004 nm 0.006 nm 0.009 nm In the case of electrons the critical wavelength shift is very large. Hence, the collision damping theory has to be used throughout the entire spectrum. For the ions, however, the statistical theory is valid, with an exception in the very center of the spectral line where the collision damping theory has to be applied. This exception becomes less important for the higher members of the Balmer series. 4.1.2 The unified theory With the so-called semi quantum mechanical unified theory it is possible to combine the pressure broadening by electrons with the Stark splitting caused by the ions. However, it is not possible to include the ion pressure broadening. A detailed description of this method can be found in [61]. Starting with the electron pressure broadening, the radiated power of an emitting system can be written as [62]: P(ω) = 4ω4 3c2X i,f δ(ω−ωif )Di|ˆ D|fE 2ρi |{z } I(ω) (4.3) It is summed over all initial states |ii, multiplied by their occupation probability ρiand summed over all final states |fiof the entire system. ˆ Dis the transition dipole moment of the entire system. The sum can be interpreted as the spectral line profile I(ω) which is the Fourier transform of an auto correlation function Φ(t): Φ(t) = X i,f,j eiωif t|hi|exj|fi|2ρi(4.4) Several assumptions are made to find the auto correlation function of the system. The 40 4.1. Theory of Stark broadening in a plasma perturbing electrons are treated as classical point charges (thus semi quantum mechanical) moving, in the case of a neutral particle as the emitting atom, along straight lines. Moreover, it is assumed that the electrons are unperturbed by the presence of the emitting atom. The reason for this is that the average energy of the interaction between the atom and the electron is small with respect to the kinetic energy of the electrons. This assumption is called the classical path approximation. In addition it is assumed that collisions leading to a broadening of the spectral line occur much more often compared to those causing transitions between different energy levels (the so-called impact approximation). The Schr¨odinger equation of this problem can be written as: i~dΨ(t) dt = [H0+He pert(t) + Hion pert(E)] Ψ(t) (4.5) with H0being the Hamiltonian of the unperturbed system, He pert(t) is the time dependent interaction Hamiltonian due to electron collisions and Hion pert(E) = e~r ~ Eis the interaction Hamiltonian which depends on the electric field ~ Eproduced by the ions. The auto correlation function of this system, with the assumptions described above, is then: Φ(t) = ~ dif if exp −i(Hf(E)−Hi(E))t ~+ Ωi,f ti′f′~ d∗ i′f′(4.6) where H(E) = H0+Hion pert(E) is the Hamiltonian of the initial and final states i, f. The sub levels i′, f′of a certain energy level are generated by the perturbation due to the electron collisions. This perturbation is described with the perturbation operator Ωi,f . As the perturbation is proportional to n4, with nthe principal quantum number of the energy level, the effect of electron collisions on the lower level is neglected: Ωi,f ≈Ωi. Nguyen-Hoe, Drawin and Herman [63] calculated the collision operator which was used for this work: Ωi=−"4πnee4a2 0 3~22m πkBTe1/2#0.6342 + ln 1 ǫ~ri·~ri a2 0 (4.7) with ǫ=4π1/2~e (3m)1/2kB n2n1/2 e Te (4.8) where a0is the Bohr radius, neis in cm−3and Tis in K. The Fourier transform of equation 4.6 leads to the final expression of the spectral line shape: 41 4 Diagnostic I(ω) = 1 π ∞ Z0 dE W(E) Re ~ dif × ×**if iω −i(Hi(E)−Hf(E)) ~−Ωi−1 i′f′++~ d∗ i′f′(4.9) First the spectral line broadening due to electron collisions (collision damping theory) is calculated for a given Stark splitting of the energy levels caused by a certain electric field strength produced by the ions multiplied by its probability of occurring W(E), which will be derived in the next section (statistical theory). Then the total profile is obtained by integrating over all possible electric field strengths. As mentioned above, the influence of the ion collision damping, valid in the line center (see chapter 4.1.1), has to be neglected in the unified theory. But here an additional Zeeman splitting due to a magnetic field can easily be included, section 4.2.1. 4.1.3 Statistical theory The perturbing ions are statistically distributed and produce so-called electric micro fields. In the case of hydrogen emitters, these electric fields lead to the well known Stark splitting. The energy levels split into 2n−1 sub levels. The frequency splitting of a transition is proportional to the electric field caused by an elementary charge eof distance r,E=1 4πǫ0 e r2(linear Stark effect): ∆ω=3 2 ~ m ∆nk r2(4.10) with nk=n·k,k= 0; ±1; ··· ± (n−1). This yields a symmetric splitting of the transition lines between two energy levels which becomes larger with higher upper principal quantum number. An average frequency shift is derived by weighting the shift of the individual components with their line strength [64] ∆nk=PS∆nk/PSk.C, introduced in equation (4.1): C=3 2 ~ m∆nk(4.11) For the Balmer lines Hβ(n= 3 →2) up to Hγ(n= 7 →2) one gets: C= (10.4; 20.5; 27.3; 42.7) ·10−4m2 s The problem is the determination of the electric field produced by the statistically distributed ions. With Ndisturbing ions of charge ein the volume Vthe total field strength at the place of the emitting atom, situated at the origin of a Cartesian coordinate system, 42 4.1. Theory of Stark broadening in a plasma is E=PNEi. The probability that the field strength Ekproduced by the kth particle is between Ekand Ek+dEkis equivalent to the probability that the kth particle is in the volume element drk. The probability that all Nions produce a field strength in the range of E+dE is thus given by: W(E)dE =Z...Zδ(E− N X i=1 Ei)gN VNd~r1, d~r2, . . . d~rNdE (4.12) where gNis the correlation function of the N-particle system. The approximation of statistically independent particles (gN= 1) producing a Coulomb field results in the Holtsmark distribution function [65]: W(β) = 2 πβ ∞ Z0 vsin vexp "−v β3/2#dv (4.13) with the relative field strength β=E/E0and the normal field strength E0, given by: E0=2.61 4πǫ0 en2/3 e(4.14) Baranger and Mozer [66, 67] introduced two components of the micro field, produced by the electrons and ions, respectively. With this, correlations between the perturbing particles can be considered and gNbecomes: g2(~r1,~r2)≈ − e2 4πǫ0kBT|~r1−~r2|exp −|~r1−~r2| λD(4.15) Furthermore the field produced by the kth particle is shielded by the other particles and instead of a Coulomb field a Debye field is produced: Ek=e 4πǫ0r2 k1 + rk λDexp −rk λD(4.16) with the Debye shielding length: λD=rǫ0kBT e2ne (4.17) A measure of this effect is the ratio between the average distance of the particles r0, with 4 3πner3 0= 1, and the Debye length. The limiting case r0/λD→0 is equivalent to the Holtsmark distribution. The distribution function W(E) for several values of r0/λD including the Holtsmark one is shown in Figure 4.1a. W(β) shows for large βa decay proportional to β−5/2. This results in a decay of the Stark broadened line wings that is proportional to ∆λ−5/2, which is a well known observation. 43 4 Diagnostic W (β) 0 1 2 3 4 5 6 7 8 9 10 β 0.0 0.2 0.4 0.6 r0/λD = 0.0 r0/λD = 0.2 r0/λD = 0.4 1019 1020 1021 1022 ne (m-3) 0.01 0.10 1.00 T = 1 eV T = 10 eV T = 25 eV r0/λD (a) (b) Figure 4.1: Probability distribution function from Mozer and Baranger [67] for different values of r0/λd(a). The limit case r0/λD→0 is equivalent to the Holtsmark distribution. Quotient r0/λDfor different temperatures versus the electron density (b). In Figure 4.1b the fraction r0/λDis shown for different densities and temperatures. For typical parameters at ASDEX Upgrade one can assume r0/λD≈0 and use the Holtsmark distribution function. Only at very low temperatures Te≈1 eV and high densities ne>1·1021 m−3are values of r0/λD>0.2 reached and deviations from the Holtsmark distribution have to be considered. 4.1.4 Model Microfield Method A different approach to calculate the Stark broadening in a plasma, named the model microfield method (MMM), was derived by Brissaud and Fritsch [68]. Considering only dipole interactions the time dependent electric micro field produced by the plasma electrons and ions is needed. Here, the field strength jumps instantaneously between constant values in a stochastic way [69]: E(t) =              E0for 0 ≤t≤t0 E1for t0≤t≤t1 E2for t1≤t≤t2 . . . (4.18) The information from the previous condition is not just lost with a new jump but at any time (a so-called kangaroo process [68, 70]). Then the probability density for the duration of the occurrence of a given field strength, ω(t|E), is given by: ω(t|E) = µ(E)e−µ(E)t(4.19) with the jump frequency µ(E). The auto correlation function for the field strength of 44 4.2. Influence of other broadening mechanism this stochastic process is: Φ(t) = ∞ Z0 dE E2W(E) ∞ Zt dt′µ(E)e−µ(E)t′(4.20) with W(E) being the probability distribution function (section 4.1.3). The jump frequency µ(E), equation 4.19, is derived by setting the correlation function of the statistical process, equation 4.20, equal to the correct auto correlation function of the problem. The auto correlation function for a field produced by statistical independent perturbers including Debye shielding is given in [71] to be: Φ(t) = 4πnee2 tr2m πkBT1 + τ2−√πτ τ2+3 2eτ2erfc(τ)(4.21) with τ=ωplt/√2 and the error function erfc(τ) = 2 √π ∞ Zτ e−t2dt (4.22) With this, the Schr¨odinger equation (4.5) can be solved exactly. The big advantage of this approach is that both, strong (Stark splitting) and weak (pressure broadening) collisions can be described. Moreover, through the superposition of two stochastic processes, the perturbation of electrons and ions can be calculated uniformly. Hence, the ion pressure broadening has not to be neglected. Based on this theory, Stehl´e and Hutcheon have calculated and published Stark broadened spectral lines for several members of the Lyman and Balmer series for a wide density and temperature range [72, 73]. At present these profiles are the most accurate ones with an uncertainty of about 10% and widely accepted. In Figure 4.2 a comparison of different Stark broadened Balmer line profiles calculated with the unified theory and MMM profiles published by Stehl´e and Hutcheon are shown. The unified theory profiles have narrower line centres due to the ion pressure broadening which has to be neglected in this theory. This leads to broader line wings. In agreement with section 4.1.1 this effect becomes less important with higher upper principal quantum number. Considering further that the line centre is smeared out by folding the Stark profile with an additional Doppler profile, see section 4.2.2, the difference between the two theories becomes negligible for the higher members of the Balmer series. 4.2 Influence of other broadening mechanism In addition to the Stark broadening there are other broadening mechanisms that have to be considered. The magnetic field present in a tokamak causes Zeeman splitting of the 45 4 Diagnostic energy levels, and the temperature of the emitting atom leads to Doppler broadening. Finally, the entrance slit of the spectrometer causes a line broadening referred to as the instrument function. In the following these mechanisms will be introduced and their influence with respect to the Stark broadening will be discussed. 485.9 486.0 486.1 486.2 486.3 486.4 λ (nm) 0 5 10 15 20 25 Intensity (a.u.) HβUnified Theory MMM 433.8 433.9 434.0 434.1 434.2 434.3 434.4 λ (nm) 0 5 10 15 20 25 Intensity (a.u.) 409.8 409.9 410.0 410.1 410.2 410.3 410.4 410.5 λ (nm) 0 3 6 9 12 Intensity (a.u.) 396.5 396.7 396.9 397.1 397.3 397.5 λ (nm) 0 2 4 6 8 10 Intensity (a.u.) Hγ HδHε Figure 4.2: Stark profile of ne= 1 ·1020 m−3for different Balmer lines calculated with the unified theory compared to the MMM profiles published by Stehl´e [73]. 4.2.1 Zeeman splitting A magnetic field results in a splitting of the atomic energy levels and hence to a broadening of the spectral line. The corresponding Hamilton operator in equation 4.5 now depends also on the magnetic field (Hi,f (E, B)). The Schr¨odinger equation is then written as: hH0+e 2mc ~ B(~ L+ 2~ S) + e~ E~ri|Ψi=E|Ψi(4.23) ~ Lis the orbit angular momentum and ~ Sthe spin. Following the calculations of Nguyen-Hoe et. al. [63] this equation can be solved with first order calculation of perturbations. The result is an Eigenvalue equation for the 46 4.2. Influence of other broadening mechanism x y z E E E z x γ B Figure 4.3: Geometry of the perturbation of an emitting atom due to a B-field and an E-field. unperturbed states, which is for ~ B=Bz(see Fig. 4.3) written as: "Lz ~+A −x(1 −(cos γ)2)1/2 a0 +zcos γ a0!# |{z } K |Ψi=ζ|Ψi(4.24) γis the angle between ~ Eand ~ B, see Fig. (4.3). It holds further: A=ea0E ~ωL ωL=eB 2mc (4.25) ζ=E−En 0 ~ω0−1En 0=−e2 2a0 1 n2(4.26) The state of an energy level |Ψican be written as a linear combination of states with different combinations of quantum numbers (with the new quantum number i=l2+l+ m+ 1): |Ψi= n2 X i=1 ai|n, ii(4.27) Then, equation 4.24 results in: n2 X i=1 (K−ζ)ai|n, ii= 0 (4.28) Solving this n2×n2Eigenvalue equation yields n2Eigenvalues ζdescribing the energy of the perturbed levels. For each Eigenvalue ζthere are n2Eigenvectors aispanning the state of the perturbed levels (eq. 4.27). With this, equation 4.9 can be solved for the case of an additional uniform magnetic field. 47 4 Diagnostic In Figure 4.4 profiles of different Balmer lines calculated for typical parameters of ASDEX Upgrade divertor plasmas with and without additional Zeeman splitting are shown. The influence of the Zeeman splitting on the line broadening can be neglected for the higher members of the Balmer series. H 485.9 486.0 486.1 486.2486.3486.4 λ (nm) 0 5 10 15 20 25 Intensity (a.u.) βB = 0 T B = 2.5 T 433.8 433.9 434.0 434.1 434.2434.3434.4 λ (nm) 0 5 10 15 20 25 Intensity (a.u.) 409.8 409.9 410.0 410.1 410.2410.3410.4410.5 λ (nm) 0 3 6 9 12 Intensity (a.u.) 396.5 396.7 396.9 397.1397.3397.5 λ (nm) 0 2 4 6 8 10 Intensity (a.u.) Hγ HδHε Figure 4.4: Stark profile of ne= 1 ·1020 m−3for different Balmer lines calculated with the unified theory with and without an additional magnetic field of B= 2.5 T. 4.2.2 Doppler broadening Besides the Stark broadening and the Zeeman splitting there is also the Doppler broadening influencing the line profile. The Doppler broadening is caused by the thermal motion of the emitting neutral particles with temperature Tn. In a thermal equilibrium the velocity distribution is a Maxwellian and the spectral intensity distribution is given by: I(λ) = 1 √π γ exp "−λ−λ0 γ2#γ=λ0r2kBTn mc2(4.29) In order to be able to evaluate nefrom the Stark broadening one is constrained to a fixed Doppler broadening. Therefore, Tn= 5 eV is assumed, which is the maximum 48 4.3. Diagnostic Setup and data evaluation Franck-Condon dissociation energy of recycled H2molecules. The Doppler broadening mainly influences the central part of the line, while the wings show still the pure Stark profile due to the weak ∆λ−5/2decay. Nevertheless, in Figure 4.5 the FWHM of a Stark and Doppler broadened Dǫline is shown for various neand Tnvalues as an indication for the influence of the Doppler broadening on the Stark profile. For densities larger than ne≈4·1019 m−3the FWHM is insensitive to small changes around Tn= 5 eV. FWHM for Dε (nm) 1018 1019 1020 ne (m-3) 2 4 6 8 10 12 Tn (eV) 0.05 0.07 0.07 0.10 0.10 0.13 0.13 0.16 0.16 0.20 0.20 0.25 0.25 0.30 0.30 0.35 0.35 0.40 0.40 0.50 0.50 0.04 0.12 0.20 0.29 0.37 0.46 0.54 Figure 4.5: FWHM of a Stark and Doppler broadened Dǫline. 4.3 Diagnostic Setup and data evaluation 4.3.1 Diagnostic setup Figure 4.6 shows the geometry of the lines of sight (LOS) in the divertor of ASDEX Upgrade used for the Stark broadening measurement. This setup allows the determination of nein the inner and outer divertor strike point region. The collected light is transmitted via optical fibres with a diameter of df= 400 µm to a Czerny Turner like spectrometer. For this work, two identical spectrometers were available. The polished ends of the fibres are mounted directly in front of the entrance slit of the spectrometer. The light is then dispersed with a reflection grating of 2400 lines/mm and focused onto an EM-CCD camera. The spectrometer is equipped with commercial camera lenses. The collimating lense has a focal length fof 280 mm and an F-number of 4 while for the focusing lense these parameters are f= 180 mm and F= 2.8. The different focal lengths yield a demagnification of 180/280 of the image on the CCD chip. The size of the CCD chip is 656 pixels in the horizontal and 496 pixels in the vertical direction with a pixel size 49 4 Diagnostic 1.5 2.0 2.5 3.0 3.5 4.0 Time (s) 0.0 0.5 1.0 1.5 2.0 ΓD (1e22 (m-2s-1) 1.5 2.0 2.5 3.0 3.5 4.0 Time (s) 0.0 0.5 1.0 1.5 2.0 ΓD (1e22 m-2s-1) 0 200 400 600 ΓD (1e22 m-2s-1) SBD with S/XB ION SBD with S/XB ION SBD with α/RB ION outer divertor inner divertor inner divertor Figure 4.10: Time traces of ΓD0measured by ionization gauges and calculated from SBD measurements for the inner and outer divertor of discharge #24456. the evaluation of the neutral flux density with the α/RB method was done for the first time. 56 Chapter 5 Experimental investigations on divertor detachment In this chapter the experimental results concerning divertor detachment will be shown. Before presenting the obtained classification of divertor detachment in section 5.2, the setup of the discharges and the diagnostics used will be introduced in section 5.1. Thereafter, in section 5.3, the effect of N2seeding and of a magnetic perturbation field on the detachment process as well as the observation of divertor plasma oscillations will be shown. 5.1 Experiment and diagnostic Setup 5.1.1 Discharge setup A series of ohmic and L-mode density ramp discharges has been performed at ASDEX Upgrade to study the detachment of the divertor. Since 2007, the plasma facing surfaces of ASDEX Upgrade are completely covered with tungsten [74]. All discharges of this series were in lower single null divertor configuration with a lower triangularity of δ= 0.36, a plasma current of Ip= 1 MA, a toroidal magnetic field of Bt= 2.5 T and a safety factor of q95 ≈4. The electron cyclotron resonance heating, ECRH, power was varied from discharge to discharge. The fuelling species was changed between deuterium and hydrogen and the field direction was changed between forward field (ion B×∇B drift towards the lower divertor, sec. 2.3.2) and reversed field, see Table 5.1. Due to the alignment of the divertor tiles, the magnetic helicity has to remain constant. Thus Btand Iphave to be changed simultaneously in reversed field operation. Within one shot additional nitrogen was puffed into the divertor, in order to trigger the detachment via removal of power in the SOL by impurity line radiation. Another discharge was performed with an externally applied magnetic perturbation, MP, field (Tb. 5.1). 57 5 Experimental investigations on divertor detachment Table 5.1: Table of plasma parameters that were varied during the series of density ramp discharges. shot # PECRH[kW] Gas Field special 27098 0 D forward 27099 400 D forward 27100 600 D forward 27101 900 D forward 27102 900 D forward MP field 27326 600 D forward N2seeding 27283 0 D reversed 27284 900 D reversed 27286 1300 D reversed 27360 0 H forward 27361 1000 H forward In Figure 5.1 time traces of various plasma parameters for the discharge #27100 are shown. The current flat top was reached at 1.3 s and a stable magnetic configuration at 1.8 s. The strike point positions where then kept constant within a tolerance of 1 cm, see Figure 5.1b. This magnetic configuration in the divertor is shown in Figure 5.2. Also shown in Figure 5.2 is what will be called later on the inner and outer scrape-off layer, namely the high and low field side divertor SOL, respectively. The strike point positions had to be kept constant to measure the time evolution of the divertor plasma with fixed geometry in order to exclude any geometric effects during the evolution of the detachment. The gas fuelling ramp starts 150 ms after the stable magnetic configuration has been reached. The gas input was thereby increased from 1·1021 up to 1·1022 atoms/s with a rate of 1·1021 atoms/s2. Then the rate was increased to 3 ·1021 atoms s−2and the fuelling was ramped up until the density limit occurred. The fuelling ramp leads to a continuous increase of the plasma density and to the development of the detachment in the divertor. This fuelling scheme was not changed within the series of discharges except for the one with additional nitrogen seeding. 5.1.2 Diagnostic setup Flush mounted Langmuir triple probes measure the ion saturation current density, jsat, and the electron density, ne,t and temperature, Te,t at the divertor targets at the positions shown in Figure 5.2a. The ion flux, ΓD+, is then calculated dividing jsat by the elementary charge e, assuming pure deuterium plasmas. The spatial probe separation in poloidal 58 5.1. Experiment and diagnostic Setup 0.0 0.5 1.0 1.5 2.0 2.5 -2 -1 0 1 2 0.0 0.5 1.0 1.5 2.0 0 1 2 3 Time (s) 0 2 4 6 0 1 2 3 Time (s) 0.0 0.5 1.0 1.5 2.0 ne core (1e19 m-2) ne edge (1e19 m-2) Fueling (1e22 at s-1) IP (MA) BT (T) ECRH (MW) PTOT (MW) PRAD (MW) PTarget (MW) PNET (MW) Strike Pointin ∆S (cm) Strike Pointout ∆S (cm) (a) (c) (e) (d) (b) Figure 5.1: Time traces of a representative discharge #27100. Plasma current (blue) and toroidal magnetic field (red) (a), relative positions of the inner (red) and outer (blue) strike point position (b), applied ECRH power (green), total heating power including ohmic heating (black) and total radiated power (c), plasma fuelling (blue), central (green)and peripheral (cyan) line integrated plasma density (d), net power to the divertor targets (red) and total power at the inner and outer target (black) measured by IR. direction is ≈2 cm in the inner and ≈2.5 cm in the outer divertor. The temporal resolution is ∆t= 0.035 ms. The electron density in the divertor volume is determined with the SBD diagnostic [58], see section 4.3.1. The geometry of the extended line of sight setup is also shown in Figure 5.2a. Fast AXUV diode bolometers measure the radiation between 1 eV and 8 keV [78]. This measurement is not absolutely calibrated and has a time resolution of 200 kHz. The positions of the the bolometer chords as well as the ionization gauges are shown in Figure 5.2b. When these experiments were carried out, the interesting gauges behind the inner and outer divertor (see sec. 4.4, fig. 4.6) were out of order. In principal, the power flux onto the divertor targets can be calculated from the Langmuir probe measurements according to equation 2.12. However, as mentioned in section 2.1.2, the absolute value of the sheath heat transmission factor γis not well known and varies for different divertor operating regimes. The target power flux density is in addition routinely measured by an infrared camera (IR). In low recycling divertor conditions this measurement can be used to deduce γ[16]. But, in high recycling or especially in detached conditions the IR measurement does not work anymore. The IR camera measures light at a wavelength of 4.7µm±1µm. In this range, there also exists a deuterium line of the Pfund series (n= 7 →n= 5) at λ= 4.65 µm. On top of 59 5 Experimental investigations on divertor detachment this, there are also molecular deuterium bands present in this spectral IR range. With the transition from attached to detached conditions, the neutral density in the divertor increases and therefore, the atomic and molecular deuterium radiation increases. In addition, recombination can become dominant, which preferably populates the higher nstates such as the upper level of this Pfund-line. The target temperature (and therefore the IR emission from the target) decreases, however, and is then strongly disturbed by this stray radiation. In order to verify this, one can make a power balance. In Figure 5.1e the net power to the divertor targets, Pnet, and the total power Pton the inner and outer target measured by IR is shown. The net power is given by Pnet =Ptot −dW/dt−Prad, where Ptot,Prad (Fig. 5.1c) are the total heating power including ohmic heating and the total radiated power measured by bolometry, respectively, and dW/dtis the change of the stored energy. Ptis derived by integrating the power flux density over the entire target in poloidal and toroidal direction. It can bee seen, that at t≈2.3 s Ptexceeds Pnet. This is physically impossible and most likely the effect of the mentioned stray radiation. Therefore, no target heat flux measurements are discussed in the following. 1.10 1.20 1.30 1.40 1.50 1.60 1.70 -1.20 -1.10 -1.00 -0.90 -0.80 -0.70 -0.60 R (m) z (m) ∆R=0 ∆S = 30 ∆S = 0 ∆S = 15 ∆S = 0 ∆S = 10 ∆R = -15 1.10 1.20 1.30 1.40 1.50 1.60 1.70 R (m) F11 F20 F4 V2 inner SOL outer SOL (a) (b) Figure 5.2: (a): LOS for Stark broadening (blue) and fixed Langmuir probes (red). Also shown is the ∆Sand ∆Rcoordinate. (b): AXUV LOS (blue), ionization gauges (red) and vertical interferometer chord (green). 5.1.3 The degree of detachment Similar to a previous work at JET [79] the notation of degree of detachment, DOD, is used as a marker for the onset and the magnitude of detachment. It is defined as the ratio of the calculated (Φcalc D+) and measured (Φmeas D+) ion flux to the target. Following the simple Two-Point-Model, the ion flux reaching the divertor target is proportional to the square 60 5.1. Experiment and diagnostic Setup of the upstream separatrix density nsep u, see section 2.2.2 and equation 2.28. Furthermore, for Ohmic and L-Mode discharges it has been shown that nsep uscales approximately linearly with the line integrated plasma density, ¯ne[80]. Therefore Φcalc D+is deduced from a horizontal edge interferometer measurement and the degree of detachment is then calculated as: DOD = Φcalc D+ Φmeas D+ =C1·(nsep u)2 Φmeas D+ =C·¯n2 e Φmeas D+ (5.1) The total ion flux to the entire target is obtained by integrating over all Langmuir probe measurements along the divertor surface: Φmeas D+= 2πZΓD+(S)R(S)dS ≈2πX iprobes ΓD+(i)R(i)·S(i+ 1) −S(i−1) 2(5.2) It should be noted that the large separation between the third and the second uppermost probe in the inner divertor (Fig. 5.2a) results in an additional uncertainty of Φmeas D+. To determine the two constants Cin Eq. 5.1 for the inner and outer divertor, the mean values of Φmeas D+(1.8 s < t < 1.9 s) before the fuelling ramp are set equal to Φcalc D+. At this time the inner divertor is already in a high recycling regime although this is the lowest achievable main plasma density in these density ramp discharges. When the divertor plasma can be described by the simple Two-Point-Model, then Φcalc D+= Φmeas D+and DOD = 1. The main assumptions of the model are that there is no significant energy and pressure loss along a field line, see section 2.2.2. Simply speaking, when the pressure drops along a field line, hence detachment begins, Φmeas D+becomes less than Φcalc D+ and DOD >1. There could be other mechanisms leading to a less steep rise of Φmeas D+compared to the TPM scaling such as e.g. a change of the ratio between conducted and convected heat flux, see equations 2.23 and 2.28. Therefore the onset of detachment at JET was defined when the DOD calculated with the peak ion flux becomes larger than 2 while the DOD calculated with the integrated ion flux is below 2. For this work, in contrast, the onset of detachment is defined when Φmeas D+rolls over. The DOD is only used as a guide line, as it will be shown that the roll over of Φmeas D+does not necessarily coincide with the condition of the degree of detachment being lower than one. 61 5 Experimental investigations on divertor detachment 5.2 Evolution of divertor detachment - the three detachment states The main observation of this work is that the detachment process in ohmic and L-mode can be divided into three different states. In the first state, which will be called the onset state, the first deviation from the simple Two-Point-Model scaling occurs. In the second one, the fluctuating state, radiative fluctuations in the inner SOL close to the X-point occur. When these fluctuations vanish, complete detachment over a large target area sets in, giving this third state the name complete detachment state. Furthermore, the characteristics of these states are a combination of both the inner and outer divertor conditions, meaning that the behaviour of both divertors is coupled. These divertor conditions will be described in the following for forward field direction and deuterium fuelling (section 5.2.1), for forward field direction and hydrogen fuelling (section 5.2.2) and for reversed field direction and deuterium fuelling (section 5.2.3). 0 1 2 4 5 1e22 (s-1) (OS) (FS) (CDS) 0 4 10 12 1e22 (s-1) 2 3 4 5 P (MW m-2) x-point Prad 2.0 2.5 3.0 3.5 Time (s) 3 6 9 12 f (kHz) ΦD+(scl) = 4.7e-17*ne 2 ΦD+(me) outer ΦD+(me) ΦD+(scl) = 9.1e-17*ne 2 inner (a) (c) (e) (f) 1 10 100 inner DOD (OS) (FS) (CDS) 1 2 3 4 5 ne (1e19 m-2) 2 4 6 8 10 outer DOD (b) (d) 2 6 8 3 Figure 5.3: Left: Calculated and measured total ion flux to the inner (a) and outer target (c), line integrated radiated power (e) measured by an AXUV diode (orange chord in Figure 5.2b) and its power spectrum (f). Right: DOD as a function of the line integrated peripheral plasma density for the inner (b) and outer (d) divertor of discharge #27100. Note the logarithmic scale of (b). The three detachment states (OS), (FS) and (CDS) are marked. 62 5.2. Evolution of divertor detachment - the three detachment states 5.2.1 The three detachment states in forward field In the following, the evolution of detachment in the inner and outer divertor with forward field direction is described. Representative for all discharges of this series, which are made in forward field, measurements of the discharge #27100 (Fig. 5.1, Tb. 5.1) are shown. The absolute values presented here are only valid for this specific discharge. The qualitative trends of the various parameters during the three detachment states are, however, valid for all discharges made in forward field with deuterium. 0 10 20 30 40 inner ∆S (cm) ne,V (m-3) SBDne,V (m-3) SBD (b)(b) 4.0 13.6 23.2 32.8 42.4 1e19 0 5 10 15 outer ∆S (cm) (OS) (FS) (CDS) ne,V (m-3) SBDne,V (m-3) SBD (c)(c) 4.0 13.4 22.9 32.3 41.7 1e19 -14 -12 -10 -8 -6 -4 -2 x-point ∆R (cm) (OS) (FS) (CDS) ne,V (m-3) SBD ne,V (m-3) SBD (a)(a) 8.0 11.8 15.6 19.4 23.2 1e19 0 5 10 15 20 inner ∆S (cm) ne,t (m-3) LPne,t (m-3) LP (d)(d) 0.0 0.7 1.3 2.0 2.6 1e19 0 5 10 15 outer ∆S (cm) ne,t (m-3) LPne,t (m-3) LP (e)(e) 0.0 2.0 4.0 6.0 8.1 1e19 0 5 10 15 20 inner ∆S (cm) Te,t (eV)Te,t (eV) (f)(f) 0.0 8.9 17.9 26.8 35.7 0 5 10 15 outer ∆S (cm) Te,t (eV)Te,t (eV) (g)(g) 0.0 11.8 23.5 35.3 47.1 2.0 2.5 3.0 3.5 Time (s) 0 5 10 15 20 inner ∆S (cm) ΓD+ (m-2s-1)ΓD+ (m-2s-1) (h)(h) 0.0 8.0 15.9 23.9 31.8 1e21 2.0 2.5 3.0 3.5 Time (s) 0 5 10 15 outer ∆S (cm) ΓD+ (m-2s-1)ΓD+ (m-2s-1) (i)(i) 0.0 57.9 115.9 173.8 231.7 1e21 Figure 5.4: Horizontal (a) and vertical (b,c) line integrated ne,V profile in the divertor volume and ne,t (d,e), Te,t (f,g) and ΓD+(h,i) target profiles in the inner and outer divertor, respectively, of discharge #27100. The three detachment states are marked. 63 5 Experimental investigations on divertor detachment Figure 5.3 shows the measured and scaled temporal evolutions of ΦD+and the corresponding DOD as a function of the line integrated peripheral plasma density of the inner and outer divertor. From this, the onsets of detachment of the inner and outer divertors are set to t≈2 s (¯ne≈1.5·1019 m−2) and t≈2.85 s (¯ne≈3.3·1019 m−2), respectively. Before the onset of the inner divertor detachment at t < 2 s, ΦD+to the inner divertor is higher than that to the outer divertor. The ratio of both corresponds to the ratio of the constants C, see Figure 5.3a,b: Φin D+/Φout D+= 9.1/4.7 = 1.9 The target profiles of ne,t,Te,t and ΓD+measured by LP and the line integrated density profiles in the divertor volume measured by SBD as a function of time are shown in Figure 5.4. The ∆Rcoordinate for the inner vertical SBD LOS in Figure 5.4a is the distance from the X-point along a horizontal line, the origin is at the X-point position and negative values are in the inner SOL (see Fig. 5.2a). Before the onset of the inner divertor detachment (t < 2 s) peak ion fluxes of ΓD+≈2·1022 m−2s−1close to the inner strike point and ΓD+≈1.5·1022 m−2s−1close to the outer strike point are measured, respectively. Their ratio of Γin D+/Γout D+= 1.3 is more symmetric than the total ion flux ratio of Φin D+/Φout D+= 1.9. This means that the inner ion flux profile is broader compared to the profile of the outer divertor which indicates that the inner divertor is already in a higher recycling regime, as mentioned above. The electron density in the divertor volume is below the measurement range of ne> 4·1019 m−3of the SBD in both the inner and outer divertor. This is expected as the density at the targets, measured by LP, is below 1.5·1019 m−3, which corresponds to a density at the recycling zone of ne,V ≈2·ne,t ≈3·1019 m−3(section 2.2.1, equation 2.19). The onset of detachment state The start of the onset state is defined when the first deviation from the Two-Point-Model scaling occurs. This happens in the inner divertor, see above, where the measured ΦD+ increases less strongly than the TPM scaling. Inner divertor During this state, the ion flux close to the inner strike point, ∆S≈ 1 cm rolls over and drops to ΓD+≈1·1022 m−2s−1with increasing upstream density (Fig. 5.4h). This is also visible in the total ion flux to the inner divertor which further deviates from the TPM scaling (Fig. 5.3a) and the DOD increases (Fig. 5.3b). Also ne,t close to the strike point decreases with increasing upstream density, but, in contrast, increases in the far SOL at ∆S≈14 cm up to ne,t ≈2.3·1019 m−3at the end of the onset state (Fig. 5.4d). This is consistent with the radiation distribution measured by foil bolometry, shown in Figure 5.5. The radiation is higher in the inner far SOL than close to the strike point. In addition, the electron density in the volume increases up 64 5.2. Evolution of divertor detachment - the three detachment states 1.0 1.2 1.4 1.6 1.8 R (m) -1.2 -1.0 -0.8 -0.6 z (m) #27100 t = 2.2 s Figure 5.5: Total radiation distribution from foil bolometry in the divertor at one time point during the onset state for #27100. to ne,v ≈1.3−2.3·1020 m−3(Fig. 5.4a,b). All in all, this indicates that the plasma is partially detached from the inner strike point region at the end of this state. Outer divertor The outer divertor is still attached, in the conduction limited regime and follows the simple TPM (DOD= 1) throughout this state (Fig. 5.3b,d). With increasing upstream density, the maximum of ΓD+and ne,t increases during this state up to 4·1022 m−2s−1and 1.4·1019 m−3, respectively, while Te,t drops to 25 eV (Fig. 5.4i,e,g). The electron density in the volume stays below 4 ·1019 m−3(Fig. 5.4c). The fluctuating detachment state This state is defined by the appearance of radiative fluctuations which are situated close to the X-point in the inner SOL. During this state, the core plasma fuelling becomes less efficient. Although the amount of the fuelling gas is steadily increased, the core plasma density seems to saturate (Fig. 5.1d, t≈2.9 s). The characteristics of these fluctuations and the evolution of the divertor plasma parameters during this state are described in the following. The X-point fluctuations The transition to this state is determined with a sudden onset of a fluctuation band of f≈5.5 kHz (Fig. 5.3e,f), measured with the AXUV diodes, which is observed for the first time. The width of this fluctuation band is ∆f≈3 kHz and the amplitude is about 1.5 times the original radiation level, which can be seen in the time trace of an AXUV diode (Fig. 5.6). There is currently no other diagnostic available measuring with such a high sampling rate in the according region in order to trace these fluctuations back to the electron temperature or to the density or to a combination of both. 65 5 Experimental investigations on divertor detachment 8 kHz ≈rmD mH·5.5 kHz = 1.4·5.5 kHz = 7.7 kHz (5.3) 0 4 10 1e22 (s-1) (OS) (FS) (CDS) 0 5 10 15 20 1e22 (s-1) 1.5 2.5 3.5 4.5 P (MW m-2) x-point Prad 2.0 2.5 3.0 3.5 4.0 Time (s) 3 6 9 12 f (kHz) ΦD+(scl) = 8.7e-17*ne 2 ΦD+(me) outer ΦD+(me) ΦD+(scl) = 13.7e-17*ne 2 inner (a) (c) (e) (f) 1 10 inner DOD (OS) (FS) (CDS) 1 2 3 4 ne (1e19 m-2) 1 2 3 4 5outer DOD (b) (d) 8 6 2 Figure 5.12: Left: Calculated and measured total ion flux to the inner (a) and outer target (c), line integrated radiated power (e) measured by an AXUV diode (orange chord in Figure 5.2b) and its power spectrum (f). Right: DOD as a function of the line integrated peripheral plasma density for the inner (b) and outer (d) divertor of discharge #27362. Note the logarithmic scale of (b). The three detachment states are marked. 5.2.3 The three detachment states in reversed field In this section the evolution of the divertor plasma is described when Btand Ipare reversed and compared to the forward field case. Representative for all discharges of the series which are made in reversed field measurements of the discharge #27284 (Tb. 5.1) are shown. When these discharges were carried out, the foil bolometry was not available. Therefore, no measurements of the radiation distribution in the divertor can be shown here. As in forward field, there are three different states during the evolution of detachment. The qualitative development of the target parameters ne,t,Te,t and ΓD+ in the inner, respectively outer target in reversed field is rather comparable to the outer, 72 5.2. Evolution of divertor detachment - the three detachment states respectively the inner target in forward field. Whereas the density in the divertor volume evolves quite similar in both field directions. 0 1 2 4 5 1e22 (s-1) (OS) (FS) (CDS) 0 5 10 15 1e22 (s-1) 2.5 3.5 4.5 P (MW m-2) x-point Prad 2.0 2.5 3.0 3.5 Time (s) 3 6 9 12 f (kHz) ΦD+(scl) = 12.7e-17*ne 2 ΦD+(me) outer ΦD+(scl) = 3.5e-17*ne 2 ΦD+(me) inner (a) (c) (e) (f) 1 10 inner DOD (OS) (FS) (CDS) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 ne (1e19 m-2) 2 4 6 8 10 outer DOD (b) (d) 3 Figure 5.13: Left: Calculated and measured total ion flux to the inner (a) and outer target (c), line integrated radiated power (e) measured by an AXUV diode (orange chord in Figure 5.2b) and its power spectrum (f). Right: DOD as a function of the line integrated peripheral plasma density for the inner (b) and outer (d) divertor of discharge #27284. Note the logarithmic scale of (b). The three detachment states are marked. The measured and calculated temporal evolutions of ΦD+and the corresponding DOD as a function of the line integrated peripheral plasma density of the inner and outer divertor are shown in Figure 5.13. The onsets of detachment (roll over of ΦD+) of the inner and outer divertors are therefore at t≈2.4 s (¯ne≈2.1·1019 m−2) and t≈2.5 s (¯ne≈2.5·1019 m−2), respectively. Before the start of the fuelling ramp, t < 1.9 s, the total ion flux to the outer target is larger than to the inner target, Φout D+/Φin D+= 3.6 (Fig. 5.13a,c). This ratio is less symmetric compared to the forward field case and, contrary to forward field, in favour of the outer divertor. Figure 5.14 shows the inner and outer target profiles of ne,t,Te,t and ΓD+as well as the density measurements in the inner and outer divertor volume. Before the start of the fuelling ramp, peak ion fluxes of ΓD+≈8·1021 m−2s−1and ΓD+≈5.2·1022 m−2s−1close 73 5 Experimental investigations on divertor detachment 0 10 20 30 40 inner ∆S (cm) ne,V (m-3) SBDne,V (m-3) SBD (b)(b) 4.0 14.4 24.7 35.1 45.4 1e19 0 5 10 15 outer ∆S (cm) (OS) (FS) (CDS) ne,V (m-3) SBD ne,V (m-3) SBD (c)(c) 4.0 10.4 16.8 23.2 29.6 1e19 -14 -12 -10 -8 -6 -4 -2 x-point ∆R (cm) (OS) (FS) (CDS) ne,V (m-3) SBD ne,V (m-3) SBD (a)(a) 8.0 15.7 23.4 31.0 38.7 1e19 0 5 10 15 20 inner ∆S (cm) ne,t (m-3) LPne,t (m-3) LP (d)(d) 0.0 1.2 2.3 3.5 4.7 1e19 0 5 10 15 outer ∆S (cm) ne,t (m-3) LPne,t (m-3) LP (e)(e) 0.0 1.2 2.4 3.7 4.9 1e19 0 5 10 15 20 inner ∆S (cm) Te,t (eV)Te,t (eV) (f)(f) 0.0 5.3 10.7 16.0 21.3 0 5 10 15 outer ∆S (cm) Te,t (eV)Te,t (eV) (g)(g) 0.0 12.4 24.9 37.3 49.7 2.0 2.5 3.0 3.5 Time (s) 0 5 10 15 20 inner ∆S (cm) ΓD+ (m-2s-1)ΓD+ (m-2s-1) (h)(h) 0.0 12.2 24.3 36.5 48.6 1e21 2.0 2.5 3.0 3.5 Time (s) 0 5 10 15 outer ∆S (cm) ΓD+ (m-2s-1)ΓD+ (m-2s-1) (i)(i) -0.2 39.4 79.0 118.6 158.2 1e21 Figure 5.14: Horizontal (a) and vertical (b,c) line integrated ne,V profile in the divertor volume and ne,t (d,e), Te,t (f,g) and ΓD+(h,i) target profiles in the inner and outer divertor, respectively, of discharge #27284. The three detachment states are marked. 74 5.2. Evolution of divertor detachment - the three detachment states to the inner and outer strike point are measured, respectively. The onset of detachment state As in forward field, the start of the onset state is defined by the first deviation from the TPM scaling. This happens, similar to forward field, in the inner divertor. Contrary to forward field, the X-point fluctuations appear already in this state. Their amplitude grows during this state until, at the end of this state, its maximum is reached. Inner divertor Contrary to forward field, the measured total ion flux increases more strongly compared to the TPM scaling (Fig. 5.13a). Thus, the flux enhancement occurs now in the inner divertor and the DOD falls below unity (Fig. 5.13b). During this state ΓD+and ne,t increase up to ΓD+≈5·1022 m−2s−1and ne,t ≈6·1019 m−3, respectively, and then roll over. The target temperature first decreases with increasing ne,t and ΓD+ and increases when ne,t and ΓD+roll over (Fig. 5.14d,f,h). Associated with the roll over, a high density front of ne,V ≈2·1020 m−3develops in the SOL at ∆S≈7 cm, see Figure 5.14b. It should be noted that, while ΓD+increases between t= 2.1 s and t= 2.3 s, there seems to be a shift of ΓD+back to ∆S≈4 cm at t= 2.2 s (Fig. 5.14h). But it is more likely that the peak of the ion flux profile moves between to probe positions in this case. Outer divertor The measured ΦD+follows the TPM scaling throughout this state and the DOD is 1, see Figure 5.13b,d. The peak position of ΓD+and ne,t remains constant during the discharge (Fig. 5.14e,i). ΓD+rises up to ≈1.6·1023 m−2s−1and ne,t up to ≈5·1019 m−3. Similar to the inner divertor in forward field, the electron temperature at the target increases with increasing ΓD+and ne,t throughout this state (Fig. 5.14g). The density in the volume close to the strike point increases up to ≈1.5·1020 m−3, see Figure 5.14c. The fluctuating detachment state In reversed field, the start of this state is defined when the strength of the X-point fluctuations reaches its maximum, see Figure 5.13f. The X-point fluctuations Contrary to forward field, two frequency bands, one at f≈4.5 kHz and one at f≈9 kHz are observed (Fig. 5.13f). The width of each of these frequency bands is ∆f≈3 kHz, which is similar to forward field. The maximum of the fluctuations is still located in the inner SOL close to the X-point, see figure 5.15. Their spatial extent, however, is larger than in forward field and seems to expand into the outer divertor SOL. 75 5 Experimental investigations on divertor detachment 1.2 1.3 1.4 1.5 1.6 1.7 R (m) -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 z (m) 0.0 1.4 2.9 4.3 5.8 Horizontal LOS (a.u.) 0.0 5.3 10.6 15.9 21.2 Vertical LOS (a.u.) Figure 5.15: Intensity of the fluctuations for all AXUV channels of discharge #27284. The colour-code represents the strength. Inner divertor During this state, the ion flux and the target density steadily drop further to ΓD+≈5·1021 m−2s−1and ne,t ≈7·1018 m−3, respectively (Fig. 5.14d,h). Furthermore, the profile of ne,t is getting broader. The target temperature first increases further up to Te,t ≈13 eV and then rolls over within this state (Fig. 5.14f). Associated with the further decrease of ΓD+and ne,t, the high density front at the strike point region (∆S < 10 cm) rises up to ne,V ≈3.7·1020 m−3and then rolls over when Te,t rolls over (Fig. 5.14b). Linked to the fluctuations high density fronts of ne≈3·1020 m−3(Fig 5.14a,b) develop in the inner far SOL (∆S≈15 cm) and X-point region (∆R≈ −2 cm). This is similar to forward field. Contrary to forward field, the X-point high density front reaches its maximum at the end of the fluctuating state. Outer divertor ΦD+, ΓD+and ne,t roll over at the start of this state (Figs. 5.13b, 5.14e,i) and the DOD exceeds unity (Fig. 5.13d). The target temperature steadily increases throughout this state up to Te,t ≈50 eV (Fig. 5.14g). Furthermore Te,t strongly fluctuates, which is most likely linked to the radiative X-point fluctuations. As the time resolution of the Langmuir probes is too slow, a correlation analysis with the AXUV diodes can not, however, be made. Associated with the further decrease of ΓD+and ne,t, the high density front at the strike point region increases up to ne≈3·1020 m−3during this state (Fig. 5.14c). 76 5.2. Evolution of divertor detachment - the three detachment states The complete detachment state The beginning of the complete detachment state is defined, similar to forward field, when the radiative X-point fluctuations vanish. Inner divertor At the start of this state, the target parameters at the strike point region (∆S < 10 cm) have already reached very low values of ΓD+<2·1021 m−2s−1, ne,t <3·1018 m−3and Te,t <2 eV (Fig. 5.14d,f,h). Also the high density front in this region has vanished (Fig. 5.14b), indicating that the plasma is completely detached from the inner strike point region. Moreover, similar to forward field, the high density front from the inner strike point region moves upwards along the field lines well above the X-point (Fig. 5.14a,b). 0 10 20 30 40 inner ∆S (cm) (OS) (FS) (CDS) ne,V (m-3) SBD ne,V (m-3) SBD (a)(a) 4.0 14.4 24.7 35.1 45.4 1e19 0 5 10 15 outer ∆S (cm) (OS) (FS) (CDS) ne,V (m-3) SBD ne,V (m-3) SBD (b)(b) 4.0 10.4 16.8 23.2 29.6 1e19 2.0 2.5 3.0 3.5 Time (s) 0 10 20 30 40 inner ∆S (cm) Dδ/DεDδ/Dε (e)(e) 2.3 2.7 3.1 3.5 3.8 2.0 2.5 3.0 3.5 Time (s) 0 5 10 15 outer ∆S (cm) Dδ/DεDδ/Dε (f)(f) 2.8 3.0 3.3 3.5 3.8 0 10 20 30 40 inner ∆S (cm) Radiance (Ph m-2sr-1s-1)Radiance (Ph m-2sr-1s-1) (c)(c) 0.0 17.1 34.2 51.4 68.5 1e17 0 5 10 15 outer ∆S (cm) Radiance (Ph m-2sr-1s-1)Radiance (Ph m-2sr-1s-1) (d)(d) 0.0 13.3 26.5 39.8 53.0 1e17 Figure 5.16: Time traces of the line integrated density (a,b), the emissivity of Dδ(c,d) and the line ratio Dδ/Dǫ(e,f) in the inner and outer divertor volume, respectively of discharge #27284. Outer divertor The ion flux and the density at the target drop further during this state (Fig. 5.14e,i). Similar to the inner divertor in forward field, the electron temperature at the strike point region (∆S≈5 cm) starts to decrease (here to Te,t ≈6 eV at the end of the discharge) while there is a short strong increase of Te,t in the private flux region (Fig. 5.14g). The high density front in the strike point region (∆S < 10 cm, Fig. 77 5 Experimental investigations on divertor detachment 5.14c) is reduced by ≈50% to ne≈1.5·1020 m−3during this state. The position of the peak ne,V moves slightly upstream, but, contrary to forward field, stays in the strike point region until the end of the discharge. Evidence for volume recombination and low divertor temperatures Similar to forward field, there is evidence for volume recombination and therefore electron temperatures below ≈1 eV in the inner and outer divertor. Figure 5.16 shows the density in the divertor volume, the emissivity of Dδand the line ratio Dδ/Dǫ. It can be seen again that the line emission increases when the high density front has moved away from the target (below the blue dotted line in Fig. 5.16a,c), indicating temperatures of ≈1.5 eV when the emission reaches its maximum. When the line emission decreases, the Dδ/Dǫline ratio increases, and electron temperatures below ≈1 eV can be expected in the regions below the red dotted lines in Figure 5.16. 5.3 Additional effects In this section, the effect of additional N2seeding and an additional magnetic perturbation field on the detachment process will be presented. Furthermore it will be shown that, under certain conditions, the divertor plasma oscillates between the onset and fluctuating detachment state back and forth. 5.3.1 Effect of impurity seeding during the fluctuating state It was mentioned in section 2.2.3 that, besides increasing the main plasma density, the temperature can be reduced by injecting additional impurities. In this section it will be shown how N2seeding alters the detached divertor plasma conditions. In ASDEX Upgrade, it is possible to puff impurities below the divertor dome into the plasma in a feedback controlled way [81], which then cool the divertor plasma via line radiation. The amount of injected nitrogen is controlled with a shunt measurement of the thermoelectric current into the outer divertor target, yielding an approximation for the divertor temperature, Tt,sh [81]. Effect of N2seeding during the fluctuating state Such a feedback controlled N2puffing was applied during the fluctuating detachment state in forward field. This discharge #27326 is an identical repeat of the reference discharge #27100 (Table 5.1) with the following exception. When the fluctuating detachment state was established, the fuelling gas puff and hence the plasma density were kept constant. Then the N2seeding was applied. In Figure 5.17a time traces of the 78 5.3. Additional effects 25 0 1 2 3 4 (1e22 at s-1) ne (1e19 m-2) D Fuelling N Puff 0 5 10 15 20 Tt,sh (eV) requested 2.0 2.5 3.0 3.5 4.0 4.5 Time (s) 2 6 10 14 f (kHz) (a) (b) (c) 12 8 4 measured Figure 5.17: Time traces of (a) Dfuelling (blue), N2puff (red), line integrated core plasma density (green); (b) requested (black) and measured (blue) Tt,sh; (c) spectrogram of an AXUV diode of discharge #27326. applied D and N2puff as well as the line integrated plasma density are shown. The feedback impurity gas puff starts at 2.5 s and is controlled such that Tt,sh is decreased from ≈12 to ≈2 eV. As mentioned before, this is just an approximation of the divertor temperature. The requested Tt,sh as well as the measured one is shown in Figure 5.17b. Due to the delay of the temperature response on the injected N2and the feedback controller itself, N2was puffed intermittently. This is why there are oscillations of Tt,sh around the requested value. Figure 5.18 depicts ΓD+at the target and ne,V in the divertor. With the decrease of the temperature due to the N2seeding, ΓD+on the inner and outer target is reduced by ≈50% (Fig. 5.18d,e). The frequency of the X-point fluctuations is lowered to ≈1 kHz (Fig. 5.17c) during phases where the Tt,sh oscillations are around the minimal temperature values. The frequency at the maxima starts at f≈5.5 kHz for Tt,sh = 12 eV and decreases to f≈3 kHz for Tt,sh = 4 eV. Moreover, the densities of the high ne,V fronts in the inner far SOL, inner X-point region and outer strike point region, characteristic for the fluctuating detachment state, are also reduced by ≈50% (Fig. 5.18a,b,c) during the phases where Tt,sh is close to a local minimum. 79 5 Experimental investigations on divertor detachment 0 10 20 30 40 inner ∆S (cm) ne,V (m-3) SBDne,V (m-3) SBD (b)(b) 4.0 13.5 23.0 32.4 41.9 1e19 0 5 10 15 outer ∆S (cm) (OS) (FS; w N2)(CDS) ne,V (m-3) SBD ne,V (m-3) SBD (c)(c) 4.0 12.0 20.0 27.9 35.9 1e19 -14 -12 -10 -8 -6 -4 -2 x-point ∆R (cm) (OS) (FS; w N2)(CDS) ne,V (m-3) SBD ne,V (m-3) SBD (a)(a) 8.0 11.5 14.9 18.4 21.8 1e19 2.0 2.5 3.0 3.5 4.0 4.5 Time (s) 0 5 10 15 20 inner ∆S (cm) ΓD+ (m-2s-1)ΓD+ (m-2s-1) (d)(d) 0.0 8.7 17.4 26.0 34.7 1e21 2.0 2.5 3.0 3.5 4.0 4.5 Time (s) 0 5 10 15 outer ∆S (cm) ΓD+ (m-2s-1)ΓD+ (m-2s-1) (e)(e) 0.0 46.2 92.3 138.5 184.6 1e21 Figure 5.18: Horizontal (a) and vertical (b) line integrated ne,V profile and ΓD+(d) in the inner divertor. Vertical (c) line integrated ne,V profile and ΓD+(e) in the outer divertor of #27326. The three detachment states are marked. 80 5.3. Additional effects High power H-mode discharges with N2seeding A similar effect is observed in high power, high density H-mode discharges. N2seeding is routinely used in these high power discharges to reduce the power load to the outer divertor target. Besides this cooling effect, N2seeding leads to an improved confinement [82]. The underlying physics of this confinement improvement is not yet completely understood [83]. 0 10 20 30 40 ∆S (cm) PF 2.0 2.5 3.0 3.5 4.0 4.5 Time (s) -15 -10 -5 0 ∆R (cm) 35.0 46.4 57.7 69.1 0 2 4 6 8 10 NBI (MW) N-puff (1e22 atoms s-1) 0 10 20 30 F20 (1e22 m-2s-1) F11 (1e22 m-2s-1) V2 (1e18 m-2) (a) (b) (c) ne (m-3) (d) ne (m-3) 25.0 43.3 61.7 80.0 1e19 1e19 Figure 5.19: Time traces of (a) NBI heating (red), N2puff (green); (b) ΓD(red & magenta), ne,V from V2; horizontal (c) and vertical (d) line integrated ne,V profile in the inner divertor of discharge #26302. In Figure 5.19 time traces of such a discharge with Ip= 1 MA, Bt=−2.5 T and ¯ne≈ 8.2·1019 m−2are shown. The NBI heating power was increased stepwise from 5 MW to 10 MW and a constant N2puff was applied at t= 3.5 s. In the phase without N2puff a high density front around 5·1020 m−3is measured in the upper part of the inner divertor via the Stark broadening diagnostic (Fig. 5.19c,d). This is supported by a vertical interferometer measurement. The position of the interferometer chord (V2) is shown in 81 5 Experimental investigations on divertor detachment pressure in the inner divertor is low (Fig. 5.23). It is remarkable that in JET during the same state sub-oscillations in the Dαsignal with much higher frequency (with respect to the frequency of the plasma oscillations) were observed, as stated in [86]. 88 Chapter 6 Summary and discussion of the experimental results 6.1 Summary During the evolution of divertor detachment three different distinct states where found wherein the behaviour of the inner and outer divertor is strongly coupled. The characteristics of these detachment states will be summarized with respect to the forward field case, which was the most extensively investigated case. The start of the first detachment state, the onset state, is defined when the first deviation from the Two-Point-Model (TPM) scaling occurs. This happens in the inner divertor with the roll over of the ion flux density, ΓD+, (DOD>1) and the target electron density, ne,t, close to the strike point. Associated with this roll over, the electron density in the inner divertor volume, ne,V , starts to increase. The outer divertor follows the TPM scaling (DOD= 1) throughout this state, i.e. ΓD+and ne,t increases with increasing upstream density, whereas the target temperature, Te,t, decreases (consistent with equations 2.26-2.28). # 27100 t = 2.5 s # 27100 t = 2.9 s # 27100 t = 3.5s (a) (b) (c) Figure 6.1: Total radiation distribution from foil bolometry in the divertor for three different time points of #27100. See text for explanations. The appearance of radiative fluctuations characterizes the start of the second, the fluc89 6 Summary and discussion of the experimental results tuating detachment state. These fluctuations have a mean frequency of f≈5.5 kHz, a width of ∆f≈3 kHz and are situated in the inner SOL close to the X-point. In hydrogen, the mean frequency is increased by the square root of the mass ratio of both species, i.e. f≈8 kHz. At the beginning of this state, the total ion flux, ΦD+, to the inner divertor and ΓD+and ne,t close to the inner strike point suddenly increase. In addition, there is a jump of the peak ΓD+and ne,t position in the strike point region from ∆S≈1 cm to ∆S≈5 cm at the transition to the fluctuating state. With increasing upstream density, ΓD+and ne,t at the strike point region (∆S≈5 cm) roll over. After the roll over of ΓD+and ne,t at the strike point region, Te,t in this region increases. This behaviour is consistent, since the momentum loss factor, which accounts for the momentum, and therefore ΓD+and ne,t, removal in equation 2.24, causes an increase of the temperature (eq. 2.26). After the roll over, ne,V increases further. In order to remove momentum via CX-collisions, a high neutral density (gas-target) must exist in front of the target (sec. 2.2.3). At the boundary of this gas-target in the SOL, the plasma parameters still follow the TPM scaling (e.g ne∝¯n3 e, eq. 2.27). The density in the divertor volume should therefore continue to increase with increasing upstream density, being in agreement with the measured evolution. The position and spatial extend of this high density front can be approximated by the distribution of the total radiation in the inner divertor (red circle in Fig. 6.1a). During the fluctuating detachment state, high density fronts develop also in the inner far SOL and X-point region, whose estimated positions are indicated by the red circles in Figure 6.1b. According to the bolometric measurement, it is also possible that this is just one density front rather than two. In any case, however, the density front in the inner divertor expands into the inner far SOL at ∆S≈15 cm, consistent with the measured increase of the ion flux and target electron density in this region. Therefore, a mechanism must exists, which brings more particles to the far SOL, possibly caused by an increase of the turbulent radial transport (eq. 2.44) in this region. At the end of the fluctuating state, the fuelling of the main plasma becomes less efficient, i.e. although the fuelling puff is constantly increased, the main plasma density almost saturates. Based on the stability theory of detached plasmas (sec. 2.2.3), the main plasma density cannot be increased further by gas puffing at a certain point. Then, the dense plasma buffer in the SOL must increase and move towards the X-point (sec. 2.2.3). Indeed, a decrease of ne,V at the inner strike point region and an increase of ne,V in the inner far SOL and X-point region is measured during the phase in which the main plasma density increases less strongly than the fuelling puff (compare also Fig.6.1a,b). The total ion flux to the outer divertor first increases more strongly than the TPM scaling (DOD<1) and then rolls over during the fluctuating detachment state. Consequently, ne,V steadily increases. The effect of DOD<1, namely the flux enhancement, will be discussed below. 90 6.1. Summary The transition to the complete detachment state is defined when the radiative X-point fluctuations vanish. At this transition, the inner and outer divertor simultaneously start to detach completely from the strike point region. The complete detachment is defined here when the target parameters ΓD+,ne,t and Te,t drop to significant lower values and, the main point, when the high density front in the strike point region decreases (In contrast, the onset of detachment is defined here by the roll over of the total ion flux, ΦD+). In the outer divertor, the high density front moves out of the area covered by the SBD diagnostic. In the inner divertor, the movement of the high density front during this state from the target towards and even above the X-point can be monitored. This is consistent with the total radiation distribution before the complete detachment state (6.1b) and at the end of this state (6.1c). It was shown by means of spectroscopy, that, once the high density front has moved away from the target, recombination is dominant and temperatures are below ≈1 eV in the region between the high density front and the target. This is expected, as first a high density is necessary in order to remove momentum from the plasma, slowing down the plasma flow to the target. This triggers, in combination with temperatures below ≈1 eV, the recombination process. In addition, the total radiated power in the main plasma and SOL almost equals the total applied heating power at the end of the complete detachment state (Fig. 5.1c). This indicates that more than ≈90% of the power entering the SOL is radiated before reaching the target. The main differences between the forward field case and the reversed field case are summarized in the following. In reversed field, the radiative X-point fluctuations consist of two frequency bands of f≈4.5 kHz and f≈9 kHz, their width of ∆f≈3 kHz is similar to the forward field case. The spatial extent of the fluctuations is larger compared to forward field and seems to expand into the outer divertor SOL. In reversed field, their amplitude grows already in the onset state and the maximum amplitude is reached in the fluctuating state. In forward field, before the onset of detachment, the total ion flux, ΦD+, to the inner target is larger than to the outer target. In reversed field the total ion flux to the outer target is larger. The first deviation from the TPM scaling is, in forward field, a less steep rise of ΦD+compared to the scaling (DOD >1) and in reversed field a stronger increase (DOD <1, the flux enhancement). The finally achieved DOD is for both field directions larger in the inner than in the outer divertor. The ratio of DOD(in)/DOD(out) becomes more symmetric in reversed field (≈50 in forward field, ≈1.5 in reversed field). Furthermore, the effect of N2seeding during the fluctuating state in forward field was investigated. With additional N2seeding during the fluctuating detachment state, the nevalues of the high density fronts in the inner far SOL, inner X-point region and outer strike point region are reduced by ≈50%. ΦD+to the inner and outer target is reduced by ≈25%. Also the frequency of the radiative X-point fluctuations is reduced 91 6 Summary and discussion of the experimental results to f≈1 kHz with N2seeding. A similar effect is observed in high power, high density H-Mode discharges. Here, the density reduction of the high density front in the inner far SOL is confirmed with a vertical interferometer measurement. In addition, a reduction of the neutral fluxes by ≈50% is measured in the far SOL with N2seeding compared to non seeding phases. Finally, the effect of an additional magnetic perturbation, MP, on the detachment process was studied. Detachment proceeds similarly with and without MP until the outer ΦD+ rolls over. With MP, this roll over is followed by an abrupt and strong drop of ΦD+in the outer divertor, and by the disappearance of the radiative X-point fluctuations and the high density fronts in the inner far SOL and X-point region. Moreover, the detachment of the inner and outer divertor proceeds faster with MP. 6.2 Discussion The observations, summarized above, gave rise to questions, for which possible theories will be discussed in the following. Ion flux asymmetry Before the onset of detachment, in forward field, the ratio of the total ion flux reaching the inner and outer divertor is asymmetric and in favour of the inner divertor (Φin D+/Φout D+= 1.9). When the field direction is changed, this ratio is still asymmetric but now being in favour of the outer divertor (Φout D+/Φin D+= 3.5). A possible explanation of this, as proposed in [43], is the combination of the radial drift, Γdr r, and the poloidal drift in the private flux region (PF), Γdr Θ, induced by ~ E×~ Bforces (sec. 2.3.2). In forward field, Γdr ris directed from the outer SOL across the separatrix into the PF and from the PF into the inner SOL (Fig. 2.2b). The poloidal drift flow, Γdr Θ, in the PF is directed from the outer to the inner divertor (Fig. 2.2a). For similar conditions, such a flow in the PF has been measured in JT-60U [87] and ASDEX Upgrade [88] and was associated with Γdr Θ. Thus, the combination of both Γdr rand Er×Bin the private flux region brings more particles to the inner divertor in forward field and more particles to the outer divertor in reversed field and can explain these asymmetries. Furthermore, the finally achieved DOD is, for both field directions, larger in the inner divertor. This is consistent, as these ~ E×~ Bdrifts should become less important or even negligible at high densities (sec. 2.3.2). In addition, for both field directions the roll over of ΦD+happens first in the inner divertor. The ratio of the peripheral line integrated plasma density at the roll over in the inner and outer divertor is in reversed field ¯ne,in/¯ne,out ≈2.1/2.5 = 0.84. In forward field this ratio is ¯ne,in/¯ne,out ≈ 1.5/3.3 = 0.76. Taking the second roll over (see next point) in forward field, the ratio is ¯ne,in/¯ne,out ≈2.9/3.3 = 0.88, which is comparable to reversed field and indicates that 92 6.2. Discussion the influence of the ~ E×~ Bdrifts became negligible. # 27100 t = 1.8 s # 27100 t = 2.9s (a) (b) Figure 6.2: Total radiation distribution in the divertor for two different time points of #27100. See text for explanations. The two roll overs in forward field In forward field, two roll overs of ΓD+are observed in the inner divertor strike point region, one at the onset state and one at the fluctuating detachment state. A possible reason for the early first roll over followed by a second roll over in the inner divertor in forward field could be a geometric effect of the divertor structure. The lower tile of the inner divertor target is tilted towards the separatrix, i.e. the angle between the target normal and the horizontal axis is negative (white arrow in Fig. 6.2a). In the onset state the ion flux profile is radially not very broad, which is supported by the total radiation distribution (Fig. 6.2a). Recycled neutrals are released from the lower inner target and released in a cos2distribution cone around the target normal, hence back to the strike point region (white arrow in Fig. 6.2a). This would enhance the neutral pressure in the inner strike point region, which increases the probability for CX-collisions to remove momentum, thus the ion flux would decrease, as observed. At the transition to the fluctuating state, a mechanism sets in which brings more particles to the far SOL, i.e. to the upper tile of the inner target (Fig. 6.2a). Once the ion fluxes to this upper tile are strong, and therefore recycling from this tile becomes strong, the situation should change. The upper tile curves backwards, i.e. the angle between the target normal and the horizontal axis becomes positive. If recycling takes place at this upper tile (high ion fluxes are measured in this region during the fluctuating state, confirmed by the radiation distribution Fig. 6.2b), neutrals will be released into regions further upstream (white arrows in Fig. 6.2b). This should change the divertor plasma conditions and could be the reason for the second increase and roll over of the ion flux in the inner divertor. In order to verify this theory, similar discharges can be made with different positions of the strike point. With a lower strike point, a higher density would be needed to push the ion flux to the upper tile of the inner divertor. 93 6 Summary and discussion of the experimental results Most of the outer target, however, is constantly tilted away from the separatrix. In reversed field, ΦD+in the outer divertor1scales longer with the TPM compared to forward field, then rolls over and decreases continuously. No second roll over is observed, which is consistent with this divertor geometry model. In the high density, high power H-mode, discussed in section 5.3.1, high densities, target ion fluxes and neutral fluxes are measured at the entrance of the inner divertor (indicated with the white circle in Fig. 6.2b) without N2seeding. Recycled neutrals originating from this target region should have a much higher probability to reach the main plasma, where they are ionized and cool the main plasma, than the neutrals which are released from the strike point area and mainly ionize in the SOL. With N2seeding, the high density region at the entrance of the inner divertor was measured to shrink, which should result in less recycled neutrals reaching the main plasma. This then could allow for higher pedestal temperatures, which where observed in improved H-Modes with N2seeding [83] and suggested to be the explanation for the increased confinement of improved H-Modes with N2seeding. Flux enhancement The flux enhancement, which is defined here when the total ion flux is larger than the Two-Point-Model scaling, occurs in the outer divertor in forward field and in the inner divertor in reversed field. In forward field2, during the fluctuating state, a high electron density is measured in the inner far SOL and X-point region, while the density in the strike point region is reduced (see the radiation distribution 6.2b as an indication). Recycled neutrals, originating from the strike point region, could therefore pass the inner SOL, the private flux region and reach the outer SOL. Namely, the inner divertor strike point region becomes transparent for neutrals (blue arrows in Fig. 6.2b). It has been shown previously at ASDEX Upgrade [89] that, under similar conditions, the inner divertor becomes transparent for neutrals and the neutral fluxes measured in the inner divertor and private flux region are equal. These neutrals, which reach the outer divertor SOL, will ionize there. This leads to additional radiation losses (fpow >0 in equation 2.25) in the outer SOL. As a consequence, the ion flux at the target increases (eq. 2.28), consistent with the observations. In addition, these ionized neutrals should provide an additional particle source in the outer SOL, resulting in a fraction of power being convected (fconv >0). This may explain the increase of the outer target temperature (eq. 2.26) during the flux enhancement phase, while the target ion flux and density also increase. In total, this would then be a combination, or competition, of the fpow >0 and fconv >0 effects. 1As in forward field the inner divertor receives the higher ion flux before the onset of detachment while in reversed field this is the outer divertor, these two cases are compared 2In the explanation for reversed field, the inner and outer divertor would simply change 94 6.2. Discussion Radiative X-point fluctuations Once the X-point fluctuations are triggered, a high electron density is measured at the X-point region. This indicates, that a certain fraction of recycled neutrals reaches the X-point and are ionized there, connected with the appearance of the fluctuations. Whether this is a necessary condition to trigger the fluctuations cannot, however, be proven here. But once the fluctuations are triggered, also a higher recycling is taking place at the upper tile of the inner divertor (white arrows in Fig. 6.2b). As mentioned before, recycled neutrals originating from the upper tile have a higher probability to reach the X-point than recycled neutrals coming from the strike point region. It was shown that, with N2seeding the frequency can be reduced and the necessary amount of injected N2depends on the heating power. As with power removal in the SOL due to N2seeding, a lower hydrogen recycling is needed to sustain the same target parameters (sec. 2.2.3) and a reduction of the ion flux to the upper tile of the inner divertor with N2seeding was measured. This indicates that there is a connection between the recycling taking place at the upper tile of the inner divertor and the radiative X-point fluctuations. Furthermore, the frequency of the fluctuations depend on the square root of the mass of the fuelling species and the ion sound speed csis inversely proportional to the square of the mass (eq.2.7). One may assume that ions or filaments, originating at the X-point due to the ionization of recycled neutrals, flow with csfrom the X-point to the inner or outer target. An assumption of Ti=Te= 15 eV and α= 1 gives cs≈38 km/s. With the connection length from the inner X-point to the outer divertor along the SOL, Lc≈84 m, this yields a characteristic frequency of f≈0.5 kHz which is by far too slow. The connection length to the inner divertor is Lc≈15 m, yielding a characteristic frequency of f≈2.5 kHz. This is still a factor of ≈2.5 too low but of the same order of magnitude and possibly within the uncertainties (The determination of Lcclose to the Xpoint is uncertain due to the large flux expansion there). It cannot be verified, however, whether the density oscillates with the frequency of the fluctuations between the high density front at the X-point and the inner strike-point region, as the time resolution of the Stark broadening diagnostic and the Langmuir probes is too slow. New, or faster, diagnostics are therefore needed to gain more information on this topic. Divertor plasma oscillations Finally at medium to high densities, with the heating power close to the L-H transition threshold, a situation occurs where the divertor plasma oscillates back and forth between the onset state and the fluctuating detachment state. A possible explanation of these oscillations is, that, although no H-mode is achieved, a better confinement is reached. This would lead to a better particle confinement of the main plasma, to a decrease of the upstream density and to the re-attachment of the inner divertor. This then may change the recycling properties of the inner divertor, which can influence the main plasma properties as discussed above. Thus the better confinement 95 6 Summary and discussion of the experimental results is lost, the upstream density increases, the inner divertor detaches and a kind of limit cycle is established. This theory is rather speculative and should be verified with further experiments. A theory exists, however, which states that a minimum neutral density at the X-point is necessary to achieve the H-mode [90]. Moreover, the characteristics how the various plasma parameters oscillate are similar to those of the divertor plasma oscillations previously found at JET. It is therefore likely that the two states of the divertor plasma oscillations are the same for ASDEX Upgrade and JET. Furthermore, in JET high frequent sub oscillations (with respect to the frequency of the plasma oscillations) in the Dαsignal were found during one state, as stated in [86]. Compared to the oscillations found here, this is the fluctuating detachment state where the radiative X-point fluctuations are observed. All together this is a strong hint that these divertor plasma oscillations are the same for AUG and JET. As a consequence, the onset and fluctuating detachment states should also have existed at JET. The experiments in JET where carried out with the Mk I divertor which was an open horizontal carbon divertor. The actual ASDEX Upgrade divertor is a closed vertical tungsten divertor. If theses states have existed in these JET experiments, then the presented classification of divertor detachment is independent of machine size, divertor geometry and divertor material. In order to confirm this, dedicated experiments at different machines need to be performed. 96 Chapter 7 Conclusions and outlook The next-step fusion experiment, ITER, must rely on the divertor being detached in order to avoid damage on the divertor material. Therefore, an understanding of the detachment process is crucial. This thesis focuses on the experimental investigation of the process of divertor detachment. Divertor detachment is achieved by a reduction of the temperature in the divertor via increasing the main plasma density or seeding of additional impurities. With a reduction of the temperature, volumetric processes such as charge exchange collisions and recombination become dominant. These processes lead to a strong reduction of the ion flux and plasma pressure in front of the divertor target. As a consequence, the region of high electron density is retracted from the target and a knowledge of the electron density distribution in the divertor volume is necessary to understand the detachment process. The first part of this thesis was the installation and verification of a diagnostic determining the electron density in the divertor volume, which is based on the spectroscopic measurement of the Stark broadening of the Balmer lines. Initial problems with reflected stray-radiation have been solved and first measurements were successfully compared for consistency with other diagnostics, such as Langmuir probes and neutral pressure gauges. Thereby, neutral hydrogen fluxes in detached conditions have been evaluated from spectroscopy for the first time, yielding good agreement with neutral fluxes measured by the pressure gauges. The detachment process was then, as the main part of this thesis, investigated with an extensive set of density ramp L-mode discharges with different heating powers, fuelling species and magnetic field directions. Usually, divertor detachment was studied by comparing upstream parameters, such as electron density and temperature, with target parameters, without having knowledge of the distribution of these parameters between the upstream region and the target. Furthermore, it was mainly focused on the outer divertor, because the outer divertor is the more crucial one in terms of power deposited on the target. In this thesis, emphasis was put on the evolution of the electron density 97 BIBLIOGRAPHY [45] M. Groth, J.A. Boedo, N.H. Brooks, R.C. Isler, A.W. Leonard, G.D. Porter, J.G. Watkins, W.P. 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URL http://dx.doi.org/10.1088/0741-3335/39/2/007. 108 Acknowledgements The work presented here would not have been possible without the help and motivation of many colleagues of the ASDEX Upgrade team, not least through the significant support of the people I do thankfully acknowledge in the following. First of all my sincere thank is owed to Prof. M. Kaufmann for giving me the opportunity to perform this thesis at the IPP under his academic supervision. I also want to thank Prof. A. Peeters for his considerate willingness to judge my work. My special gratitude goes to my advisors Dr. M. Wischmeier and Dr. A. Scarabosio who guided me through the challenges of my work. With their continuous encouragement, dedication and consolidated knowledge about SOL physics they were always available to give advice. I extend my deepest thanks to my group leader Dr. R. Dux who introduced me to the world of spectroscopy and has always been willing to answer each and every one of my questions. I am very grateful to Dr. H.W. M¨uller who was in charge of the Langmuir probes and evaluating the probe data. I thank M. Bernert for operating the AXUV diodes and for the valuable discussions on tomographic reconstructions and fluctuations. For the development and maintenance of the SBD diagnostic and the in-vessel work, I am indebted to the Gef¨assmannschaft, in particular M. Ebner and F. Springer, and especially to our spectroscopy group technician A. Mayer. I am also grateful to Prof. A. Kallenbach, Dr. W. Suttrop and Dr. C. Fuchs for fruitful discussions and helpful comments. For the proof-reading of the manuscript a special thank goes to M. Dunne and Dr. R. McDermott. I also want to thank my room mates S. Fietz, B. Geiger, P. de Marn´e, P.A. Schneider, the daily visitors J. Boom, I. Classen, M. Willensdorfer, E. Viezzer, C. Vorpahl and the Skat crew T. Happel and P. Sauter for creating a nice atmosphere and having interesting, not only scientific, discussions.