Characterization of the ion pedestal in low and high collisionality plasmas

University of Seville Master in Nuclear Physics Characterization of the ion pedestal in low and high collisionality plasmas Diego Jos´e Cruz Zabala Supervisor: Eleonora Viezzer Departamento de F´ısica At´omica, Molecular y Nuclear Facultad de F´ısica Resumen El modo de alto confinamiento (H-mode) es un r´egimen muy importante para futuros dispositivos de fusi´on. En este r´egimen, el confinamiento global se incrementa y se desarrolla una estructura de pedestal en los perfiles. Sin embargo, todav´ıa falta una comprensi´on completa de c´omo es formado. En este r´egimen, el perfil de la velocidad toroidal de las impurezas presenta un m´ınimo local cerca de la ´ultima superficie de flujo magn´etico cerrada y, bajo ciertas condiciones, las impurezas en el borde del plasma pueden rotar en direcci´on opuesta comparada con el centro del plasma. Una base de datos sobre el pedestal ha sido compilada con datos de ASDEX Upgrade para intentar progresar en la comprensi´on de la f´ısica del pedestal. Esta tesis est´a enfocada en el estudio del perfil de la temperatura i´onica y del perfil de la velocidad toroidal de las impurezas, obtenidos con el sistema ”charge exchange recombination spectroscopy”, a baja y alta colisionalidad. La correlaci´on entre las caracter´ısticas del pedestal y el m´ınimo en la velocidad toroidal de las impurezas ha sido estudiada. Se ha observado que el m´ınimo en la velocidad toroidal de las impurezas alcanza valores negativos en descargas de baja colisionalidad, mientras que es positivo en descargas de alta colisionalidad. Adem´as, la posici´on del m´ınimo de la velocidad toroidal de las impurezas est´a correlacionada con la posici´on de la parte superior de los pedestales de la temperatura i´onica y densidad en descargas de alta colisionalidad, mientras que, para descargas de baja colisionalidad, solo est´a correlacionada con la posici´on de la parte superior del pedestal de la temperatura i´onica. 3 Abstract The high confinement mode (H-mode) is a very important regime for future fusion devices. In this regime, the global confinement is increased and a pedestal structure is developed in the profiles. However, a complete understanding of how it is formed is still missing. In this regime, the toroidal impurity velocity profile exhibits a local minimum close to the separatrix and, under certain conditions, the impurities at the plasma edge can rotate in the opposite direction compared to the plasma core. A pedestal database was compiled with data from ASDEX Upgrade to try to progress in understanding the pedestal physics. This thesis is focussed on the study of the ion temperature and toroidal impurity velocity profiles, obtained with the charge exchange recombination spectroscopy system, at low and high collisionality. A correlation between the characteristics of the pedestal with the minimum in the toroidal impurity velocity was studied. It has been observed that the minimum in the toroidal impurity velocity reaches negative values in low collisionality discharges, while it is positive in high collisionality discharges. Moreover, the position of the minimum in the toroidal impurity velocity is correlated with the position of the ion temperature and density pedestal tops in high collisionality discharges, while it is only correlated with the position of the ion temperature pedestal top in low collisionality discharges. 5 Contents 1 Introduction 9 1.1 Nuclearfusion.................................. 9 1.2 Magnetic confinement and tokamak . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Goals....................................... 13 2 Theory overview 14 2.1 Particledrifts .................................. 15 2.1.1 E×B-drift ............................... 15 2.1.2 ∇B-drift................................. 15 2.1.3 Curvaturedrift ............................. 16 2.2 Particleorbits.................................. 16 2.3 H-mode and Edge Transport Barrier . . . . . . . . . . . . . . . . . . . . . 17 2.4 Edge Localized Modes (ELMs) . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 Diagnostics 21 3.1 Electron temperature and density measurements . . . . . . . . . . . . . . . 21 3.2 Ion temperature and impurity rotation measurements . . . . . . . . . . . . 23 3.3 Profilealignment ................................ 25 3.4 ELMsynchronization.............................. 27 4 Database 28 4.1 Pedestal characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.1.1 Modified hyperbolic tangent function (mtanh method) . . . . . . . 29 4.1.2 Splinemethod.............................. 30 4.2 Databaseparameters.............................. 30 7 5 Results 34 5.1 Comparison between profiles at low and high ν∗............... 34 5.2 Dependency of ωmin ton ν∗........................... 35 5.3 Correlations between positions of pedestal top and ωmin t........... 39 6 Summary and conclusions 42 8 Chapter 1 Introduction 1.1 Nuclear fusion It is well known that the world’s increasing energy consumption demands for new clean and abundant source of energy for the future. Fusion energy is one of the most prominent candidates to meet these demands. This kind of energy is produced in the Sun and in all the stars. The energy is obtained when two light nuclei fuse to a heavier one. In order to produce this reaction, the kinetic energy of the nuclei has to be high enough to overcome the Coulomb repulsion. Increasing the kinetic energy means increasing the temperature, which has to be of the order of hundreds of million of degrees in order that fusion can take place. At high temperatures a gas is fully ionized. This state of the matter is called plasma. The main characteristic of a plasma is that its kinetic energy is much higher than its potential energy. On Earth, the most prominent fusion reaction is between deuterium (D) and tritium (T), two isotopes of hydrogen (H): 2D+3T→4He +n+ 17.6MeV (1.1) The high cross-section (see figure 1) and high energy yield makes the D-T reaction the most favourable one [1]. The products of the reaction are 4He and neutrons. Dis present in water. Approximately 0.015% of the hydrogen in ocean water is deuterium. However, Tis not present in nature since it has half life of about 12 years. In order to produce T, the neutrons produced in the main fusion reaction are used to produce another reaction with lithium 6Li +n→4He +3T+ 4.8MeV (1.2) 9 16 CHAPTER 2. THEORY OVERVIEW where v⊥is the velocity perpendicular to the magnetic field. In this case, the direction and value of the drift is different for ions and electrons as the ∇Bdrift depends on charge and mass of the particle. 2.1.3 Curvature drift As the particles gyrate along the magnetic field lines, they follow curved field lines and therefore feel a centrifugal force. The expression of the curvature drift is vcurv =−mv2 k qB3∇B×B(2.8) where vkis the parallel velocity to the magnetic field. Similar to the ∇B-drift, the curvature drift depends on the sign of the charge and on the mass so that the direction and value of the drift are different for ions and electrons. 2.2 Particle orbits As mentioned above, a charged particle moving in a magnetic field gyrates around a magnetic field line while the guiding centre moves with constant velocity. The drifts introduced in the previous section result in two types of guiding centre orbits if collisions are not taken into account [1]. Particles with a sufficient large velocity parallel to the magnetic field gyrate continuously around the torus. These are called the passing particles. Figure 2.2(a) shows an example of a passing particle orbit. In a torus, the magnetic field is stronger in the inner region (high field side) than in the outer region (low field side) due to the 1/R dependence of the toroidal magnetic field. When a particle is moving to a higher magnetic field region, v⊥increases as a consequence of the conservation of the magnetic moment µ. Then, vkdecreases due to the conservation of the energy. At a certain point vk= 0 and the particle will be reflected to the outer region and gets trapped in a magnetic mirror, which is produced due to the force on the magnetic moment, F=µ∇kB. This type of orbit is called banana because of its shape in a poloidal plane projection. An example of a trapped particle orbit is shown in figure 2.2(b). Figure 2.2 also shows the last closed flux surface, also called separatrix. E=1 2mv2=1 2m(v2 ⊥+v2 k) ; µ= 1 2mv2 ⊥ B.(2.9) 2.3 H-MODE AND EDGE TRANSPORT BARRIER 17 Figure 2.2: Poloidal plane projection of a passing orbit (a) and a banana orbit (b). 2.3 H-mode and Edge Transport Barrier In divertor tokamaks, a high energy confinement regime is obtained when enough power is injected [3]. The high energy confinement regime, called H-mode, is characterised by an increase of density and temperature compared to the low energy confinement regime (L-mode). The transition from L-mode to H-mode results in an increase in plasma confinement by approximately a factor of 2. During the transition into H-mode, an edge transport barrier (ETB) evolves causing a reduced level of particle and heat transport perpendicular to the magnetic field. The ETB causes a steepening of the density and temperature gradients, and consequently pressure gradient at the plasma edge (see figure 2.3). The toroidal impurity velocity profile in H-mode discharges exhibits a very deep well close to the separatrix which can have negative values under certain conditions [4]. The profiles develop a pedestal structure within the ETB, which causes the improvement of the confinement in the H-mode as reflected in the increase of the stored energy shown in blue in figure 2.4(a). When the NBI is turned on, the stored energy, electron temperature and density increase and the plasma enters in the H-mode. 18 CHAPTER 2. THEORY OVERVIEW Figure 2.3: Typical profiles in H-mode discharges. The pedestal tops are the top of the pedestal structure. The scrape of layer (SOL), where the magnetic field lines are not closed, is represented in grey. 2.4 EDGE LOCALIZED MODES (ELMS) 19 Figure 2.4: a) Time traces of ECRH power, NBI and plasma stored energy (WMHD). b) Electron temperature and density. c) Thermo-currents in the divertor which is used as an ELM monitor. 2.4 Edge Localized Modes (ELMs) The H-mode regime is accompanied by Edge Localized Modes, which are cyclic instabilities that expel particles and energy [5,6]. ELMs have been observed in all tokamak devices when they are operating in H-mode. ELMs eject particles from the pedestal region, causing a degradation of the pedestal structure in density, temperature and pressure profiles. After an ELM, the profiles recover their steep gradients until the next ELM occurs. The physics triggering of an ELM is not well known yet, but it is believed that they are linked to the large gradients of the edge profiles. The most prominent candidate to explain the ELMs is the peeling-ballooning stability limit. The peeling stability limit implies a limit on the edge plasma current, while the ballooning stability limit results in a limit on the edge pressure gradient. Figure 2.5 shows a comparison between the temperature profiles before and after an ELM. The profiles experience a degradation as a consequence of the ELM. The ELMs act also as a regulator of the impurities since these are also ejected during an ELM. The common way to detect an ELM is an increase of a thermo-current in the divertor due to the particles which are ejected. Figure 2.4 c) shows the the thermo- 20 CHAPTER 2. THEORY OVERVIEW Figure 2.5: Comparison between temperature profiles before and after an ELM. currents in the divertor. A spike in the signal indicates an ELM. There are two big ELMs around 1.54 s and 1.59 s. During these two ELMs, the stored energy decreases a little bit, due to the degradation of the pedestal. For future fusion devices like ITER, it is very important to mitigate or suppress the ELMs to avoid damage of the machine, while maintaining the improved confinement of the H-mode. Chapter 3 Diagnostics High-resolution diagnostics are key to fusion research. The pedestal region is a very thin region (thinner than 2 cm on AUG) with large gradients that needs very high spatial and temporal resolution. In order to characterize properly the pedestal region, the time resolution has to be good enough to measure in-between two ELMs. In this section, the diagnostics that have been used during this thesis will be introduced (see figure 3.1). 3.1 Electron temperature and density measurements In this work, the electron temperature (Te) has been measured with the electron cyclotron emission (ECE) and Thomson scattering (TS) diagnostics. For the density (ne), laser interferometry (DCN), impact excitation spectroscopy on a lithium beam (LIB) and Thomson scattering (TS) were used. The TS diagnostic gives information on electron temperature and density and thus, allows us to align both with respect to the separatrix position, as shown in section 3.3. A brief overview is introduced in the next sections. Electron cyclotron emission (ECE) The ECE diagnostic gives information on Te. It measures the emission of electron radiation at its angular cyclotron frequency ωc,e =eB/meand its harmonics ωk,e =kωc,e. Assuming that the electron temperature is the radiation temperature and that electrons follow a Maxwellian distribution, the intensity at the cyclotron frequency follows Planck‘s law of 21 22 CHAPTER 3. DIAGNOSTICS Figure 3.1: Toroidal (left) and poloidal (right) view of the diagnostics used during this thesis at AUG. black-body radiation. At high temperatures, this results in the Rayleigh-Jeans expression Iω=ω2 2π2c2kBTe.(3.1) In a tokamak, the toroidal magnetic field, which is the dominant part of the total magnetic field, varies like 1/R. This dependency allows us to associate the emission to a radial position. The assumption of black-body is only valid if the plasma is optically thick. If the plasma is not optically thick, as at the plasma edge due to the decrease in the density, the black-body law is not applicable. Due to this effect, the ECE measurements exhibit a peak close to the separatrix. Hence, in this region, the ECE data have not been used for fitting the electron temperature profile. At AUG, the ECE system has a spatial resolution of 1 cm and a temporal resolution of 1 µs [7,8]. Thomson scattering (TS) The Thomson scattering system measures the electron temperature (Te) and density (ne). The TS diagnostic is based on the elastic scattering of an electromagnetic wave by a charged particle. When an electromagnetic wave reaches the plasma, it accelerates the particles and the wave is scattered. The particles have velocities with respect to the initial 3.2 ION TEMPERATURE AND IMPURITY ROTATION MEASUREMENTS 23 and scattered waves and, due to the Doppler effect, the frequency of the scattered wave is shifted. Due to the difference between electron and ion mass, mainly the electrons are accelerated. It is common to measure the scattered wave at 90◦. The width of the scattered wave signal gives a measure of Te. The intensity of the signal gives information about ne. At AUG, there are two TS diagnostics, one viewing the plasma core and one the edge. The edge system has a spatial resolution of 3 mm and the core system has a resolution of 25 mm [9]. The TS diagnostic can measure every 8 ms. Due to its high resolution, the edge system is proper to characterize the pedestal region. Impact excitation on a lithium beam The lithium beam diagnostic injects high energy Li atoms in order to measure the density. When the Li atoms interact with the plasma, they are excited and emit radiation [10]. The profile of this radiation is correlated with the density. Due to several effects, the Li beam is attenuated when it penetrates the plasma. Hence, the Li beam diagnostic only gives information on the outermost region of the density profile. At AUG, the Li beam diagnostic has a spatial resolution of 5 mm and a temporal resolution of 50 µs [11]. DCN laser interferometry The DCN diagnostic takes advantage of the interaction of the electrons with electromagnetic waves adding the dependence on the variation of the plasma refractive index N. A phase shift is obtained when comparing the propagation of an electromagnetic wave through the plasma with the propagation through the vacuum. This phase is directly correlated with the line-integrate density through the beam path. At AUG, this diagnostic has a temporal resolution of 300 µs [12]. 3.2 Ion temperature and impurity rotation measurements The most common technique to measure ion temperature and impurity rotation is charge exchange recombination spectroscopy (CXRS) [13]. The CXRS diagnostic measures the spectral lines emitted due to charge transfer from neutral to impurity ion species: AZ++D→A(Z−1)+∗+D+→A(Z−1)+ +hν +D+.(3.2) 24 CHAPTER 3. DIAGNOSTICS Figure 3.2: Typical spectrum measured with a CXRS diagnostic at AUG. The FWHM (Full Width at Half Maximum) is correlated to the temperature and the shift ∆λis correlated to the toroidal impurity velocity. Figure taken from [14]. The neutrals are usually deuterium (D) or hydrogen (H) and are injected via neutral beam injection. The light emitted is analyzed with a spectrometer. Each species emits at a different wavelength and the measured spectrum gives information on its temperature and rotation. In particular, the temperature is derived from the width of the signal and velocity is derived from the Doppler shift (see figure 3.2). The lines of sight (LOS) of the CXRS system are the viewing lines of the plasma where the diagnostic is pointing at. The active line comes from the points where the LOS intercept the neutral beam. The passive lines are emitted at the plasma edge, due to charge exchange with thermal neutral deuterium and electron impact excitation [15]. The impurities that are usually measured at AUG are boron (B) and nitrogen (N) but in helium (He) plasmas the main ion can be measured. Usually low Z impurities are measured because they are fully ionized, while high Z impurities have a smaller concentration in the plasma and they are not fully ionized throughout the whole plasma. Figure 3.2 shows the spectral radiance obtained with one of the edge CXRS systems at AUG [16, 17]. The full width at half maximum (FWHM) of the spectral radiance is directly correlated with the temperature of the measured species: T=mc2 8ln(2)λ2 0e2FWHM2(3.3) where mis the mass of the measured species, cis the speed of light, λ0is the theoretical wavelength of emission and eis the electron charge. The shift due to Doppler effect 3.3 PROFILE ALIGNMENT 25 provides the rotation velocity vtof the considered species ∆λ λ=vt·eLOS c(3.4) where eLOS is the unit vector along the LOS. Note that vt=ωt×R. In this thesis, two CXRS systems at AUG have been used to characterise the edge profiles [16,17]: the toroidal edge CXRS system, which has a spatial resolution of 1-3 mm, and the poloidal edge CXRS system, which has a spatial resolution of 3-5 mm in the steep gradient region. Both CXRS systems have a standard temporal resolution of 2.3 ms but it can be turned down to 50 µs [17]. 3.3 Profile alignment The different profiles are obtained by combining the data of various diagnostics. The magnetic equilibrium is assumed to be toroidally symmetric. As the diagnostics measure at different toroidal and poloidal positions, small uncertainties in the radial position can arise when mapping the profiles onto the magnetic equilibrium. Thus, the measured profiles of the different diagnostics have to be aligned in order to reduce uncertainties in the radial position. This adjustment is very important in the ETB region which has a spatial extent of only 1.5-2 cm at AUG. The steep gradients in the ETB allow to reduce the uncertainties down to 2-3 mm [18]. Power balance and parallel heat transport studies based on a 1D heat conduction model [19, 20] determine that electron temperature at the separatrix has to be approximately 100 eV in H-mode discharges of AUG. The procedure to align the profiles is the following: first, the Teprofile from TS is shifted to obtain 100 eV at the separatrix. Then, the Te profile measured with ECE is shifted to match the profile measured with TS. As mentioned above, TS gives information on Teand ne. The shift used for the TS Teprofile is applied to the TS neprofile. After that, the lithium beam neprofile is shifted to match the TS neprofile. Thus, the Teprofile and neprofile are aligned. The Tiprofile, measured with the CXRS systems, is aligned by shifting Tisuch that the position of the steepest gradients matches the one of Te. This assumption is valid for high collisionality discharges as at high collisionality the ions and electrons are well coupled [21]. The uncertainty in the alignment between Teand Tiis less than 5 mm. The toroidal impurity velocity (ωt) profile is intrinsically aligned to the Tiprofile because they are measured with the same diagnostic. Figure 3.3 shows an example of the experimental data before and after the alignment. 32 CHAPTER 4. DATABASE Figure 4.5: Typical safety factor (left) and collisionality (right) profiles. where j=i, e, stands for electrons or ions, νjis the collision frequency and ωbj is the bounce frequency. The expressions used to calculate the electron and ion collisionality [23] are the following ν∗ e= 0.0012 ·qR3/2 0Zeff ne[1019m−3] r1/2(Te[keV ])2(4.4) ν∗ i= 4.9·10−5·qR3/2 0Z4 eff (17.3−1 2ln(ni[1020m−3]) + 3 2ln(Ti[keV ]))ni[1019m−3] r1/2(Ti[keV ])2(4.5) where qis the safety factor, R0is the major radius, Zeff is the effective charge state , ris the radial coordinate and is the ratio between the minor and the major radius =a/R0. Figure 4.5 shows a typical qprofile and collisionality profile. Note that the safety factor and collisionality go to infinite at the separatrix. The characteristics of a plasma depends on the elements of which it is composed. The database includes deuterium, hydrogen and helium discharges. In some discharges, impurity seeding, usually nitrogen, is applied. When applying impurity seeding it has been observed differences in the location of the density pedestal top [24]. The amount of gas introduced in the plasma per unit of time is the fuelling. The triangularity δand the elongation κare parameters that describe the shape of the plasma. Both parameters refer to the separatrix poloidal cross section shape. The elongation is bigger when the shape looks more thinner (see black shape in figure 4.6a) and the triangularity is bigger when the shape looks more like a triangle (see black shape in figure 4.6b). Table 4.1 shows the range the parameters included in the database. Pheat is the heating power, fELM is the ELM frequency, Ipis the plasma current and Btis the toroidal magnetic field. 4.2 DATABASE PARAMETERS 33 Figure 4.6: a) Separatrix of a high (low) elongation discharge in black (red). b) Separatrix of a high (low) triangularity discharge in black (red). Parameter Range Pheat 3.5 - 15.4 [MW] fELM 32.4 - 201.7 [Hz] Ip0.62 - 1.14 [MA] Bt1.97 - 2.5 [T] δ0.18 - 0.40 κ1.59 - 1.74 ν∗ e(ρ= 0.97) 0.62 - 4.20 ν∗ i(ρ= 0.97) 0.24 - 3.15 Dfuelling 0 - 2.81 [1022 part/s] Hfuelling 0 - 2.56 [1022 part/s] Nfuelling 0 - 2.47 [1022 part/s] Table 4.1: Range of the parameters included in the database. Chapter 5 Results The pedestal is a very important region to understand the behaviour of the plasma. The impact of the collisionality on the profiles as well as understanding the relation of the position (value) of the different pedestals with the position (value) of the minimum in the toroidal impurity velocity could help to progress in pedestal physics. This section shows the results obtained during this thesis. 5.1 Comparison between profiles at low and high ν∗ This section will show the main differences between profiles at high and low collisionality. Figure 5.1 shows time traces of discharge #33207. In this discharge, four times windows were analyzed. From the first time window (black) to the second one (red) the NBI power is increased. The toroidal impurity velocity increases in the core but decreases in the edge. Furthermore, the density decreases and ion and electron temperature increase. Comparing the second (red), third (blue) and fourth (green) time windows, the NBI power is constant but the deuterium fuelling decreases. The toroidal impurity velocity in the core keeps constant but it decreases at the edge. Again, density decreases and ion and electron temperature increase. Expressions 4.4 and 4.5 show that the collisionality decreases when the density decreases and when the temperature increases, while keeping the safety factor constant. This behaviour is observed in the temporal evolution of the selected time windows in this discharge. Thus, the collisionality in this discharge is decreasing in all analyzed time windows. Specifically, the ion collisionality at ρpol = 0.97 goes from 1.31 to 0.24. Figure 5.2 compares the profiles in the first time window (highest collisionality) with the profiles in the fourth time window (lowest collisionality). As mentioned above, 34 5.2 DEPENDENCY OF ωMIN TON ν∗35 Figure 5.1: Time traces: a) plasma current, toroidal magnetic field and safety factor at the flux surface containing 95% of the total poloidal flux inside the separatrix, b) plasma stored energy, c) NBI, ECRH and radiation power, d) density, e) fuelling, f) ELM frequency, g) toroidal velocity, h) electron and ion temperature of discharge #33207. Analyzed times windows are highlighted in colours. the temperature is higher in the low collisionality case and the density is higher in the high collisionality case. Furthermore, the ion temperature is larger than the electron temperature at low collisionality. At high collisionality, the ion and electron temperature are coupled and at low collisionality they are decoupled. The minimum in the toroidal velocity is negative in the low collisionality case and positive in the high collisionality case [25]. 5.2 Dependency of ωmin ton ν∗ This section describes the correlations between the minimum in the toroidal impurity velocity profile with the collisionality. The relation between the values of Ti,Teand neat the pedestal top with the value of the minimum in the toroidal impurity rotation profile 36 CHAPTER 5. RESULTS Figure 5.2: Comparison between profiles of discharge #33207 at low collisionality (red) and high collisionality (black). 5.2 DEPENDENCY OF ωMIN TON ν∗37 Figure 5.3: Correlations between the values of Tped.top i,Tped.top e,nped.top eand ωmin tin the four time windows selected of the discharge #33207. for the four time windows considered in discharge #33207 is represented in figure 5.3. When the density decreases and the temperature increases, i.e collisionality decreases, the value of the minimum in ωtdecreases reaching negative values. As mentioned in the previous section, the minimum in the toroidal impurity velocity changes sign when collisionality is low enough. Negative values of the toroidal impurity velocity means that the particles are moving in the counter-current direction and in opposite direction of the plasma core. Figure 5.3 will be reproduced in figure 5.4 including all the time windows of the database. The trend is the same in both figures. When the temperature increases enough (or the density is low enough), the minimum in the toroidal impurity velocity becomes negative as the collisionality is decreasing. In figure 5.4, a linear fit is included for deuterium discharges (black) and for deuterium with nitrogen seeding discharges (blue). The fits of the temperature data without nitrogen seeding are slightly steeper than the fits to the 38 CHAPTER 5. RESULTS Figure 5.4: Correlations between the values of Tped.top i,Tped.top e,nped.top eand ωmin tfor all the database. data with seeding. The fit to the density data without nitrogen seeding has an offset of around 5 krad/s with respect to the fit to the data with nitrogen seeding. To confirm the dependency of the minimum in ωton the collisionality, both quantities are represented in figure 5.5. The collisionality is taken at ρ= 0.97. When the collisionality is low enough, the minimum in ωtreaches negative values, while for high values of the collisionality, the minimum in ωtis positive. The uncertainties in the collisionality shown in figure 5.5 are calculated via Gaussian error propagation using uncertainties of temperature and density. Uncertainties in the major radius, safety factor and Zeff have not been taken into account. Error bars are only included for one data point on each graph for clarity. This database shows a robust dependence of ωton ν∗including changes in shape, plasma current, fuelling, ELM frequency and toroidal magnetic field. 5.3 CORRELATIONS BETWEEN POSITIONS OF PEDESTAL TOP AND ωMIN T39 Figure 5.5: Correlations between collisionality and ωmin t. 5.3 Correlations between positions of pedestal top and ωmin t The objective of this section is to identify correlations between the position of the pedestals and the minimum in the toroidal impurity velocity. Figure 5.6 shows the position of ωmin t versus the position of nped.top eand Tped.top ifor the whole database. Including all points of the database, no correlation between position of the ωmin tand the position of nped.top eis observed. However, when limiting the parameter space to ν∗ i>0.9 (high collisionality), 0.20 < δ > 0.26, Ip>1MA and 5 MW < Pheat <16 MW, shows a clear trend between the radial position of ωmin tand nped.top eand Tped.top i. Figure 5.7 shows that the radial position of ωmin tis located at nped.top eand ωmin tmoves outwards when Tped.top iand nped.top emove outwards. This dependence is also studied at low collisionality. The results for low collisionality are shown in figure 5.8. In this case, there is no correlation between the position of ωmin tand the position of nped.top e, but there is a correlation between the position of ωmin tand the position of Tped.top i. This suggest that the physics mechanism setting the pedestal may be different at low and high collisionality. Note, however, that the uncertainties of the radial profile alignment are larger at low collisionality as the electrons and ions are more decoupled and, hence, the assumption of ρ(∇Ti) = ρ(∇Te) may not be valid. The trends observed in figures 5.7 and 5.8 are clear, but it is important to mention that the data included in the figures have uncertainties. The positions derived from Teand ne profiles have a uncertainty of 5 mm due to the spatial resolution of the diagnostics, that corresponds to 0.01 in ρat AUG. On the other hand, the positions derived from Tiand 40 CHAPTER 5. RESULTS Figure 5.6: Correlations between position of the minimum in the toroidal impurity velocity and position of nepedestal top (left) and position of Tipedestal top (right). Figure 5.7: Repetition of figure 5.6 for only high collisionality discharges. The dash line is the identical line y=x. Figure 5.8: Repetition of figure 5.6 for only low collisionality discharges. 5.3 CORRELATIONS BETWEEN POSITIONS OF PEDESTAL TOP AND ωMIN T41 ωtprofiles have two sources of uncertainties: the spatial resolution of the diagnostics and the uncertainties due to the radial profile alignment.