Comparison of runaway electron generation parameters in small, medium-sized and large tokamaks-A survey of experiments in COMPASS, TCV, ASDEX-Upgrade and JET

PAPER Comparison of runaway electron generation parameters in small, medium-sized and large tokamaks—A survey of experiments in COMPASS, TCV, ASDEX-Upgrade and JET To cite this article: V.V. Plyusnin et al 2018 Nucl. Fusion 58 016014 View the article online for updates and enhancements. Related content Formation and termination of runaway beams in ITER disruptions J.R. Martín-Solís, A. Loarte and M. Lehnen - Runaway electron beam generation and mitigation during disruptions at JET-ILW C. Reux, V. Plyusnin, B. Alper et al. - Runaway electrons in MGI experiments in TEXTOR S A Bozhenkov, M Lehnen, K H Finken et al. - Recent citations The effect of resonant magnetic perturbation on the electron density threshold of runaway electron generation during disruptions on J-TEXT Z F Lin et al - Dissipation of runaway current by massive gas injection on J-TEXT Y N Wei et al - MeV range particle physics studies in tokamak plasmas using gamma-ray spectroscopy M Nocente et al - This content was downloaded from IP address 37.158.234.192 on 20/07/2020 at 11:51 1 © 2017 Instituto Superior Tecnico Printed in the UK Nuclear Fusion Comparison of runaway electron generation parameters in small, medium-sized and large tokamaks—A survey of experiments in COMPASS, TCV, ASDEX-Upgrade and JET V.V.Plyusnin1, C.Reux2, V.G.Kiptily3, G.Pautasso4, J.Decker5, G.Papp4, A.Kallenbach4, V.Weinzettl6, J.Mlynar6, S.Coda5, V.Riccardo3, P.Lomas3, S.Jachmich7, A.E.Shevelev8, B.Alper3, E.Khilkevitch8, Y.Martin5, R.Dux4, C.Fuchs4, B.Duval5, M.Brix3, G.Tardini4, M.Maraschek4, W.Treutterer4, L.Giannone4, A.Mlynek4, O.Ficker6, P.Martin9, S.Gerasimov3, S.Potzel4, R.Paprok6, P.J.McCarthy10, M.Imrisek6, A.Boboc3, K.Lackner4, A.Fernandes1, J.Havlicek6, L.Giacomelli11, M.Vlainic12, M.Nocente11,13 , U.Kruezi3, COMPASS team6, TCV team5, ASDEX-Upgrade team, EUROFusion MST1 Teama and JET contributorsb EUROFusion Consortium, JET, Culham Science Centre, Abingdon, OX14 3DB, United Kingdom 1 Instituto de Plasmas e Fusão Nuclear, Instituto Superior Tecnico, Universidade de Lisboa, Lisboa, Portugal 2 CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France 3 CCFE, Culham Science Centre, Abingdon, OX14 3DB, United Kingdom 4 Max-Planck-Institut fur Plasmaphysik, Garching D-85748, Germany 5 Swiss Plasma Centre, EPFL, CH-1015 Lausanne, Switzerland 6 IPP AS CR, Za Slovankou 3, CZ-18200 Prague, Czechia 7 Laboratoire de Physique des Plasmas-Laboratorium voor Plasmafysica, ERM/KMS, B-1000 Brussels, Belgium 8 Ioffe Institute, St. Petersburg, 194021, Russian Federation 9 Consorzio RFX, corso Stati Uniti 4, 35127 Padova, Italy 10 Department of Physics, University College Cork, Cork, Ireland 11 Istituto di Fisica del Plasma, CNR, Milano, Italy 12 Department of Applied Physics, Ghent University, Sint-Pietersnieuwstraat 41, Technicum B4, Ghent B-9000, Belgium 13 Dipartimento di Fisica ‘G. Occhialini’, Università di Milano-Bicocca, Milano, Italy E-mail: vladislav[email protected] Received 17 January 2017, revised 6 August 2017 Accepted for publication 26 September 2017 Published 8 November 2017 Abstract This paper presents a survey of the experiments on runaway electrons (RE) carried out recently in frames of EUROFusion Consortium in different tokamaks: COMPASS, ASDEX- Upgrade, TCV and JET. Massive gas injection (MGI) has been used in different scenarios for RE generation in small and medium-sized tokamaks to elaborate the most efficient and reliable ones for future RE experiments. New data on RE generated at disruptions in COMPASS and ASDEX-Upgrade was collected and added to the JET database. Different accessible parameters of disruptions, such as current quench rate, conversion rate of plasma current into V.V. Plyusnin etal Printed in the UK 016014 NUFUAU © 2017 Instituto Superior Tecnico 58 Nucl. Fusion NF 10.1088/1741-4326/aa8f05 Paper 1 Nuclear Fusion IOP International Atomic Energy Agency a See the author list of [59]. b See the author list of [60]. 2018 1741-4326 1741-4326/18/016014+15$33.00 https://doi.org/10.1088/1741-4326/aa8f05 Nucl. Fusion 58 (2018) 016014 (15pp) V.V. Plyusnin etal 2 runaways, etc have been analysed for each tokamak and compared to JET data. It was shown, that tokamaks with larger geometrical sizes provide the wider limits for spatial and temporal variation of plasma parameters during disruptions, thus extending the parameter space for RE generation. The second part of experiments was dedicated to study of RE generation in stationary discharges in COMPASS, TCV and JET. Injection of Ne/Ar have been used to mock-up the JET MGI runaway suppression experiments. Secondary RE avalanching was identified and quantified for the first time in the TCV tokamak in RE generating discharges after massive Ne injection. Simulations of the primary RE generation and secondary avalanching dynamics in stationary discharges has demonstrated that RE current fraction created via avalanching could achieve up to 70–75% of the total plasma current in TCV. Relaxations which are reminiscent the phenomena associated to the kinetic instability driven by RE have been detected in RE discharges in TCV. Macroscopic parameters of RE dominating discharges in TCV before and after onset of the instability fit well to the empirical instability criterion, which was established in the early tokamaks and examined by results of recent numerical simulations. Keywords: Tokamak, disruptions, runaway electrons, hard x rays (Some figuresmay appear in colour only in the online journal) 1. Introduction Disruptive termination of plasma discharges is one of the most critical issues for tokamak operations. International thermonuclear experimental reactor (ITER) is based on the tokamak concept [1, 2]. Together with excessive electro magnetic forces and heat loads onto plasma facing components (PFC) the major disruption in tokamaks causes an induction of strong electric fields occurring during thermal quench (TQ) and plasma current decay stage—current quench (CQ). If these electric fields are strong enough to overcome the dissipative effect of the Coulomb collisions, they accelerate plasma electrons into runaway regime [3–7]. Such runaway electrons (RE) will be accelerated ever more rapidly because the dissipative collisional friction decreases with increase of electron velocity. Unlimited acceleration will inevitably lead to the relativistic energies acquired by RE. Major disruptions in tokamaks often resulted in generation of large populations of high-energy RE. Large number of spontaneous and intentional major disruptions in the JET tokamak led to generation of RE beams with the energies from several MeV till to several tens of MeV and current values sometimes exceeding 2.5 MA [8–13]. Generation of intense RE beams with relativistic energies has been detected during major disruptions in TORE Supra [14], JT-60U [15] and TFTR [16]. The density of RE generated during disruptions in these large tokamaks was high enough to create post-disruption current plateaux with values up to 60–70% of the pre-disruptive plasma currents [11]. Such intense RE beams constitute a serious problem for the safety operation of tokamaks since the interaction of these beams with surrounding PFC resulted in high heat loads, sputtering and melting of the first wall materials. In TORE Supra the RE beam damaged the actively cooled limiter and caused the water leak into vacuum vessel [14]. Experimental trend in disruption generated RE [11] suggests that ITER disruptions could generate much higher RE currents resulting in much severe consequences when relativistic RE beams will interact with the first wall. Significant efforts in theoretical studies and numerical modelling of the RE generation during disruptions have been done to investigate the trend in this process toward the domain of ITER operational parameters ([1, 2] and references cited therein). The main mechanism responsible for generation of large RE currents during disruptions in ITER is considered to be an avalanching of secondary RE. These secondary RE are generated due to close distance electron–electron col lisions between existing seed RE and thermal electrons, thus the latter become runaway [17–19]. The RE avalanching is not possible without the RE seeds that can exist in pre-disruptive plasmas, or they can be produced due to several processes during TQ and CQ [9–11, 20]. The first known source for seed RE is the Dreicer acceleration [4–7]. Performed in recent decades studies allowed characterization of other mechanisms, which could be responsible for the creation of RE seeds, in addition to the Dreicer generation. One of such mechanisms is hot tail runaway generation [21–23]. The energetic particles in the tail of initial distribution function of high temperature plasma need longer time to slow down than those in low energy part of the distribution if the plasma cools down sufficiently fast. These energetic particles constitute a hot tail of the mainly cold post-TQ electron distribution. Due to the increase of electric fields in TQ and CQ a significant part of this hot tail can be converted into RE. Also, it was pointed out that even a small sources, such as the tritium decay and Compton scattering of γ-rays emitted by activated wall on plasma electrons, would be sufficient to generate significant RE populations during CQ [24]. In [25] it was shown, that interaction of high energy RE with the first wall also could cause an additional yield of the high-energy electrons (with MeV energies) from surrounding surfaces. Simulations of runaway process, which might occur at major disruptions in ITER without mitigation, demonstrate Nucl. Fusion 58 (2018) 016014 V.V. Plyusnin etal 3 the possibility to generate RE currents with up to 10 MA in multi-MeV energy range (for example [26]). Localized interaction of such intense RE beams with surrounding surfaces inevitably will result in inacceptable loads and evaporation of the Be first wall [27]. Therefore, in the tokamak-reactor, such as ITER, the generation of RE is inacceptable. To prevent detrimental consequences of disruptions and RE generation events the efficient methods for disruption mitigation and suppression/avoidance of runaway process are essential. Massive gas injection (MGI) is considered as a part for the prospective design of disruption mitigation system in ITER (ITER-DMS) to suppress/avoid detrimental effects of major disruptions and generation of intense RE beams. Significant advances in experimental studies of MGI capabilities and characterization of the methods for the fast plasma shutdown have been achieved during recent years [28, 29]. Despite that MGI demonstrated the ability to mitigate a majority of severe processes caused by disruptions, a set of problems related to RE avoidance/suppression is still unresolved [12, 13]. To overcome existing problems a detailed knowledge of runaway generation physics and improved models for simulation of interaction of RE beams with large quantities of injected impure gases are required. This paper presents a survey of the first series of experiments on RE generation carried out in frames of EUROFusion Consortium program [30–32] in small and medium-sized (MST) European tokamaks—in COMPASS, TCV and ASDEX-Upgrade. Results of these experiments have been analysed in comparison to the data collected in experiments on RE generation carried out in JET with PFC made from carbon (JET-C) and in JET with ITER-like wall (JET-ILW). In one group of experiments the parameters of disruption generated RE have been studied depending on increase of the device experimental parameters: magnetic field (B0), plasma current (Ipl), etc. The RE data collected in ASDEX-Upgrade and COMPASS was included into database elaborated in experiments on disruptions and RE in JET-C and JET-ILW [11, 25, 33]. A detailed analysis was dedicated to study of the RE parameters evolution depending on geometrical sizes of tokamak experiments. This analysis has demonstrated conformity of the recent results from small and medium sized tokamaks [30–32] to the data on RE obtained earlier in large tokamaks [11–13, 25, 33]. Another part of experiments was dedicated to the study of RE generation parameters in stationary tokamak discharges. A scenario of RE generation under stationary conditions constitutes the subject of a special attention due to the convenient possibility to measure reliably the plasma parameters during onset, growth and loss of relativistic RE [34, 35]. This stationary RE generation scenario was developed in experiments with low plasma density on COMPASS and TCV. Using the measured plasma parameters the RE generation dynamics was quantified in frames of conventional theory of runaways. Obtained data was compared to the data collected in the JET stationary RE discharge [35]. Parameters of the observed RE generation events, such as critical fields and energies, have been analysed to highlight the differences and similarities of RE generation in low-density and moderate density plasmas. MGIs into stationary RE discharges in TCV and COMPASS were used for establishing the operational regimes for future experiments on the RE beam dissipation. RE avalanche events after MGI into RE discharges have been detected and studied in TCV. The events associated to the kinetic instability driven by RE have been observed and studied in TCV. Obtained results are in adequate conformity with the statements formulated in frames of the theory for kinetic instability driven by relativistic RE. 2. Diagnostics for RE detection and measurements of RE parameters Relativistic RE interacting with background plasma and neutrals produce a bremsstrahlung hard x-ray emission (HXR) in the sub-MeV and MeV energy ranges. Also RE produce γ-radiation and photo-neutrons hitting the elements of PFC. Measurements of these radiations in different time points and subsequent numerical processing of the obtained data provide the information on different RE parameters, such as mean and maximum energies of RE populations, their spatial locations, etc. The HXR detectors are used to register the RE generation in the ASDEX-Upgrade disruption experiments. The neutron spectrometry diagnostic used on ASDEX-Upgrade has demonstrated that maximal energy of RE in disruptions has reached up to ≈10 MeV. In JET the HXR emission is measured with the set of horizontally and vertically viewing NaI(Tl), Bi4GeO12 (usually referred as BGO) and LaBr3 spectrometers. The JET neutron/γ-emission profile monitor with highly collimated detectors is routinely used for neutron and γ-rays measurements. These diagnostics allow the measurements of spatial distribution of HXR emission sources in the JET plasma crosssection. The data from vertically viewing HXR spectro meter on JET has been numerically processed using the DeGaSum code [36] to study the evolution of the RE distribution function (REDF) in disruptions and during the stationary discharge. Reconstruction of REDF from the measured HXR spectra revealed the generation of RE population with maximal energies up to ≈7–8 MeV and with mean energy ≈2.5–3 MeV in stationary discharge [35]. Similar or even higher mean RE energies were measured in JET-ILW disruptions [12, 13, 33]. The maximum RE energy in disruptions reached up to 12– 15 MeV (sometimes up to 20–25 MeV) [25, 33]. A detailed analysis of the RE parameters inferred on the basis of HXR spectrometry and other methods could be found in [8, 11, 25, 33, 36]. The HXR bremsstrahlung, which is radiated following the relativistic electrons scattering on the background plasma ions, is characterized by very narrow forward radiation pattern with angular half-width about of θ ~ 1⁄γ0, (γ0 is relativistic param eter of energetic electrons). Two narrow radiation patterns with angular half-size θ ≈ 0.06–0.1 have been detected by vertical and horizontal HXR cameras in JET [35] indicating that maximum energies of electrons scattered on background ions could be Wmax ≈ 5–8 MeV. One can see that angular characteristics of the measured HXR radiation Nucl. Fusion 58 (2018) 016014 V.V. Plyusnin etal 4 and the processed data from the HXR spectroscopy yielded similar values on RE energy allowing cross-verification. On TCV a photo-multiplier tube for Hard x-rays (PMTX) is routinely used for measurements of the HXR emission and detection of RE generation. This detector is placed outside the torus, in the machine hall. Due to the large production of energetic HXRs following the RE generation in stationary discharges or during post-disruption RE plateaux the other HXR diagnostics (with energy thresholds ≈20 keV and ≈200 keV) usually saturate and only the PMTX camera could be effectively used for detection of RE generation regimes. Two NaI(Tl) scintillation detectors with photomultipliers for HXR measurements were used during RE experiments in COMPASS. Since these detectors are not shielded, they are characterized by the energy threshold ≈50 keV. Also for measurements of HXR a detector based on ZnS(Ag) scintillator with photomultiplier was used. This detector was shielded with 10 cm of lead. The distance of both detectors from the tokamak main axis is ≈4 m. A detailed description of the diagnostics used in COMPASS experiments also could be found elsewhere [31]. During the RE dominated discharges in COMPASS the synchrotron radiation from RE beam was directly measured by an infrared camera [37]. 3. RE generated during disruptions in Tokamaks Series of experiments in ASDEX-Upgrade and COMPASS have been carried out in order to design the reliable scenario of disruptions with RE generation and to create the basis for future experiments on RE studies in small and medium-sized tokamaks. Disruption scenarios with RE generation in both tokamaks are based on the MGI disruption scenario developed in JET for RE studies [12, 13]. In JET the disruption mitigation valves (DMVs) have been used for injection of Ar, Ne, Xe and Kr. This scenario is described in detail elsewhere [12, 13]. Similarly to JET, the fast injections of large amount of impure gases have been used to trigger the disruptions in limiter configurations in ASDEX-Upgrade and COMPASS [30–32]. The sequence of events in disruptions triggered by MGI is similar to those caused by constant gas puff [10, 11], but occurring in significantly shorter time. These processes are well known and their detailed phenomenological and quantitative descriptions can be found in many publications [9–13, 24, 33, 38]. The main characteristics are: after MGI the plasma develops strong MHD activity; The growth of MHD modes enables penetration of the impurity gas into plasma centre; This process resulted in the cooling of plasma core and formation of the hollow electron temperature profiles [11, 38]. Following these phases the complete plasma energy collapse occurs very quickly. The RE generation scenario in ASDEX-Upgrade is based on L-mode Ohmic circular plasma discharges with inner limiter (R0 = 1.65 m, apl = 0.5 m) and Ipl ⩽ 0.8 MA at B0 = 2.5 T. The injection of 0.05–0.2 bar·l of Ar from the piezo-electric in-vessel valve resulted in characteristic rise of MHD activity and disruptions [30]. To optimize the RE generation at disruptions the low-density plasmas (〈ne〉 ≈ (2.5–3.6) · 1019 m−3) were heated by 2–2.5 MW of ECRH applied for 0.1–0.2 s immediately before Ar/Ne injections. Disruptions were well reproducible with typical thermal quench time tTQ ≈ 0.001 s. Figure1 presents an example of temporal evolution of plasma parameters in the scenario for study of RE generation during disruptions in ASDEX-Upgrade. Disruption of the discharge #32034 was induced by MGI from the piezo-electric valve, which was triggered at t = 1.0 s (vertical dash-dot line in figure1). Usually, major disruption occurs during small time after valve triggering (~4–10 ms, depending on the injected gas type and quantity). In this pulse the disruption occurred in ~5 ms after valve triggering. The maximum of plasma current time derivative on CQ stage was ≈−250 MA s−1. CQ evolution fits well to decay function with characteristic e-folding time tCQ ≈ 2.8 ms. Transition of the plasma current evolution from exponential decay into slow decaying plateau well coincides to the detection of HXR emission and photo-neutrons indicating the generation of RE with energies up to 10 MeV. RE current plateaux with up to 0.4 MA and duration up to 0.4 s have been measured in series of disruptions dedicated to the RE studies in ASDEX-Upgrade. Disruptions in hydrogen plasmas in ASDEX-Upgrade resulted in RE plateaux comparable to those obtained in deuterium, while the slightly lower RE currents were achieved in helium. MGI from the second DMV (triggered on 70th ms Figure 1. ASDEX-Upgrade discharge #32034: scenario for study RE generation at disruptions; disruption was induced by MGI triggered at t = 1.0 s (vertical dash-dot line); disruption time is t ≈ 1.005 s; rectangle pulse of 2.1 MW ECRH is indicated by dot-filled shape; plasma current time derivative maximum on CQ stage is ≈−250 MA s−1; ohmic CQ evolution fits well to decay function with characteristic e-folding time tCQ ≈ 2.8 ms; noticeable deviation of current plateau evolution from exponential decay well corresponds to detection of HXR emission. Nucl. Fusion 58 (2018) 016014 V.V. Plyusnin etal 5 after the first injection) resulted in obvious suppressing effect on RE plateaux and allowed a study of dissipative effects of the MGI of high-Z gases on RE beams [30]. Similar scenario for RE generation studies has been developed in COMPASS: the circular plasma (R0 = 0.56 m, apl ≈ 0.2 m) with carbon limiter from the high field side (HFS) and additional one from the low field side (LFS) for the vessel protection [31]. Experimental magnetic field was B0 = 1.15 T and plasma currents were 80 ⩽ Ipl ⩽ 140 kA. An average electron density was kept relatively low (〈ne〉 ≈ (0.8–2.2)· 1019 m−3) in order to maximize the RE generation rate. Figure 2 presents an example of RE generation in COMPASS during disruption of pulse #10825. MGI was triggered at t = 0.98 s with the active injection phase lasted till to disruption event (≈0.003 s). The maximum of plasma current time derivative on CQ stage was ≈−130 MA s−1. CQ evolutions in many disruptions fit well to decay function with characteristic e-folding time tCQ ≈ 0.5 ms. Detection of the HXR emission coincides to appearance of RE current plateau with value up to 30 kA. Sometimes the COMPASS disruptions resulted in RE current plateaux with values up to 60 kA. COMPASS data was added to the data on disruption generated RE in tokamaks. The data on RE currents generated in tokamak disruptions shows an increasing trend with increase of the total plasma current from small and medium-sized devices toward JET (figure 3). The data plotted in figure4 shows that the higher RE currents are generated in devices with the larger plasma minor radius ( I RE_Ave ∝a2 pl ). Figure 5 presents the data on RE generated in different tokamaks versus toroidal magnetic fields. In this Figurethe data from smaller devices is added to the data on RE collected in JET-C and JET-ILW [11, 25, 33]. One can see, that values of RE plateaux measured in COMPASS disruptions at B0 = 1.15 T and currents Ipl ⩽ 120 kA are similar to the JET data at B0 =1.2 T and currents 1 MA ⩽ Ipl ⩽ 1.2 MA. The MGI disruptions in ASDEX-Upgrade at current Ipl ≈ 0.8 MA and B0 =2.5 T resulted in RE plateaux with values similar to those obtained in JET at B0 =2–2.4 T, but with pre-disrup- tion plasma currents in JET at least two times higher: 1.4 MA ⩽ Ipl ⩽ 2 MA [11, 25, 33]. It is likely that maximum of RE current values generated in disruptions scales as a function, which is proportional to B2 0 . In figure5 the dotted line represents the function f(B0) = ε2 0·B2 0 , where ε0 = apl/R0 = 0.33, Figure 2. RE generation scenario in the COMPASS disruptions: RE plateau with ≈25–30 kA generated after disruption triggered by Ar injection in discharge #10825; MGI was triggered at t = 0.98 s; the injection active stage is indicated by filled area; disruption time is ≈0.983 s; plasma current time derivative maximum on CQ stage is ≈−130 MA s−1; ohmic CQ evolution fits well to decay function with characteristic e-folding time tCQ ≈ 0.5 ms; noticeable deviation of current plateau evolution from exponential decay well corresponds to detection of HXR emission. Figure 3. Disruption generated RE currents versus plasma currents in small, medium-sized and large tokamaks. Figure 4. Generation of RE currents in COMPASS, ASDEX- Upgrade and JET depending on plasma minor radius; solid line represents a function of a2 pl . Nucl. Fusion 58 (2018) 016014 V.V. Plyusnin etal 6 which corresponds to the JET geometry sizes. Note, that ASDEX-Upgrade geometry provides ε0 = apl/R0 ≈ 0.303 and for COMPASS case: ε0 = apl/R0 ≈ 0.36. Generation of RE beams with the measured currents about of tens/hundreds kA at magnetic fields B0 = 1–1.2 T in JET-ILW and COMPASS evidently indicates the absence of background for statements about existence of the threshold for RE generation on toroidal magnetic field value [2]. Maximum values of the RE current generated in ASDEX- Upgrade disruptions reached up to one half of pre-disruption plasma currents I RE Ipl ⩽ 0.5, while the RE current plateaux in COMPASS sometimes reached up to I RE I pl ≈ 0.66 of pre-dis- ruption values (figure 6(a)). This data on conversion rate of plasma current into runaways is quite similar to the recent JET-ILW results confirming observed earlier apparent weak sensitivity of the current conversion rate versus Ipl values and geometrical sizes of experiments [11–13, 21, 22]. Unlike the current conversion rate, the CQ rate Iγ= 1 Ipl dIpl dt revealed strong dependence on the scale of experiments (figure 6(b)). The CQ process is usual driver for generation of high E —one of the determining factors for RE generation. In JET [11] the value of RE currents generated in disruptions has demonstrated almost linear dependence versus values of plasma current time derivatives ( dI pl dt ) evaluated on the beginning of CQ. From the CQ rate the average RE generation rate γRE = 1 jRE dj RE dt , where jRE =ecnRE , can be quantified when a measurable deviation of the plasma current from the exponential decay due to RE is detected, or even when RE plateaux are measured [11, 25, 33]. During RE plateau total plasma current is constant Itot =Ipl +IRE and its time derivative is zero. Meanwhile, the plasma resistive current decays with characteristic e-folding time τCQ [8–13]. So that, dI RE dt = −dIpl dt on the beginning of RE plateaux. Therefore, if the evolution of the plasma cross-section during CQ is known from magnetic measurements, one can evaluate the growth of RE in time using: d dt jREdS= −dIpl dt . Figure 7 summarizes the dependence of RE current conversion rate versus CQ rate values at disruptions. One can see that CQ rates in smaller devices should be approximately 10 times higher than in large tokamaks in order to cause comparable RE generation at disruptions. Simple calculation using the CQ data from figures6(b) and 7 shows that CQ rate evolution from COMPASS to JET depends not only on Ipl, B0, ne, Te, etc, but also on the value of plasma total inductance determined by the major and minor plasma radii of the devices: Lp = µ0 · R0 · (ln(8R0/ap)–2). In the same time, measured CQ rates allowed to deduce the ranges of average post-disruption plasma temperatures: Te ⩽ 7 eV in COMPASS, Te ⩽ 10 eV in ASDEX-Upgrade and Te ⩽ 20 eV in JET. Therefore, the devices with larger geometrical sizes and higher plasma operational parameters, i.e. large tokamaks [2], provide wider limits of the spatial and temporal evolutions of plasma parameters during disruptions, thus extending the parameter space for RE generation. Small and medium sized tokamaks revealed characteristics of RE in MGI disruptions similar to those in JET-C and JET-ILW. However, significant differences in RE parameters have been found also. In particular, the RE experiments in COMPASS (with carbon limiter) have demonstrated obvious non-increasing trend in generated RE currents versus plasma current time derivatives (figure 8(a)). This result is quite different from the data collected in JET-C, where the stable increasing trend of generated RE current versus plasma current time derivative was found [11]. Note that this JET-C trend is based on the data obtained in spontaneous disruptions and those triggered by slow gas puff. In contrast to this data from JET-C, MGI experiments in JET-ILW did not demonstrate such an obvious trend [33]. The change of plasma current direction in COMPASS also resulted in certain differences in runaway generation parameters. This difference could be linked to the change of the helicity direction at unchanged directions of the plasma particles drifts due to grad-B. It is expected to extend the data presented in figure8(b), because, the availability of a small number of this data may be misleading. Despite the observed similarity in the sequence of processes during disruptions, a strong difference between the RE plateau current average densities in JET-ILW and ASDEX- Upgrade has been found. The pre-disruptive average densities of plasma currents have been evaluated: 〈 jpl〉 ≈ 0.5 MA m−2—in JET and 〈 jpl〉 ≈ 0.8 MA m−2—in ASDEX-Upgrade (figure 9). After disruptions the average current densities of RE plateaux in JET remained close to pre-disruption values. Sometimes the increase of average RE current density was observed achieving almost 2 times larger values at the time of plateau termination. Meanwhile, during ASDEX- Upgrade disruptions the runaway acceleration provided the average density of RE plateaux about 2–3 times lower relatively to pre-disruptive values and there were no indications for similar to JET increase of the RE current density during plateaux. This result could be explained by the fact that characteristic e-folding time of plasma current decay in JET is 8 ⩽ tCQ ⩽ 12 ms, which is significantly larger than in ASDEX- Upgrade (tCQ ≈ 2–3 ms). Therefore, sustained for a longer Figure 5. RE generation versus toroidal magnetic fields in small, medium-sized and large tokamaks (compare to data presented in figure7 of [11]); dotted line represents a function of ε2 0·B2 0 , where ε0 = apl/R0 ≈ 0.33 as in JET (in COMPASS: ε0 = apl/R0 ≈ 0.35; in ASDEX-Upgrade: ε0 = apl/R0 ≈ 0.303). Nucl. Fusion 58 (2018) 016014 V.V. Plyusnin etal 7 time the runaway process in JET provides accumulation of higher RE density. With the increase of RE fraction in total current during CQ the generation process is self-limited by the decrease of electric field. At the sufficient decrease of electric fields the generation of new REs is ceased and the remaining plateau current is carried by RE. The second possible reason for the observed difference between parameters of RE plateaux in JET and ASDEX- Upgrade is the difference between the values of lost plasma currents due to the current peeling effect. This effect inevitably occurs during fast inward motion of the plasma on CQ and it should result in higher electric fields due to the additional loss of the corresponding magnetic flux [39]. Yet another reason for observed difference could be the substantially shorter gas travelling distance from in-vessel valve to the plasma after MGI in ASDEX-Upgrade. As a result, the faster gas penetration, better its assimilation and more effective RE dissipation could be achieved. Similarly to the results from the D-IIID tokamak [28], the ASDEX-Upgrade experiments have shown dissipative effects of the second MGI of Ar/Ne on RE beams for both, far and close located injection valves [30]. In contrast to D-IIID [28] and ASDEX-Upgrade [30] the dissipative effect of secondary MGI on already accelerated RE beam was not achieved in JET [12, 13]. These JET experiments have demonstrated the presence of low temperature but dense enough post-disruption background plasma ( ¯ ne ⩽ 1020 m−3), which fills almost all vacuum volume comprising the space of open magnetic field lines and nested magnetic surfaces formed by RE beam current [12, 13]. Interacting with background hydrogen neutrals and impurity ions relativistic RE, both, well confined and already drifted out, can generate secondary (not runaway) electrons [40–43]. The ionization cross-section of hydrogen by relativistic electron is described in [40]. Subsequently, for an ion Xi with ionization potential IXi and having NXi outer shell electrons the formula for crosssection ionization by relativistic electron with energy characterized by Lorentz factor γ0 was derived in the form [41, 42] given below: σ Xi=7.24 ·10−20 N Xi I Xi ·γ 2 0 γ2 0−1 (15.85 −ln(IXi)+2ln(γ0)) . (1) In [42, 43] it was pointed out that relativistic electron ionization could generate low temperature electrons with mean energy ~40 eV. Analysis of the spectroscopy data measured during the runaway plateaux in JET indicates the presence of argon lines with wavelengths corresponding to 3- and 4-times ionized Ar. This data well corresponds to the statement above, since to achieve observed Ar ionization stages the background plasma should have significant electron temperature 10 eV ⩽ Te ⩽ 20 eV [44]. Therefore, the ionization of background gas by RE serves as a source for plasma cloud, which surrounds the RE beam [12, 13]. It is obvious, that such plasma will have a screening effect on the penetration of the injected gas [45] to the location of RE beam thus decreasing the effect of the second MGI. Figure 6. Conversion of plasma currents into RE currents—chart (a), and CQ rates in disruptions with RE generation—chart (b) in small medium-sized and large tokamaks. Figure 7. Dependence of conversion rate of plasma resistive currents into RE currents versus CQ rates at disruptions in tokamaks (values of disrupted currents are given in header). Nucl. Fusion 58 (2018) 016014 V.V. Plyusnin etal 8 4. RE in stationary discharges in TCV, COMPASS and JET 4.1. Runaway critical energies and runaway critical electric fields in tokamaks Transient nature of disruptions does not allow reliable measurements of plasma parameters evolution. Modelling of RE generation at disruptions is still very complicated task also, since it requires an inclusion of many parameters, which are strongly varied during disruptions. Therefore, a scenario of RE generation in stationary discharges in tokamaks constitutes a subject of special attention due to possibility to measure reliably plasma parameters during onset, growth and loss of relativistic RE [34]. This steady-state scenario with low plasma density was used in the second group of experiments in COMPASS and TCV. Obtained data on RE generation dynamics was compared to the data measured during RE stationary phase of the JET discharge JPN #86078 [35]. The baseline scenario for RE studies in TCV is: L-mode, inner wall limited Ohmic discharges (R0 = 0.89 m, apl = 0.25 m) at B0 = 1.43 T, plasma currents Ipl ⩽ 200 kA and average plasma density 〈ne〉 ⩽ 3·1019 m−3. Conditions for measurable RE generation during flattop were achieved by controlled plasma density ramp-down (figure 10). RE in COMPASS are normally produced during the current ramp-up phase providing the measurable seed RE population detected using HXR diagnostics. The baseline scenario for RE studies is: B0 = 1.15 T, 90 kA ⩽ Ipl ⩽ 150 kA, 〈ne〉 ⩽ 3 · 1019 m−3, Ohmic inner wall limited discharge in L-mode. Using different fuelling scenarios the RE populations could be generated (figure 11) allowing studies of MHD effects on RE confinement [31]. Similarly to the JET data, plasma parameters in COMPASS and TCV have been numerically processed in order to minimize the effect of the data large scattering (filtering noise, etc) onto results of numerical evaluation of runaway dynamics. All measured parameters were used in simulation of runaway generation in radially averaged model with the aid of iterative method [20]. In this modelling the value of effective ion charge (Zeff) was used as iterative parameter and calculated using the equationof plasma electro-conductivity on the basis of measured plasma current, loop voltage (Vloop), electron temperature (Te) and density 〈ne〉. Analysis of stationary RE discharges in COMPASS, TCV and JET [35] has shown that the primary (Dreicer) process Figure 8. A study of RE generation at inversion of plasma current direction in COMPASS disruptions: (a)—plasma currents and B0 are in co-direction; (b)—plasma currents and B0 are in counter-direction. Figure 9. Comparison of average RE current plateaux densities in ASDEX-Upgrade (a) and in RE plateaux in JET-C and in JET-ILW (b) generated during disruptions triggered by MGI. Nucl. Fusion 58 (2018) 016014 V.V. Plyusnin etal 15 ORCID iDs A. Kallenbach https://orcid.org/0000-0003-0538-2493 A.E. Shevelev https://orcid.org/0000-0001-7227-8448 O. Ficker https://orcid.org/0000-0001-6418-9517 A. 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