Phenomenological modeling of the suprathermal electron generation during magnetic field line reconnections in Experimental Advanced Superconducting Tokamak

Phenomenological modeling of the suprathermal electron generation during magnetic field line reconnections in Experimental Advanced Superconducting Tokamak

The strong suprathermal electron generation is modeled in conditions of bursts of the strong MHD plasma activity in the Experimental Advanced Superconducting Tokamak (EAST) when magnetic field line reconnections took place. Because of the fast changes in the magnetic flux during these magnetic field...

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Datum:2017
Hauptverfasser: Marchuk, Yu.M., Pankratov, I.M.
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Veröffentlicht: Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2017
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spelling irk-123456789-1221122017-06-28T03:02:36Z Phenomenological modeling of the suprathermal electron generation during magnetic field line reconnections in Experimental Advanced Superconducting Tokamak Marchuk, Yu.M. Pankratov, I.M. Магнитное удержание The strong suprathermal electron generation is modeled in conditions of bursts of the strong MHD plasma activity in the Experimental Advanced Superconducting Tokamak (EAST) when magnetic field line reconnections took place. Because of the fast changes in the magnetic flux during these magnetic field line reconnections the instant bursts of the induced electric field occur. The instant changes in suprathermal electron density during these bursts of the induced electric field have been analyzed. Моделируется сильная генерация надтепловых электронов в условиях коротких вспышек сильной МГД-активности плазмы при перезамыкании магнитных силовых линий в Experimental Advanced Superconducting Tokamak (EAST). В результате быстрых изменений магнитного потока во время таких перезамыканий магнитных силовых линий индуцируются короткие вспышки электрического поля. Проанализированы мгновенные изменения плотности надтепловых электронов при этих вспышках индуцированного электрического поля. Моделюється сильна генерація надтеплових електронів в умовах коротких сплесків сильної МГД-активності плазми при перемиканні магнітних силових ліній в Experimental Advanced Superconducting Tokamak (EAST). В результаті швидких змін магнітного потоку під час таких перемиканнь магнітних силових ліній індукуються короткі сплески електричного поля. Проаналізовані миттєві зміни густини надтеплових електронів під час цих сплесків індукованого електричного поля. 2017 Article Phenomenological modeling of the suprathermal electron generation during magnetic field line reconnections in Experimental Advanced Superconducting Tokamak / Yu.M. Marchuk, I.M. Pankratov // Вопросы атомной науки и техники. — 2017. — № 1. — С. 6-9. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS: 52.55.Fa; 52.35.Bj; 52.35.Vd http://dspace.nbuv.gov.ua/handle/123456789/122112 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
topic Магнитное удержание
Магнитное удержание
spellingShingle Магнитное удержание
Магнитное удержание
Marchuk, Yu.M.
Pankratov, I.M.
Phenomenological modeling of the suprathermal electron generation during magnetic field line reconnections in Experimental Advanced Superconducting Tokamak
Вопросы атомной науки и техники
description The strong suprathermal electron generation is modeled in conditions of bursts of the strong MHD plasma activity in the Experimental Advanced Superconducting Tokamak (EAST) when magnetic field line reconnections took place. Because of the fast changes in the magnetic flux during these magnetic field line reconnections the instant bursts of the induced electric field occur. The instant changes in suprathermal electron density during these bursts of the induced electric field have been analyzed.
format Article
author Marchuk, Yu.M.
Pankratov, I.M.
author_facet Marchuk, Yu.M.
Pankratov, I.M.
author_sort Marchuk, Yu.M.
title Phenomenological modeling of the suprathermal electron generation during magnetic field line reconnections in Experimental Advanced Superconducting Tokamak
title_short Phenomenological modeling of the suprathermal electron generation during magnetic field line reconnections in Experimental Advanced Superconducting Tokamak
title_full Phenomenological modeling of the suprathermal electron generation during magnetic field line reconnections in Experimental Advanced Superconducting Tokamak
title_fullStr Phenomenological modeling of the suprathermal electron generation during magnetic field line reconnections in Experimental Advanced Superconducting Tokamak
title_full_unstemmed Phenomenological modeling of the suprathermal electron generation during magnetic field line reconnections in Experimental Advanced Superconducting Tokamak
title_sort phenomenological modeling of the suprathermal electron generation during magnetic field line reconnections in experimental advanced superconducting tokamak
publisher Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate 2017
topic_facet Магнитное удержание
url http://dspace.nbuv.gov.ua/handle/123456789/122112
citation_txt Phenomenological modeling of the suprathermal electron generation during magnetic field line reconnections in Experimental Advanced Superconducting Tokamak / Yu.M. Marchuk, I.M. Pankratov // Вопросы атомной науки и техники. — 2017. — № 1. — С. 6-9. — Бібліогр.: 14 назв. — англ.
series Вопросы атомной науки и техники
work_keys_str_mv AT marchukyum phenomenologicalmodelingofthesuprathermalelectrongenerationduringmagneticfieldlinereconnectionsinexperimentaladvancedsuperconductingtokamak
AT pankratovim phenomenologicalmodelingofthesuprathermalelectrongenerationduringmagneticfieldlinereconnectionsinexperimentaladvancedsuperconductingtokamak
first_indexed 2025-07-08T21:08:46Z
last_indexed 2025-07-08T21:08:46Z
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fulltext ISSN 1562-6016. ВАНТ. 2017. №1(107) 6 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2017, № 1. Series: Plasma Physics (23), p. 6-9. PHENOMENOLOGICAL MODELING OF THE SUPRATHERMAL ELECTRON GENERATION DURING MAGNETIC FIELD LINE RECONNECTIONS IN EXPERIMENTAL ADVANCED SUPERCONDUCTING TOKAMAK Yu.M. Marchuk1, I.M. Pankratov1,2 1V.N. Karazin Kharkiv National University, Kharkov, Ukraine; 2Institute of Plasma Physics of the NSC KIPT, Kharkov, Ukraine The strong suprathermal electron generation is modeled in conditions of bursts of the strong MHD plasma activity in the Experimental Advanced Superconducting Tokamak (EAST) when magnetic field line reconnections took place. Because of the fast changes in the magnetic flux during these magnetic field line reconnections the instant bursts of the induced electric field occur. The instant changes in suprathermal electron density during these bursts of the induced electric field have been analyzed. PACS: 52.55.Fa; 52.35.Bj; 52.35.Vd INTRODUCTION Runaway electron generation is a fundamental physical phenomenon. At the same time the runaway electrons during major disruptions can cause a serious damage of plasma-facing-component surfaces in large tokamaks like ITER [1, 2]. The strong electric fields induced during the tokamak disruption can generate a lot of these runaways. The energy of runaway electrons can reach as high as tens of Megaelektronvolt. 1. RUNAWAY GENERATION Runaway electrons are generated when the electron energy exceeds a critical energy at which the electric field driving force is equal to the minimum frictional drag force in the plasma. There are primary runaway generation ( ||0 0p p , Dreicer generation [3]) and secondary runaway generation ( ||0 0p p , avalanche generation [4]). The inequality 0.25 / /0 (2 )cr effp p Z  (1) determines the runaway region of primary generation process [5] and the inequality 0.54 0 12 (2 ) / 3cr effp p Z   (2) determines the runaway region of secondary generation process [6], where / /0p and 0p are the initial values of the electron longitudinal and transverse (with respect to magnetic field) momenta, respectively, and 2 3 2 0 / // 4cr e ep e m n L E . (3) Here, e and me are the charge and the resting mass of the electron, ne is the plasma density L is the Coulomb logarithm, Zeff is the effective ion charge number, E// is the tokamak toroidal induced electric field and c is the velocity of light. The avalanche formed as a result of the secondary generation with avalanche time tav [7]: / /12 (2 ) / 9av e efft m cL Z eE  . (4) 2. RUNAWAY EAST DISCHARGE The runaway ohmic discharge #28957 in EAST was performed in the limiter configuration with the toroidal magnetic field B0 = 2 T, the plasma current Ip = 250 kA, the central line-averaged density <ne> = 2.2×1019 m−3, the plasma major radius R = 1.86 m and the minor radius a = 0.45 m (see, e.g. [8]). At the plasma center, the electron temperature Te ≈ 0.55 keV was obtained using a soft x-ray pulse height analysis (PHA) system during the plasma current flat-top phase (duration of impulse was 5 s). MHD modes m/n=1/1 (the soft x-ray signal) and m/n=2/1 (the Mirnov coil signals) existed in the plasma, where m and n are the poloidal and toroidal mode numbers. Runaway electrons were created by the ohmic coil during the start-up phase of the discharge. The runaway electrons were located around the q = 2 rational magnetic surface (ring-like runaway electron beam (see, e.g., [8]). In shot #28957 three types of events were observed during the stepwise increases in the non-thermal ECE signal [9]: 1. The MHD (m/n=2/1) small amplitude spikes (type I events, small non-thermal ECE jumps) emerged approximately every 0.02 s and coincided with sawtooth m/n=1/1 peaks. 2. Huge MHD spikes (type II events) emerged approximately every 0.5 s. 3. Larger amplitude MHD (m/n=2/1) spikes (type III events) were observed approximately every 0.3 s after each huge MHD spike (type II events). In cases II-III types events the MHD (m/n=2/1) spikes were not correlated with the m/n=1/1 sawtooth oscillations peaks. Due to the local runaway generation processes, local changes in the plasma current density profile should occur (around the q = 2 rational magnetic surface, where the runaway electrons are located). The tearing mode stability depends rather sensitively on the current- density gradient in the vicinity of the resonant surface ISSN 1562-6016. ВАНТ. 2017. №1(107) 7 [10]. These local changes in the plasma current density profile near the q = 2 rational magnetic may be the trigger for the strong enhancement of the MHD activity (m/n=2/1 spikes). The generation of suprathermal electrons should be enhanced during these MHD spikes because of the fast changes in the magnetic flux (squeezing and reconnection of the magnetic field lines). As result of these changes in magnetic flux the bursts of induced electric fields occurred [10]. During these bursts of the induced electric field E//, electron runaway region increased because the value of pcr dropped (see Eqs. (1)- (3)). The abrupt growth in the suprathermal electron population occurred during these bursts of E//. In Ref. [9] conclusion was made that the step-like non- thermal ECE jumps may be explained by the abrupt growth in the suprathermal electron generation (number of runaways) during MHD m/n=2/1 spikes. In Ref. 8 the runaway energy E ≈ 30 MeV was deduced for EAST shot #28957 and conclusion was made that the secondary runaway generation process should take place with avalanche time tav ≈ 0.5s (EAST #28957 parameters: E// ≈ 0.1 V/m, Zeff ≈ 3, and L ≈ 15). The value of tav ≈ 0.5 s is of the same order as the value of the time of strong MHD activity (0.3 s or 0.5 s intervals). The time behavior of runaway electron density nr is described by the following well-known equation (see, e.g., [11-13]):             || , r rr e e lav n t n tdn n t t t dt tt E     (5) where  4 2 2 3 04 ,e e e n t L m v    || , D E E   3 2 0 , 4 e D e e n L E T  (6)        11 1 416 ZZ effeff t K Z eeff        . (7) -------------------------------------------------------------------- The first term in right part of Eq. (5) describes primary generation, second term describes secondary generation and last term describes the runaway loss. Solution of Eq. (5) has the next form:                        t t lav r tE tdtn 0 || 11 exp                                 t t t t lav eeer tE tdntdtn 0 0 || 0 11 exp   . (8) Because of a very short time of the MHD m/n=2/1 spikes, the linear time dependence of changes of the bursting electric field was taken for modeling (Fig.1):                     20 21 2 0 11 1 0 100 || ., ;, ;, ;, ttE ttt tt EE ttt tt EE tttE tE br br m br br m     (9) Fig. 1. Model for bursting electric field The instant change in suprathermal electron density during the burst of induced electric field is given by:         3 3( 1) 2 160 3 04 4 21 2 exp 2 Z eff effm e br r br br av m av le eff K ZE n n t E t E tem L Z                                       1 1 2 2 0 00 0 exp exp , 2 2 br br br br br br av m av l av m av l dtI t t t t dtI t t t t t E t E t t E t E t                              (10) where   3( 1)3 2 16 0 0 0 ( 1)1 exp , 4 effZ eff m m m ZE I t t E E E t t E E                                     , .m D E E   (11) 8 ISSN 1562-6016. ВАНТ. 2017. №1(107) Eq. (10) describes of instant change in suprathermal electron density at the time of the fast reconnection of magnetic field lines that was accompanied by the burst of induced electric field. Reconnections of magnetic field lines leads to the stochastization of magnetic field lines. Rapid changes of synchrotron spot structure and intensity during EAST experiments were result of changes in the runaway beam structure owing this stochastization. Recall, the synchrotron radiation is used for the direct observation of the runaway beam image. The loss term in Eq (10) describes the radial drift of suprathermal electrons due to this magnetic turbulence. This equation is used for modeling of experiments in tokamak EAST. Note, in Refs. [12, 13] the equation (5) was used for modeling of disruption generated runaways in JET by including secondary runaway generation with the value of avalanche time, tav , which was obtained in Ref. [7] (see Eq. (4)). This modeling of a JET disruption showed that here the secondary runaway generation plays a dominant role. 3. MODELLING OF THE SUPRATHERMAL ELECTRON GENERATION DURING HUGE MHD SPIKES In modeling the same plasma parameters were used that were in the EAST shot #28957 (see Table). Plasma parameters for modeling of #28957 The plasma parameters Value E0 in Eq. (9) 0.1 V/m Em in Eq. (9) (0.9…5) V/m ED 16 V/m Plasma density, ne 2.2×1019 m-3 Effective ion charge, Zeff 3 Coulomb logarithm, L 15 Electron temperature, Te 550 eV K(Zeff) 0.5 Fig. 2. Instant changes in the suprathermal electron density on amplitude of bursting electric field Huge MHD spike (type II events) was modeled for assumed range of the induced electric field from 0.9 to 5 V/m. The calculation was performed by a standard program Microsoft Excel which realized Simpson method for numerical integration. In Fig. 2 the phenomenological modeling result of instant changes in suprathermal electron density is presented (curve 1 corresponds to 2.5 ms of burst duration (2τbr), curve 3 for 3.75 ms, curve 2 for 1.7 ms). These three values of burst durations are result of data analysis from Ref. 9. They are in good agreement with EAST experiments. Note, the value Em=12 V/m of induced electric field was found during a series of minor disruptions in the T-10 tokamak [14]. CONCLUSIONS The dependence of instant changes in suprathermal electron density from amplitude of bursting electric field during the strong MHD plasma activity in EAST has been investigated. We plan to use obtained results for further comparison with EAST experiments. ACKNOWLEDGEMENTS We thank Dr. R.J. Zhou for useful and fruitful discussions. REFERENCES 1. ITER Physics Basis, Chapter 3: MHD stability, operational limits and disruptions // Nucl. Fusion. 1999, v. 39, № 12, p. 2175-2389. 2. Progress in the ITER Physics Basis, Chapter 3: MHD stability, operational limits and disruptions // Nuclear Fusion. 2007, v. 47, № 6, p. S128-S202. 3. H. Dreicer. Electron and ion runaway in a fully ionized gas. 1 // Physcal Review. 1959, v. 115, № 2, p. 238-249. 4. Ya.A. Sokolov // JETP Letter. 1979, v. 29, p. 218- 220. 5. V. Fuchs, R.A. Cairns, C.N. Lashmore-Davies, M.M. Shoucri. Velocity-space structure of runaway electrons // Phys. Fluids. 1986, v. 29, № 9, p. 2931- 2936. 6. N.T. Besedin, I.M. Pankratov. Stability of a runaway electron beam // Nuclear Fusion. 1986, v. 26, № 6, p. 807-812. 7. I.M. Pankratov, N.T. Besedin. Runaway electron secondary generation // Proc. 23th EPS Conf. on Contr. Fusion and Plasma Physics, Kiev. 1996, v. 20C, part. 1, p. 279-282. 8. R.J. Zhou, I.M. Pankratov, L.Q. Hu, M. Xu, J.H. Yang. Synchrotron radiation spectra and synchrotron radiation spot shape of runaway electrons in Experimental Advanced Superconducting Tokamak // Phys. Plasmas. 2014, v. 21, p. 063302. 9. I.M. Pankratov, R.J. Zhou, L.Q. Hu. Runaway electron generation as possible trigger for enhancement of magnetohydrodynamic plasma activity and fast changes in runaway beam behavior // Phys. Plasmas. 2015, v. 22, p. 072115. 10. D. Biskamp. Magnetic Reconnection in Plasmas. Cambridge: “Cambridge University Press”, 2000. 11. R. Jaspers, N.J. Lopes Cardozo, F.C. Schuller, K.H. Finken, T. Grewe, G. Mank. Disruption generated runaway electrons in TEXTOR and ITER // Nuclear Fusion. 1996, v. 36, № 3, p. 367-373. ISSN 1562-6016. ВАНТ. 2017. №1(107) 9 12. I.M. Pankratov, R. Jaspers, K.H. Finken, I. Entrop. Secondary generation of runaway electrons and its detection in tokamaks // Proc. 26th EPS Conf. On Contr. Fusion and Plasma Physic. Maastricht. 1999, v. 23J, p. 597-600. 13. R.D. Gill, B. Alper, M. De Baar, T.C. Hender, M.F. Johnson, V. Riccardo. Behaviour of disruption generated runaways in JET // Nuclear Fusion. 2002, v. 42, № 8, p. 1039-1044. 14. P.V. Savrukhin, E.A. Shestakov. A study on the effects of magnetohydrodynamic perturbations on nonthermal beam formation during the current decay phase of disruptions in the T-10 tokamak // Nuclear Fusion. 2015, v. 55, p. 043016. Article received 20.12.2016 ФЕНОМЕНОЛОГИЧЕСКОЕ МОДЕЛИРОВАНИЕ ГЕНЕРАЦИИ НАДТЕПЛОВЫХ ЭЛЕКТРОНОВ ПРИ ПЕРЕЗАМЫКАНИИ МАГНИТНЫХ СИЛОВЫХ ЛИНИЙ В EXPERIMENTAL ADVANCED SUPERCONDUCTING TOKAMAK Ю.Н. Марчук, И.М. Панкратов Моделируется сильная генерация надтепловых электронов в условиях коротких вспышек сильной МГД- активности плазмы при перезамыкании магнитных силовых линий в Experimental Advanced Superconducting Tokamak (EAST). В результате быстрых изменений магнитного потока во время таких перезамыканий магнитных силовых линий индуцируются короткие вспышки электрического поля. Проанализированы мгновенные изменения плотности надтепловых электронов при этих вспышках индуцированного электрического поля. ФЕНОМЕНОЛОГІЧНЕ МОДЕЛЮВАННЯ ГЕНЕРАЦІЇ НАДТЕПЛОВИХ ЕЛЕКТРОНІВ ПРИ ПЕРЕМИКАННІ МАГНІТНИХ СИЛОВИХ ЛІНІЙ В EXPERIMENTAL ADVANCED SUPERCONDUCTING TOKAMAK Ю.М. Марчук, І.М. Панкратов Моделюється сильна генерація надтеплових електронів в умовах коротких сплесків сильної МГД- активності плазми при перемиканні магнітних силових ліній в Experimental Advanced Superconducting Tokamak (EAST). В результаті швидких змін магнітного потоку під час таких перемиканнь магнітних силових ліній індукуються короткі сплески електричного поля. Проаналізовані миттєві зміни густини надтеплових електронів під час цих сплесків індукованого електричного поля.

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