On the possibility for the resonance ELM-generation mechanism by the injection of the neutral particle beam in tokamak

It is known that in plasmas with a magnetic field the Hall electric field is generated at the expense of the charge separation on the magnetic Debye radius rB=|B|/(4pene). In addition, the plasma current equilibrium can arise, where the charged particles are drifting in the crossed electric and magn...

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Дата:	2007
Автор:	Gordeev, A.V.
Формат:	Стаття
Мова:	English
Опубліковано:	Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2007
Назва видання:	Вопросы атомной науки и техники
Теми:	Magnetic confinement
Онлайн доступ:	https://nasplib.isofts.kiev.ua/handle/123456789/110323
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Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:	On the possibility for the resonance ELM-generation mechanism by the injection of the neutral particle beam in tokamak / A.V Gordeev // Вопросы атомной науки и техники. — 2007. — № 1. — С. 3-5. — Бібліогр.: 7 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine

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spelling	nasplib_isofts_kiev_ua-123456789-1103232025-02-10T01:38:43Z On the possibility for the resonance ELM-generation mechanism by the injection of the neutral particle beam in tokamak Про можливості резонансного механізму генерації ELM при інжекції пучка нейтральних часток у токамаках О возможности резонансного механизма генерации ELM при инжекции пучка нейтральных частиц в токамаках Gordeev, A.V. Magnetic confinement It is known that in plasmas with a magnetic field the Hall electric field is generated at the expense of the charge separation on the magnetic Debye radius rB=\|B\|/(4pene). In addition, the plasma current equilibrium can arise, where the charged particles are drifting in the crossed electric and magnetic fields. Such a situation can be realized in tokamaks as a result of the ionization processes for the beams of the energetic neutral particles that are injected in tokamaks in order to increase the plasma density and temperature. In this presentation, the generation of the resonance instability for the azimuthal drifting flux of the ions and electrons crosswise to the strong magnetic field is considered. Відомо, що в плазмі з магнітним полем генерація холловського електричного поля за рахунок поділу зарядів відбувається на магнітному дебаєвському радіусі rB=\|B\|/(4pene). При цьому можливо утворення плазмової токової рівноваги, де заряджені частки дрейфують у схрещених електричному і магнітному полях. Така ситуація може бути реалізована в токамаках як наслідок процесів іонізації пучка енергійних нейтральних часток, інжектуємих у токамаки, з метою підвищення густини плазми і її температури. Розглянуто генерацію резонансної нестійкості азимутальних потоків іонів і електронів, що дрейфують поперек сильного магнітного поля. Известно, что в плазме с магнитным полем генерация холловского электрического поля за счёт разделения зарядов происходит на магнитном дебаевском радиусе rB=\|B\|/(4pene). При этом возможно образование плазменного токового равновесия, где заряженные частицы дрейфуют в скрещённых электрическом и магнитном полях. Такая ситуация может быть реализована в токамаках в результате процессов ионизации пучка энергичных нейтральных частиц, инжектируемых в токамаки, с целью увеличения плотности плазмы и её температуры. Рассмотрена генерация резонансной неустойчивости азимутальных потоков ионов и электронов, дрейфующих поперёк сильного магнитного поля. This paper has been partially supported within the System of the Initiative Projects of Russian Research Centre “Kurchatov Institute” 2007 Article On the possibility for the resonance ELM-generation mechanism by the injection of the neutral particle beam in tokamak / A.V Gordeev // Вопросы атомной науки и техники. — 2007. — № 1. — С. 3-5. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 52.30.Ex, 52.35.We, 52.55.-s https://nasplib.isofts.kiev.ua/handle/123456789/110323 en Вопросы атомной науки и техники application/pdf 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	Magnetic confinement Magnetic confinement
spellingShingle	Magnetic confinement Magnetic confinement Gordeev, A.V. On the possibility for the resonance ELM-generation mechanism by the injection of the neutral particle beam in tokamak Вопросы атомной науки и техники
description	It is known that in plasmas with a magnetic field the Hall electric field is generated at the expense of the charge separation on the magnetic Debye radius rB=\|B\|/(4pene). In addition, the plasma current equilibrium can arise, where the charged particles are drifting in the crossed electric and magnetic fields. Such a situation can be realized in tokamaks as a result of the ionization processes for the beams of the energetic neutral particles that are injected in tokamaks in order to increase the plasma density and temperature. In this presentation, the generation of the resonance instability for the azimuthal drifting flux of the ions and electrons crosswise to the strong magnetic field is considered.
format	Article
author	Gordeev, A.V.
author_facet	Gordeev, A.V.
author_sort	Gordeev, A.V.
title	On the possibility for the resonance ELM-generation mechanism by the injection of the neutral particle beam in tokamak
title_short	On the possibility for the resonance ELM-generation mechanism by the injection of the neutral particle beam in tokamak
title_full	On the possibility for the resonance ELM-generation mechanism by the injection of the neutral particle beam in tokamak
title_fullStr	On the possibility for the resonance ELM-generation mechanism by the injection of the neutral particle beam in tokamak
title_full_unstemmed	On the possibility for the resonance ELM-generation mechanism by the injection of the neutral particle beam in tokamak
title_sort	on the possibility for the resonance elm-generation mechanism by the injection of the neutral particle beam in tokamak
publisher	Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate	2007
topic_facet	Magnetic confinement
url	https://nasplib.isofts.kiev.ua/handle/123456789/110323
citation_txt	On the possibility for the resonance ELM-generation mechanism by the injection of the neutral particle beam in tokamak / A.V Gordeev // Вопросы атомной науки и техники. — 2007. — № 1. — С. 3-5. — Бібліогр.: 7 назв. — англ.
series	Вопросы атомной науки и техники
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first_indexed	2025-12-02T12:50:39Z
last_indexed	2025-12-02T12:50:39Z
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fulltext	MAGNETIC CONFINEMENT Problems of Atomic Science and Technology. 2007, 1. Series: Plasma Physics (13), p. 3-5 3 ON THE POSSIBILITY FOR THE RESONANCE ELM-GENERATION MECHANISM BY THE INJECTION OF THE NEUTRAL PARTICLE BEAM IN TOKAMAK A.V. Gordeev RRC “Kurchatov Institute”, Moscow, Russia, e-mail: gordeev@dap.kiae.ru It is known that in plasmas with a magnetic field the Hall electric field is generated at the expense of the charge separation on the magnetic Debye radius ( )eB en4Br π= r . In addition, the plasma current equilibrium can arise, where the charged particles are drifting in the crossed electric and magnetic fields. Such a situation can be realized in tokamaks as a result of the ionization processes for the beams of the energetic neutral particles that are injected in tokamaks in order to increase the plasma density and temperature. In this presentation, the generation of the resonance instability for the azimuthal drifting flux of the ions and electrons crosswise to the strong magnetic field is considered. In this case, the generation of the resonance instability by the account of the ion inertia is obtained for the fast magnetosonic oscillations by Biω>>ω [ ( )cmBez iiBi r =ω is the ion cyclotron frequency], when the resonance condition pi0kv ω±=−ω ( )22 z 2 pi 1 0pi ck+ωγ=ω − is valid for some points ( is the oscillation frequency, v0 is the beam velocity of the charged particles, 1 Brk −≤ is the oscillation wave vector, ωpi is the ion plasma frequency). The considered instability corresponds to the parameter range 0ii 22 ii cvmn4Bcmn4 π>>>>π . PACS: 52.30.Ex, 52.35.We, 52.55.-s 1. INTRODUCTION The problem of the plasma heating and the equilibrium confinement in tokamaks is the main problem in the project ITER [1]. As it follows from [1,2], the problem of the stable equilibrium itself and in particular the problem of the ELM generation in tokamaks, as yet, far enough from the complete resolution. It is not ruled out that it is just the inclusion of this problem in the complicated numerical codes which is not favorable for the elucidation of the ELM mechanism. In the presented paper the attempt is made by way of example for the cylindrical model of the tokamak to consider the resonance instability which arises quite naturally by the propagation through plasma of the energetic particles’ flux. The instability considered is suggested as the physical mechanism of the ELM. In this case, the energetic particles can be generated as a result of the ionization of the neutral particles’ fluxes, which usually used for the increasing of the plasma density and temperature in tokamaks [1]. It is known, that by the injection of the charged particles of the high energy in the plasma with the magnetic field the propagation of this beams on the account of the Hall electric field [3,4] arises. In the case of the plasma cylinder with the longitudinal magnetic field Bz due to the absence of the unidirectional stationary azimuthal electric field Eθ the azimuthal particle drift on the account of the radial electric field Er arises. Thus, in contrast to the considered in [5] plane case, in the cylindrical geometry by the presence of the longitudinal magnetic field the drifting rotation of the plasma flux occurs. One can show that the drift plasma fluxes turn out to be unstable relative to the fast magnetosonic oscillations near the lower hybrid range of frequency. In addition, the characteristic size scale of these oscillations is about the magnetic Debye radius ( )eB en4Br π= . The presented instability is proposed as the ELM – generation mechanism. 2. THE MAIN EQUATIONS Further on, the case will be considered when the energy of the injected particles is essentially larger than the thermal energies of the tokamak particles, so the particles temperatures will not be taken into account. Therefore, for the describing of the ion and electron motion in the strong electric and magnetic fields the relativistic equations for the cold particles are used ]Bv[ c ez Eez dt pd i,e i,e i,e i,e rrr r ×+= (1) and Maxwell equations t E c 1)vnvnz( c e4]B[ eeiii ∂ ∂ +− π =×∇ r rrr , ]E[ t B c 1 r r ×∇= ∂ ∂ − , )nnz(e4E eii −π=⋅∇ r . (2) Here i,evr is the electron and ion velocities, i,ei,ei,e vmp rr γ= , 22 i,e cv11 r −=γ , i,en are the electron and ion densities, zi is the ion charge number, ze = -1, E r is the electric field, B r is the magnetic field. 3. THE DERIVATION OF THE DISPERSION RELATION FOR THE RESONANCE INSTABILITY OF THE DRIFT FLUX OF IONS AND ELECTRONS In the considered frequency range, the large electron mobility along the magnetic field B0 is of the essential importance. Then by neglecting the electron inertia in the transverse direction one can obtain the following equation relative E in the WKB approximation (see also [6]): mailto:gordeev@dap.kiae.ru 4 0E)s(k ds Ed 2 02 2 =− θ θ , 22 2 pi 2 0 2 pi 22 0 ~ ~ 1)s(k Ω−Ω ΩΩ Λ+Ω+Ω−= , (3) Here kc ω =Ω , 0k k~ β−Ω θ , 22 i i 22 i2 pi kcm nez4π =Ω , 2 0 2 ii 0 B cmn4π =Λ ,       +Ω γ =Ω 2 2 z2 pi2 0 2 k k1 , 0r mk =θ , 2 z 22 kkk += θ . Here m is the integer. Here, one can consider that the spatial region r, where the drifting flux settles down, corresponds to the characteristic radius r0>> r, what allows to neglect the cylindrical effects. In the following presentation, because of the inequality θ<< kk z , one can consider that ( )θθ = ksignkk and ( ) 0vksign~ θ−Ω=Ω . 4. THE RESONANCE PLASMA INSTABILITY FOR THE AZIMUTHAL DRIFTING FLUX OF IONS AND ELECTRONS From the equation (3) one can see that the effective interaction of the drifting flux with the electromagnetic oscillations occurs in the poles, where pi0vk ω±=−ω θ , ( )22 z 2 pi 1 0pi ck+ωγ=ω − . Here, the values v0 and piω are determined by the ion flux parameters, and the frequency is determined by the ground plasma. Of course, the drifting flux goes through the ground plasma. However, in the calculations the drifting fluxes and the ground plasma will be spatially separated. This procedure results in the diminishing of the instability increment without any change of the physical mechanism. By the further investigations within the frame of the Eq.(3), we take approach from that used in the paper [7]. As one can see from the Figure, in the region of the azimuthal flux there exists the pole-pole well ( )21 s,s , The plasma velocity profile and the contour in the complex plane and in the region of the ground plasma there exists the zero – zero well (s1,s2). Both these regions correspond to the negative values of )s(k 2 0 . For the construction of the perturbations that go to zero by ±∞→s , one must use the Landau rule when one should add to the frequency the small positive imaginary quantity: ε+ω→ω i , where > 0. With this procedure in mind, the electric field E , that by ( )1sRes < to the left of the pole potential well ( )21 s,s goes to zero and is equal to         = ∫θ s s 0 0 1 dskexp k BE , (4) after the passage through the pole 1s is transformed inside the pole potential well ( )21 s,s into the traveling wave [7] ( )[ ] ( )                 π −− − = ∫θ s s 2 04/12 0 1 4 dsskiexp sk BE , (5) that after the passage through the pole 2s for ( )2sRes > turns to the exponentially increasing solution by the moving away from the 2s . In this case, by the sewing the solution, that increases by the going away from the pole 2s , with the exponentially descending solution to left of the potential well ( )21 s,s for 12 sss << , one can obtain the connection condition between the coefficients A and B ( ) ( ) ( )         −−≅        −− ∫∫ 1 2 2 1 s s 0 q s s 2 0 dssk2expA1dsskiexpiB . (6) In addition, because of the exponentially weak connection between oscillations in the regions ( )21 s,s and ( )21 s,s the dispersion relation is determined by the equation       +π=−∫ 2 1q)s(kds 2 1 s s 2 0 , q = 1, 2, 3,… (7) Now, multiplying equation (3) by the complex conjugate electric field amplitude *E θ and then subtracting from the obtained expression the complex conjugated quantity, one can arrive, after the integration with respect to s, at the following relation: ( ) ( ) = Ω∂ ∂ − Ω ∫ Re k sk dsIm 2 0 s s 2 0 2 1 ( ) ( )         −Ω ∫ 1 2 02exp~ s s dssksign , (8) where ( ) ( ) ( )( )[ ]         Ω−Ω ΩΩ ΛΩ+Ω−= Ω∂ ∂ 2 22 2 pi 2 0 2 0 ~Re ~ReRe2 Re k Thus, the instability there exists, when ( )Ω~sign has the opposite values in the potential wells ( )21 s,s and ( )21 s,s . This is the case, when ( ) 0Re >Ω for the ground plasma and ( ) 0~Re <Ω for the drifting flux of ions and electrons. This relation gives for the ion beams with the density ne ~ 1011 cm-3 the increment ( )ΩIm ~ 108 s-1. 5 5. CONCLUSIONS Within the framework of the investigated instability one can explain the relaxation oscillations that arise by the generation of the ELM disturbances [1]. Indeed, the considered instability is determined by the resonance condition pi0vk ω±=−ω θ , where the value of is somewhat less than the ion plasma frequency that corresponds to the ground plasma. By the arising of the ELM perturbations, the density decrease of the ground plasma in the edge region occurs what results in the decrease of the ion plasma frequency and the value of itself. This must lead to the violation of the resonance condition and also to the termination of the instability. As a result, the plasma density increases and the ELM generation arises anew. ACKNOWLEDGEMENT This paper has been partially supported within the System of the Initiative Projects of Russian Research Centre “Kurchatov Institute”. REFERENCES 1. ITER PHYSICS BASIS // Nuclear Fusion. 1999, v.39, N12. 2. Book of Abstracts of the 33 European Physical Society Conference on Plasma Physics, Roma, Italy, June 19-23, 2006. 3. A.V. Gordeev, T.V. Losseva // Plasma Physics Reports. 2005, v.31, N1, p.26. 4. A.V.Gordeev // Plasma Physics Reports. 2006, v.32, N9, p.780. 5. A.V. Gordeev// Proceedings of the 22nd Symposium on Plasma Physics and Technology, Prague, June 26-29, 2006 / Czechoslovak Journal of Physics, v.58, 2006, Suppl. B, p.73. 6. V.D. Shafranov // Reviews of Plasma Physics /ed. by M.A. Leontovich. New York: “Consultants Bureau”. 1967, v.3. 7. A.V.Gordeev, L.I. Rudakov// Sov. Phys. JETP. 1969, v.28, p.1226. ELM A. . , ( )eB en4Br π= r . , . , , . , . Biω>>ω [ ( )cmBez iiBi r =ω - ], pi0kv ω±=−ω ( )22 z 2 pi 1 0pi ck+ωγ=ω − ( - , v0 - , 1 Brk −≤ - , ωpi - ). 0ii 22 ii cvmn4Bcmn4 π>>>>π . ELM . , ( )eB en4Br π= r . , . , , . , . Biω>>ω [ ( )cmBez iiBi r =ω - ], pi0kv ω±=−ω ( )22 z 2 pi 1 0pi ck+ωγ=ω − ( - , v0 - , 1 Brk −≤ - , ωpi - ). 0ii 22 ii cvmn4Bcmn4 π>>>>π .

On the possibility for the resonance ELM-generation mechanism by the injection of the neutral particle beam in tokamak

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