Tearing mode in the cylindrical tokamak

Furth, H. P.

doi:10.1063/1.1694467

Cited by 543 publications

(352 citation statements)

References 9 publications

Supporting

Mentioning

334

Contrasting

Unclassified

Order By: Relevance

“…1): Families II and III are frequently referred to as "peaked" and "flat" profile shapes (Ref. [3]). The results for the intermediate "broad" shape (p=2) are not presented hera, but they are similar to those for 5v.…”

Section: Numerical Resultsmentioning

confidence: 99%

Current relaxation time scales in toroidal plasmas

Mikkelsen

1989

Physics of Fluids B: Plasma Physics

View full text Add to dashboard Cite

An approximate normal mode analysis of plasma current diffusion in tokamaks is presented.The work is based on numerical solutions of the current diffusion equation in cylindrical geometry. Eigenvalues and eigenfunctions are shown for a broad range of plasma conductivity profile shapes. Three classes of solutions are considered which correspond to three types of tokamak operation. Convenient approximations to the three lowest eigenvalues in each class are presented and simple formulae for the current relaxation time scales are given. DISCLAIMERThis report was prepared as an account or work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any Irgal liability or responsi bility for the accuracy, completeness, or usefulness or any information, apparatus, product, or process disclosed, or represents that ils use would not infringe privately owned rights. Refer ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recomnjendation, or favoring by the United States Government or any agency thcrcol. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. tariff ^ DiiSTiilBUriOf} flF THIS BGCUMEHT IS UNLIMITED T. INTRODUCTIONThe time scale for current diffusion is often Che longest pLasma time scale in a tokamak. It therefore plays an important role in large tokamak design and operation. In the TFCX preconceptual design study, for example, the lengths of the louet-hybrid-driven current rampup and ignited burn phases were determined by current diffusion time scales.An understanding of current relaxation is also required in interpreting the resuLts of noninductive current drive experiments where purely external measurements of the toroidal electric field are used to infer the inductively driven current inside the plasma. Such a procedure is valid onLy if the inductively driven current has reached its equilibrium value.The current relaxation time scale is often referred to as the "skin time." the purpose of the present work is to endow that phrase with quantitative meaning in the context of typical tokamak operation. This is done by solving a normal mode problem for each of three types of tokamak operation; the eigenvalues of the normal modes are then related to the current relaxation time scales. where the displacement current has been dropped froii the second equation, Tokamak geometry is approximated throughout this work by cylindrical geometry;toroidal mode-coupling, elongation, and triangularity, etc., are ignored. The "toroidal" current density is assumed to be related to the "toroidal" electric field by a simple Ohm's law:where we restrict attention to cases in which the noninductively driven current, j., and the conductivity, o, are constant in time.We...

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

Current relaxation time scales in toroidal plasmas

Mikkelsen

1989

Physics of Fluids B: Plasma Physics

View full text Add to dashboard Cite

show abstract

“…Обсуждения с окружающими, в том числе с В.Д. Шафрановым, поначалу не об-наружили каких-либо других достойных кандидатов на их роль, кроме модной на тот момент тиринг-неустойчивости [21]. Однако было не ясно почему рост l i вызывает их подавление.…”

Section: удержание и макроскопическая устойчивостьunclassified

V.D. Shafranov, in the Years of Tokamak Formation

Mirnov¹

2016

PAST-TF

View full text Add to dashboard Cite

Троицкий институт инновационных и термоядерных исследований, г. Троицк, Москва, Россия 2 Национальный исследовательский ядерный университет «МИФИ», Москва, РоссияАкадемик Виталий Дмитриевич Шафранов, ушедший от нас 9 июня 2014 г., по праву считается одним из отцов-основателей теории магнитного удержания термоядерной плазмы. Его имя ассоциируется со многими аспектами равновесия и устойчивости плазмы в замкнутых магнитных ловушках. Уравнение Грэда-Шафранова и шафрановский сдвиг являются ключевыми поня-тиями в теории равновесной, осесимметричной тороидальной плазмы, а предел Крускала-Шафранова давно признан как фун-даментальное ограничение тороидального тока в плазме, необходимое для поддержания макроскопической стабильности в то-камаках. Наконец, им совместно с академиком Л.А. Арцимовичем была впервые предложена концепция токамаков с некруглым сечением, что привело к развитию современного направления D-образных токамаков, таких как JET, и предложена идея полои-дального дивертора, необходимого для работы практических термоядерных устройств, таких как ИТЭР. Эта статья в честь па-мяти В.Д. Шафранова призвана отразить его участие в некоторых малоизвестных аспектах ранних термоядерных исследований и ту ключевую роль, которую он сыграл в них в эпоху становления концепции токамака.Ключевые слова: токамак, Шафранов, шафрановский сдвиг, уравнение Грэда-Шафранова, предел Крускала-Шафранова. V.D. SHAFRANOV, IN THE YEARS OF TOKAMAK FORMATION S.V. Mirnov 1, 2 1 Troitsk Institute for Innovation and Fusion Research (TRINITI), Troitsk, Moscow, Russia 2 National Research Nuclear University «MEPhI», Moscow, RussiaAcademician Vitaly Dmitrievich Shafranov, who died on 9 June 2014, is rightly regarded as one of the founding fathers of the theory of magnetic confinement of fusion plasma. His name is being associated with many aspects of plasma equilibrium and stability of the closed magnetic traps. The Grad-Shafranov equation and the Shafranov shift are key concepts in axisymmetric toroidal plasma equilibrium theory, while the Kruskal-Shafranov limit is universally recognised as a fundamental limit on the toroidal plasma current, essential for maintaining macroscopic stability in tokamaks. With academician L.A. Artsimovich he introduced the concept of tokamaks with noncircular cross-sections which has led to the development of the current high-performance tokamak devices, such as JET, and to the poloidal divertors, necessary for the operation of a practical fusion devices such as ITER. This paper in honor of his memory is intended to reflect his involvement in some unknown aspects of the early fusion research and the key role, which Shafranov played in the era of the formation of the tokamak concept. ПРЕДИСЛОВИЕСтатья, предлагаемая читателю, в своей основной части повторяет статью автора «Shafranov and tokamaks», недавно опубликованную на английском языке в Journal of Plasma Phys. (2016, vol. 82, 515820102). А именно является её первоначальной русской версией. Чтобы стать более адекватной для восприятия зарубежным читателем, русская ...

show abstract

“…Thus, in particular, the (now .. classical") FKR stability criterion was studied in det~il for various tokamak current profiles. 9 The relation ' . .…”

Section: ·(Fkr)mentioning

confidence: 99%

Introduction to the linear theory of tearing instabilities

Hazeltine¹

1978

View full text Add to dashboard Cite

Tearing mode in the cylindrical tokamak

Cited by 543 publications

References 9 publications

Current relaxation time scales in toroidal plasmas

Current relaxation time scales in toroidal plasmas

V.D. Shafranov, in the Years of Tokamak Formation

Introduction to the linear theory of tearing instabilities

Contact Info

Product

Resources

About