You need JavaScript to view this

Stabilization by Shear and Negative V''; Stabilisation au Moyen du Croisement de Lignes de Champ et de l'Emploi d'un V'' Negatif; Stabilizatsiya spomoshch'yu shira i otritsatel'nogo V{sup ;} Estabilizacion por Cizallamiento y Empleo de V'' Negativa

Conference:

Abstract

A criterion is derived for the stability against gravitational interchange of toroidal systems by using the hydrodynamic equation with finite resistivity. The stability depends on an expression that reduces to the sign of the second derivative of the volume per unit flux (V'') in the case that the plasma does not surround any ''floating'' conductors. If this condition is violated, then a ''rapid'' resistive instability results. If the condition is satisfied, then both the resistive growth rate and the critical {beta} against ''ballooning'' modes depend on a figure of merit rR{sub c}/L{sup 2} where r is plasma radius, L is length along field lines between ''good'' and ''bad'' regions, Re the mean radius of curvature and {gamma} is a shape factor depending on the design. A similar consideration applies to ''kinking'' modes. Using the results of numerical calculations, we will discuss the structure, stability properties and figure of merit of several ''stagnation-point'' solutions having the negative-V'' property. The principle here is to create directions of favorable {Delta}B, then cause the rotational transform to be weakened in the favorable regions (reaching a null at the stagnation point). The negative contributions to V'' are then weighted heavily, becoming infinite at the stagnation  More>>
Authors:
Furth, H. P.; Killeen, J.; [1]  Rosenbluth, M. N.; [2]  Coppi, B. [3] 
  1. Lawrence Radiation Laboratory, Livermore, CA (United States)
  2. General Atomic Division, General Dynamics Corporation and University of California (San Diego), La Jolla, CA (United States)
  3. University of California (San Diego), La Jolla, CA (United States)
Publication Date:
Apr 15, 1966
Product Type:
Conference
Report Number:
IAEA-CN-21/106
Resource Relation:
Conference: Conference on Plasma Physics and Controlled Nuclear Fusion Research, Culham (United Kingdom), 6-10 Sep 1965; Other Information: 20 refs., 12 figs.; Related Information: In: Plasma Physics and Controlled Nuclear Fusion Research Vol. I. Proceedings of a Symposium on Plasma Physics and Controlled Nuclear Fusion Research| 792 p.
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BALLOONING INSTABILITY; EQUILIBRIUM; PERFORMANCE; PERIODICITY; PLASMA; ROTATIONAL TRANSFORM; STABILITY; STAGNATION POINT; TUBES
OSTI ID:
22117281
Research Organizations:
International Atomic Energy Agency, Vienna (Austria)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISSN 0074-1884; TRN: XA13M2207073902
Submitting Site:
INIS
Size:
page(s) 103-125
Announcement Date:
Aug 01, 2013

Conference:

Citation Formats

Furth, H. P., Killeen, J., Rosenbluth, M. N., and Coppi, B. Stabilization by Shear and Negative V''; Stabilisation au Moyen du Croisement de Lignes de Champ et de l'Emploi d'un V'' Negatif; Stabilizatsiya spomoshch'yu shira i otritsatel'nogo V{sup ;} Estabilizacion por Cizallamiento y Empleo de V'' Negativa. IAEA: N. p., 1966. Web.
Furth, H. P., Killeen, J., Rosenbluth, M. N., & Coppi, B. Stabilization by Shear and Negative V''; Stabilisation au Moyen du Croisement de Lignes de Champ et de l'Emploi d'un V'' Negatif; Stabilizatsiya spomoshch'yu shira i otritsatel'nogo V{sup ;} Estabilizacion por Cizallamiento y Empleo de V'' Negativa. IAEA.
Furth, H. P., Killeen, J., Rosenbluth, M. N., and Coppi, B. 1966. "Stabilization by Shear and Negative V''; Stabilisation au Moyen du Croisement de Lignes de Champ et de l'Emploi d'un V'' Negatif; Stabilizatsiya spomoshch'yu shira i otritsatel'nogo V{sup ;} Estabilizacion por Cizallamiento y Empleo de V'' Negativa." IAEA.
@misc{etde_22117281,
title = {Stabilization by Shear and Negative V''; Stabilisation au Moyen du Croisement de Lignes de Champ et de l'Emploi d'un V'' Negatif; Stabilizatsiya spomoshch'yu shira i otritsatel'nogo V{sup ;} Estabilizacion por Cizallamiento y Empleo de V'' Negativa}
author = {Furth, H. P., Killeen, J., Rosenbluth, M. N., and Coppi, B.}
abstractNote = {A criterion is derived for the stability against gravitational interchange of toroidal systems by using the hydrodynamic equation with finite resistivity. The stability depends on an expression that reduces to the sign of the second derivative of the volume per unit flux (V'') in the case that the plasma does not surround any ''floating'' conductors. If this condition is violated, then a ''rapid'' resistive instability results. If the condition is satisfied, then both the resistive growth rate and the critical {beta} against ''ballooning'' modes depend on a figure of merit rR{sub c}/L{sup 2} where r is plasma radius, L is length along field lines between ''good'' and ''bad'' regions, Re the mean radius of curvature and {gamma} is a shape factor depending on the design. A similar consideration applies to ''kinking'' modes. Using the results of numerical calculations, we will discuss the structure, stability properties and figure of merit of several ''stagnation-point'' solutions having the negative-V'' property. The principle here is to create directions of favorable {Delta}B, then cause the rotational transform to be weakened in the favorable regions (reaching a null at the stagnation point). The negative contributions to V'' are then weighted heavily, becoming infinite at the stagnation point. We consider three types of solution: (1) Linear periodic-multipole arrays, by using helical Script-Small-L = 2 and 4, or Script-Small-L = 3 ''shaping fields'' with natural stagnation points; and by superimposing Script-Small-L = 0 and 2, Script-Small-L = 1 and 3, or Script-Small-L = 0 and 3 ''corrugating fields'', to create favorable {Delta}B regions. (2) Helical equilibria, by using gross helical curvature to create the favorable VB regions and stagnating the rotational transform by means of a current on an axial conductor, around which the helical equilibrium flux-tube is wound. (3) Toroidal equilibria, by using the gross toroidal curvature to create the favorable {Delta}B regions. The rotational transform is generated by a helical Script-Small-L = 2 winding and stagnated by an auxiliary poloidal field. (author) [French] Les auteurs etablissent un critere de stabilite a l'egard de l'interchange gravitationnel dans les dispositifs torriidaux a l'aide de l'equation hydrodynamique dans laquelle on tient compte d'une reistivite finie. La stabilite depended'une expression qui se reduit au signe de la derivee seconde du volume par unite de flux (V'') lorsque le plasma n'entoure pas de conducteurs . Si cette condition n'est pas remplie, il se produit une instabilite resistive 'rapide'. Si elle l'est, le taux de croissance de l'instabilite resistive ainsi que la valeur critique de {beta} au-dela de laquelle se produit le mode de 'ballonnement' dependent d'un nombre caracteristique a (rR{sub c}/L{sup 2}) y ou r est le rayon de plasma, L la distance separant les 'bonnes' et les 'mauvaises' regions mesuree le long des lignes de forces, R{sub c} le rayon moyen de courbure et {gamma} un facteur de forme qui depend des details de la configuration. Des considerations semblables s'appliquent a des 'modes en serpentements ' . En se fondant sur les resultats de calculs numeriques, les auteurs etudient la structure, les proprietes de stabilite, ainsi que le nombre caracteristique de plusieurs solutions a 'points de stagnation ' pour lesquelles V'' est negatif. La methode consiste, dans ce cas, a creer des directions ou {Delta}B est favorable et a provoquer ensuite l'affaiblissement de la transformee rotationnelle dans les regions favorables (pour atteindre la valeur zero au point de stagnation). Les facteurs contribuant a rendre V'' negatif sont alors fortement ponderes et deviennent infinis au point de stagnation. Les auteurs examinent trois types de solutions: 1. Des dispositifs lineaires a multipoles periodiques, au moyen de 'champs modelants' helicoiedaux (du type Script-Small-L = 2 et 4 ou Script-Small-L = 3) presentant des points de stagnation naturels auxquels on superpose des 'champs de gaufrants' (du type Script-Small-L = 0 et 2, Script-Small-L = 1 et 3 ou Script-Small-L = 0 et 3), pour creer les regions a {Delta}B favorable. 2. Des equilibres helicoiedaux au moyen de la courbure heli'cbidale globale pour creer des regions a {Delta}B favorable, la stagnation de la transformee rotationnelle etant obtenue a l'aide d'un courant circulant sur un conducteur axial, autour duquel s'enroule le tube de flux en equilibre dont la forme est helicoiedale. 3. Des equilibres toroiedaux, au moyen de la courbure toroiedale globale, pour creer les regions a {Delta}B favorable. La transformee rotationnelle est engendree par un enroulement helicoiedal du type Script-Small-L = 2. Sa stagnation est obtenue par un champ poloiedal auxiliaire. (author) [Spanish] Se establece en la presente memoria un criterio de estabilidad respecto del intercambio gravitatorio en los sistemas toroidales, usando la ecuacion hidrodinamica en la cual se tiene en cuenta una resistividad finita. La estabilidad depende de una expresion que se reduce al signo de la derivada segunda del volumen por unidad de flujo (V'') en el caso de que el plasma no rodee a ningun conductor 'flotante'. Si esta condicionlno se cumple aparece una inestabilidad resistiva rapida mientras que, en caso contrario, tanto el indice de aumento de la inestabilidad resistiva como el valor critico de {beta} mas alla del cual se manifiesta el modo de 'inflacion' depende de un valor caracteristico Tilde-Operator rRc {gamma}/L{sup 2}, donde r es el radio del plasma, L la distancia que separa las zonas 'buenas' {gamma} 'malas', medida a lo largo de las lineas de fuerza, R{sub c} el radio de curvatura medio, y {gamma} un factor de forma que depende de detalles de la configuracion. Analogas consideraciones se aplican a los modos 'serpenteados'. Sobre la base de los resultados de los calculos numericos, los autores analizan la estructura, las propiedades de estabilidad y el valor caracteristico de varias soluciones de 'punto de estancamiento' para las cuales V'' es negativa. El metodo consiste en crear direcciones en que {Delta}B es favorable y debilitar luego la transformada rotacional en las regiones favorables (para alcanzar el valor cero en el punto de estancamiento). Los factores que contribuyen al valor negativo de V'' se ponderan entonces marcadamente, llegando a ser infinito en el punto de estancamiento. Los autores consideran tres tipos de solucion: 1) Disposiciones lineales de multipolos periodicos, mediante campos 'modeladores' helicoidales (del tipo Script-Small-L = 2 y 4 o Script-Small-L = 3) que presentan puntos de estancamiento naturales a los que se superponen 'campos de acanaladura' (del tipo Script-Small-L = 0 y 2, Script-Small-L s 1 y 3, o bien Script-Small-L = 0 y 3) pata crear regiones de {Delta}B favorable. 2) Equilibrios helicoidales, empleando la curvatura helicoidal de caracter global para crear las regiones de {Delta}B favorable y estancando la transformada rotacional mediante una corriente que circula por un conductor axial, alrededor del cual se arrolla el tubo de flujo en equilibrio, de forma helicoidal. 3) Equilibrios toroidales empleando la curvatura toroidal de caracter global para crear las regiones de {Delta}B favorable. La transformada rotacional se genera mediante un devanado helicoidal del tipo Script-Small-L = 2 y se logra el estancamiento mediante un campo poloidal auxiliar. (author) [Russian] Dlja ustojchivosti otnositel'no gravitacionnoj zhelobkovoj neustojchivosti toroidal'nyh sistem vyvoditsja kriterij putem ispol'zovanija gidrodinamicheskogo priblizhenija s konechnym udel'nym soprotivleniem. Ustojchivost' zavisit ot vyrazhenija, kotoroe svoditsja k znaku vtoroj proizvodnoj velichiny ob''ema na edinicu potoka (V''); v tom sluchae, kogda plazma ne okruzhena kakimi-libo ''plavajushhimi'' provodnikami. Esli jeto uslovie narushaetsja, to voznikaet ''bystraja'' rezistivnaja neustojchivost'. Esli jeto uslovie vypolnjaetsja, to kak dissipativnyj inkrement, tak i kriticheskoe {beta} dlja ''balonnyh'' mod zavisjat ot velichiny Tilde-Operator rRc {gamma}/L{sup 2} , gde g - radius plazmy, L - dlina vdol' linij polja mezhdu ''horoshimi'' i ''plohimi'' oblastjami, R{sub c} srednij radius krivizny i, nakonec, {gamma} formfaktor, zavisjashhij ot detal'noj konstrukcii. Podobnye soobrazhenija rasprostranjajutsja i na vintovye mody. Ispol'zuja rezul'taty chislennyh raschetov, my obsudim strukturu, ustojchivost' i preimushhestva neskol'kih reshenij so ''stacionarnoj tochkoj'', imejushhih otricatel'noe V''. Princip sostoit v tom, chtoby sozdat' napravlenija blagoprijatnogo VB, a zatem sozdat' vrashhatel'noe preobrazovanie, oslabljaemoe v blagoprijatnyh oblastjah (dostigaja 0 v stacionarnoj tochke). Otricatel'nye vklady v velichinu V'' priobretajut bol'shoj ves, stanovjas' beskonechnymi v stacionarnoj tochke. Rassmatrivajutsja tri tipa reshenija: 1) Linejnye periodicheski-mul'tipol'nye rjady S ispol'zovanija vintovyh 1 = 2 i 4, ili 1=3 ''formirujushhih polej'' s estestvennymi stacionarnymi tochkami; i putem nalozhenija 1 = 0 i 2, 1 = 1 i 3, ili 1 = 0 i 3 ''gofrirujushhih polej'', dlja togo, chtoby sozdat' blagoprijatnye oblasti {Delta}B. 2) Vintovoe ravnovesie putem ispol'zovanija bol'shoj vintovoj krivizny s cel'ju sozdanija blagoprijatnyh oblastej {Delta}B i ostanovki vrashhatel'nogo preobrazovanija s pomoshh'ju toka na osevom provodnike, vokrug kotorogo navita vintovaja trubka dlja ravnovesnogo potoka. 3) Toroidal'noe ravnovesie s ispol'zovaniem bol'shoj toroidal'noj krivizny dlja sozdanija blagoprijatnyh oblastej {Delta}B. Vrashhatel'noe preobrazovanie sozdaetsja s pomoshh'ju spiral'nyh vitkov 1 =2 i stacionarnaja tochka obrazuetsja blagodarja vspomogatel'nomu poloidal'nomu-polju. (author)}
place = {IAEA}
year = {1966}
month = {Apr}
}