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Theoretical Studies of Electron Injection and E-Layer Build-Up in Astron; Etudes Theoriques sur l'Injection d'Electrons et la Formation de la Couche E dans l'Astron; Teoreticheskie izucheniya ehlektronnoj inzhektsii i narashchivaniya sloya-E v ustanovke ''Astron''; Estudios Teoricos de Electrones y Formacion de la Capa E en la Instalacion Astron

Conference:

Abstract

High intensity beams of relativistic electrons injected into the Astron device can be trapped in part by the action of coherent electromagnetic self-forces. Through the appropriate design of external passive circuitry, axial electrostatic blow-up of the azimuthally injected beam can be prevented or inhibited. The self-forces result in a spread of particles in z-P{sub z} phase space, and part of the beam is trapped at the expense of the loss of the rest. In addition to this effect, for sufficiently high beam currents, the coupling of the relativistic beam to the passive circuitry can lead to significant loss of axial momentum through energy dissipation. A one-dimensional model of the actual Astron geometry has been investigated theoretically. Green's functions for the self-electric and self-magnetic fields have been calculated analytically and incorporated into the Vlasov equation governing the axial motion of the electrons. Results of the calculation allow some qualitative comparison with experimental results from the Astron experiment. As envisioned, the trapped electrons will form a cylindrical layer of sufficient intensity so that the self-magnetic field is comparable to the applied field. The mathematical model for the build-up of the electron layer and the self-field is the time-dependent Vlasov equation coupled with  More>>
Authors:
Killeen, J.; Neil, V. K.; Heckrotte, W. [1] 
  1. Lawrence Radiation Laboratory, Livermore, CA (United States)
Publication Date:
Apr 15, 1966
Product Type:
Conference
Report Number:
IAEA-CN-21/95
Resource Relation:
Conference: Conference on Plasma Physics and Controlled Nuclear Fusion Research, Culham (United Kingdom), 6-10 Sep 1965; Other Information: 6 refs., 11 figs.; Related Information: In: Plasma Physics and Controlled Nuclear Fusion Research. Vol. II. Proceedings of a Conference on Plasma Physics and Controlled Physics Research Nuclear Fusion Research| 1017 p.
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANGULAR MOMENTUM; ASTRON; AXIAL SYMMETRY; BEAM CURRENTS; BOLTZMANN-VLASOV EQUATION; CYLINDRICAL CONFIGURATION; DISTRIBUTION FUNCTIONS; E REGION; ELECTRON BEAM INJECTION; ENERGY LOSSES; FINITE DIFFERENCE METHOD; GREEN FUNCTION; MAGNETIC FIELDS; MATHEMATICAL MODELS; MAXWELL EQUATIONS; ONE-DIMENSIONAL CALCULATIONS; RELATIVISTIC RANGE; TIME DEPENDENCE; TRAPPED ELECTRONS
OSTI ID:
22178040
Research Organizations:
International Atomic Energy Agency, Vienna (Austria)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISSN 0074-1884; TRN: XA13M2260002484
Submitting Site:
INIS
Size:
page(s) 227-243
Announcement Date:
Jan 09, 2014

Conference:

Citation Formats

Killeen, J., Neil, V. K., and Heckrotte, W. Theoretical Studies of Electron Injection and E-Layer Build-Up in Astron; Etudes Theoriques sur l'Injection d'Electrons et la Formation de la Couche E dans l'Astron; Teoreticheskie izucheniya ehlektronnoj inzhektsii i narashchivaniya sloya-E v ustanovke ''Astron''; Estudios Teoricos de Electrones y Formacion de la Capa E en la Instalacion Astron. IAEA: N. p., 1966. Web.
Killeen, J., Neil, V. K., & Heckrotte, W. Theoretical Studies of Electron Injection and E-Layer Build-Up in Astron; Etudes Theoriques sur l'Injection d'Electrons et la Formation de la Couche E dans l'Astron; Teoreticheskie izucheniya ehlektronnoj inzhektsii i narashchivaniya sloya-E v ustanovke ''Astron''; Estudios Teoricos de Electrones y Formacion de la Capa E en la Instalacion Astron. IAEA.
Killeen, J., Neil, V. K., and Heckrotte, W. 1966. "Theoretical Studies of Electron Injection and E-Layer Build-Up in Astron; Etudes Theoriques sur l'Injection d'Electrons et la Formation de la Couche E dans l'Astron; Teoreticheskie izucheniya ehlektronnoj inzhektsii i narashchivaniya sloya-E v ustanovke ''Astron''; Estudios Teoricos de Electrones y Formacion de la Capa E en la Instalacion Astron." IAEA.
@misc{etde_22178040,
title = {Theoretical Studies of Electron Injection and E-Layer Build-Up in Astron; Etudes Theoriques sur l'Injection d'Electrons et la Formation de la Couche E dans l'Astron; Teoreticheskie izucheniya ehlektronnoj inzhektsii i narashchivaniya sloya-E v ustanovke ''Astron''; Estudios Teoricos de Electrones y Formacion de la Capa E en la Instalacion Astron}
author = {Killeen, J., Neil, V. K., and Heckrotte, W.}
abstractNote = {High intensity beams of relativistic electrons injected into the Astron device can be trapped in part by the action of coherent electromagnetic self-forces. Through the appropriate design of external passive circuitry, axial electrostatic blow-up of the azimuthally injected beam can be prevented or inhibited. The self-forces result in a spread of particles in z-P{sub z} phase space, and part of the beam is trapped at the expense of the loss of the rest. In addition to this effect, for sufficiently high beam currents, the coupling of the relativistic beam to the passive circuitry can lead to significant loss of axial momentum through energy dissipation. A one-dimensional model of the actual Astron geometry has been investigated theoretically. Green's functions for the self-electric and self-magnetic fields have been calculated analytically and incorporated into the Vlasov equation governing the axial motion of the electrons. Results of the calculation allow some qualitative comparison with experimental results from the Astron experiment. As envisioned, the trapped electrons will form a cylindrical layer of sufficient intensity so that the self-magnetic field is comparable to the applied field. The mathematical model for the build-up of the electron layer and the self-field is the time-dependent Vlasov equation coupled with Maxwell's equations. The system is axially symmetric and complete neutralization is assumed. The field components Br and B{sub z} can be derived from a stream function {psi}( r, z, t). The canonical angular momentum is a constant of the motion, hence we can consider an electron distribution function f{sub e}( r, z, P{sub r}, P{sub z}). The partial differential equations for f{sub e} and {psi} are solved numerically by using finite difference methods. The phase space consists of over 160 000 points, that is 81 in z, 12 in r, 19 in P{sub z} and 9 in P{sub r}. At each step an integration of f{sub e} over momentum space yields the current density j{sub {theta}}(r, z, t); the self-field is then computed by solving the equation for {psi}(r, z, t). In this paper a number of runs are presented, corresponding to several vacuum magnetic fields and various injection conditions. The electron distributions obtained differ widely according to the applied mirror field that is used. In all these runs, minimum-B regions are formed and some have been carried for enough to achieve field reversal. (author) [French] Des faisceaux de forte intensite d'electrons relativistes, injectes dans 1*Astron, peuvent etre pieges en partie par l'action de forces propres electromagnetiques coherentes. Par un schema approprie de circuits passifs externes, il est possible d'empecher ou d'inhiber une explosion electrostatique axiale du faisceau injecte par voie azimutale. Les forces propres donnent lieu a une diffusion de particules dans l'espace des phases z- Pz; une partie du faisceau est piegee au prix de la perte de la partie restante. En plus de cet effet, il est possible, dans le cas de courants de faisceau suffisamment eleves, que le couplage du faisceau relativiste aux circuits passifs entraine, par dissipation d'energie, une perte considerable de quantite de mouvement axiale. Les. auteurs ont etudie, du point de vue theorique, un modele unidimensionnel de la geometrie de 1*Astron. Ils ont calcule analytiquement les fonctions de Green pour les champs electriques et magnetiques propres et les ont incorporees dans l'equation de Vlassov qui regit le mouvement axial des electrons. Les resultats du calcul permettent de proceder a une comparaison qualitative avec les resultats experimentaux obtenus dans l'installation Astron. Conformement aux previsions, les electrons pieges formeront une couche cylindrique d'une intensite telle que le champ magnetique propre puisse etre compare au champ applique. Le modele mathematique expliquant la formation de la couche d'electrons et du champ propre est l'equation de Vlassov (qui est fonction du temps) couplee aux equations de Maxwell. Le systeme possede une symetrie axiale et on le suppose electriquement neutre. Les composantes du champ B{sub r} et B{sub z} peuvent etre derivees d'une fonction d'ecoulement {psi}(r, z, t). Le moment cinetique canonique est une constante du mouvement, ce qui permet de considerer une fonction de distribution des electrons du type f{sub e} (r, z, Pr, Pz). Les equations differentielles partielles pour f{sub e} et {psi} sont resolues numeriquement par des methodes de differences finies. L'espace des phases se compose de plus de 160 000 points, soit 81 dans z, 12 dans r, 19 dans P{sub z} et 9 dans P{sub r}. A chaque stade, une integration de fe sur l'espace des quantites de mouvement donne la densite du courant j{sub {theta}} (r, z, t); on calcule ensuite le champ propre en resolvant l'equation pour {psi} (r, z, t). Les auteurs presentent un certain nombre d'essais qui correspondent a plusieurs champs magnetiques dans le vide et a diverses conditions d'injection. Les distributions d'electrons obtenues different sensiblement selon le champ de miroir applique. Dans tous ces essais, il se forme des regions de B minimum, dont certaines ont ete poussees assez loin pour donner lieu a une inversion de champ. (author) [Spanish] Los haces de alta intensidad de electrones inyectados con velocidades relativistas en el dispositivo Astron,pueden ser atrapados en parte por la aceion de fuerzas propias electromagneticas coherentes. Proyectando adecuadamente los circuitos pasivos externos es posible impedir o inhibir la explosion electrostatica axial del haz inyectado en direccion azimutal. Las fuerzas propias originan una dispersion de particulas en el espacio de fases z-P{sub z}, y parte del haz es atrapado a expensas de la perdida del resto. Ademas de este efecto, para corrientes de haz suficientemente intensas el acoplamiento del haz.relativista con los circuitos pasivos puede provocar una perdida significativa de cantidad de movimiento axial debida a disipacion de energia. Los autores estudiaron teoricamente un modelo unidimensional del dispositivo Astron. Calcularon analiticamente las funciones de Green representativas de los campos propios electrico y magnetico, y las incorporaron a la ecuacion de Vlasov que rige el movimiento axial de los electrones. Los resultados de los calculos permiten establecer una comparacion cualitativa con los resultados experimentales obtenidos mediante la instalacion Astron. Tal como se suponia, los electrones atrapados forman una capa cilindrica de intensidad suficiente para que el campo magnetico propio sea comparable con el campo aplicado. El modelo matematico que explica la formacion de la capa electronica y del campo propio es la ecuacion de Vlasov en funcion del tiempo, unida a las ecuaciones de Maxwell. El.sistema tiene simetria axial y se supone electricamente neutro. Los componentes del campo B{sub r} y B{sub z} pueden deducirse a partir de una funcion de flujo {psi} (r, z, t). El momento angular canonico es una constante del movimiento, lo que permite considerar una funcion de distribucion de los electrones del tipo f{sub e} (r, z, P{sub r}, P{sub z}). Las ecuaciones diferenciales parciales en f{sub e} y {psi} se resuelven numericamente usando el metodo de las diferencias finitas. El espacio de las fases consiste en mas de 160 000 puntos, a saber 81 en z, 12 en r, 19 en P{sub z} y 9 en P{sub r} . En cada paso, la integracion de f{sub e} en el espacio de las cantidades de movimiento da la densidad de corriente j{sub {theta}} (r, z, t); el campo propio se calcula luego resolviendo la ecuacion para {psi} (r, z, t). Los autores presentan una serie de experimentos correspondientes a varios campos magneticos en el vacio y distintas condiciones de inyeccion. Las distribuciones de electrones obtenidas difieren sensiblemente segun cual sea el campo de espejo aplicado. En todos estos experimentos se forman regiones de B mfnimo y algunos se han desarrollado lo suficiente como para lograr la inversion del campo. (author) [Russian] Zahvat vysoko intensivnyh puchkov reljativistskih jelektronov, inzhektiruemyh v ustanovku Astron, mozhet chastichno osushhestvljat'sja za schet kogerentnyh jelektromagnitnyh sil. Osevoe jelektrostaticheskoe razmytie azimutal'no inzhektiruemogo puchka mozhet byt' predotvrashheno ili podavleno blagodarja sootvetstvujushhej konstrukcii vneshnej passivnoj shemy. Pod dejstviem sobstvennyh sil chasticy rasprostranjajutsja v fazovom prostranstve z-Pz, i chast' puchka zahvatyvaetsja za schet poter' drugoj chasti. V dopolnenie k jetomu jeffektu dlja dostatochno vysokih tokov v puchke svjaz' reljativistskogo puchka s passivnoj shemoj mozhet privesti k znachitel'noj potere osevogo momenta iz-za dissipacii jEhnergii. Teoreticheski byla izuchena odnomernaja model' real'noj geometrii Astrona. Funkcii Grina dlja sobstvennyh jelektricheskih i magnitnyh polej byli rasschitany analiticheskim sposobom i vvedeny v uravnenie Vlasova, kotoroe opredeljaet osevoe dvizhenie jelektronov. Rezul'taty raschetov pozvoljajut provesti nekotorye kachestvennye sravnenija s jeksperimental'nymi rezul'tatami, poluchennymi v jeksperimente na Astrone. Kak i predpolagalos', zahvachennye jelektrony obrazujut cilindricheskij sloj dostatochnoj intensivnosti, tak chto sobstvennoe magnitnoe pole sravnimo s prilozhennym polem. Matematicheskaja model' dlja narastanija jelektronnogo sloja i sobstvennogo polja javljaetsja zavisimym ot vremeni uravneniem Vlasova sovmestno s uravnenijami Maksvella. Sistema javljaetsja aksial'no-simmetrichnoj, i predpolagaetsja polnaja nejtralizacija. Komponenty polja Vg i B z mozhno vyvesti na osnovanii funkcii potoka {psi}(r, z, t). Kanonicheskij uglovoj moment javljaetsja konstantoj dvizhenija, i pojetomu my mozhem rassmatrivat' funkciju jelektronnogo raspredelenija f{sub e} (r, z, R{sub g}, R{sub g}). Differencial'nye uravnenija dlja f{sub e} i {psi} reshajutsja chislenno s ispol'zovaniem metodov konechnyh raznostej. Fazovoe prostranstvo soderzhit bolee 160 000 tochek, naprimer 81 v prostranstve g, 12 v g, 19 v P z i 9 v Rg. Na kazhdoj stupeni integracija fe po prostranstvu momenta daet plotnost' toka j{sub {theta}} (r, z, t)j sobstvennoe pole zatem vychisljaetsja putem reshenija uravnenija dlja {psi} (r, z, t). V nastojashhem doklade privoditsja celaja serija opytov, otnosjashhihsja v razlichnym vakuumnym poljam i k razlichnym uslovijam inzhekcii. Poluchennye jelektronnye raspredelenija sil'no otlichajutsja drug ot druga v zavisimosti ot primenjaemogo probochnogo polja. Vo vseh sluchajah imelo mesto obrazovanie oblastej minimal'nogo-V i v nekotoryh iz nih bylo dostignuto reversirovanie polja. (author)}
place = {IAEA}
year = {1966}
month = {Apr}
}