A study of the stability of the Z pinch under fusion conditions using the Hall fluid model

Abstract

The Hall fluid model (a quasineutral two-fluid model with Te=0) is used to investigate the effect of the Hall term on the m=0 instability in a pure Z pinch. The problem is treated numerically by a linearized initial value code. Two different equilibria are investigated. The growth rate of the fastest growing magnetohydrodynamic mode is increased for one equilibrium and reduced for the other by the inclusion of the Hall term, and in the second case new modes with high growth rates are found. The possibility of Hall term destabilization of MHD stable equilibria is suggested.

Linear analysis of magnetic and flow shear stabilization of Z-pinch instabilities

“…After several growth times the solution converges to the fastest growing mode. [14][15][16] In deriving Eqs. 1.…”

Magnetohydrodynamic simulation of solid-deuterium-initiated Z-pinch experiments

“…where Uj, k designates values at time t'_and spatial coordinates (_l)j, (_3)k" In Eqs. (19) and (20), X and Y are spatial finite-difference approximations to X and _, respectively. F.,quation_ (19) and (20) show the standard ADI coupling between unknown quantities.…”

“…U_j._ "2alonga line of constant j;thequantities atj+ 1 andj-I ireknown quantifies since theyhavethesuperscript n +l. Equations (19)and (20)areingeneral nonlinear functions of theunknown quantifies and therefore cannotbe solved directly. To solveEqs.…”

“…To solveEqs. (19)and (20), ANIMAL usesessentially a New_on-Raphsonmethod as givenby Pennmgton, 2samong others. Application of theNewton-Raphson methodtoEq.…”

Hall and two-temperature magnetohydrodynamic simulation of deuterium-fiber-initiated Z pinches

“…In addition, fiber-initiated Z pinches form low density coronal plasmas during early stages of their development; in such low density plasmas, the inverse density dependence of the finite-Larmor-radius scaled terms, such as the Hall term, can lead to their importance. Analytic and numerical work on the influence of the Hall term has equilibrium-dependent results ͑lower mϭ0 growth rates for some equilibria, higher for others͒, 16 so the close-to-the-experiment approach used in our simulations is important, to insure that realistic equilibria are evaluated.…”