Two-dimensional magnetohydrodynamic liner-on-plasma simulations for the compression phase of a magnetized target fusion system based on inverse Z pinch

Abstract

This article reports, for the first time, two-dimensional magnetohydrodynamic liner-on-plasma simulations for the compression phase of a magnetized target fusion (MTF) system with an inverse Z-pinch target. These simulations evolve the complete liner-plasma system along with the driving pulsed-power source. First, it has been demonstrated that closely coupled liner-on-plasma simulations produce results that are significantly different from loosely coupled simulations that have been reported in the literature. Second, it has been found that an initially stable plasma, satisfying the Kadomtsev criteria, and with a small initial pressure perturbation in the axial direction, remains stable all through the compression phase, even though there are large changes in the pressure and magnetic field levels. Third, a plasma that violates the Kadomtsev criteria, even by a small amount, turns out to be unstable, as predicted by theory. In practical terms, this means that it is preferable to stay well away from the stability limit, even at the cost of some reduction of initial plasma pressure. Fourth, even during the burn phase, when there is a large and rapid increase in plasma pressure due to fusion energy deposition, an initially stable plasma generally tends to remain stable, and even improves its stability margin. This observation shows that the inverse Z pinch is fairly benign as a MTF target, as an initially stable plasma remains stable during both the compression and burn phases. Fifth, certain unusual features are observed in the temperature profile—these depend upon the time scale for implosion. This has implications for plasma-surface interactions at the liner and central conductor.

A stable corridor for toroidal plasma compression

“…The stability of the global solution during compression bears some analogy to the Kadomtsev criterion in cylindrical Z-pinch experiments [27], where the pressure gradient and magnetic field shear analogously drive global instabilities. However, the equilibria here remain tokamak-like throughout the compression.…”

2-D MHD Study of Instabilities During the Compression Phase of an Inverse Z-Pinch MTF System

“…We have earlier shown that, starting with a uniform liner without perturbations, an initially-stable plasma continues to remain stable, even when initial perturbations are 6 . When instabilities are growing in the liner, however, it acts like a continuously-increasing perturbation on the plasma surface.…”

“…These parameters, evaluated at each time step, are then used to update a circuit solver to self-consistently obtain the circuit current as a function of time. Instead of solving the magnetic field diffusion equation, we used the "frozen magnetic flux" approximation 6 . Important limitations of this model, and details of validation of the model, are summarized elsewhere 6 .…”

“…The initial radial variation of magnetic field and density through the plasma is calculated such that the plasma is in MHD equilibrium and also satisfies the Kadomtsev criteria for stability against m=0 and m=1 modes. Details of these calculations are given in 6 . Initial liner and capacitor bank parameters are given in Table 1 --reasons for choosing these numbers were given in 6 .…”

Burn phase calculations and one-dimensional optimization studies for an inversez-pinch magnetized target fusion system

“…Computational studies of various MTF configurations have been reported in [1,[3][4][5]. A brief summary of such work is given in [6], and is omitted here for the sake of brevity. Compression of plasma to the megabar (million atmosphere) pressure range using metallic liners has been reported by Degnan et al [7].…”