Equilibrium and Stability of Plasmas in Stellarators

/pdf/magnetized-target-fusion-a-proof-of-principle-research-3256xwb9fk.pdf

Magnetized Target Fusion. A Proof-of-Principle Research Proposal

A wall confined plasma in an inverse-pinch configuration holds potential as a plasma target for Magnetized Target Fusion (MTF) as well as a simple geometry to study wall-confined plasma. An experiment is planned to study the inverse-pinch configuration using the Zebra Z pinch [B. S. Bauer et al., AIP Conference Proceedings Vol. 409 (American Institute of Physics, Melville, 1997), p. 153] of the Nevada Terawatt Facility at the University of Nevada, Reno (UNR). The dynamics of the discharge formation have been analyzed using analytic models and numerical methods. Strong heating occurs by thermalization of directed energy when an outward moving current sheet (the inverse pinch effect) collides with the outer wall of the experimental chamber. Two-dimensional magnetohydrodynamic simulations show Rayleigh–Taylor and Richtmyer–Meshkov like modes of instability, as expected because of the shock acceleration during plasma formation phase. The instabilities are not disruptive, but give rise to a mild level of turbu...

Magnetohydrodynamic simulation of the inverse-pinch plasma discharge

A hard-core Z-pinch plasma (metal conductor on axis) with an unstable pressure profile can rearrange itself through m=0 interchange motions to produce a stable pressure profile. In this paper the self-organization process is demonstrated in numerical simulations of an experimental plasma formation process, using a two-dimensional compressible two-fluid magnetohydrodynamic code. The stabilization process results in m=0 turbulence, which has a level of kinetic energy that is saturated typically at a few percent of the plasma thermal energy. Using idealized initial conditions for simulations with an axial sinusoidal density perturbation, it is possible to observe in detail the development of instability and then turbulence. At first a coherent Rayleigh–Taylor type motion grows exponentially, with localized isentropic heating and cooling associated with the motion. Then the bubble and spike structure breaks up and incoherent m=0 turbulence develops.

/pdf/self-organization-observed-in-numerical-simulations-of-a-3g9gysiab9.pdf

Self-organization observed in numerical simulations of a hard-core diffuse Z pinch

One‐dimensional steady‐state radial profiles of a classical Z pinch are calculated. The effects of ion thermal conduction and bremsstrahlung radiation losses are included self‐consistently, as are Ohmic heating, pressure balance, and an equation of state. It is shown that the upper current limit of approximately 1.4 MA for an equilibrium pinch found when only bremsstrahlung losses are allowed is virtually unaffected by the inclusion of ion thermal conduction. However, solutions with lower currents are now allowed. The profile‐smoothing effect of ion thermal conduction is not sufficient to produce a pressure profile stable to m=0 modes. Total losses due to radial conduction are shown to be small for a thermonuclear plasma.

Steady-state radial heat conduction in a Z pinch

The behavior of a hot, magnetized plasma brought into contact with a cold wall is studied numerically in one and two dimensions. A fully nonlinear, time‐dependent magnetohydrodynamic plasma model which includes thermal conduction, resistive diffusion, radiation, and ionization is used. The model is solved numerically with an Eulerian computer code which employs implicit finite difference methods. One‐dimensional calculations for cylindrical geometry examine the effect of the electrical properties of the wall on the plasma. Two‐dimensional calculations for cylindrical geometry show the formation of a wall‐induced instability which enhances thermal conduction losses from the plasma; the re‐emergence of short wavelengths, a new feature of unstable behavior, is evident in the calculations. Two‐dimensional calculations for toroidal geometry show that heat losses to a cold wall lead to double‐vortex convection flow of the plasma with no evidence of the formation of smaller scale convective cells.

Unstable behavior of hot, magnetized plasma in contact with a cold wall

Using the two-dimensional MHD computer code ANIMAL. The authors have computed the plasma dynamics of the preionization phase of a toroidal pinch. The physical model includes electron and ion thermal conduction, electron-ion resistivity, electron-neutral resistivity, ionization, dissociation, and line radiation all based on local thermodynamic equilibrium. The code uses ADI finite difference equations with improved boundary conditions which enable the code to follow the oscillatory motion of the plasma. A coupled electrical circuit calculation is performed. The physical model requires the specification of a minimum ionization fraction fmin to set an upper bound on the resistivity. By suitably choosing fmin, they reproduce many of the features of the preionization discharge. Our calculations have suggested a new electrical diagnostic, the measurement of intervals between zero-crossings of current and flux, which is used to help normalize the computations.

http://iopscience.iop.org/article/10.1088/0032-1028/22/3/001/pdf

The numerical computation of the preionization phase of a toroidal pinch discharge

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Unstable behavior of hot, magnetized plasma in contact with a cold wall

The numerical computation of the preionization phase of a toroidal pinch discharge