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

Abstract

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.

Imploding Liner Compression of Plasma: Concepts and Issues

“…The increase of particle density near the colder boundary, however, reduces diffusion, so the target will maintain a high temperature interior, if sufficient magnetic flux exists for thermal insulation of the hot plasma. With convection and heat transfer to the colder surroundings, a non-barotropic fluid condition (∇n×∇T = 0) leads to vorticity and circulation of wall material into the plasma target [27]; the lack of alignment of density and temperature gradients, which previously was invoked in the generalized Ohm's law as a mechanism to develop the rz-currents for rotation of an FRC, here enters as the so-called baroclinic term in the equation for the rate of change of vorticity.…”

Initial numerical studies of the behaviour of Z-pinch plasma under liner implosion conditions

“…To solve these equations, we have used the very general computer code ANIMAL -A New (Alternating Direction) Implicit Magnetohydrodynamic ALgorithm. Many of the numerical methods used in ANIMAL are reported elsewhere [14][15][16][17].…”

“…We now feel that the mesh we have used is inadequate to completely resolve the boundary layers at the liner and end plug, but, of course, additional resolution would have led to additional computational time. Lindemuth, et al [17] have examined more carefully the zoning requirements at a wall.…”

“…The end plug AB and the liner CB are assumed to be perfect electrical conductors, so that the total magnetic flux within the system remains constant except for the small amount of flux annihilation which occurs on axis. The end plug and liner are treated as rigid, cold walls, and heat conduction to the cold walls is treated in the manner reported by Lindemuth, Pettibone, et al [17]. The liner velocity for all calculations is taken to be a constant,!…”

“…Hence, the plasma experiences an initial magnetic force, and in the calculations we observe initial transients as the plasma tries to establish a steady state. Transients due to the cold walls are also observed; in essence, the initial conditions are assuming that the hot plasma is brought into contact with the cold walls at t = 0 in the manner which is used in plasma-wall studies [17][18][19]. Hence, the initial cooling rates are higher than would be observed if more realistic initial conditions were used.…”