Alan L. Hoffman

Suppression of the n=2 rotational instability in field‐reversed configurations

Compact toroid plasmas formed in field‐reversed theta pinches are generally destroyed after 30–50 μsec by a rotating n=2 instability. In the reported experiment, instability is controlled, and the plasma destruction is avoided in the TRX‐1 theta pinch through the application of octopole magnetic fields. The decay times for loss of poloidal flux and particles are unaffected by the octopole fields. These decay times are about 100 μsec based on inferences from interferometry and excluded flux measurements. The weak, rotating elliptical disturbance (controlled n=2 mode) also made possible a novel determination of the density profile near the separatrix using single‐chord interferometry. The local density gradient scale length in this region is found to be about one ion gyrodiameter.

Flux-trapping during the formation of field-reversed configurations

Flux‐trapping during the early formation phases of a field‐reversed configuration has been studied experimentally on the field‐reversed theta‐pinch TRX‐1. An annular z‐pinch preionizer was employed to permit ionization at high values of reverse‐bias flux. Contrary to previous analysis, the rate of flux loss was not governed exclusively by inertially limited plasma convection to the tube walls. At high reverse flux levels, a pressure bearing sheath was observed to form at the tube walls and the flux loss was restricted by resistive diffusion across this sheath. The characteristic time for flux loss was 0.08rt (cm) μsec, independent of the bias field and independent of the fill pressure for fill pressures above 15 mTorr D2. Octopole barrier fields were found to be effective in limiting the inertially governed flux loss at very early times before the wall sheath formed.

Particle lifetime scaling in field‐reversed configurations based on lower‐hybrid‐drift resistivity

The particle lifetime scaling for field‐reversed configurations is derived in the limit where classical resistivity is negligible and anomalous resistivity is dominant. This scaling is shown to have the form τN∝S4(1+C/S)3, where S is the ratio of the major radius to ion Larmor radius. The term in parentheses represents a contribution from open field line confinement which is very significant for present small‐S field‐reversed configurations since C has a typical value of 50. The open field line confinement only loses importance for reactor‐sized plasmas with major radii approaching 1 m.

Inductive Field-Reversed Configuration Accelerator for Tokamak Fueling

Compact toroids can be used for fueling other fusion devices by accelerating them to high enough velocities to penetrate strong magnetic fields. In the simplest analysis, the kinetic energy density of a flux-excluding object {1/2}pv{sup 2} must exceed the magnetic field energy density B{sup 2}/2{mu}{sub 0} of the field to be pushed aside. Field reversed configurations (FRCs) are a type of compact toroid that are particularly efficient for this application due to their high density and thus lower required energy per unit mass. FRCs are also formed and accelerated inductively, thus minimizing possible impurity contamination. The Tokamak Refueling by Accelerated Plasmoids (TRAP) experiment was built to develop the inductive acceleration method and test the ability of high-velocity FRCs to penetrate transverse magnetic fields. Simple models have been developed for both the acceleration and penetration processes to determine fueler parameters required for a given tokamak field. Experimental results are given for the acceleration process. Half-milligram FRCs with number densities of 10{sup 22} m{sup {minus}3} were accelerated to velocities of 200 km/s, sufficient to fuel tokamaks with Tesia magnetic fields. The technology is easily extendable to much higher FRC densities and velocities, sufficient to fuel the largest, highest-field tokamaks.

A single-fluid model for shock formation in MHD shock tubes

A simple single-fluid model is presented which accounts for the behaviour of MHD shock producing devices in which the shock and the driving current sheet are unseparated. By means of both characteristic and similarity solutions, it is shown that unusual plasma behaviour is a simple consequence of the fluid equations of motion. The important parameters in determining the performance of MilD shock tubes are the width of the current sheet at breakdown (related to the magnetic Reynolds number) and the current sheet Mach number with respect to the gas at rest. It is shown that, under many conditions, separation is more likely to be achieved with a decrease , rather than an increase , in current sheet speed. Lowering the Mach number is more influential in causing the shock to form at the front of the current sheet than raising the magnetic Reynolds number.

Plasma wall sheath contributions to flux retention during the formation of field‐reversed configurations

Flux loss during field reversal on the TRX‐1 field‐reversed θ pinch is found to be much less than predicted by the inertial model of Green and Newton. This can be explained by a pressure bearing, conducting sheath which naturally forms at the wall and limits the flux loss. A one‐dimensional (r‐t) magnetohydrodynamic (MHD) numerical model has been used to study the formation and effectiveness of the sheath. The calculations are in excellent agreement with experimental measurements over a wide range of operating parameters. The results indicate that good flux trapping can be achieved through the field reversal phase of FRC formation with much slower external field reversal rates than in current experiments.

Experiments and Calculations in an Inverse Pinch

Experiments on the production of collisional shocks in an inverse pinch magnetohydrodynamic shock producing device are described. These experiments are related to the numerical techniques in an accompanying paper in order to explain the observed phenomena. The position of a shock in the rear of a current sheet driven through argon is accounted for by the calculation of relevant plasma parameters and their comparison to previous similarity solutions. The forward position of a shock in helium and hydrogen is similarily explained. The effect of shock produced dissociation in hydrogen is observed by its effect on the gas conductivity and current sheet diffusion. The detailed influence of Mach number and magnetic Reynolds number on shock position is examined experimentally, and methods are proposed for successfully producing high‐speed separated shocks.

Calculations of Gas Conductivity in Magnetohydrodynamic Shock Producing Devices

The simple scalar conductivity based on electron collisions with other particles is shown to be the governing parameter in determining current sheet diffusion and energy dissipation in magnetohydrodynamic shock producing devices. Simple methods are developed for calculating this scalar conductivity based on previous similarity solutions and experimental measurements of current sheet growth. These methods are shown to be applicable to inverse pinch experiments described in an accompanying paper, where the gas velocity in regions of the current sheet is constant. The position of the shock, through its influence on the gas velocity, is shown to exert a dominant influence on the current sheet diffusion.