J. P. Freidberg

Vlasov‐Fluid Model for Studying Gross Stability of High‐β Plasmas

A model is presented which provides a more realistic description of the gross stability properties in high‐β plasmas than that given by ideal magnetohydrodynamics.

Rotational instabilities in a theta pinch

The stability of a rotating ϑ pinch is investigated in the context of the finite Larmor radius fluid equations. The main result is the discovery of an unstable m=1, n=0 mode (m is the azimuthal mode number and n is the number of radial modes) whose threshold is the lowest of any unstable mode. A comparison with experiment indicates that this mode may be the one responsible for the m=1 ’’wobble’’ instability observed in high temperature ϑ pinches.

Rigid Drift Model of High‐Temperature Plasma Containment

A model is proposed which appears to be consistent with certain recent high‐temperature plasma heating and confinement experiments, whose behavior is not adequately described by magnetohydrodynamics.

Lower hybrid drift instability at low drift velocities

The behavior of the lower hybrid drift instability is investigated in the low drift velocity regime by including the effects of the magnetic field on the ions. It is found that the mode is transformed from the nonresonant lower hybrid drift instability to the resonant ion cyclotron drift instability as the drift velocity Vd decreases and is finally stabilized when Vd/Vti∼ (me/mi)1/2.

Kink instabilities in a high‐β tokamak

A toroidal, circular cross section, sharp‐boundary model of a high‐pressure tokamak with currents confined to the surface, is tested for stability against kink modes. It is shown that for β > 0.21 e, where e is the inverse aspect ratio, the model is unstable to the n = 1 kink mode (n is the mode number the long way) for all values of the safety factor above and below the Kruskal‐Shafranov limit. Along the n = 1 marginal stability line m = 2 (m is the mode number the short way) is found to be the dominant harmonic.

Magnetohydrodynamic Stability of a Diffuse Screw Pinch

The magnetohydrodynamic stability of a diffuse screw pinch is investigated in an attempt to explain certain discrepancies between experiment and sharp boundary theory. It is found that the stability of a diffuse pinch is fairly sensitive to the Bθ profile and can lead to large differences from the sharp boundary model. By suitably adjusting Bθ in the diffuse profile, the original discrepancy between experiment and theory is removed.

Magnetohydrodynamic stability of a sharp boundary model of tokamak

Calculations of critical β for a sharp boundary, constant pressure model of tokamak are presented. The analysis is valid for arbitrary β, arbitrary aspect ratio, and arbitrary plasma cross section. Specific results are given for the circle, ellipse, triangle, square, and doublet cross sections.

Resonant particle effects on finite Larmor radius stabilization

It is shown that the threshold for instability of a one‐dimensional Vlasov‐fluid screw pinch is identical to that in ideal magnetohydrodynamics, for arbitrary ion gyroradius. That is, there is no absolute finite Larmor radius stabilization, although the growth rates for the Vlasov‐fluid model can be much lower. It is the ions in resonance with the real part of the mode frequency which are responsible for maintaining the instability beyond the value of ρi/a for which ’’finite Larmor radius stabilization’’ would have occurred. An analytical expression for the growth rate near the marginal point is derived using the finite Larmor radius expansion. The expression exhibits the expected scaling with β and Larmor radius.

Kink instabilities in a high‐β tokamak with elliptic cross section

A toroidal, elliptic cross‐section, sharp‐boundary model of a high‐pressure tokamak with currents confined to the surface, is tested for stability against kink modes. It is shown that the optimum configuration corresponds to a vertical ellipse in which the ratio of the major to minor axes is 2.2. For this case, the maximum critical β for stability against kink modes is β = 0.37a/R. For β > 0.37a/R the model is unstable for all values of the safety factor above and below the Kruskal‐Shafranov limit.

Stability of two‐dimensional magnetohydrodynamic equilibria

A numerical procedure is presented for computing the stability of high β, diffuse two‐dimensional magnetohydrodynamic equilibria. The method is tested on the problem of the bumpy θ pinch with arbitrary size bumpiness.