L. D. Pearlstein

Analytic equilibria with quadrupole symmetry in the paraxial limit

Mirror equilibria for arbitrary mirror ratio and flux‐tube eccentricity are obtained to leading order in the plasma pressure (beta expansion) in the paraxial limit (axial scale lengths long compared with radial scale lengths). The solutions are given in terms of quadratures over known functions. The theory is applied to a tandem‐mirror configuration.

Finite Beta Stabilization of the Drift‐Cone Instability

An analytic expression giving the drift‐cone stability criterion of a finite‐beta plasma is derived using a mirror‐ratio‐dependent loss‐cone ion distribution. This is used to determine a beta limit for stability which is found to be insensitive to changes in mirror ratio and plasma temperature.

Finite Larmor radius equations in an arbitrary near‐theta pinch geometry

A set of fluid‐like equations is derived which describes the stability of a diffuse, high β, arbitrary, near‐ϑ pinch configuration. The equations simultaneously include geometric effects which drive ideal magnetohydrodynamic instabilities and kinetic effects which give rise to finite Larmor radius stabilization. A simple heuristic procedure is given for determining these equations in addition to a full derivation starting from basic principles.

‘‘Moderate‐m’’ ballooning modes in quadrapole stabilized tandem mirrors

The beta limits on the central cells of nonaxisymmetric tandem mirrors due to moderate‐m ballooning modes are studied. Both finite Larmor radius (FLR) effects and corrections associated with the finite extent of the ballooning modes in the plane perpendicular to B are retained. The assumption of short perpendicular wavelength together with the large ellipticity of the flux surfaces near the magnetohydrodynamic (MHD) anchor cells allows a reduction of the three‐dimensional problem into a sequence of three one‐dimensional problems. The marginal stable boundary for the Mirror Fusion Test Facility (MFTF‐B) (National Technical Information Service Document Nos. 82020108 and UCID‐19359) is calculated and compared with that obtained from a low mode number calculation.

Plasma return currents in a magnetic field

Whereas plasma return currents along a magnetic field arise for an electromagnetic diffusion time, it is found that appreciable plasma return currents perpendicular to a magnetic field are not induced for built‐up times slow compared with an Alfven transit time.

Critical Length Criteria for Mirror Machines

Critical scale lengths for stability of mirror devices are determined. The analysis proceeds via a modified WKB technique which adds the effect of wave amplification due to the presence of singularities of the dielectric function. The approximate answers so determined compare favorably with the numerical solution of the appropriate equations. Results for large and small mirror ratios are presented. It is found that irrespective of the character of the wave in the infinite medium limit (e.g., drift‐cone or stable negative energy wave) stabilization is effected at roughly the same magnetic scale length for all but the longest axial wavelength modes.

Straight‐Line Orbit Approximation in Periodic Systems

It is shown that the plasma response function, in a system whose particle orbits are periodic, is accurately approximated by the infinite medium response function for real frequencies when the bounce time is sufficiently spread.

Theoretical Aspects of Astron Buildup by Multiple Pulses

The time asymptotic response to an incoming current source in the presence of a partially built up E layer in the astron geometry is examined. A one‐dimensional Vlasov model which considers only motion in the exial direction (perpendicular to the current direction and tank radius) is studied. It is shown that (1) A back current is induced in the E layer. (2) A new dissipation mechanism (Landau damping) occurs in the E layer as well as in the resistors. (3) The dissipation in the layer causes particle scattering that leads to axial expansion which competes with contraction due to the addition of current. The net effect for a neutralized layer can lead to a saturation in E layer strength, a behavior encountered in numerical experiment. For the unneutralized layer, however, this situation is not nearly as severe and there appears to be a parameter range where stacking should occur.

Hollow equilibrium and stability of a relativistic electron beam propagating in a preionized channel

A short pulse of relativistic electrons propagating along a preionized channel of high conductivity may assume a hollow equilibrium profile as a result of induced plasma currents. In this configuration the pulse is neutrally stable with respect to lateral expulsion from the channel by the induced currents. The properties of a thin hollow shell equilibrium are derived.