Nicholas A. Krall

Stabilization of Hot Electron Plasma by a Cold Background

A stabilizing effect of cold plasma, distinct from line tying, is described, and its influence on the flute stability of a hot‐electron plasma is evaluated.

Finite β Effects in a Weakly Unstable Plasma

The effect of finite plasma pressure (β) on the interchange mode is calculated in the finite Larmor radius limit. The method follows earlier zero β calculations of Rosenbluth and Simon, expanding the Vlasov equation with the ion Larmor radius ai considered small compared with the plasma radius L. The plasma pressure is taken to be zero order in ai/L. A differential equation is obtained for the stability properties of systems with arbitrary radial dependence of density, electric field, magnetic field, and β. Several simple examples show that increasing β moves marginally flute unstable systems to stability, if the change in β does not include violent changes in the density and field profiles.

TRAPPING INSTABILITIES IN A SLIGHTLY INHOMOGENEOUS PLASMA

The stability of an infinite collisionless plasma with a small density gradient in the x direction (using the collisionless Boltzmann equation and Maxwells equations) confined by a static magnetic field in the z direction, is studied. Unstable modes are found at frequencies near multiples of the ion‐cyclotron frequency Ωi. These modes are electrostatic oscillations transverse to the magnetic field, and have very short wavelengths λ ∼ vd/Ωi, where vd is the (small) drift occasioned by the magnetic‐field inhomogeneity. The phase velocity of the wave is comparable to vd, and resonant interaction leads to the growth. Typical growth rates are large, α ∼ (me/mi) Ωi, but the effect of the instability is minimized by the extremely short wavelength.

Stability of a Slightly Inhomogenous Plasma

Slightly inhomogeneous plasmas are studied to determine their stability against growing longitudinal electrostatic oscillations. The procedure is to expand Maxwells equations and the collisionless Boltzmann equation about e = 0, corresponding to a uniform plasma, where the expansion parameter e characterizes the particle density gradient. It is found that the shift in the eigenfrequency of the oscillation is of order e2; this shift is a real number to order e2 if the eigenfrequency for the corresponding uniform plasma, e = 0, is a real number. Transverse modes are also examined for some special directions of propagation, with similar results. It is observed that this expansion procedure would not reproduce instabilities associated with particle drifts.

One-dimensional transport models with local and nonlocal lower-hybrid-drift waves in field-reversed configurations

The one‐dimensional transport theory for field‐reversed configurations has been reexamined taking into account global lower‐hybrid‐drift turbulence. Extending previous work for nonlocal electrostatic lower‐hybrid‐drift theory, the spatial character of lower‐hybrid‐drift eigenmodes have been determined in the separatrix region of a field‐reversed configuration. Surprisingly, it has been found that the transport model based on the more comprehensive ‘‘global’’ theory of the lower‐hybrid‐drift theory results in transport coefficients which are very similar to those based on the simple ‘‘local’’ lower‐hybrid‐drift theory. The reason for this is as follows. The nonlocal theory of the lower‐hybrid‐drift predicts a sequence of eigenmodes with differing eigenvalues and spatial extent. It is found that if a particular eigenmode is considered and the radial points which mark its radial extent are noted, then the eigenfrequency and growth rate associated with that eigenmode will have approximately the same value as ...

Nonlinear Limit of a Drift Instability Related to Auroral Bombardment

The nonlinear development of the low‐frequency transverse‐drift instability is calculated. Although quasi‐linear theory might be expected to be valid for such a mode, wave scattering is required to saturate the mode spectrum. The effect of the fully developed instability is a coordinate displacement, and a shift in vz. If applied to the radiation belts, this instability would predict auroral bombardment localized in radius, occurring in the lower density large‐gradient regions of the particle distribution.

Rayleigh‐Taylor Instability in a Stabilized Linear Pinch Tube

Kerr cell photographs through a mesh anode have shown growing flute patterns on the interior luminous surface of the plasma cylinder. These appeared when the pressure of the enclosed axial field reversed the initial inward acceleration, as is expected for the accelerational hydromagnetic analog of the Rayleigh‐Taylor instability. The measured growth rates ranged from about one‐half to the full value predicted by simple theory. This agreement extended over a range of operational tube conditions. As predicted, application of an interior stabilizing field from a central wire erased the visible fluting.

Microwave heating of the ELMO Bumpy Torus relativistic electron ring

A model for microwave heating of electron rings in the ELMO Bumpy Torus configuration is analyzed using a relativistically correct quasi‐linear formulation. The spatial locations of heating by the different electron‐cyclotron harmonics are calculated. The steady‐state ring energy and the microwave power required to sustain the rings are determined by balancing the line‐averaged heating rate against classical collisional and radiative energy loss processes. Although ring formation is generally attributed to the second harmonic electron‐cyclotron resonance, the calculations show that fundamental heating also plays a critical role in ring start‐up and steady state. The model predicts ring power requirements for EBT which are consistent with previous estimates.

Invariance of the Magnetic Moment for Short Wavelength Perturbations

Minimum B configurations are magnetic field configurations whose strength increases toward the periphery. It is demonstrated that low-frequency electrostatic instabilities (e.g., universal instabilities) preserve the magnetic moment as an adiabatic invariant and hence are stabilized by the minimum B configurations. (D.L.C.)

Electron ring startup model for ELMO Bumpy Torus

The microwave power requirements for EBT electron ring startup are calculated based on the assumption that the ring electrons originate as runaways accelerated by the first harmonic resonance of the extraordinary mode. The calculated microwave power threshold for startup is consistent with the experimental data for the microwave power requirements deduced from the C–T transition points. The ring model is also compatible with the experimentally observed ring location if the subsequent heating and toroidal drift motion of the energetic electron after the initial startup is considered in determining the ring spatial structure.