J. L. Shohet

Ballooning mode calculations in stellarators

A magnetohydrodynamic (MHD) ballooning mode formalism and calculation is developed to show how a field‐line‐following code can be used to study MHD stability. The asymptotic analysis of the ballooning equation yields the Mercier condition. It is shown that first‐order equilibrium effects on the vacuum fields from finite pressure cancel the intrinsically destabilizing term of the Mercier condition. A ballooning unstable solution is found in a Heliac configuration that has a magnetic well at zero beta and a rotational transform that increases radially outward.

Plasma heating by Alfvén wave excitation in the Proto‐Cleo stellarator

Alfven wave heating experiments have been done in the Proto‐Cleo l=3, seven field period stellarator. The Alfven waves were excited by a helical wave launcher which surrounds the entire torus. Doubling of both the electron and ion temperatures was observed with electrons and ions heated independently by the wave. The effectiveness of the heating changes, as predicted by theory, when experimental parameters were varied. Evidence of the existence of Alfven wave resonant surfaces in the plasma were also observed. Some enhanced plasma loss occurred when Alfven wave heating was applied to the plasma. Several possible mechanisms for this enhanced loss were studied but no clear explanation was found.

PLASMA ELECTRON VELOCITY DISTRIBUTIONS DETERMINED FROM THE POLARIZATION OF FREE--FREE BREMSSTRAHLUNG.

The degree of polarization of the free‐free bremsstrahlung from a plasma, as measured by Compton scattering, may be used to determine the electron velocity distribution. In this experiment, a hot electron plasma was made by means of electron cyclotron resonance heating in a magnetic mirror. The measured degree of polarization varied as mirror ratio and amount of lower off‐resonance heating were changed. A theoretical computation of polarization, utilizing a nonrelativistic quantum mechanical theory, which matched the experimental conditions, showed that either a loss‐cone or a Harris distribution could fit the observed data, except when lower off‐resonance heating filled the loss cone. Under these conditions, only the Harris distribution was correct.

Free‐Free Bremsstrahlung from a Plasma with an Anisotropic Electron Velocity Distribution

Measurements of two properties of the emitted free‐free bremsstrahlung from an electron cyclotron resonance plasma were made. These were the radiation intensity and the spatial distribution of the photons as a function of angle with respect to the magnetic field axis. The intensity was maximum for directions of observation along the field lines. The spectral distribution showed that the average emitted x‐ray photon was more energetic along the field lines than across them. A theoretical development has been made which considers quantum‐mechanical, nonrelativistic transitions, which correspond to the conditions of the experiment. The theory predicts the observed measurements and also, in the limit of low energy photons, (nonquantum mechanical transitions) corresponds to previous developments.

ELECTROMAGNETIC INSTABILITY IN AN ELECTRON CYCLOTRON RESONANCE PLASMA.

An electron cyclotron resonance plasma was produced in a magnetic mirror field. Measurements of electron density, electron temperature, stored energy density, electron energy distribution, plasma light variations, and particle fluxes were made. An instability characterized by microwave emission below the electron cyclotron frequency, bursts of high‐energy x‐rays, particle losses along the magnetic axis, and variations in stored energy density was observed. The dispersion relation for transverse electromagnetic waves propagating in a plasma with an anisotropic Maxwellian electron velocity distribution with loss cones was solved numerically using parameters characteristic of this experiment and was found to yield instability frequencies and growth rates which agreed well with those observed.

Measurement of the Anisotropic Energy Distribution of Electrons in an Electron Cyclotron Resonance Plasma

The anisotropy of the electrons in an electron cyclotron resonance plasma has been measured by means of the plasma diamagnetism and particle end flux out of a uniform magnetic field region. Measurements of x rays produced by the plasma were also made.

Transit-time magnetic pumping of an electron beam in the Proto-Cleo stellarator

A traveling wave was launched around the Proto‐Cleo stellarator to attempt transit‐time magnetic pumping of a pulsed electron beam moving along the magnetic field lines. An apparent loss of the beam was seen when transit‐time magnetic pumping was applied. A random walk diffusion of the beam with a step size determined by the radial E×B drift in the wave poloidal electric field agrees well with the experimental results.

Radio frequency breakdown and electron confinement time in a stellarator

Radio frequency (u2009f=350 kHz) inductive breakdown has been studied in a toroidal stellarator. The time delay between the application of the radio frequency pulse and the buildup of detectable plasma density is measured as a function of the discharge parameters. It is shown that the confinement time of energetic electrons (∼100 eV), produced during the breakdown, may be deduced from the breakdown characteristics. The experimentally determined confinement times are compared with predictions of neoclassical transport theory and are found to have functional dependence on the discharge parameters approximately consistent with plateau scaling, but to be shorter than predicted by the neoclassical diffusion model.

Surface modes in magnetized fully ionized plasma

Density fluctuations in a semi‐infinite fully ionized plasma in the presence of a uniform magnetic field are investigated using a direct variational principle. ’’Two‐stream’’ distribution functions are included to allow for the expected discontinuity in velocity space at the boundary. The microscopic boundary conditions incorporate both specular reflection and diffuse scattering effects. The shape of the density fluctuation spectrum is very dependent on the orientation of the wave vector (k) with respect to the direction of the magnetic field. The spectrum also shows evidence of both ion and electron surface effects which become enhanced with the increase in diffuse scattering contributions at the boundary.

Plasma effects on the absorption spectrum for the ordinary mode in a magnetized plasma

The rate of energy absorption for electrons in a plasma is calculated from the emission, including plasma effects through the index of refraction. The net absorption is obtained for the case of propagation perpendicular to an applied dc magnetic field. The dispersion relation for cyclotron harmonic waves is solved numerically to obtain wavenumbers as functions of excitation frequency. This gives the index of refraction required to find the net absorption rate. Spectra for various temperatures and densities are found by integration over the electron velocity distribution.