David B. Beard

Cyclotron Radiation from Magnetically Confined Plasmas

The cyclotron emission from a hot, completely ionized, magnetically confined plasma has been estimated by computing the absorption of an incident plane wave. The harmonics of the fundamental cyclotron frequency, which are emitted perpendicular to the magnetic field direction, were summed over and also treated individually. Because of the Doppler effect and the relativistic variation in mass the behavior of the electrons and the electromagnetic properties of the medium are functions of electron velocity.Assuming a Maxwell‐Boltzmann distribution in electron velocity, the polarization of the plasma was computed by integrating over electron velocity. Solution of Maxwells equations yielded the absorption of an incident wave, and thus, from Kirchhoffs relation, the emission of the plasma was determined. The entire calculation was carried out nonrelativistically to first order in v2/c2, and at temperatures too low for fluctuations to play a dominant role.

Synchrotron Radiation Losses from Energetic Plasmas

The synchrotron emission from plasma electrons having an isotropic Maxwell‐Boltzmann velocity distribution has been numerically computed as a function of electron temperature, radiation frequency, and the angle between the radiation propagation vector and the magnetic field. The total emission at high temperatures from a cylindrical plasma volume was found to be greater than earlier estimates of others valid at lower temperatures due to contributions at frequencies higher than the critical frequency at which the plasma becomes semitransparent. The increase is temperature dependent. For a 10‐m‐diameter plasma the increase for a typical plasma is 32% at an electron temperature of 20 keV and rises to 140% at 200 keV electron temperature. The effect of reflectors in diminishing the loss of radiated energy is very much reduced at high temperatures. If r is the over‐all microwave reflectivity of the material walls surrounding the plasma, the loss is diminished approximately by (1 − r)0.8 for kT = 10 keV, by (1 ...

Relativistic Calculation for Cyclotron Radiation from Hot Plasmas

The equation of motion of an electron in a time-dependent electric field and constant magnetic field is given for the case where insignificant changes in electron energy are neglected. This equation is expanded to give an evaluation for propagation perpendicular to the magnetic field for an oscillator of a given resonant frequency. Equations are given for the refractive index, Maxwell- Boltzmann distribution in energy, and the absorptivity of a plasma. (B.O.G.)

Line Shapes and Intensities for Disk Sources Used in an Homogeneous Magnetic Field Beta‐Ray Spectrometer with New and Conventional Slit Geometries

This paper is primarily concerned with the effect on the line profile shape and intensity of the angle φ, the angle made by the projection of the electron velocity vector on a plane perpendicular to the instrument axis at the source with the radius of the source point. Quantitative results are quoted for several geometries. The line profile, expected intensity, and optimum source size for a commonly used slit geometry utilizing an entrance slit for take‐off angle selection is found to differ significantly from previously quoted results, the intensity for the same half‐width for optimum source size being 46% of the earlier work. A new slit geometry consisting of an additional baffle near the source which restricts φ is discussed and is found to improve the expected intensity for the same line half‐width by 24% for an optimized Hubert slit system which is already found in this paper to be 28% better than the best of previous slit geometries. Finally, a geometry which selects φ properly is shown to remove al...

Synchrotron Radiation from Mirror Machine Geometries

The radiation due to the orbiting of electrons in a confining magnetic field has been numerically integrated over a thermal velocity distribution perpendicular to the magnetic field as a function of frequency of emitted radiation and the angle the radiation propagation vector makes with the magnetic field. The general dependence of the emission on angle and frequency has been examined by the use of various approximations and is shown to agree with the numerical calculations. Our result for a velocity distribution perpendicular to the magnetic field more nearly corresponds to Drummond and Rosenbluths previous angular dependence than with Trubnikovs result for an isotropic velocity distribution.

Comment on the Angular Dependence of Plasma Synchrotron Emission

A numerical study was made of plasma emission from a plasma with a two- dimensional velocity distribution limited to directions perpendicular to the magnetic field. It was found that the Drummond-Rosenbluth approximation is extremely good for an electron gas whose velocity vector is essentially perpendicular to the confining magnetic field.