Thomas B. Kaiser

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.

Ballooning modes in quadrupole tandem mirrors

Ballooning modes in tandem mirrors with quadrupole vacuum field symmetry are investigated in the limits of zero gyroradius and large aspect ratio. The eigenmode equation derived from the guiding‐center energy principle is reduced to one dimension by the use of an eikonal representation of the cross‐field variation of the perturbation. The eigenvalue problem is solved numerically and the structure of the local dispersion relation examined in order to derive conditions for marginal stability. Applications to the TMX‐U and MFTF‐B tandem‐mirror experiments are presented.

Finite Larmor radius and wall effects on the M=1 ballooning mode at arbitrary beta in axisymmetric tandem mirrors

The equation for the m=1 ballooning mode is derived; the dominant finite Larmor radius terms force the mode to be rigid. A dispersion relation with the wall near the plasma is obtained for arbitrary β, and it is also shown that with the wall at infinity only the vacuum curvature contributes to all orders in β.

Rigid ballooning modes in tandem mirrors

Stability of tandem mirrors to rigid‐displacement ballooning modes is studied using vacuum field geometry. Results show substantial improvement in values of beta over those predicted by ‘‘infinite‐m’’ theory. Previous work has shown that kinetic effects stabilize these latter short‐wavelength modes, suggesting that only the rigid mode survives.

One- and two-dimensional simulations of ultra-short-pulse reflectometry

Ultra-short-pulse reflectometry is studied by means of the numerical integration of one- and two-dimensional full-wave equations for ordinary and extraordinary modes propagating in a plasma. The numerical calculations illustrate the use of the reflection of ultra-short-pulse microwaves as an effective probe of the density or magnetic profile in the presence of density or magnetic fluctuations in the plasma. Bragg resonance effects can be identified in the reflected signals, which give information on fluctuations. It is also demonstrated that ultra-short-pulse reflectometry can be used to perform correlation reflectometry measurements in which correlation lengths for density fluctuations are deduced from the observed cross-correlation function of phase shifts as a function of frequency.

Comments on ’’Relaxation processes in plasmas with magnetic field’’

Velocity sapce fokker−planc coefficients obtained in an investigation of the temperature relaxation of a magnetizaed plasma differ from those obtained by other workers in thensor structue. Although the diffusion tensor is in error, it is shown that the relaxation rates are unaffected by the mistake.

The influence of end‐plate potential control on magnetohydrodynamic normal modes and stability in mirror machines

By adjusting the electrostatic potential on the end plates of a mirror plasma, the plasma’s magnetohydrodynamic (MHD) stability can be altered. Furthermore, the plasma’s MHD response to low‐frequency modulation of the end plates can be used to pump unwanted ions that collect in a thermal barrier. Here, precise boundary conditions are derived for the MHD equations of motion to model an end plate separated from the plasma by a sheath.

One- and two-dimensional simulations of ultra-short-pulse reflectometry (abstract)

Ultra-short-pulse reflectometry is studied by means of the numerical integration of one- and two-dimensional full-wave equations for ordinary and extraordinary modes propagating in a plasma. The numerical calculations illustrate the use of the reflection of ultra-short-pulse microwaves as an effective probe of the density or magnetic profile in the presence of density or magnetic fluctuations in the plasma. Bragg resonance effects can be identified in the reflected signals, which give information on fluctuations. It is also demonstrated that ultra-short-pulse reflectometry can be used to perform correlation reflectometry measurements in which correlation lengths for density fluctuations are deduced from the observed cross-correlation function of phase shifts as a function of frequency.