Harold Weitzner

Propagation and absorption of electromagnetic waves in fully relativistic plasmas

The propagation and absorption of electromagnetic waves in a relativistic Maxwellian plasma are investigated by solving the uniform plasma dispersion relation. Both the Hermitian and the anti‐Hermitian parts of the plasma conductivity tensor σ are calculated relativistically. The Bessel functions occurring in σ are not expanded, and many cyclotron harmonic terms are included at high temperatures. The dispersion relation is solved numerically for perpendicular propagation, k∥ =0, where the relativistic effects are maximum and are not masked by Doppler broadening, which has been more thoroughly investigated. It is found that relativistic broadening has a substantial effect on wave dispersion, shifting the extraordinary mode right‐hand cutoff and the upper‐hybrid resonance to higher magnetic field with increasing temperature. Above a critical temperature, the cutoff disappears entirely. There is a broad range of temperatures, 20 keV≤Te ≤500 keV, for which the wavenumber k⊥ differs significantly from both the...

An eikonal expansion of the Vlasov–Maxwell equations valid near cyclotron resonance

In the usual formulations of geometrical optics, the physics of the medium enters the equations through a conductivity tensor operator σ. An essential assumption in the subsequent expansion is that the magnitude of σH, the Hermitian part of σ, is much smaller than σA, the anti‐Hermitian part. In a finite temperature plasma with ωpe∼‖Ωe‖, this condition is always violated sufficiently close to cyclotron resonance, even though in many cases the waves are weakly damped and k is slowly varying. Simultaneously expanding the Vlasov equation and Maxwell equations and taking explicit account of the relative magnitude of the electric field components in the ordering scheme yields a formalism in terms of real rays, real eikonal functions, and slowly varying amplitude that is valid at cyclotron resonance. It is assumed that ωpe∼‖Ωe‖∼ω are large, that ω≃‖Ωe‖, and that vek/ω is small. It is shown that when the waves are weakly damped at cyclotron resonance, the ray trajectories are, to leading order, exactly those of ...

Green's Function for Two‐Dimensional Magnetohydrodynamic Waves. I

As an extension of an earlier paper the Greens function is evaluated for the Lundquist equation linearized about uniform magnetic field, constant matter density, and zero flow velocity. It is assumed that all quantities are functions of two space variables and time only. In the general magnetic field configuration considered here a pure Alfven disturbance no longer exists; there is instead a wave with properties of both the Alfven and fast‐slow disturbance.

A convergent spectral representation for three‐dimensional inverse magnetohydrodynamic equilibria

By rearranging terms in a polar representation for the cylindrical spatial coordinates (R,φ,Z), a renormalized Fourier series moment expansion is obtained that possesses superior convergence properties in mode number space. This convergent spectral representation also determines a unique poloidal angle and thus resolves the underdetermined structure of previous moment expansions. A conformal mapping technique is used to demonstrate the existence and uniqueness of the new representation.

Report of panel 3: Concept improvement

The charge to Panel 3 was to look at the idea of concept improvements in the context of US DOE management of the magnetic fusion program. The panel suggested that if DOE were commited to the idea of concept improvement, it needed to overcome the existing impression it was not receptive to new ideas. In part the long time scale for development of fusion energy, coupled with the rate of change of scientific programs and research based on emerging knowledge, means that in general the program will be much different ten to twenty years in the future. To be able to meet this changing direction, the US program must maintain an openness to look at promising alternative ideas, spend money on developing the ideas, and consider funding some to intermediate development levels. Stellerator research was offered as one alternative to consider in light of present international work. The panel urged supporting the development of new concepts and ideas, as well as continued support for plasma physics basic research.

Magnetohydrodynamic and double adiabatic stability of compact toroid plasmas

The linear stability of compact toroids is examined in the magnetohydrodynamic and double adiabatic models. The long‐thin approximation in ideal magnetohydrodynamics is used to investigate tilting and shifting modes in field reversed configurations without toroidal fields. A necessary and sufficient condition is obtained and used to show that the combination of flux surface shaping and profile flatness results in stability to a class of transverse modes in a region about the O point. The double adiabatic model yields for general confined plasmas a sufficient condition for stability in the form of six ordinary differential equations along each field line. Further reduction of the condition to a single second‐order equation depends on the sign of ∂S/∂B, where S(ψ,B)=p∥B5/p3⊥ is a combination of the two entropies. Strong stabilizing effects of pressure anisotropy are shown.