Stephen E. Bodner

Electron heating due to parametric instability turbulence

The turbulent electron heating due to laser‐plasma instabilities at the critical density (laser frequency equals plasma frequency) is considered. In the regime where the laser energy is much less than the plasma thermal energy, simulations show that the wave energy spectrum takes on approximate k−2 shape concomitant with the formation of a suprathermal electron tail. Test particle calculations demonstrate that these tails are produced by velocity space diffusion due to the plasma waves. Quasilinear theory predicts a linear heating rate and an exponential shape for the electron tail, in agreement with the simulation result. The fluid equations, including mode coupling terms, are solved, and it is found that the instability saturation level and k−2 spectrum are due to mode coupling. Using the resulting fields, the electron distribution function is evolved, giving reasonable heating rates and suprathermal tail formation. Calculations in the underdense region (laser frequency greater than plasma frequency) sh...

Parametric instability thresholds and their control

It is shown that the “swelling” of the laser electric field must be included in threshold estimates for the electrostatic instabilities excited by a laser near the critical density. Random amplitude modulation of the laser is found to lead to an increased instability threshold.

Turbulence Theory with a Time‐Varying Wiener‐Hermite Basis

A theory of homogeneous turbulence in an incompressible fluid is formulated. The field variable v(r, t) is expanded in terms of a complete set of an ideal random basis, the first term of which is Gaussian. Since the ideal basis follows the actual fluid motion, there should be no incorrect relation between large and small eddies.

NONLINEAR DYNAMICS OF A SINGLE HARMONIC LOSS-CONE FLUTE MODE.

The nonlinear evolution of a single‐wavelength, longitudinal flute mode with frequency near a harmonic of the cyclotron frequency is determined. It is shown that only a small‐amplitude wave is needed to destroy the linearly coherent contributions of different gyrating particles to the perturbed charge density. This nonlinear smearing of the cyclotron resonance is accomplished by vortex filament motion of the hot particles in phase space, and leads to rapid stabilization and subsequent damping of the linearly unstable resonant modes that occur in hot‐cold multicomponent loss‐cone systems. In such a system with a typical hot‐particle Larmor radius R, a mode with wave vector k gains energy from the low‐velocity, inverted population hot particles until an energy is attained of the order (kR)−2 times the hot‐particle kinetic energy. This field energy then decays, being absorbed by the high‐velocity, normally populated hot particles.

Quasi-linear theory in the non-resonant region

By solving for the changes 〈Δν〉 and 〈ΔνΔν〉 for a particle, it is shown that there is no diffusion equation for non-resonant particles when the electric field wave is damping. By indirect means it is then shown for this case that the appropriate quasi-linear solution for ƒ 1 (к, ν, t) is proportional to ∂ƒ 0 (ν, 0)/∂ν rather than ∂ƒ(ν, t)/∂ν.