Barry S. Newberger

Structure and Scaling Laws of Laser-Driven Ablative Implosions

A stationary, spherical flow model gives the form of laser‐driven ablation fronts and scaling laws for the dependence of implosion parameters on laser wavelength, pusher atomic number, and other input quantities.

New sum rule for products of Bessel functions with application to plasma physics

In our investigations of the linear theory of the stability of relativistic beam‐plasma systems immersed in a magnetic field we have been led to consider sum rules for an infinite series of products of Bessel functions of the form J∞n = −∞(n jJ2n)/ (n+μ). In this work we report on the sum of this series treated as a special case of a more general infinite series. We also mention the extension of the results beyond the range of the parameters for which formulae are explicitly given and indicate how intermediate results obtained may be useful in their own right. Finally, an additional application of our result is indicated.

A Relativistic Plasma Dispersion Function

A relativistic plasma dispersion function is defined, and its analytic properties discussed. Using this function, it should prove possible to formulate relativistic plasma linear theory in a particularly simple form for study either analytically or numerically. As an example, the dispersion relation for Langmuir waves in a one-dimensional relativistic plasma is solved and compared against the results of computer simulations. Agreement is good for waves of phase velocity either above or below the speed of light, Two appendices are provided, the first giving several expansions and other representations of the dispersion function, the second discussing numerical methods for its evaluation. Contour plots of the function are included.

Simulation of cyclotron wave growth in a helical slow wave structure

Growth of large amplitude coherent cyclotron waves on unneutralized relativistic electron beams has been studied analytically and numerically. The mechanism for growth is the unstable coupling of helical waveguide modes with relativistic electron beam cyclotron waves. Approximate analytic growth rates are found to be in good agreement with the exact numerical solution of the linearized plasma equations on a self‐consistent cylindrical beam equilibrium. Particle simulations performed in cylindrical geometry quantitatively confirm the theory. The calculations were conducted in both an infinite medium and realistically terminated configuration. In the latter, matched impedances on the helix were required to reduce transients and unwanted reflections to tolerable levels. Saturation in both cases is due either to convection or, in sufficiently long waveguides, growth of the wave until it physically intersected the helix.

Relativistic Linear Theory in the Absence of External Fields

The dielectric tensor for a multi-component, homogeneous, field-free relativistic plasma is derived in manifestly covariant form. From the dielectric tensor, linear dispersion relations are obtained explicitly when each component of the plasma is isotropic in its rest frame. If the components are relativistic Maxwellians, these dispersion relations are expressible in terms of the relativistic plasma dispersion function. Special attention is given to the Weible and two-stream instabilities and to the normal modes of a quiescent, hot electron gas. For the last case the dispersion relations are solved numerically and compared against computer simulation data. An appendix applies the formalism to cold plasmas.

Electrostatic two‐stream instability for a scattered relativistic electron beam and collisional plasma

The Vlasov stability theory of the two‐stream instability of a scattered relativistic electron beam in a collisional plasma is presented. New analytic results demonstrating the effect of a small but finite scatter (temperature) on the cold beam dispersion relation are given. These provide a basis for a discussion of the continuous transition, with increasing scatter, from the hydrodynamic to kinetic regime of instability. Numerical solutions of the dispersion relation are presented to illustrate some general features observed as well as trends in scaling with the beam parameters.

Computer Simulation of Collective Ion Acceleration by Discrete Cyclotron Modes

Extensive analytical studies suggest that significant currents of high energy ions can be obtained by collective acceleration via large amplitude cyclotron waves in a non-neutral intense relativistic electron beam. We have already demonstrated this acceleration mechanism in fully self-consistent two-dimensional computer simulations for low ion current and energy. However, the simulations employed a packet of cyclotron waves created ad hoc upstream of the acceleration region. Acceleration was limited by phase-mixing and damping of the packet. Here, we shall present results of our ongoing effort to simulate, first, realistic growth of large amplitude, single frequency cyclotron waves in the relativistic electron beam and, second, acceleration of various ion currents with those waves.

The Initial Value Problem in Relativistic Plasma

The Landau problem in relativistic plasma is considered in detail. It is shown how all modes in the plasma arise through proper treatment of the inverse Laplace transforms without imposition of any external conditions. A correct derivation of the asymptotic behavior of the electric field is included and estimates of the contribution of more rapidly decaying Landau modes are made analytically and are compared with numerical computations.

Diffusive processes in the cross‐field flow of intense plasma beams

We consider magnetic field diffusion in the presence of strongly magnetized electrons (ωceτc 0>1) as a mechanism for the rapid penetration observed in cross‐field flows of high‐β plasma beams. The diffusion has been investigated in several cases which are amenable to analytic solution. The flux penetration times are found to be insensitive to the particular configuration. Comparison with two experiments is made. Agreement within the limits of the experiments is found. Both require an anomalous collision rate which is consistent with observed fluctuations in one case but apparently not the other.

Steady‐state plasma production and fluid flow in ion beams with step‐function density profiles

The steady‐state fluid equations for plasma production and transverse flow in an ion beam with a step‐function density profile are solved exactly in both slab and cylindrical geometries. The beam edge is treated as both a neutral and a non‐neutral sheath. In the former, the beam density falls from its value inside the beam to zero in a distance much greater than a Debye length, while in the latter the Debye length is much greater than the beam falloff distance. Physical solutions with plasma density profiles which decrease monotonically from the beam center are shown not to exist for negative ion beams with a non‐neutral sheath.