Edward P. Lee

Resistive hose instability of a beam with the Bennett profile

The resistive hose instability of a self‐pinched relativistic beam is examined with emphasis placed on the important case of the Bennett current profile JB(r) ∝ (1+r2/a2)−2. Previously known results applicable to a general profile are recovered and extended in several directions. An essential new feature in this study is the use of distributed particle mass to model orbital phase‐mixing effects produced by the anharmonic pinch field. Resonant growth is considerably reduced, and the instability when viewed in the beam reference frame is shown to be convective rather than absolute. The peak amplitude of a disturbance wave packet moves from the point of its inception in the beam pulse toward the pulse tail. The disturbance subsequently damps if the pulse length is finite; thus, propagation over distances that are long compared with the particle betatron wavelength is possible. The predicted growth rate and group velocity of the mode are shown to be in fair agreement with the results of numerical simulation.

Kinetic theory of a relativistic beam

A Fokker–Planck equation is derived to study the evolution of a stable, low‐current beam propagating in a gas‐plasma medium. Small‐angle scattering of the beam particles by the medium causes diffusion in the phase space projected transverse to the direction of propagation. The projected components of dynamical friction vanish. As a result, there is a continued input of energy into the transverse particle motions, which is taken up in expansion against the pinch field. A quasi‐static Bennett equilibrium, with isothermal distribution of transverse momenta, is shown to be a similarity solution of the Fokker–Planck equation with scale radius increasing in accord with Nordsieck’s formula. An H theorem is proved and the Bennett distribution is shown to minimize both H and −d H/d t; hence, it is the time‐dependent asymptotic state. The predicted current profile and radius are shown to be in fair agreement with experiment.

Measurements of hose instability of a relativistic electron beam

The observed disruption of a self‐focused, relativistic electron beam propagating through a gas is shown to result from the growth of m=1 (’’kink’’ or ’’hose’’) perturbations. Measurements of the frequency dependence of the spatial amplification rate are presented. An upper cutoff to the frequency range for hose amplification is observed, in agreement with a theoretical model that includes the damping effects of a spread in the particle betatron frequency.

Filamentation of a heavy-ion beam in a reactor vessel

A heavy‐ion beam driver for inertial confinement fusion is subject to filamentation instability over a broad range of beam and plasma background conditions. The case of a beam injected into a gas‐filled reactor vessel, where finite pulse length and propagation distance play an important role in limiting mode growth, is analyzed. The effects of transverse thermal spread, spherical convergence to the pellet, and finite magnetic decay rate of eddy currents are included in this treatment. It is concluded that a cold beam will be severly disrupted unless the product of magnetic plasma frequency and propagation time is not large compared with unity. If this condition is not met, mode growth may still be limited to about six e folds by adding transverse velocity spread such that the pulse tail is in a state of pinch equilibrium. However, this approach causes much of the pulse to be lost by thermal expansion.

Radial expansion of self-focused, relativistic electron beams

Measurements of the radial expansion from gas scattering of a low ν/γ relativistic electron beam are presented. The measured current density profiles approach a Bennett shape, as predicted theoretically, and the rate of expansion of the beam radius with distance is in good agreement with the predictions of an envelope equation. locus has been determined. It terminates at zero temperature at

Low‐frequency hydromagnetic kink mode of a relativistic beam

An analysis of the stability of the kink mode of a relativistic charged‐particle beam propagating in a toroidally confined plasma is presented. The essential feature is the treatment of the beam as a distinct component of the system having finite velocity and inertia in addition to its current. To simplify the analysis, the plasma background is assumed to be a pressureless, uniform fluid obeying the laws of perfect magnetohydrodynamics while the beam is treated as a cold, rigid body. To simulate toroidal geometry, periodic boundary conditions are imposed in the axial direction of a straight, cylindrical volume. The walls of the cylinder have perfect conductivity. A strong solenoidal field is externally imposed, but the beam is the only source of the poloidal field. It is found that a modification of the stability condition of Kruskal and Shafranov applies; the onset of instability corresponds to the appearance of closed particle orbits rather than the more severe condition of closed field lines. The maxim...

The beamline for the second axis of the Dual Axis Radiographic Hydrodynamic Test Facility

During normal DARHT II operation, the beam exiting the accelerator will be well characterized by its nominal design parameters of 20-MeV, 2000-Amperes, 2-/spl mu/sec-pulse length, and 3 cm-mr unnormalized emittance. Normal operation will have the beam delivered to a beam dump via several DC magnets. A 2-way kicker magnet is used to deflect portions of the beam into the straight ahead beamline leading to either a diagnostic beamline or to the converter target beamline. During start up and or beam development periods, the beam exiting the accelerator may have parameters outside the acceptable range of values for normal operation. The Enge beamline must accommodate this range of unacceptable beam parameters, delivering the entire 80 KiloJoule of beam to the dump even though the energy, emittance, and/or match is outside the nominal design range.

Transport of intense ion beams

Abstract The maximum transportable current for an ion beam is determined by considerations of focal strength, space charge equilibrium and stability, structural practicality, and emittance. These factors are described within the context of a heavy ion driver for inertial confinement fusion. Recent supporting results from particle-in-cell simulations and transport experiments will be described.

Hollow equilibrium and stability of a relativistic electron beam propagating in a preionized channel

A short pulse of relativistic electrons propagating along a preionized channel of high conductivity may assume a hollow equilibrium profile as a result of induced plasma currents. In this configuration the pulse is neutrally stable with respect to lateral expulsion from the channel by the induced currents. The properties of a thin hollow shell equilibrium are derived.

Low‐Current Relativistic Beam Equilibria

A simple procedure yields isotropic beam equilibria with given current profile and energy distribution in the limiting case of the beam current small compared with the Alfven current.