W. R. Shanahan

Linear theory of a cold relativistic beam propagating along an external magnetic field

The linear theory of a cold relativistic electron beam propagating parallel to an external magnetic field and through a cold, homogeneous plasma is investigated. The electromagnetic dispersion relation is solved numerically and compared with analytical predictions based on the electrostatic approximation. It is found that electromagnetic effects are important for determining the entire unstable spectrum. However, except for the strong magnetic field regime, the maximum growth rates and corresponding frequencies are in agreement with those predicted by the electrostatic approximation. In the strong magnetic field regime the two−stream spectrum is found to be much narrower in angle than predicted by the electrostatic approximation. In the moderate and strong magnetic field regime the growth rate of waves propagating at large angles with respect to the beam are independent of beam energy.

Vacuum propagation of solid relativistic electron beams

An investigation of equilibrium, stability, and space‐charge‐ limiting current of a solid relativistic beam propagating along a finite external magnetic field has been carried out and compared with experiments. The concept of a rigid‐rotor equilibrium is only approximately valid when the beam current is much less than the Alfven critical current. Typically, low‐voltage beams rotate fastest at the beam edge whereas high‐voltage beams rotate fastest near the beam axis. A limited investigation of the rigid rotor stability condition indicates, at worst, a weak instability may be present if the rigid‐rotor equilibrium is artificially imposed, and no instability at all for a self‐consistent equilibrium. Numerical solutions for the space‐charge limiting current and relativistic factor on axis are presented and compared with two‐dimensional, cylindrical, space‐ and time‐dependent simulations. Analytical expressions for the limiting current are valid for ωc/ωb≳5, where ωc is the cyclotron frequency and ωb is the b...

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.

Filamentation instability of a radially finite relativistic electron beam

A study of the filamentation of a radially bounded relativistic electron beam propagating through a background plasma is presented. Through a careful consideration of all relevant boundary terms, both geometrically modified bulk as well as surface waves are exhibited. Approximate formulae for the growth rates of the two species of modes are derived. While no finite geometry effects arise to vitiate the stability criteria previously derived for the bulk modes in the homogeneous case, that found for the surface modes is slightly more stringent. Stability requires an external magnetic field twice as strong as that predicted by previous analyses. This added stringency is created by additional terms in the boundary conditions, which are displayed here for the first time. Selected numerical results demonstrate that the filamentation instability is unlikely to be the source of the strong beam disruption observed in recent experiments.

Characterization and suppression of zero‐frequency cyclotron waves on relativistic electron beams

Zero‐frequency cyclotron waves, which can be excited by a variety of static perturbations, produce large‐scale disruption of relativistic electron beam equilibria. A study of their basic nonlinear properties and an examination of methods with which to achieve their effective suppression are presented. A simple set of envelope equations based on the signal‐particle equations of motion is derived. Both analytic and numerical solutions are obtained for the case of a uniform magnetic guide field. The envelope equations are then used to investigate methods of suppression. It is found that although a spatially steeply rising magnetic field is a key component in achieving such suppression, initial beam momentum flaring plays a crucial role. Relativistic, fully electromagnetic particle‐in‐cell simulations designed to examine methods of suppression are presented.

Simulation of slow cyclotron wave growth on a scattered relativistic electron beam

Simulations demonstrating effective growth of slow cyclotron waves on a beam exhibiting a scattered distribution of particle velocities are described. No dramatic changes from the cold beam results for the dispersive properties are observed, but significant modifications of radial eigenmode structure appear.

A Phase Modulated Collective Ion Accelerator

The possibility of constructing compact, highcurrent traveling wave ion accelerators through employment of relativistic electron beam collective modes has been suggested often in recent years. A new mechanism based upon temporal modulation of the beam kinetic energy has been studied by us, using both analytic and numerical tools. Preliminary linear studies for the slow cyclotron beam mode indicate that such a mechanism can yield efficient acceleration to ion velocities of roughly 0.5 c in a simple, straight-walled waveguide. Numerical simulations have been performed to verify the theory and investigate nonlinear wave/particle interactions.

A Computational Study of One Aspect of Autoresonant Acceleration

Excitation and suppression of zero-frequency cyclotron waves on a relativistic electron beam in a parameter regime appropriate to autoresonant collective ion acceleration are examined through numerical simulation. The excitation mechanism considered is that of anode shorting, while suppression is achieved through a combination of nonadiabatic change in the guide magnetic field and the introduction of a finite radial velocity divergence in the beam. Some brief remarks are included concerning the effect of a scattered beam distribution.

Multidimensional theory of the inhomogeneous beam‐plasma instability

A combined analytic and numerical study of the effect of a plasma density gradient on the beam‐plasma instability is presented. After a thorough discussion of the qualitative aspects of this problem, emphasis is placed on the development of a theory which can reveal the interplay between the gradient and the multidimensional aspects of the instability. Using fluid equations, a differential equation is derived for the electrostatic potential. An integral representation for the solution of this equation is derived and its asymptotic evaluation presented. Explicit comparison is made between this asymptotic result and a direct numerical integration of the basic equations. The predictions of the theory are presented for the two‐dimensional case, both for the case in which the beam propagates along the direction of the gradient and for that in which the beam is propagating at an angle to this direction. Some brief remarks are made concerning the fully three‐dimensional case.