A STUDY OF THE STABILITY OF A RELATIVISTIC PARTICLE BEAM PASSING THROUGH A PLASMA

Technical Report · Mon Oct 01 04:00:00 EDT 1962

DOI:https://doi.org/10.2172/4749414· OSTI ID:4749414

Mjolsness, R C

The disperslon law is derived for small amplitude disturbances of the spatially non-uniform steady state conflguratuon of a relativistic particle beam of finite cross section and infinite length passing through a low temperature dense plasma. First, a macroscopic analysis is given in which Maxwell's equatlons are supplemented by fluid equations for the beam and plasma effects are accounted for by means of a scalar conductivity. A more realistic treatment of the plasma is then obtained by introducing a variable tensor conductivity and appropriate boundary conditions, permitting the effects of Hall currents, density and temperature gradients, and metal walls to be assessed. Finally, the analysis is refined by treating the beam particles by means of the collisionless Boltzmann equation while maintaining the scalar conductivity description of the plasma. Use of the orbit integral technique for solving the Boltzmann equation permits the perturbed beam current to be expressed as an integral over the perturbed field variables, and the relativistic dynamics and the geometry of the configuration greatly increase the tractability of the expressions. Introduction of appropriate Hankel transforms of the field variables leads to an integral form for Maxwell's equations and to the expression of the stability problem as a set of three linear, coupled integral equations. A formal solution of these equations is given, and the dispersion relation is seen to appear as a solvability condition for the equations. Asymptotic evaluations of the formal expressions are given for the case of low frequency, long wavelength disturbances and high frequency, highly localized disturbances. 55 references. (auth)

• Research Organization: Los Alamos Scientific Lab., N. Mex.; and Princeton Univ., N.J. Palmer Physical Lab.
• DOE Contract Number: W-7405-ENG-36
• NSA Number: NSA-17-015345
• OSTI ID: 4749414
• Report Number(s): LA-2802
• Country of Publication: United States
• Language: English

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BEAMS
BESSEL FUNCTIONS
BIBLIOGRAPHY
BOLTZMANN EQUATION
BOUNDARY CONDITIONS
CONFIGURATION
CROSS SECTIONS
CURRENTS
DENSITY
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
DISPERSION THEORY
ELECTRIC CONDUCTIVITY
ELECTRODYNAMICS
ELECTROMAGNETISM
ELEMENTARY PARTICLES
EQUATIONS
FIELD THEORY
FLUID FLOW
FREQUENCY
HALL EFFECT
INTEGRALS
MATHEMATICS
MAXWELL EQUATIONS
MECHANICS
METALS
ORBITS
PARTICLES
PHYSICS
PLASMA
QUANTUM MECHANICS
RELATIVITY THEORY
SCATTERING
SCATTERING AMPLITUDE
STABILITY
TEMPERATURE
TENSORS
THERMODYNAMICS
TRANSPORT THEORY
VECTORS
VESSELS