Theory of the resistive hose instability in relativistic electron beams

Journal Article · Fri Aug 01 04:00:00 EDT 1980 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.863170· OSTI ID:5152126

Uhm, H S; Lampe, M

A theory of the resistive hose instability is developed for an infinitely long relativistic electron beam propagating parallel to an applied axial magnetic field. Complete space-charge neutralization by the ambient plasma and paraxial flow (p/sup 2//sub z/>>p/sup 2//sub r/+p/sup 2//sub theta/) are assumed. An integro-differential eigenvalue equation is derived from Vlasov--Maxwell theory for the general case, and this equation is reduced to an ordinary differential equation by using a model in which the class of beam electrons with a given transverse energy displaces as a rigid component. The model introduced spread betatron frequency in a natural way that includes correlations to radial position. Using a variational technique, an approximate dispersion relation is found for arbitrary density profile and is evaluated in closed form for either the Bennett or square profile. Stability properties are illustrated and discussed in detail for a square profile, including the influence of the applied magnetic field (stabilizing), proximity to a conducting guide (stabilizing), and partial current neutralization (destabilizing).

• Research Organization: Naval Surface Weapons Center, White Oak, Silver Spring, Maryland 20910
• OSTI ID: 5152126
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 23:8; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700107* -- Fusion Energy-- Plasma Research-- Instabilities
BEAM-PLASMA SYSTEMS
BEAMS
BOLTZMANN-VLASOV EQUATION
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
EIGENVALUES
ELECTRON BEAMS
ENERGY RANGE
EQUATIONS
HOSE INSTABILITY
INSTABILITY
LEPTON BEAMS
MAGNETIC FIELDS
MAXWELL EQUATIONS
NORMAL-MODE ANALYSIS
PARTICLE BEAMS
PLASMA INSTABILITY
PLASMA MICROINSTABILITIES
RELATIVISTIC RANGE
VARIATIONAL METHODS