Theory of the resistive hose instability in relativistic electron beams. Memorandum report

Technical Report · Mon Nov 26 04:00:00 EST 1979

OSTI ID:5057123

Uhm, H S; Lampe, M

A Vlasov-Maxwell 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(z)/sup 2/ >> p(r) /sup 2/ + p(theta)/sup 2/) are assumed. The analysis is performed for rigid-rotor and cold laminar flow equilibria. An integro-differential eigenvalue equation is obtained for the general case, and is reduced to an ordinary differential equation in either the cold laminar flow limit or the case of a square beam density profile. Using a variational technique, an approximate dispersion relation is found for arbitrary density profile, and 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 Research Lab., Washington, DC (USA)
• OSTI ID: 5057123
• Report Number(s): AD-A-078189
• Country of Publication: United States
• Language: English

Related Subjects

640301* -- Atomic
Molecular & Chemical Physics-- Beams & their Reactions
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BEAMS
BOLTZMANN-VLASOV EQUATION
BOUNDARY LAYERS
DENSITY
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
ELECTRON BEAMS
ENERGY RANGE
EQUATIONS
FLUID FLOW
HOSE INSTABILITY
HYPOTHESIS
INSTABILITY
LAMINAR FLOW
LAYERS
LEPTON BEAMS
MAGNETIC FIELDS
PARTICLE BEAMS
PHYSICAL PROPERTIES
PLASMA INSTABILITY
PLASMA MICROINSTABILITIES
RELATIVISTIC RANGE
VARIATIONS
WALLS