A kinetic theory of the extraordinary-mode perturbations in cylindrical relativistic magnetrons

Journal Article · Sun Mar 01 04:00:00 EST 1992 · Physics of Fluids B; (United States)

DOI:https://doi.org/10.1063/1.860217· OSTI ID:5130908

Uhm, H S ^[1]

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1. Naval Surface Warfare Center, 10903 New Hampshire Avenue, White Oak, Silver Spring, Maryland 20903-5000 (United States)

Stability properties of the extraordinary-mode perturbations in a relativistic electron flow generated inside a cylindrical magnetron are investigated within the framework of the linearized Vlasov--Maxwell equations. The stability analysis is carried out under the assumptions that the layer is thin and relatively tenuous, and that the phase velocity of the perturbed waves is very close to the mean drift velocity of the layer. The perturbed distribution function of the extraordinary-mode perturbations is calculated by integrating along the electron orbit. The eigenvalue equation is derived and solved separately in the vacuum and layer regions by properly matching boundary conditions at the inter-regional surface. Solution in the vacuum region includes the resonator and cylindrical curvature effects. A closed algebraic dispersion relation is obtained for the synchronous modes, whose phase velocity is very close to the mean drift velocity of the layer. Analytical investigation of the dispersion relation is carried out for the resonance modes, whose eigenfrequency is very close to the vacuum modes in the magnetron circuit. The necessary and sufficient condition for instability is obtained for the resonance modes. It is shown that typical growth rates of the instability are a few percent of the electron cyclotron frequency.

• OSTI ID: 5130908
• Journal Information: Physics of Fluids B; (United States), Journal Name: Physics of Fluids B; (United States) Vol. 4:3; ISSN 0899-8221; ISSN PFBPE
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700330* -- Plasma Kinetics
Transport
& Impurities-- (1992-)
700340 -- Plasma Waves
Oscillations
& Instabilities-- (1992-)
700350 -- Plasma Production
Heating
Current Drive
& Interactions-- (1992-)
ANALYTICAL SOLUTION
BOUNDARY CONDITIONS
CONFIGURATION
CYCLOTRON FREQUENCY
CYLINDRICAL CONFIGURATION
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
DISTRIBUTION FUNCTIONS
EIGENVALUES
ELECTRON DENSITY
ELECTRON TUBES
ELECTRONIC EQUIPMENT
ENERGY RANGE
EQUATIONS
EQUIPMENT
FUNCTIONS
INSTABILITY GROWTH RATES
KINETIC EQUATIONS
MAGNETRONS
MAXWELL EQUATIONS
MICROWAVE EQUIPMENT
MICROWAVE TUBES
ORBITS
PARTIAL DIFFERENTIAL EQUATIONS
PHASE VELOCITY
RELATIVISTIC RANGE
VELOCITY