Diffusion with varying drag; the runaway problem

Thesis/Dissertation · Wed Jan 01 04:00:00 EST 1986

OSTI ID:5319575

Rollins, D K

The motion of electrons in an ionized plasma of electrons and ions in an external electric field is studied. A probability distribution function describes the electron motion and is a solution of a Fokker-Planck equation. In zero field, the solution approaches an equilibrium Maxwellian. For arbitrarily small field, electrons overcome the diffusive effects and are freely accelerated by the field. This is the electron-runaway phenomenon. The electric field is treated as a small perturbation. Various diffusion coefficients are considered for the one dimensional problem, and the runaway current is determined as a function of the field strength. Diffusion coefficients, non-zero on a finite interval are examined. Some non-trivial cases of these can be solved exactly in terms of known special functions. The more realistic case where the diffusion coeffient decays with velocity are then considered. To determine the runaway current, the equivalent Schroedinger eigenvalue problem is analyzed. The smallest eigenvalue is shown to be equal to the runaway current. Using asymptotic matching, a solution can be constructed which is then used to evaluate the runaway current. The runaway current is exponentially small as a function of field strength. This method is used to extract results from the three dimensional problem.

• Research Organization: California Inst. of Tech., Pasadena (USA)
• OSTI ID: 5319575
• Country of Publication: United States
• Language: English

Related Subjects

640420* -- Fluid Physics-- Properties & Structure of Fluids-- (-1987)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
ELECTRIC FIELDS
ELECTRONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
FOKKER-PLANCK EQUATION
FUNCTIONS
LEPTONS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
RUNAWAY ELECTRONS