Linear longitudinal oscillations in collisionless plasma diodes with thin sheaths. Part I. Method
A method is proposed for treating linear longitudinal perturbations in one-dimensional collisionless plasma diodes with a uniform plasma region and thin electrode sheaths. The method is comprehensive in that it allows for very general equilibrium, initial, boundary, and external-circuit conditions. Upon Laplace-transforming the Vlasov and Poisson equations in both space and time, appropriate evaluation of all pertinent relations leads to a set of 2+2n/sub sigma/(n/sub sigma/ is the number of particle species) coupled integral equations in x and v for the following quantities (which are the time Laplace transforms of the respective physical perturbations): j/sub e/(..omega..) (external-circuit current density), E(x,..omega..) (electrostatic field), f/sup sigma//sub l/(v>0,..omega..), and f/sup sigma//sub r/(v<0,..omega..) (velocity distribution functions of the plasma-bound particles at the left- and right-hand plasma boundaries, respectively), where sigma is the species index. The formal solution of these integral equations and the inverse Laplace transformation (..omega -->..t) are discussed in general terms. In particular, it is shown that the intrinsic eigenfrequencies are given by the zeros of the coefficient determinant of the integral equations. A comparison with previous treatments is given, and it is concluded that extensions of the method proposed to more general systems should be feasible.
- Research Organization:
- Plasma Theory and Simulation Group, Electronics Research Laboratory, University of California, Berkeley, California 94720
- DOE Contract Number:
- AT03-76ET53064
- OSTI ID:
- 6731481
- Journal Information:
- Phys. Fluids; (United States), Vol. 27:7
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
COLLISIONLESS PLASMA
PLASMA WAVES
BOLTZMANN-VLASOV EQUATION
BOUNDARY CONDITIONS
CALCULATION METHODS
DISTRIBUTION FUNCTIONS
EIGENVALUES
ELECTRODES
EQUILIBRIUM
LAPLACE TRANSFORMATION
ONE-DIMENSIONAL CALCULATIONS
PLASMA SHEATH
POISSON EQUATION
THERMIONIC DIODES
DIFFERENTIAL EQUATIONS
DIODE TUBES
ELECTRON TUBES
EQUATIONS
FUNCTIONS
INTEGRAL TRANSFORMATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
THERMIONIC TUBES
TRANSFORMATIONS
700108* - Fusion Energy- Plasma Research- Wave Phenomena