Accession Number : AD0699957

Title :   DOUBLE LAPLACE TRANSFORMATION IN MIXED BOUNDARY-INITIAL VALUE PROBLEMS AND ITS APPLICATION TO MULTI-COMPONENT PLASMAS,

Corporate Author : ILLINOIS UNIV URBANA COORDINATED SCIENCE LAB

Personal Author(s) : Evans,Kenneth Edward , Jr

Report Date : DEC 1969

Pagination or Media Count : 93

Abstract : The application of the double Laplace transform (Laplace transformation in both space and time) to the solution of systems of linear, homogenous, hyperbolic, partial differential equations with real, constant coefficients is treated. The purpose of this treatment is to discuss comprehensively a method whereby the mixed boundary-initial value problem for these equations can be solved. The treatment is limited to one-dimensional systems. Certain features of the double Laplace transform method which appear in the solution of equations of the type described are examined in detail. Two of these features are the important role played by the characteristics of the partial differential equations and the restrictions among the boundary and initial conditions which are necessary for a well-defined solution. The method is applied to the moment equations for a multi-component plasma, and the connection between the general solution and the usual 'normal mode' solution is discussed. The case of a monoenergetic beam injected into a cold, semi-infinite plasma is treated in detail. The effect of the collisions of the plasma particles with the background is included. A solution for the growth of an initial thermal disturbance in the plasma is obtained. This treatment yields the first picture of the relationship between the temporal and spatial growth in a finite, unstable plasma. (Author)

Descriptors :   (*PLASMAS(PHYSICS), PARTIAL DIFFERENTIAL EQUATIONS), (*PARTIAL DIFFERENTIAL EQUATIONS, *INTEGRAL TRANSFORMS), BOUNDARY VALUE PROBLEMS, BOUNDARY VALUE PROBLEMS, ELECTRON BEAMS, STABILITY, THESES

Subject Categories : Numerical Mathematics
      Plasma Physics and Magnetohydrodynamics

Distribution Statement : APPROVED FOR PUBLIC RELEASE