CONTINUITY BETWEEN A SOLUTION OF THE VLASOV EQUATION IN ONE DIMENSION AND THE MOVEMENT OF A SYSTEM OF PARTICLES
Among the extensive work done in recent years to derive Kinetic equations rigorously, the Vlasov equation affords a very interesting case, as it is possible to dispense with statistical assumptions on the initial microscopic state. Indeed it was shown by several authors that, given a solution of the Vlasov equation, a system of a large number of particles could be found so that its exact motion remained close, in a certain sense, to the Vlasov distribution function. These derivations were made, however, by smoothing out the Coulomb force at short distances. Whereas the 3 dimensional problem with the true Coulomb force appears very difficult, the one dimensional problem is much easier. A derivation is presented in this report for the latter case, by using the true one dimensional equivalent of the Coulomb force, i.e., a constant repulsive force between two points, the singularity being a change of sign of the force at the position of the point producing it. The discrepancy between a distribution function in phase space f(x,v) and a set of points (x-i,v-i) is measured simply by comparing the double primitive integrals A(x,v) dxdv, between limits alpha to X and alpha to V, dxdv to the number of points x-i LAMBDA X and v-i LAMBDA V.
Bibliographic Reference: AVAILABILITY: WRITE TO CEA MENTIONING REPORT EUR-CEA-FC-1222 FR, 1984
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Record Number: 1989123082500 / Last updated on: 1987-01-01
Available languages: fr