THE WATER BAG MODEL
The Vlasov equation describes the motion of an ideal incompressible fluid in a 2N-dimensional (q,p) phase space where q and p are N-dimensional canonical coordinate and momentum vectors. The configuration of this phase fluid is represented by a distribution function f(q,p) which evolves with time according to the equation where V = dq/dt and F = dp/dt. The force per unit mass F is obtained by solving a field equation and may be determined partly be external sources and partly by internal sources that are functionals of f itself. The example discussed in this paper is that of a two- dimensional electron phase fluid neutralized by a uniform positive background charge. The acceleration alpha - (e/m)E(x,t) is independent of density and is due to an electric field E that satisfies Poisson's equation: where omega-p**2 = (4pin-oe**2)/m, e is the electronic charge m the electronic mass, n-o the mean particle density, and 2V a normalization factor. In the "water bag model", an analytic calculation of the behavior of electron beams, in which a bounded region of uniform density evolves as an incompressible fluid in phase space, the curves become stretched and distorted as the motion proceeds, our program therefore adds extra points in order to maintain accuracy. Eventually the calculation terminates (slowness of the computation or to lack of storage space) until this point is reached the water bag technique is capable of considerable accuracy at a small cost in computer time, and therefore it provides a useful addition to the other methods that are available.
Bibliographic Reference: PUBLISHED IN "METHODS IN COMPUTATIONAL PHYSICS", VOL. 9 (1970), PP. 87-134 BY ACADEMIC PRESS, NEW YORK (USA)
Record Number: 1989125022000 / Last updated on: 1987-02-01
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