Nonlinear BernsteinGreeneKruskal wave equilibria subject to global energy and momentum conservation constraints
Abstract
The class of BernsteinGreeneKruskal (BGK) solutions to the nonlinear VlasovPoisson equations are examined within the context of the conservation of (spatially averaged) number, momentum and total energy, imposed as ancillary global constraints that connect the final saturated BGK state to a specified initial distribution function f(x,v,O). While imposing three conservation constraints of course does not uniquely determine the final BGK state, it does not remove a large degree of ambiguity as to whether particular classes of solutions are accessible from given initial conditions. It also permits a determination of important features of the final BGK state (e.g., saturation amplitude, wave phase velocity, etc.) in terms of properties of the initial distribution functions.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 September 1982
 Bibcode:
 1982STIN...8314386D
 Keywords:

 Bernstein Energy Principle;
 Electron Beams;
 Nonlinear Equations;
 Wave Propagation;
 Conservation;
 Energy Transfer;
 Momentum;
 Poisson Equation;
 Vlasov Equations;
 Waveforms;
 Communications and Radar