Patches of electrons and electron sheets for the 1-D Vlasov-Poisson equation
Thesis/Dissertation
·
OSTI ID:5537405
The author studies two classes of weak solutions for the 1-D Vlasov-Poisson equation describing plasma flows - patches of electrons and electron sheets. These solutions are analogous to patches of vorticity and vortex sheets for the 2-D vorticity equation. First, the existence of a given electron density is proved. It is shown that the corresponding flow map is Lipschitz continuous globally in time - so any initially smooth curve evolving with the flow remains rectifiable. Then the contour dynamics equation is derived for evolution of the boundaries z ({alpha}, t) of electron layers. The existence and uniqueness of smooth z({alpha}, t) is proved up to the time t{asterisk} of folding formation. The author designs a numerical method, proves its second-order convergence, and computes several numerical solutions. Finally, he derives equations for evolution of regularized and limit electron sheets. He designs numerical methods, proves their second-order convergence, and computes several numerical solutions. He derives a large class of exact solutions z ({alpha}, t).
- Research Organization:
- California Univ., Berkeley, CA (USA)
- OSTI ID:
- 5537405
- Country of Publication:
- United States
- Language:
- English
Similar Records
Two methods for the study of vortex patch evolution on locally refined grids
On long time asymptotics of the Vlasov-Poisson-Boltzmann equation
Higher order vortex methods with rezoning
Thesis/Dissertation
·
Sun May 01 00:00:00 EDT 1994
·
OSTI ID:10165790
On long time asymptotics of the Vlasov-Poisson-Boltzmann equation
Journal Article
·
Mon Dec 31 23:00:00 EST 1990
· Communications in Partial Differential Equations; (United States)
·
OSTI ID:5354948
Higher order vortex methods with rezoning
Technical Report
·
Sun May 01 00:00:00 EDT 1988
·
OSTI ID:7193992