Nonlinear stability theorem for rotating coherent structures in a non-neutral plasma column
- Plasma Physics Laboratory, Princeton University, Princeton, New Jersey (USA)
- Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts (USA)
A nonlinear stability theorem is developed for arbitrary-amplitude, two-dimensional coherent structures, {ital n}{sub {ital R}}({theta} {minus} {omega}{sub {ital r}} {ital t}) and {phi}{sub {ital R}}({theta} {minus} {omega}{sub {ital r}} {ital t}), in a strongly magnetized, low-density ({omega}{sup 2}{sub {ital pe}}/{omega}{sup 2}{sub {ital ce}} {much lt} 1) non-neutral plasma column confined radially by a uniform axial magnetic field {ital B}{sub 0}{cflx e}{sub z}. Here, a grounded, perfectly conducting, cylindrical wall is located at radius {ital r} = {ital r}{sub {ital w}}, and {omega}{sub {ital r}} = const is the angular rotation velocity of the coherent structures about the cylinder axis ({ital r}=0). A cold-fluid guiding-center model based on the continuity-Poisson equations is used to describe the nonlinear evolution of the electron density {ital n}{sub {ital e}}({ital r},{theta},{ital t}) = {ital n}{sub {ital R}} + {delta}{ital n}{sub {ital e}} and electrostatic potential {phi}({ital r},{theta},{ital t}) = {phi}{sub {ital R}} + {delta}{phi}. Making use of global (spatially averaged) nonlinear conservation constraints, it is shown that {partial derivative}{ital n}{sub {ital R}}({psi}{sub {ital R}})/{partial derivative}{psi}{sub {ital R}} {le} 0 is a sufficient condition for nonlinear stability of the rotating equilibrium state ({phi}{sub {ital R}},{ital n}{sub {ital R}}) to arbitrary-amplitude perturbations {delta}{ital n}{sub {ital e}} and {delta}{phi}.
- OSTI ID:
- 5299977
- Journal Information:
- Physics of Fluids B; (United States), Journal Name: Physics of Fluids B; (United States) Vol. 3:9; ISSN 0899-8221; ISSN PFBPE
- Country of Publication:
- United States
- Language:
- English
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