Lyapunov stability of relativistic fluids and plasmas

Journal Article · Tue Dec 31 23:00:00 EST 1985 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.865952· OSTI ID:6280424

Holm, D D; Kupershmidt, B A

Lyapunov stability of relativistic ideal fluid and plasma equilibria is studied analytically using the energy-Casimir method. Two- and three-dimensional relativistic equilibria in a fixed bounded domain are investigated within the framework of the macroscopic multifluid plasma model. Linearized Lyapunov stability conditions and stability norms are given, accounting for warm-plasma effects as well as relativistic and electromagnetic effects. The resulting Lyapunov stability conditions are compared to spectral stability analyses for relativistic cold plasmas in various examples and special cases, including (1) non-neutral electron flow in a planar diode and (2) circularly symmetric plasma flow enclosed in a coaxial waveguide. These linearized stability results can be extended readily to nonlinear Lyapunov stability conditions for finite-amplitude perturbations by employing standard convexity arguments for the Lyapunov functions given here. The relativistic stability conditions are shown to reduce either to their nonrelativistic counterparts or to trivial identities in the nonrelativistic limit.

• Research Organization: Center for Nonlinear Studies and Theoretical Division, MS B284, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 6280424
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 29:1; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANALYTICAL SOLUTION
ANNULAR SPACE
CONFIGURATION
DIODE TUBES
ELECTRON TUBES
ENERGY RANGE
FLUIDS
LYAPUNOV METHOD
PLASMA
PLASMA DRIFT
PLASMA SIMULATION
RELATIVISTIC PLASMA
RELATIVISTIC RANGE
SIMULATION
SPACE
STABILITY
THERMIONIC DIODES
THERMIONIC TUBES
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
WAVEGUIDES