Kinetic effects on Alfven wave nonlinearity. II. The modified nonlinear wave equation

Journal Article · Thu Feb 01 04:00:00 EST 1990 · Physics of Fluids B; (USA)

DOI:https://doi.org/10.1063/1.859329· OSTI ID:7163570

Spangler, S R ^[1]

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1. Department of Physics and Astronomy The University of Iowa, Iowa City, Iowa 52242 (USA)

The study of kinetic effects on Alfven wave nonlinearity is continued. Previously obtained expressions for the perturbed (by an Alfven wave) ion and electron distribution functions are used to obtain a nonlinear wave equation for parallel-propagating, circularly polarized waves. The results are cast in the form of a modified version of the familiar derivative nonlinear Schroedinger equation. The approach in obtaining this equation is a hybrid one; fluid theory is used to the greatest extent possible, and kinetic theory is introduced where the correction is believed to be most important. Fluid theory at two levels of sophistication is employed. The first uses a simple scalar pressure term. This approach yields physical insight and illuminates the field-aligned fluid flow and the associated plasma density perturbation as a major contributor to Alfven wave nonlinearity. The second approach employs a tensor pressure term that in general will be necessary. The results indicate that kinetic effects in general produce a nonlinear wave equation that is of a different functional form than the derivative nonlinear Schroedinger equation, as previously reported by Mjolhus and Wyller (Phys. Scr. {bold 33}, 442 (1986); J. Plasma Phys. {bold 40}, 229 (1988)). The coefficient of the derivative cubic term depends on the plasma beta in a way which, in general, is quite different from the fluid expression. In addition, a functionally novel term appears in the modified equation. The magnitude of this term, named the nonlocal term'' by Mjolhus and Wyller, can be large when the plasma beta is comparable to unity. The susceptibility of the modified equation to modulational instability is studied. Kinetic effects cause modulational instability of wave packets, even when fluid theory would predict modulational stability. This modulational instability occurs for both right- and left-hand polarized waves.

• OSTI ID: 7163570
• Journal Information: Physics of Fluids B; (USA), Journal Name: Physics of Fluids B; (USA) Vol. 2:2; ISSN 0899-8221; ISSN PFBPE
• Country of Publication: United States
• Language: English

Related Subjects

640107* -- Astrophysics & Cosmology-- Planetary Phenomena
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALFVEN WAVES
CHARGED PARTICLES
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
ELECTRONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
FLUID FLOW
FUNCTIONS
HYDROMAGNETIC WAVES
IONS
LEPTONS
MAGNETIC FIELDS
MODIFICATIONS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
PLASMA DENSITY
PLASMA PRESSURE
POLARIZATION
SCALARS
SCHROEDINGER EQUATION
WAVE EQUATIONS
WAVE PROPAGATION