Exact evaluation of the quadratic longitudinal response function for an unmagnetized Maxwellian plasma

Journal Article · Sun Jul 15 04:00:00 EDT 2012 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4737603· OSTI ID:22072551

Layden, B; Cairns, Iver H; Robinson, P A ^[1]; Percival, D J ^[2]

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1. School of Physics, University of Sydney, Sydney, NSW 2006 (Australia)
2. Defence Science and Technology Organisation, P.O. Box 1500, Edinburgh, SA 5111 (Australia)

The quadratic longitudinal response function describes the second-order nonlinear response of a plasma to electrostatic wave fields. An explicit expression for this function in the weak-turbulence regime requires the evaluation of velocity-space integrals involving the velocity distribution function and various resonant denominators. Previous calculations of the quadratic longitudinal response function were performed by approximating the resonant denominators to facilitate the integration. Here, we evaluate these integrals exactly for a non-relativistic collisionless unmagnetized isotropic Maxwellian plasma in terms of generalized plasma dispersion functions, and correct certain aspects of expressions previously derived for these functions. We show that in the appropriate limits the exact expression reduces to the approximate form used for interactions between two fast waves and one slow wave, such as the electrostatic decay of Langmuir waves into Langmuir waves and ion sound waves, and the scattering of Langmuir waves off thermal ions.

• OSTI ID: 22072551
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 7 Vol. 19; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
COLLISIONLESS PLASMA
DISPERSION RELATIONS
DISTRIBUTION FUNCTIONS
EXACT SOLUTIONS
INTEGRALS
ISOTROPY
LANGMUIR FREQUENCY
NONLINEAR PROBLEMS
PLASMA WAVES
RESPONSE FUNCTIONS
SCATTERING
SOUND WAVES
TURBULENCE