Statistical Models of Power-law Distributions in Homogeneous Plasmas
- Space Sciences Laboratory, University of California, Berkeley, CA 94720 (United States)
A variety of in-situ measurements in space plasmas point out to an intermittent formation of distribution functions with elongated tails and power-law at high energies. Power-laws form ubiquitous signature of many complex systems, plasma being a good example of a non-Boltzmann behavior for distribution functions of energetic particles. Particles, which either undergo mutual collisions or are scattered in phase space by electromagnetic fluctuations, exhibit statistical properties, which are determined by the transition probability density function of a single interaction, while their non-asymptotic evolution may determine the observed high-energy populations. It is shown that relaxation of the Brownian motion assumptions leads to non-analytical characteristic functions and to generalization of the Fokker-Planck equation with fractional derivatives that result in power law solutions parameterized by the probability density function.
- OSTI ID:
- 21510089
- Journal Information:
- AIP Conference Proceedings, Vol. 1320, Issue 1; Conference: Festschrift on modern challenges in nonlinear plasma physics: Honoring the career of Dennis Papadopoulos, Halkidiki (Greece), 15-19 Jun 2010; Other Information: DOI: 10.1063/1.3544343; (c) 2010 American Institute of Physics; ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ASYMPTOTIC SOLUTIONS
BROWNIAN MOVEMENT
COLLISIONS
DIFFUSION
DISTRIBUTION
DISTRIBUTION FUNCTIONS
FLUCTUATIONS
FOKKER-PLANCK EQUATION
FUNCTIONAL ANALYSIS
HOMOGENEOUS PLASMA
INTERACTIONS
PARTICLES
PHASE SPACE
PROBABILITY
PROBABILITY DENSITY FUNCTIONS
RELAXATION
STATISTICAL MODELS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MATHEMATICAL MODELS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
SPACE
VARIATIONS