Non-Maxwellian distribution functions in flaring coronal loops. Comparison of Landau-Fokker-Planck and BGK solutions

Solar Physics ◽  
1988 ◽  
Vol 117 (1) ◽  
pp. 123-133 ◽  
Author(s):  
N. N. Ljepojevic ◽  
P. MacNeice
Keyword(s):  
Distribution Functions ◽  
Maxwellian Distribution ◽  
Coronal Loops ◽  
Fokker Planck

scholarly journals Non-Linear Langevin and Fractional Fokker–Planck Equations for Anomalous Diffusion by Lévy Stable Processes

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 760 ◽  
Author(s):  
Johan Anderson ◽  
Sara Moradi ◽  
Tariq Rafiq
Keyword(s):  
Anomalous Diffusion ◽  
Transport Coefficient ◽  
Numerical Solutions ◽  
Distribution Functions ◽  
Space Distribution ◽  
Non Linear ◽  
Non Local ◽  
Local Transport ◽  
Fokker Planck Equations ◽  
Fokker Planck

The numerical solutions to a non-linear Fractional Fokker–Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degrees of fractionality of the stable Lévy distribution as solutions to the FFP equation. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy and modified transport coefficient. The transport coefficient significantly increases with decreasing fractality which is corroborated by analysis of experimental data.

scholarly journals Measuring heat flux from collective Thomson scattering with non-Maxwellian distribution functions

2019 ◽  
Vol 26 (3) ◽  
pp. 032104 ◽  
Author(s):  
R. J. Henchen ◽  
M. Sherlock ◽  
W. Rozmus ◽  
J. Katz ◽  
P. E. Masson-Laborde ◽  
...  
Keyword(s):  
Heat Flux ◽  
Thomson Scattering ◽  
Distribution Functions ◽  
Maxwellian Distribution ◽  
Collective Thomson Scattering

Comparison Between Theoretical Values and Simulation Results of Transport Coefficients for the Dissipative Particle Dynamics Method

2004 ◽  
Author(s):  
Akira Satoh
Keyword(s):  
Transport Coefficients ◽  
Dissipative Particle Dynamics ◽  
Planck Equation ◽  
Equation Of Motion ◽  
Particle Dynamics ◽  
Momentum Conservation ◽  
Distribution Functions ◽  
Fokker Planck Equation ◽  
Dynamics Method ◽  
Fokker Planck

In the present study, we have derived an expression for transport coefficients such as viscosity, from the equation of motion of dissipative particles. In the concrete, we have shown the Fokker-Planck equation in phase space, and macroscopic conservation equations such as the equation of continuity and the equation of momentum conservation. The basic equations of the single-particle and pair distribution functions have been derived using the Fokker-Planck equation. The solutions of these distribution functions have approximately been solved by the perturbation method under the assumption of molecular chaos. The expression of the viscosity due to dissipative forces has been obtained using the approximate solutions of the distribution functions. Also, we have conducted non-equilibrium dynamics simulations to investigate the influence of the parameters, which have appeared in defining the equation of motion in the dissipative particle dynamics method.

Effects of Landau Damping and Collision on Stimulated Raman Scattering with Various Phase-Space Distributions

2021 ◽  
Author(s):  
Shanxiu XIE ◽  
Yong CHEN ◽  
Junchen YE ◽  
Yugu CHEN ◽  
Na PENG ◽  
...  
Keyword(s):  
Growth Rate ◽  
Raman Scattering ◽  
Stimulated Raman Scattering ◽  
Deep Understanding ◽  
Distribution Functions ◽  
Maxwellian Distribution ◽  
Landau Damping ◽  
Hot Electron ◽  
Collisional Damping ◽  
Stimulated Raman

Abstract Stimulated Raman scattering (SRS) is one of the main instabilities affecting the success of the fusion ignition. Here, we study the relationship between Raman growth and Landau damping with various distribution functions combining the analytic formulas and Vlasov simulations. The Landau damping obtained by Vlasov-Poisson simulation and Raman growth rate obtained by Vlasov-Maxwell simulation are anti-correlated, which is consistent with our theoretical analysis quantitatively. Maxwellian distribution, flattened distribution, and bi-Maxwellian distribution are studied in detail, which represent three typical stages of SRS. We have also demonstrated the effects of plateau width, hot-electron fraction, hot-to-cold electron temperature ratio, and collisional damping on the Landau damping and growth rate. It gives us a deep understanding of SRS and possible ways to mitigate SRS through manipulating distribution functions to a high Landau damping regime.

scholarly journals FOKKER–PLANCK EQUATION FOR FRACTIONAL SYSTEMS

2007 ◽  
Vol 21 (06) ◽  
pp. 955-967 ◽  
Author(s):  
VASILY E. TARASOV
Keyword(s):  
Phase Space ◽  
Power Systems ◽  
Fractional Power ◽  
Planck Equation ◽  
Distribution Functions ◽  
Fractional Integrals ◽  
Fractional Systems ◽  
Fokker Planck Equation ◽  
Bogoliubov Equations ◽  
Fokker Planck

The normalization condition, average values, and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A fractional (power) system is described by the fractional powers of coordinates and momenta. These systems can be considered as non-Hamiltonian systems in the usual phase space. The generalizations of the Bogoliubov equations are derived from the Liouville equation for fractional (power) systems. Using these equations, the corresponding Fokker–Planck equation is obtained.

Sign in / Sign up

Export Citation Format

Share Document