scholarly journals On application of stochastic differential equations for simulation of nonlinear wave–particle resonant interactions

2021 ◽  
Vol 28 (9) ◽  
pp. 092904
Author(s):  
A. S. Lukin ◽  
A. V. Artemyev ◽  
A. A. Petrukovich
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Nonlinear Wave ◽  
Resonant Interactions

Stochastic differential equations for modeling of nonlinear wave-particle interaction

2021 ◽  
Author(s):  
Alexander Lukin ◽  
Anton Artemyev ◽  
Anatoly Petrukovich
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Nonlinear Wave ◽  
Inhomogeneous Plasma ◽  
Electron Distribution Function ◽  
Wave Spectrum ◽  
Particle Interaction ◽  
Resonant Interaction ◽  
Radiation Belts ◽  
Model Parameters

<p>The charged particle resonant interaction with electromagnetic waves propagating in an inhomogeneous plasma determines the dynamics of plasma populations in various space plasma systems, such as shock waves, radiation belts, and plasma injection regions. For systems with small wave amplitudes and a broad wave spectrum, such resonant interaction is well described within a framework of the quasi-linear theory, which is based on the Fokker-Planck diffusion equation. However, in systems with intense waves, this approach is inapplicable, because nonlinear resonant effects (such as phase bunching and phase trapping) and non-diffusive processes play an essential role in the acceleration and scattering of charged particles. In this work we consider a generalized approach for modelling of wave-particle resonant interaction for intense coherent waves. This approach is based on application of stochastic differential equations for simulation resonant scattering and trapping. To test and verify an applicability of this approach, we use a simple model system with high-amplitude electrostatic whistler waves and energetic electrons propagating in the Earth radiation belts. We show that the proper determination of the model parameters allows us to describe the dynamics of the electron distribution function evolutions dominated by nonlinear resonant effects. Moreover, the proposed approach significantly reduces the calculation time in comparison with test particles methods generally used for simulations of nonlinear wave-particle interactions.</p>

Stochastic Differential Equations for Power Law Behaviors

2012 ◽  
Author(s):  
Bo Jiang ◽  
Roger Brockett ◽  
Weibo Gong ◽  
Don Towsley
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Power Law

scholarly journals Strong Solution Existence for a Class of Degenerate Stochastic Differential Equations

2020 ◽  
Vol 53 (2) ◽  
pp. 2220-2224
Author(s):  
William M. McEneaney ◽  
Hidehiro Kaise ◽  
Peter M. Dower ◽  
Ruobing Zhao
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Strong Solution ◽  
Solution Existence
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