scholarly journals An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks

2021 ◽  
pp. 110772
Author(s):  
L. Chacón ◽  
D. Daniel ◽  
W.T. Taitano
Keyword(s):  
Kinetic Equation ◽  
Runaway Electron ◽  
Asymptotic Preserving

Comparison of relativistic runaway electron avalanche rates obtained from Monte Carlo simulations and kinetic equation solution

2001 ◽  
Vol 29 (3) ◽  
pp. 430-438 ◽  
Author(s):  
L.P. Babich ◽  
E.N. Donskoy ◽  
I.M. Kutsyk ◽  
A.Yu. Kudryavtsev ◽  
R.A. Roussel-Dupre ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Kinetic Equation ◽  
Monte Carlo Simulations ◽  
Runaway Electron ◽  
Electron Avalanche ◽  
Equation Solution

scholarly journals An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena

2018 ◽  
Vol 9 (2) ◽  
pp. 61-75
Author(s):  
Abdelghani Bellouquid ◽  
Jacques Tagoudjeu
Keyword(s):  
Kinetic Equation ◽  
Kinetic Model ◽  
Small Parameter ◽  
Kinetic Models ◽  
Numerical Approach ◽  
Test Cases ◽  
Equivalent Formulation ◽  
Asymptotic Preserving ◽  
Standard Methods ◽  
Asymptotic Preserving Scheme

Abstract In this paper, we propose a numerical approach to solve a kinetic model of chemotaxis phenomena. This scheme is shown to be uniformly stable with respect to the small parameter, consistent with the uid-di usion limit (Keller-Segel model). Our approach is based on the micro-macro decomposition which leads to an equivalent formulation of the kinetic model that couples a kinetic equation with macroscopic ones. This method is validated by various test cases and compared to other standard methods.

scholarly journals On the relativistic large-angle electron collision operator for runaway avalanches in plasmas

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
O. Embréus ◽  
A. Stahl ◽  
T. Fülöp
Keyword(s):  
Growth Rate ◽  
Kinetic Equation ◽  
Electric Field ◽  
Runaway Electron ◽  
Large Angle ◽  
Collision Operator ◽  
Electron Collision ◽  
Runaway Electrons ◽  
Avalanche Effect ◽  
Coulomb Collisions

Large-angle Coulomb collisions lead to an avalanching generation of runaway electrons in a plasma. We present the first fully conservative large-angle collision operator, derived from the relativistic Boltzmann operator. The relation to previous models for large-angle collisions is investigated, and their validity assessed. We present a form of the generalized collision operator which is suitable for implementation in a numerical kinetic equation solver, and demonstrate the effect on the runaway-electron growth rate. Finally we consider the reverse avalanche effect, where runaways are slowed down by large-angle collisions, and show that the choice of operator is important if the electric field is close to the avalanche threshold.

Deep Impurities with Collision Delay

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Wave Function ◽  
Kinetic Equation ◽  
Elastic Scattering ◽  
Response Function ◽  
Plasma Oscillation ◽  
Impurity Scattering ◽  
Fermi Momentum ◽  
Screening Length ◽  
Plasma Mode ◽  
Dissipative Mechanism

The linearised nonlocal kinetic equation is solved analytically for impurity scattering. The resulting response function provides the conductivity, plasma oscillation and Fermi momentum. It is found that virial corrections nearly compensate the wave-function renormalizations rendering the conductivity and plasma mode unchanged. Due to the appearance of the correlated density, the Luttinger theorem does not hold and the screening length is influenced. Explicit results are given for a typical semiconductor. Elastic scattering of electrons by impurities is the simplest but still very interesting dissipative mechanism in semiconductors. Its simplicity follows from the absence of the impurity dynamics, so that individual collisions are described by the motion of an electron in a fixed potential.

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