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A Particle Method for the Multispecies Landau Equation
José A Carrillo1, Jingwei Hu2, Samuel Q Van Fleet2
1Mathematical Institute, University of Oxford, Oxford, OX2 6GG UK.
Acta Applicandae Mathematicae
|October 24, 2024
Summary
This study extends a particle method for plasma simulations to multiple species, ensuring conservation laws and Maxwellian equilibrium. The method demonstrates second-order accuracy for complex plasma dynamics.
Area of Science:
- Plasma Physics
- Computational Physics
- Kinetic Theory
Background:
- The Landau collision operator models grazing collisions in plasmas.
- A deterministic particle method exists for single-species Landau equation.
- This method uses regularization and Dirac delta functions.
Purpose of the Study:
- Extend the deterministic particle method to multispecies plasmas.
- Analyze conservation properties (mass, momentum, energy) and entropy decay.
- Investigate equilibrium distribution and temperature conditions.
Main Methods:
- Regularization of the multispecies Landau collision operator.
- Weak form of the regularized Landau equation.
- Time evolution governed by ordinary differential equations for Dirac delta functions.
Main Results:
- The method conserves mass, momentum, and energy.
- Equilibrium distribution is Maxwellian.
- A critical condition ensures species-independent equilibrium temperature.
- Convergence study shows approximately 2nd order accuracy.
Conclusions:
- The extended particle method accurately simulates multispecies plasmas.
- It preserves fundamental physical quantities.
- It achieves Maxwellian equilibrium under specific conditions.
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