Hybrid particle-spectral method for kinetic plasma simulations

Technical Report · 07 February 2024

DOI:https://doi.org/10.2172/2377696· OSTI ID:2377696

Chapurin, Oleksandr ^[1]; Koshkarov, Oleksandr ^[1]; Delzanno, Gian Luca ^[1]; Roytershteyn, Vadim ^[2]; Brady, Peter T. ^[1]; Chiodi, Robert Michael ^[1]; Harnish, Cale Charles ^[1]; Livescu, Daniel ^[1]

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1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
2. Space Science Institute, Boulder, CO (United States)

A hybrid model for numerical solutions of the Vlasov–Poisson equations is presented, which blends spectral and particle approaches. The model splits the distribution function for plasma species into both spectral and particle representations in the velocity space to combine the advantages of each approach. The spectral representation leverages asymmetrically weighted Hermite basis, whereas the particle representation leverages the particle-in-cell method. Configuration phase space is decomposed with the Fourier method, which is well suited for periodic problems. We derive conservation equations for mass, momentum, and energy for the proposed combined method. It is shown that the coupling error between the two methods is absent in the semi-discrete setting (not taking into account time discretization). Finally, numerical test cases are presented simulating a weak electron beam interaction with plasma, leading to beam–plasma instability. The initially localized electron beam evolved into a highly non-equilibrium distribution function in the velocity space. A small growth rate and the resonance nature of instability make it difficult to obtain accurate solutions for purely particle methods due to noise, which falls as ~1/$$\sqrt{N_p}$$ with a number of particles. At the same time, purely spectral methods may require a large number of modes to capture the highly nonequilibrium state of the evolved beam. We show that the hybrid method is well suited for such problems: it reproduces the linear stage as well as nonlinear dynamics with sufficient accuracy using a highly non-equilibrium distribution function.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: 89233218CNA000001
• OSTI ID: 2377696
• Report Number(s): LA-UR--23-32602
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY