An Explicit Energy-Conserving Particle Method for the Vlasov–Fokker–Planck Equation

Abstract. We propose an explicit particle method for the Vlasov–Fokker–Planck equation that conserves energy at the fully discrete level. The method features two key components: a deterministic and conservative particle discretization for the nonlinear Fokker–Planck operator (also known as the Lenard–Bernstein or Dougherty operator) and a second-order explicit time integrator that ensures energy conservation through an accuracy-justifiable correction. We validate the method on several plasma benchmarks, including collisional Landau damping, two-stream instability, and Weibel instability, demonstrating its effectiveness.