6D phase space collective modes in Vlasov-Maxwell system

Plasma electromagnetic (EM) kinetic simulation faces two unavoidable difficulties. One arises from the fact that Maxwell equations determine a simultaneity relation between transverse electric field E ⃗ Tr and local growth rates of probability distribution function (PDF) f in Vlasov-Maxwell (V-M) simulation in Eulerian approach, so does that between E Tr and Lagrangian particles’ time-varying rates which refers to displacement of f -element in 6 D phase space in V-M simulation in Lagrangian approach, and macroparticles’ accelerating rates in Particle-in-Cell (PIC) simulation. These simultaneous with E Tr are termed as bottom objects’ growth rates (BOGRs) in this work. Directly solving the BOGRs needs to diagonalize a large full matrix, and hence often be approximated. The other arises from the fact that Lagrangian particles’ time-histories should uniformly converge with respect to the time-step. This severe requirement is difficult to be satisfied and hence some of Lagrangian particles’ time-histories lose fidelity. We propose a strict alternative method free from two difficulties. The initial-value problem of V-M system can be interpreted by 6 D phase space allowed deformation of an initial f -profile. By virtue of a more compact description of f , in which a conditional probability density function (C-PDF) well reflects some macroscopic conservation laws behind the V-M system, we can interpret the initial-value problem of f in terms of 6 D standing-wave oscillation in the C-PDF. A key subtle difference between microscopic scalar field and microscopic vector field can also lead to a similar scheme of particle simulation. PACS: 52.65.-y.