# [PEM21-P05] Study of anisotropic electrons distributed around the wake of an ionospheric sounding rocket by a 1D Vlasov-Poisson simulation

Keywords:wake, sounding rocket, Vlasov-Poisson simulation, velocity distribution function, ionosphere

In order to investigate inhomogeneity of hot electrons around the rocket wake, we are now developing a Vlasov-Poisson code. In the simulation with this code, we can calculate wake filling process of ambient ions and electrons in one-dimensional space along the X-axis, which is parallel to the ambient magnetic field. The grid spacings of the space and of the velocity spaces of electrons and ions are ΔX = λ

_{D}(λ

_{D}: Debye length), ΔV

_{e}= 0.1V

_{the}(V

_{the}: thermal velocity of electrons), and ΔV

_{i}= 0.0025V

_{the}, respectively. The range of the space is -600λ

_{D}≤X≤600λ

_{D}, and a void is set at -25λ

_{D}≤X≤25λ

_{D}at the initial time. The ranges of the velocity spaces of electrons and ions are -10V

_{the}≤V

_{e}≤10V

_{the}, and -15V

_{thi}≤V

_{i}≤15V

_{thi}(V

_{thi}: thermal velocity of ions), respectively. The time step Δt is Δt=0.1ω

_{p}

^{-1 }(ω

_{p}: plasma frequency). Accordingly, the CFL (Courant-Friedrichs-Lewy) condition, which should be satisfied to carry out numerical simulations stably, is E/E

_{0}≤1 (E

_{0}= λ

_{D}ω

_{p}

^{2}m

_{e }/ e), where E is the electric field, m

_{e}is the electron mass, and e is the elementary charge. The rational CIP method [Xiao et al., CPC, 1996] is applied to solve the Vlasov equations, and Fourier transform [Birdsall and Langton, Taylor & Francis Group, 2008] is used to obtain electric fields through the Poisson’s equation. If we assume that the plasma is also flown in the y direction, the plasma distribution along the X-axis as a function of time can be understood as that as a function of distance in the y direction.

In our current code, electric oscillations whose amplitudes increase with time are observed outside the wake near the wake boundaries, which makes the CFL condition be unsatisfied at t=469Δt (corresponding to 3.4 mm downstream). However, the calculation has to be proceeded until at least t~60000Δt because we are going to check the velocity distribution functions in the region including the tail of the wake (about 0.4 m downstream) to discuss plasma waves observed in the S-520-26 rocket experiment. Therefore, the electric oscillations must be damped such as by selectively and artificially attenuating the electric fields or by making the density gradients at the wake boundaries be shallower. Even in the calculation before t=469Δt with our current code, we can see several hot electrons such as multi-stream electrons on the wake axis, and a single beam component outside the wake. The multi-stream electrons are considered to be composed of electrons periodically coming into the wake from the outside, and the single electron beam may be owing to the reflection of electrons by the polarized electric field at the wake boundaries.

In this presentation, we will describe the configuration and schemes of our simulation first, and then will show the calculation results. We will especially discuss the spatial distribution of anisotropic electrons and their generation process.