These simulations intend to reproduce fundamental processes at work when solar wind plasma parcels move away radially from the Sun, while expanding spherically in the transverse direction. Solar wind plasma expansion modifies bulk parameters of the plasma (e.g.: parallel beta, ratio between the perpendicular and the parallel temperature) in a way that promotes the onset of firehose instabilities.
Here, we simulate a simplified system, where ions and electrons are isothermal and turbulent fluctuations are absent. We let the plasma parcels expand. Different background magnetic field values are present in the two cases. We observe the onset of the electron firehose instability, after a phase of abiabatic plasma expansion.
The simulations are done with the fully kinetic Expanding Box Model (EBM) code EB-iPic3D, described in Innocenti et al 2019a, which combines a semi-implicit temporal discretization with the EB strategy, that allows to simulate at a cheap computational cost solar wind expansion in the heliosphere.


In the figure, modified from Innocenti et al, 2019a, we plot a sketch of the Expanding Box Model system. We map the advecting, expanding system of interest to a Cartesian grid, that we simulate, using the EB variable change.

Details on the code and analysis of similar simulations are provided in Innocenti et al 2019a, 2019b, 2020

Innocenti, M. E., Tenerani, A., & Velli, M. (2019). A Semi-implicit Particle-in-cell Expanding Box Model Code for Fully Kinetic Simulations of the Expanding Solar Wind Plasma. The Astrophysical Journal870(2), 66. https://iopscience.iop.org/article/10.3847/1538-4357/aaf1be/meta

Innocenti, M. E., Tenerani, A., Boella, E., & Velli, M. (2019). Onset and evolution of the oblique, resonant electron firehose instability in the expanding solar wind plasma. The Astrophysical Journal883(2), 146. https://iopscience.iop.org/article/10.3847/1538-4357/ab3e40/meta

Innocenti, M. E., Boella, E., Tenerani, A., & Velli, M. (2020). Collisionless Heat Flux Regulation via the Electron Firehose Instability in the Presence of a Core and Suprathermal Population in the Expanding Solar Wind. The Astrophysical Journal Letters898(2), L41. https://iopscience.iop.org/article/10.3847/2041-8213/aba591/meta?casa_token=zfK1N9tDdpwAAAAA:Ej9AodV8VzDHxx_ur5l8gHRwaioncEEiYsnPuFxGWqyVRNOZb920LepGqjehnXCp1zJh-LP8rA

Velli, M., Grappin, R., & Mangeney, A. (1992, October). MHD turbulence in an expanding atmosphere. In AIP Conference Proceedings (Vol. 267, No. 1, pp. 154-159). American Institute of Physics.