Numerical simulation of filling a magnetic flux tube with a cold plasma: Anomalous plasma effects

Abstract

Large‐scale models of plasmaspheric refilling have revealed that during the early stage of the refilling counterstreaming ion beams are a common feature. However, the instability of such ion beams and its effect on refilling remain unexplored. The difficulty with investigating the effect of ion‐beam‐driven instability on refilling is that the instability and the associated processes are so small‐scale that they cannot be resolved in large‐scale models. Typically, the instabilities have scale lengths of a few tens of plasma Debye length, which is a few meters at the most, and the spatial resolution in large‐scale models is at least several tens of kilometers. Correspondingly, the temporal scale of the instability is by several orders of magnitude smaller than the temporal resolution afforded by the models. In order to learn the basic effects of ion beam instabilities on refilling, we have performed numerical simulations of the refilling of an artificial magnetic flux tube. The shape and size of the tube are assumed so that the essential features of the refilling problem are kept in the simulation and at the same time the small‐scale processes driven by the ion beams are sufficiently resolved. We have also studied the effect of commonly found equatorially trapped warm and/or hot plasma on the filling of a flux tube with a cold plasma. When the warm and/or hot plasma consists of anisotropic ions and isotropic electrons, the potential barrier set up by this plasma has a drastic effect on the flow of the cold ion beams, and hence on the filling. Three types of simulation runs have been performed. In run 1 we have only a cold plasma and we treat ions kinetically and electrons are assumed to obey the Boltzmann law. In run 2 both electrons and ions in the cold plasma are treated kinetically. Run 3 is similar to run 2, but it includes an equatorially trapped plasma population as mentioned above. A comparison between the results from run 1 and run 2 reveals that in the latter type of simulation electron‐ion (e‐i) and ion‐ion (i‐i) instabilities occur and significantly modify the evolution of the plasma density distributions in the flux tube along with the total plasma content. When the electron dynamics is simplified by the assumption of the Boltzmann law, both the electron‐ion and ion‐ion instabilities are inhibited. On the other hand, when electrons are treated kinetically, the e‐i instability occurs at an early stage when ion beams are too fast to excite the i‐i instability. The former instability heats the electrons so that conditions for the latter instability are eventually met. The i‐i instability and its nonlinear evolution creates potential structures which significantly modify the filling process. In run 2 filling is enhanced over run 1 due to the trapping of the plasma in the potential structures. Run 3 with the equatorially trapped plasma consisting of hot anisotropic ions and warm isotropic electrons shows that the difference in the thermal anisotropy between electrons and ions generates electrostatic shocks in the flow of the initially fast ion beams. The propagating shocks yield extended potential structure in the flux tube. The trapping of plasma in the potential structure further enhances the filling in run 3 over that seen in run 2.