Numerical simulation of small-scale low-β magnetic flux ropes in the upper ionospheres of Venus and Mars

We use a three-dimensional macro-particle code (implicit-particle simulation) to examine the evolution of a small magnetic flux rope, where “small” means that its radius is close to the kinetic length scale of protons or electrons. Small flux ropes have been observed in the dayside ionospheres of Venus and Mars. In our simulations, we assume that the initial low-β force-free flux rope is maintained by the electron current: an electron beam flows in the flux rope along the magnetic field lines. The simulation results show that electrostatic two-stream (Buneman) instability is generated around the flux rope axis where the velocity of the electron beam is higher than the electron thermal velocity or the acoustic velocity. Electrons there are heated considerably in the direction parallel to the magnetic field by the instability, and an electron hot tube is formed. The magnetic field deviates from the initial force-free field although the helical structure of the magnetic field is maintained. These results indicate that the electron hot tubes will be evidence of flux rope formation in the low-β region, i.e., in the interaction region between the solar wind and the ionosphere, if they are found by high-resolution observations in the upper ionosphere.