Coronal Loop Model Including Ion Kinetics

Abstract

We present a kinetic coronal loop model including collisions and wave-particle interactions to study the mechanisms of loop heating. The model is based on a quasi-linear treatment of the Vlasov equation for the reduced velocity distribution functions of the protons, which are the only ions considered in the loop plasma. For the energy input into the loop, we assume that linear Alfven waves penetrate the loop from its footpoints and heat the protons via wave-particle interactions and wave absorption. Through Coulomb collisions between protons and electrons some thermal energy can be transferred to the electrons. It turns out that in such a model protons are hotter than electrons, and the scale length for proton heating along the loop is determined by the dissipation scale of the ion-cyclotron waves. Through the gyrofrequency this scale is connected to the cross section area of the loop and, thus, to the spatial variation of the magnetic field shaping the coronal loop. Furthermore, it is shown that in the case of a nearly homogeneous flux tube cross section, an almost flat temperature profile occurs along the major part of the loop with an enhanced plasma density. These plasma parameter profiles are consistent with those of loops having temperatures between 1 and 1.5 MK as observed in extreme-ultraviolet emission. However, if the magnetic field lines are more strongly diverging from the footpoints to the loop apex, the proton heating is found to be more uniform, resulting in a higher temperature and lower density along the loop. These profiles are similar to those observed in X-ray loops.