Kinetic and space charge control of current flow and voltage drops along magnetic flux tubes: 2. Space charge effects

The distribution of current‐driven electrostatic potentials along auroral magnetospheric flux tubes is studied analytically, based on the principles of quasi‐neutrality and kinetic orbital motion of electrons and ions governed by inertia, electric forces, and magnetic mirror forces. When certain particle accessibility conditions are fulfilled, the kinetics determines the electron and ion number densities as unique functions of position along the flux tube and local potential. These functions are used to define potential profiles for which electron and ion number densities everywhere match, or alternatively positions where potential jumps (double layers) may occur. Magnetospheric and ionospheric particle sources in the form of Maxwellians with loss cones depending on the total voltage drop are considered, as well as trapped particles. The potential profile generally comprises a potential jump that accounts for a sizeable fraction of the total voltage drop (only by assuming unrealistic velocity distributions of the magnetospheric electron source can solutions without a jump be found). The jump may typically occur around an altitude of 1 R E , an altitude that increases with density of the ionospheric source and that decreases with increasing density of trapped, secondary, and backscattered particles and total voltage drop along the flux tube. Below the potential jump, only small potential variations occur. Above the potential jump, the potential falls off gradually, asymptotically linear in magnetic field intensity. Only a small percentage of the potential drop occurs above an altitude of a few R E , but the weak field extending to higher altitudes is essential for quasi‐neutrality and for the current‐voltage relationship (discussed in a previous paper). Above the potential jump, the number density of particles is reduced as compared to regions without current flow and potential drops. Depending on the density of the ionospheric source, solutions are possible for total potential drops much larger than the temperature of the magnetospheric electron source. While full accessibility for the mirroring electrons tends to be locally violated, accessibility for all particles within the source cone is fulfilled in these solutions, so the current‐voltage relationship does not depend on the shape of the potential profile. Some comments are also made on transient conditions when there is no time for transport of neutralizing ions from the ionosphere.