Kinetic and space charge control of current flow and voltage drops along magnetic flux tubes:: Kinetic effects -: art. no. 8004

[1] The current-voltage characteristic of magnetospheric magnetic flux tubes is studied under rather general conditions, assuming the current to be carried by collision-free particles experiencing inertia, electric forces, and magnetic mirror forces. The approach is that of the powerful kinetic orbital motion'' theory of current collectors in plasma as developed by H. M. Mott-Smith and I. Langmuir in 1926. When C. Davisson's 1925 condition on particle access is fulfilled, the total voltage drop is uniquely determined from the current by kinetic/geometric considerations only, without considerations of the actual space charge and electrostatic potential distribution. For any velocity distribution that is isotropic within the source cone, the current-voltage characteristic is linear for sufficiently small currents. The nature of the corresponding global flux tube electric resistance is discussed. The current-voltage characteristic is given for a variety of distribution functions (where the Maxwellian case corresponds to that studied by S. Knight in 1973) including distributions with a reduced (nonisotropic) flux in the source cone. The current-voltage characteristic is also discussed for cases where the Davisson condition is not fulfilled, when the solution method provides a lower bound on the voltage for a given current. Making assumptions on the altitude extent of the voltage drop, we can also define an upper bound on the voltage for a particular current. The magnetospheric source of particles should be taken to be located at the top of the acceleration region in order to fulfill the Davisson condition. This may limit the effective magnetic mirror ratio, such that the applicability of the linear approximation to the current-voltage characteristic is more restricted, and the saturation current is moderately small, which may lead to overvoltages, a redistribution of the current, or an increased extent of the acceleration region. Joining solutions that piecewise fulfill the Davisson condition, we can derive the current flow for a rather wide range of prescribed potential distributions. Earlier works on the Knight mechanism and related theories for determining the voltage drop along a flux tube are discussed. Determination of the electrostatic potential distribution, and verification of the Davisson condition, requires considerations of the space charge (Poisson equation), to be discussed in a second paper.