Nonlinear Effects of Fluctuations in a Current‐Carrying Plasma

A current‐carrying electron‐proton plasma is studied by calculating the velocity distribution of the particles with the Lenard‐Balescu‐Guernsey form of the Fokker‐Planck equations rather than with the familiar Landau form. The Landau equations yield velocity distributions that become unstable to longitudinal ion waves when the temperature ratio Te/Ti is large and the electric field E 0 that drives the current exceeds a critical magnitude E crit. The Landau equations are then not appropriate because they do not include the effect that the fluctuations associated with these ion waves have upon the velocity distributions. The Lenard‐Balescu‐Guernsey equations show that as E 0 is increased toward E crit these fluctuations increase and affect the electron velocity distribution much as enhanced electron‐electron collisions would do. In particular, this nonlinear process reduces the electrical conductivity by a noticeable amount (a few percent in the examples given). Although one might also expect the threshold electric field for instability to be increased significantly, this effect is found to be extremely weak, if it exists.