Larmor Radius Approximation Research Articles

Electromagnetic Electron-Ion Streaming Instability

Instabilities produced by a current across a magnetic field and propagating obliquely to the field are studied in connection with the description of hydromagnetic shock waves. It is shown that there exist unstable waves of mixed polarization which can be described as coupled ion beam and whistler modes with frequencies given by ω≈k·u where u is the streaming velocity of the ions relative to the electrons. These waves are investigated in the small electron Larmor radius approximation and in the frequency range Ωi ≪ ω ≪ Ωe where Ωi and Ωe are the cyclotron frequencies of the ions and electrons, respectively. The maximum growth rate is limited by γ < 123 (meu/2miυ¯e)1/3Ωe where υ¯e is the electron thermal velocity. The effect of collisions is considered, and the possibility of observing the instability in oblique shock wave experiments is discussed.

Finite Larmor radius hydromagnetics

A complete set of fluid equations in the so-called finite Larmor radius or drift approximation is obtained by a systematic asymptotic expansion using the gyration period and radius, respectively, as small space and time parameters. The time and space scales must be linked together by velocities characterizing the plasma. In this case, these velocities are chosen to be the so-called gradient and pressure drifts, whereas in ordinary hydromagnetics the Alfvén and thermal velocities are used. This limit is particularly relevant for high temperature spatially inhomogeneous plasmas. Given this linkage, rough physical arguments are used to obtain scalings for all the other variables in the theory. Careful attention is then paid to consistency and inclusiveness in the derivation of the equations. This set is applied to the simple problem of linear wave propagation and stability in a one-dimensional inhomogeneous plasma. It provides a unified treatment of FLR wave phenomena.