Electrostatic instabilities driven by an electric current perpendicular to a magnetic field

The linear stability problem of a current flowing perpendicularly to a magnetic field is analysed. With the restriction that the growth rate should be larger than the ion cyclotron frequency, all the fast growing electrostatic modes are computed and compared. It is argued that the most significant modes of the problem (relevant to perpendicular collisionless shocks, pinches and the plasma focus) can be obtained without inclusion of effects due to gradients of the equilibrium quantities. The computations are divided into three broad categories: T e ≫ T i , T e = T i and T i = 10 T e . With the aid of computation and analysis an attempt has been made to cover the whole range of parameter space for this problem.