Ion-Ion Velocity Space Instability

An electrostatic instability caused by the difference between ${\theta }_{\mathrm{\perp ‐i}}$ and ${\theta }_{\mathrm{\Vert ‐i}}$ , the ion temperatures perpendicular and parallel to magnetic field, is discussed. Results show that the instability disappears as the ratio ${\theta }_{\mathrm{\perp ‐i}}{\mathrm{/\theta }}_{\mathrm{\Vert ‐i}}$ approaches roughly a value of 16 and also when for a given value of ${\theta }_{\mathrm{\perp ‐i}}{\mathrm{/\theta }}_{\mathrm{\Vert ‐i}}$ the ratio ${\theta }_{\mathrm{\perp ‐i}}{\mathrm{/\theta }}_{\mathrm{\Vert ‐e}}$ becomes large, ${\theta }_{\mathrm{\Vert ‐e}}$ being the electron temperature parallel to the magnetic field. From the results it is also concluded that this instability disappears, irrespective of the values of ${\theta }_{\mathrm{\perp ‐i}}{\mathrm{/\theta }}_{\mathrm{\Vert ‐i}}$ , and ${\theta }_{\mathrm{\perp ‐i}}{\mathrm{/\theta }}_{\mathrm{\Vert ‐e}}$ , whenever the plasma density is low enough so that the square of ion gyrofrequency is greater than about 2.8 times the square of ion plasma frequency.