Solitary waves in cold collisionless plasma

The propagation of finite amplitude waves in a magnetized plasma, in which thermal motion and collisions are neglected, is studied for arbitrary direction of propagation. Solutions for oblique propagation are presented, which complement the analytical solutions for propagation perpendicular to the magnetic field obtained by Adlam and Allen and others, and for parallel propagation obtained by Saffman. Oblique propagation is much more complicated than the two limiting cases in that: (1) In a given direction and at a given speed higher than the Alfvén speed there are a large number of different waves and (2) As shown by Saffman there are additional waves whose speed is less than the Alfvén speed. These submagnetic waves are investigated in the limit of infinite mass ratio, and the results compared with computer calculations. The stability of the waves against the two-stream instability is investigated and it is shown that (1) The supermagnetic waves (speed higher than Alfvén speed v_A) are destroyed by the two-stream instability unless v_A/c is sufficiently large (2) The submagnetic waves are destroyed by the two-stream instability unless the pressure is non-negligible.