COUNTERSTREAMING ELECTRONS AND IONS IN PIERCE-LIKE DIODES

The dynamics of Pierce-like diodes is investigated for ions moving wit h arbitrary velocities opposite to as well as in the direction of elec tron propagation. By application of an integral formalism that is able to account for mobile streaming ions, equilibrium solutions for the d iode in an external circuit are derived. The stability of the uniform equilibrium for the short-circuited diode and for counterstreaming spe cies is investigated. In this case, new oscillatory unstable branches appear that destabilize the diode for all values of ct, where ct is th e Pierce parameter. This contrasts with the diode with co-moving ions being stable for sufficiently small values of a. These new branches co incide with the Pierce-Buneman modes for initially resting ions. If \v (i0)\/v(e0) is increased, where v(s0) are the injection velocities (s= e,i), a stronger destabilization is observed for counterstreaming in c omparison to co-streaming with maximum growth rate in the range of v(i 0)approximate to - 2v(e0) for a hydrogen plasma. It is furthermore sho wn that the familiar picture of waves (Fourier modes) must be substant ially modified to meet the physics of bounded plasmas.