On the dispersion relation of the transit time instability in inverted fireballs

Recently discovered inverted fireballs are non-linear plasma phenomena, which are formed in hollow grid anodes with high transparency in an existing background plasma. If a sufficiently large potential is applied, accelerated electrons from the bulk start to oscillate through the grid. Experimental investigations have shown that they produce different types of plasma instabilities. One of those oscillations is a transit time instability which originates from strong electron beams that travel through the inverted fireball. This type of instability is similar to vircator reflex oscillations and produces radio frequency waves. Hence, it is suitable to convert DC signals into signals oscillating in the MHz range. This paper analyses the dispersion relation of the transit time instability for three different plasma regimes. The regimes can be divided into a collision less regime, a regime with high collisionality and one in between those former two. It is demonstrated that the plasma properties of the surrounding background plasma have a strong influence on the behavior of the instability itself