Abstract: In multi-pulse X ray photography, plasma created by earlier pulses will affect the up-coming later ones, and cause concerns on the stability of the beams. Based on the basic theory of plasma, we simulate the beam-plasma interaction and address the instability problems in different plasma density scenarios. In external magnetic field free situation, simulation shows the beam (20 MeV, 2.5 kA, 1.3 mm) exhibits different instability properties as the density of the plasma changes. For the density ratio of beam-plasma being less than 1, sausage instability appears, but the beam is generally undisturbed and the hotspot is good. For the density ratio of beam-plasma being between 10 and 100, the pinch effect of the plasma improves the focusing. Filamentation instabilities become prominent as the density ratio of beam-plasma is greater than 1000, the beam emittance grows rapidly, and the target hotspot is dispersed.