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We explore how inhomogeneity in the background plasma number density altersthe growth of electrostatic unstable wavemodes of beam plasma systems. This isparticularly interesting for blazar-driven beam-plasma instabilities, which maybe suppressed by inhomogeneities in the intergalactic medium as was recentlyclaimed in the literature. Using high resolution Particle-In-Cell simulationswith the SHARP code, we show that the growth of the instability is local, i.e.,regions with almost homogeneous background density will support the growth ofthe Langmuir waves, even when they are separated by strongly inhomogeneousregions, resulting in an overall slower growth of the instability. We also showthat if the background density is continuously varying, the growth rate of theinstability is lower; though in all cases, the system remains within the linearregime longer and the instability is not extinguished. In all cases, the beamloses approximately the same fraction of its initial kinetic energy incomparison to the uniform case at non-linear saturation. Thus, inhomogeneitiesin the intergalactic medium are unlikely to suppress the growth ofblazar-driven beam-plasma instabilities.

Growth of beam-plasma instabilities in the presence of background inhomogeneity