This chapter presents the first study of this thesis on investigating how weak, small-scale intergalactic magnetic fields affect the instability energy loss efficacy and whether the instability can still suppress the GeV cascade. The chapter describes how the magnetic field modifies the beam distribution and subsequently the linear growth rate of the electrostatic instability. Finally, a magnetic field parameter space is identified where neither the instability nor magnetic field deflection can effectively suppress the cascade, leading to an exclusion of that region.