When operated with a Hall thruster, either centrally or externally mounted, cathode discharge occurs in a magnetic field environment. Therefore, it is important to assess the influence of the magnetic field on the standalone operation of a hollow cathode to better predict device behavior when coupled with a Hall thruster. This study focuses on the influence of an applied axial magnetic field on main oscillatory phenomena in the plume of a Kr-fed sub-ampere hollow cathode. A probe array consisting of two cylindrical Langmuir probes and an emissive probe was used to assess changes in the plasma parameters and collected ion saturation current as the magnetic field strength was increased. The electron transport along the cathode-anode space was analyzed in terms of total electron collision frequency. It was shown that a higher magnetic field strength induces larger plasma densities and lower electron temperatures. Both the ionization instability and ion acoustic turbulence (IAT) energy diminished with higher magnetic field strengths when the cathode operated in plume mode before the magnetic field was applied. The total electron collision frequency as well as its main contributor, the anomalous collision frequency due to IAT, decreased at higher field strengths. Higher magnetic field strengths were shown to damp the ionization instability. The results included in this communication are the first characterization of the response