A beam‐plasma system consisting of a focused light ion beam propagating through az‐discharge plasma is analyzed for electromagnetic velocity space instabilities. In particular, the Weibel (k⋅B0=0, k⋅Vz≃0) and the whistler (k×B0≃0, k⋅Vz=0) instabilities are studied. It is found that unstable modes do not grow fast enough to affect the beam propagation in a pellet‐fusion‐reactor chamber. For k⋅Vz≳0, the instabilities convect with a velocity much less than the beam streaming velocity.