Plasma magnetohydrodynamics and macro-instability theories are briefly reviewed.Although the configuration of any EBIS is inherently susceptible to a number of classical beam instabilities, the small radial dimension of an EBIS plasma prevents modes from occurring in EBIS traps with low beam compression due to physical limitation. In EBIS devices with high electron beam compression, where the potential for beam instabilities is great, the radial dimension is smaller than the Debye length, which renders any plasma theory invalid. However, a RHIC EBIS is expected to have a diameter which is much larger than the Debye length. Hence, it may be the first EBIS, in which the various plasma theories could be valid. For this and future devices like it, a framework is established to analyze and offer remedies plasma instabilities in EBIS.