Experimental results are presented for the heating of a 4 m long plasma confined by a uniform magnetic field of 4-5 kG by an intense relativistic electron beam. The initial plasma density ranged from approximately 5 x 10 to the 13th power cu cm to approximately 3 x 10 to the 15th power cu cm, the lower density cases being partially ionized and the higher density cases highly ionized. In all cases, the energy coupled from the beam to the plasma is greater than can be explained by binary collisions between beam electrons and the plasma particles. Over most of the density range tested, 5 x 10 to the 13th power cu cm to 1.5 x 10 to the 15th power cu cm the plasma heating cannot be explained by classical processes. These results are found to be explained quantitatively by the use of a full nonlinear treatment of the electron-electron two stream instability in the kinetic regime. A review of beam plasma interaction theory and previous experiments is presented to facilitate comparison with the present results.