The end-boundary floating-surface sheath potential, electron and ion energy distribution functions (EEDf , IEDf ) in the low-pressure non-ambipolar electron plasma (NEP) are investigated. The NEP is heated by an electron beam extracted from an inductively coupled electron-source plasma (ICP) through a dielectric injector by an accelerator located inside the NEP. This plasma's EEDf has a Maxwellian bulk followed by a broad energy continuum connecting to the most energetic group with energies around the beam energy. The NEP pressure is 1-3 mTorr of N 2 and the ICP pressure is 5-15 mTorr of Ar. The accelerator is biased positively from 80 to 600 V and the ICP power range is 200-300 W. The NEP EEDf and IEDf are determined using a retarding field energy analyser. The EEDf and IEDf are measured at various NEP pressures, ICP pressures and powers as a function of accelerator voltage. The accelerator current and sheath potential are also measured. The IEDf reveals mono-energetic ions with adjustable energy and it is proportionally controlled by the sheath potential. The NEP end-boundary floating surface is bombarded by a mono-energetic, space-charge-neutral plasma beam. When the injected energetic electron beam is adequately damped by the NEP, the sheath potential is linearly controlled at almost a 1 : 1 ratio by the accelerator voltage. If the NEP parameters cannot damp the electron beam sufficiently, leaving an excess amount of electron-beam power deposited on the floating surface, the sheath potential will collapse and become unresponsive to the accelerator voltage.