A low energy electron cooling system and method for increasing the phase space intensity and overall intensity of low energy ion beams, including a vacuum chamber to allow electron beam and ion beam merging and separation, a cathode to generate the electron beam, a collector to collect the electron beam, magnetic field generation devices to guide the electrons on their desired trajectories, and electrodes to accelerate and decelerate the electron beam. By overlapping the electron and ion beams, thermal energy is transferred from the ion beam to the electron beam, which allows an increase in the phase space density and overall density of the ion beams. Advantageously, the low energy electron cooling system uses electrodes to set up electrostatic potentials that trap non-beam neutralizing-background-ions longitudinally within the electron cooling region and solenoidal fields that trap the non-beam neutralizing-background-ions radially within the electron cooling region. The trapped non-beam neutralizing-background-ions allow electron cooling currents that are vastly larger than the space charge limit of previous electron cooling devices, which leads to vastly improved functioning of the electron cooling device over previous electron cooling devices.