Neutral‐atom injection with Lorentz trapping is one of the most popular and successful methods of forming a “hot ion plasma.” It is suggested here that one could form a “hot electron plasma” by injecting ions with megaelectron volt energies and using Lorentz trapping. For example, build‐up calculations indicate that one could form in a mirror machine a 15‐keV “hot electron plasma” with a density of109 cm−3by using a 50‐&mgr; A beam ofH2+ at 60 MeV. TheH2+beam would be sent through a gas cell or foil to obtain some30 MeV H0atoms by dissociation. TheH0would then pass through the magnetic confinement field and some 15‐keV electrons would be trapped by Lorentz ionization of excitedH0. If the background gas pressure is below10−8Torr, electron‐electron scattering will determine the containment time forn ≈ 109 cm−3. Neutralization of the hot electrons can be accomplished by ionization of the residual gas as the ionization time constant is much shorter than the gasscattering time constant. Since typical scattering times are many seconds, dc operation is preferable. If one can obtain the necessary combination of ion energy and confining magnetic field strength, Lorentz electron stripping from theH−orHe−ground state can result in very high trapping efficiencies and higher plasma densities. Some advantages and uses for beam‐injected and Lorentz‐trapped hot electron plasmas are discussed.