This work describes an investigation of the effect of temperature, voltage, and rise time on the size and shape of the brightness waves of electroluminescence; sawtooth and square pulse voltage waveforms were used to excite copper‐activated phosphors in a slightly conducting medium. A model is proposed which accounts for the major features of the experiments. Electrons which have been ionized from a region of high field are trapped in another part of the phosphor particle. A field opposite in polarity to that which produced the ionization serves to sweep the conduction electrons, which are at every instant in thermal equilibrium with the traps, back into the high field region where the electrons recombine, with radiative emission. The model is successfully applied to measurements of the average electroluminescence brightness for sinusoidal excitation of a binderless phosphor layer as a function of temperature, frequency, and voltage.