Numerical Studies of Turbulent Heating

The equations of motion of electrons subject to different combinations of electrostatic waves were integrated numerically. Magnetic fields were ignored throughout. For particular choices of wave amplitude, wavenumber, frequency, and phase, and for given initial velocities, there is calculated the mean-square velocity spreading of a collection of particles subject to three different kinds of wave spectra: (a) a single monochromatic wave; (b) several (up to 10) monochromatic waves with differing phase velocities; and (c) a single wave with a random phase change at regular intervals. Heating occurs due to two basic effects: the “trapping” of particles, operative in all three spectra, and the spreading of the spectral density due to the random phase interruptions in (c). For the parameters chosen, numerical results are that the most efficient heating occurs in case (c).