Beam-driven three-dimensional electromagnetic strong turbulence

Abstract

Large scale beam-driven electromagnetic strong turbulence is investigated by numerically solving the three-dimensional electromagnetic Zakharov equations, where turbulence is driven at nonzero wavenumbers k. For electron thermal speeds ve/c ≳ 0.1, a significant fraction of driven Langmuir waves undergo electromagnetic decay into electromagnetic waves and ion-acoustic waves so that transverse waves contribute significantly to the total energy density. It is shown that as ve/c increases, the wavenumber and energy density of transverse waves produced increase. For ve/c≲0.1, beam-driven turbulence is approximately electrostatic. An approximately periodic cycle is observed, similar to previous two-dimensional electrostatic simulations, in which Langmuir waves are driven to larger mean energy densities until a series of backscatters occurs, shifting the Langmuir waves out of resonance with the driver and decreasing the wavenumber of the Langmuir waves. A low-k condensate results from which wave packets form and collapse, decreasing the mean energy density. Averaging over many of these periods, the statistical properties are calculated and the scaling behavior of the mean energy density is shown to agree well with the electrostatic two-component model prediction. When driven at nonzero k the scaling behavior is shown to depend weakly on ve/c, in contrast to when strong turbulence is driven at k = 0, where the scalings depend more strongly on ve/c.