Strong Langmuir turbulence generated by electron beams: Electric-field distributions and electron scattering

Abstract

Strong-turbulence theory is used to predict the statistics of intense Langmuir fields generated when an electron beam is injected into a plasma, and the theory of transit-time interactions is then used to calculate the beam scattering caused by the turbulent waves. The theory predicts that the distribution of field strengths will have a Gaussian tail corresponding to fields in nonlinearly collapsing coherent wave packets that are near the arrest of their collapse by damping. The functional form of the tail of the field distribution is determined by the statistical distribution of wave packets at the time of their formation, whereas its exponent depends on the arrest scale. Comparison of numerical calculations of this exponent with experimental measurements confirms the Gaussian form of the tail and implies that collapse is arrested at a scale of (16±5)λD, where the peak electrostatic energy density is of the same order as the thermal energy density, in good agreement with independent particle-in-cell calculations. Transit-time calculations of beam scattering in strong turbulence yield rms energy changes in good agreement with experimental values and mean energy changes that are well within the experimental limits. These results support the validity of the recently developed scaling theory of strong turbulence, and the predicted form of transit-time interactions with coherent wave packets.