Magnetic fluctuation energy spectra at for all three simulations, labeled as I, II, and III. The reduced energy spectra labeled as “a” are calculated from the two-dimensional energy spectra labeled as "b" by integrating on the other direction. Red lines (lower curves in the cascade regime) and blue lines (upper curves in the cascade regime) with solid circles in the reduced energy spectra correspond to and , respectively.
Time histories of quantities summed over the cascading wavenumber range for Run I (upper red line), Run II (middle blue line), and Run III (bottom green line). (a) Total magnetic fluctuation energy and (b) spectral anisotropy .
Spectral anisotropy as a function of the instantaneous for Run I (red), Run II (blue), and Run III (green). For the black-and-white version of the figure, the points for Run I correspond to , the points for Run II correspond to , and the points for Run III correspond to . Each point corresponds to a summation over the cascading wavenumber range .
Three magnetic energy ratios as functions of for three ranges of as labeled. Here the green or upper points indicate , the blue or decreasing points indicate , and the red or increasing points indicate , the magnetic compressibility. Run I and linear theory results are shown by open circles and dashed lines, respectively. The simulation results are averaged over the whole time of the computation.
Time histories of (a) parallel electron kinetic energy , (b) perpendicular electron kinetic energy , and (c) ratio of the perpendicular and the parallel electron kinetic energy. These energies are normalized to the background magnetic field energy . Here red denotes results from Run I, blue denotes results from Run II, and green denotes results from Run III. In black-and-white, Run I curves are uppermost in panels (a) and (b), and lowermost in panel (c); Run II curves are in the middle, and Run III curves are lowermost in panels (a) and (b) and uppermost in panel (c).
Differences between the late-time and initial electron velocity distributions; that is, for Run I (top), Run II (middle), and Run III (bottom).
Linear dispersion theory for whistler fluctuations in a homogeneous, collisionless, electron-proton plasma with . (a) Whistler damping rates as functions of wavenumber for four angles of propagation as labeled. (b) Whistler damping rates as functions of propagation angle for five values of wavenumber as labeled.
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