Schematic view of the nonlinear phase mixing: when the fluctuation scale is comparable to or smaller than the Larmor radius , the gyroaverage of the electric field induces a decorrelation of the distribution function at the velocity-space scale corresponding to the difference in Larmor radii . Reprinted with permission from T. Tatsuno et al., Phys. Rev. Lett. 103, 015003 (2009). Copyright 2009 American Physical Society.
Two-dimensional spectral density from one of the forward cascade simulation reported in Ref. 17. Kinetic turbulence proceeds in the position and velocity space simultaneously. Reprinted with permission from T. Tatsuno et al., J. Plasma Fusion Res. 9, 509 (2010); e-print arXiv:1003.3933. Copyright 2010 Japan Society of Plasma Science and Nuclear Fusion Research.
Schematic view of the freely decaying turbulence in the space. A diagonal Fourier-Hankel mode (indicated by the red circle) cascades towards small scales in position and velocity space according to the forward cascade of W (blue dotted arrows). Nonlinear interaction conserves both W and E, so the forward cascade must be accompanied by the excitation of larger-scale modes on the diagonal (green solid arrow), which corresponds to the inverse cascade of E.
Time evolution of the 2D spectra for run D [see Eq. (6) and Table I]. Diagonal components () are indicated by dotted lines.
Time evolution of the 2D spectra for run F [see Eq.(6) and Table I]. The diagonal () is indicated by dotted lines.
Snapshot of the (a) energy transfer function and (b)entropy transfer function at for run D [see Eqs. (29) and (30), and Table I].
Slices of the 2D spectra of run F along p axis.
Time evolution of for the runs indexed in Table I. Runs A and E correspond to the strongly collisional case; B corresponds to the marginal case; and C, D, and F correspond to the weakly collisional case.
Time evolution of the ratio of collisionless invariants for the strongly collisional (runs A and E) and marginal (run B) cases. The decay law (20) is drawn for comparison.
Time evolution of the invariants for the marginal (run B) and weakly collisional (run D) cases. Decay law of each invariant (17) is drawn for the marginal case, and fitted slopes are drawn for the weakly collisional case.
Normalized spectra for run B (see Table I).
Normalized spectra for run D (see Table I).
Index of the runs described in Sec. IV.
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