Nonlinear Phase Mixing and Phase-Space Cascade of Entropy in Gyrokinetic Plasma Turbulence

Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic turbulence; and because any physical process that produces fluctuations of the gyrophase-independent part of the distribution function may, via the entropy cascade, result in turbulent heating at a rate that increases with the fluctuation amplitude, but is independent of the collision frequency.

Figure 1

Schematic view of the nonlinear phase mixing superimposed on the potential from the Run (iii) (see Table ) at $t/{\tau }_{\mathrm{init}}=10$ and the largest wavelength mode taken out. When the fluctuation scale $\ell \lesssim \rho$, 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 ${\ell }_v=\delta v/\Omega \sim \ell$ [see (7)].

Figure 2

Time evolution of $\mathfrak{W}$ and $\mathfrak{E}$ [Eqs. (3, 4)] normalized to initial $\mathfrak{W}$. The runs (i)–(iii) are indexed in Table . Evolution of $\mathfrak{E}$ does not differ among runs significantly, and is given for run (iii).

Figure 3

Time-averaged normalized (a) wave-number (Fourier) spectra $E_h(k_{\perp })/\mathfrak{W}$ and $E_{\phi }(k_{\perp })/\mathfrak{W}$ [cf. (9)], and (b) velocity-space (Hankel) spectrum ${\widehat{E}}_g(p)/\mathfrak{W}$ for the runs indexed in Table . Theoretically predicted slopes are given for comparison.