Free Energy Cascade in Gyrokinetic Turbulence

In gyrokinetic theory, the quadratic nonlinearity is known to play an important role in the dynamics by redistributing (in a conservative fashion) the free energy between the various active scales. In the present study, the free energy transfer is analyzed for the case of ion temperature gradient driven turbulence. It is shown that it shares many properties with the energy transfer in fluid turbulence. In particular, one finds a (strongly) local, forward (from large to small scales) cascade of free energy in the plane perpendicular to the background magnetic field. These findings shed light on some fundamental properties of plasma turbulence, and encourage the development of large-eddy-simulation techniques for gyrokinetics.

Figure 1

Shell decompositions in perpendicular wave number space of the drive (${\mathcal{G}}^{\ell }$) and dissipation ($-{\mathcal{D}}^{\ell }$) terms (as well as their sum) from a Gene simulation of ITG turbulence.

Figure 2

Shell-to-shell transfer in perpendicular wave number space of entropy (a) and electrostatic energy (b) from a Gene simulation of ITG turbulence.

Figure 3

Wavenumber spectra of ${\mathcal{E}}_f$ and ${\mathcal{E}}_{\varphi }$ from a Gene simulation of ITG turbulence. Predictions from a two-dimensional theory are shown for comparison.