Energy transfer in two-dimensional magnetohydrodynamic turbulence: formalism and numerical results

The basic entity of nonlinear interaction in Navier-Stokes and the Magnetohydrodynamic (MHD) equations is a wavenumber triad ({\bf k,p,q}) satisfying ${\bf k+p+q=0}$. The expression for the combined energy transfer from two of these wavenumbers to the third wavenumber is known. In this paper we introduce the idea of an effective energy transfer between a pair of modes by the mediation of the third mode, and find an expression for it. Then we apply this formalism to compute the energy transfer in the quasi-steady-state of two-dimensional MHD turbulence with large-scale kinetic forcing. The computation of energy fluxes and the energy transfer between different wavenumber shells is done using the data generated by the pseudo-spectral direct numerical simulation. The picture of energy flux that emerges is quite complex---there is a forward cascade of magnetic energy, an inverse cascade of kinetic energy, a flux of energy from the kinetic to the magnetic field, and a reverse flux which transfers the energy back to the kinetic from the magnetic. The energy transfer between different wavenumber shells is also complex---local and nonlocal transfers often possess opposing features, i.e., energy transfer between some wavenumber shells occurs from kinetic to magnetic, and between other wavenumber shells this transfer is reversed. The net transfer of energy is from kinetic to magnetic. The results obtained from the studies of flux and shell-to-shell energy transfer are consistent with each other.Comment: 27 pages REVTEX; 14 ps figure

Calculation of renormalized viscosity and resistivity in magnetohydrodynamic turbulence

A self-consistent renormalization (RG) scheme has been applied to nonhelical magnetohydrodynamic turbulence with normalized cross helicity $\sigma_c =0$ and $\sigma_c \to 1$. Kolmogorov's 5/3 powerlaw is assumed in order to compute the renormalized parameters. It has been shown that the RG fixed point is stable for $d \ge d_c \approx 2.2$. The renormalized viscosity $\nu^*$ and resistivity $\eta^*$ have been calculated, and they are found to be positive for all parameter regimes. For $\sigma_c=0$ and large Alfv\'{e}n ratio (ratio of kinetic and magnetic energies) $r_A$, $\nu^*=0.36$ and $\eta^*=0.85$. As $r_A$ is decreased, $\nu^*$ increases and $\eta^*$ decreases, untill $r_A \approx 0.25$ where both $\nu^*$ and $\eta^*$ are approximately zero. For large $d$, both $\nu^*$ and $\eta^*$ vary as $d^{-1/2}$. The renormalized parameters for the case $\sigma_c \to 1$ are also reported.Comment: 19 pages REVTEX, 3 ps files (Phys. Plasmas, v8, 3945, 2001

Plasma beta dependence of turbulent transport suggesting an advantage of weak magnetic shear from local and global gyrokinetic simulations

A higher plasma β is desirable for realizing high performance fusion reactor, in fact, one of the three goals of JT-60SA project is to achieve a high-β regime. We investigate key physical processes that regulate the β dependence of turbulent transport in L-mode plasmas by means of both local and global gyrokinetic simulations. From local simulations, we found that the turbulent transport does not decrease as β increases, because the electromagnetic stabilizing effect is canceled out by the increase of the Shafranov shift. This influence of the Shafranov shift is suppressed when the magnetic shear is weak, and thus the electromagnetic stabilization is prominent in weak shear plasmas, suggesting an advantage of weak magnetic shear plasmas for achieving a high-β regime. In high β regime, local gyrokinetic simulations are suffered from the non-saturation of turbulence level. In global simulations, by contrast, the electromagnetic turbulence gets saturated by the entropy advection in the radial direction to avoid the zonal flow erosion due to magnetic fluctuations. This breakthrough enables us to explore turbulent transport at a higher β regime by gyrokinetic simulations