Existence of finite and anisotropic heavy ion parallel compressibility pinch in the gyrokinetic turbulence

Turbulence-driven heavy ion transport in hot magnetized plasma is investigated by means of the gyrokinetic theory and simulations. A finite heavy ion parallel compressibility pinch (${\mathrm{\ensuremath{\Gamma}}}_{s,\ensuremath{\parallel}}$) is found in the gyrokinetic framework, in contrast to the conventional understanding that ${\mathrm{\ensuremath{\Gamma}}}_{s,\ensuremath{\parallel}}$ is negligible. A perturbation theory clarifies the turbulence frequency dependence of ${\mathrm{\ensuremath{\Gamma}}}_{s,\ensuremath{\parallel}}$, resolving the discrepancy with experimental observations. It is also predicted by a nonlocal approach of the parallel advection term that ${\mathrm{\ensuremath{\Gamma}}}_{s,\ensuremath{\parallel}}$ is strongly anisotropic on a magnetic surface. The parameter dependence shows that decreasing the heavy ion mass ${m}_{s}$ strongly enhances ${\mathrm{\ensuremath{\Gamma}}}_{s,\ensuremath{\parallel}}$ through kinetic effects, leading to a deviation from the $1/{m}_{s}$ scaling. Moreover, the pinch direction can be reversed in nonlinear trapped electron mode turbulence through the inverse cascade.