Analysis Of The Hermite Spectrum In Plasma Turbulence

The properties of the Hermite spectrum associated with the linear drift-kinetic equation-as used in studies of gyrokinetic turbulence-are examined. A rigorous uniform asymptotic expression is derived for the steady-state spectrum with a Lenard-Bernstein collision operator. It is found that the spectrum is partitioned into three regions whose boundaries are determined by the ratio of the collision frequency nu to the parallel transit frequency kv(th). In the regime of small Hermite index, n, with n less than or similar to (nu/kv(th))(2/3), collisions play no role, and the free energy decays like n(-1/2) due to phase mixing. In the previously unexplored large-n regime, n >= (nu = kv(th))(2), collisions are dominant, and the decay of the free energy spectrum is extremely steep, falling off like (n/e)(-n). Most of the free energy is dissipated in the intermediate regime, (nu/kv(th))(2/3) less than or similar to n << (nu/kv(th))(2), where the asymptotic spectrum is in close agreement with the exponentially decaying "continuization" estimate. Our analysis shows that collisions act as a singular perturbation, giving rise to the intermediate regime, where collisions are significantly altering the spectrum well inside the general large-n asymptotic region. Published by AIP Publishing.