Cascades and Dissipative Anomalies in Nearly Collisionless Plasma
  Turbulence
  We develop first-principles theory of kinetic plasma turbulence governed by
the Vlasov-Maxwell-Landau equations in the limit of vanishing collision rates.
Following an exact renormalization-group approach pioneered by Onsager, we
demonstrate the existence of a "collisionless range" of scales (lengths and
velocities) in 1-particle phase space where the ideal Vlasov-Maxwell equations
are satisfied in a "coarse-grained sense". Entropy conservation may
nevertheless be violated in that range by a "dissipative anomaly" due to
nonlinear entropy cascade. We derive "4/5th-law" type expressions for the
entropy flux, which allow us to characterize the singularities
(structure-function scaling exponents) required for its non-vanishing.
Conservation laws of mass, momentum and energy are not afflicted with anomalous
transfers in the collisionless limit. In a subsequent limit of small gyroradii,
however, anomalous contributions to inertial-range energy balance may appear
due both to cascade of bulk energy and to turbulent redistribution of internal
energy in phase space. In that same limit the "generalized Ohm's law" derived
from the particle momentum balances reduces to an "ideal Ohm's law", but only
in a coarse-grained sense that does not imply magnetic flux-freezing and that
permits magnetic reconnection at all inertial-range scales. We compare our
results with prior theory based on the gyrokinetic (high gyro-frequency) limit,
with numerical simulations, and with spacecraft measurements of the solar wind
and terrestrial magnetosphere.
