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Freely decaying turbulence in two-dimensional electrostatic gyrokinetics
In magnetized plasmas, a turbulent cascade occurs in phase space at scales
smaller than the thermal Larmor radius ("sub-Larmor scales") [Phys. Rev. Lett.
103, 015003 (2009)]. When the turbulence is restricted to two spatial
dimensions perpendicular to the background magnetic field, two independent
cascades may take place simultaneously because of the presence of two
collisionless invariants. In the present work, freely decaying turbulence of
two-dimensional electrostatic gyrokinetics is investigated by means of
phenomenological theory and direct numerical simulations. A dual cascade
(forward and inverse cascades) is observed in velocity space as well as in
position space, which we diagnose by means of nonlinear transfer functions for
the collisionless invariants. We find that the turbulence tends to a
time-asymptotic state, dominated by a single scale that grows in time. A theory
of this asymptotic state is derived in the form of decay laws. Each case that
we study falls into one of three regimes (weakly collisional, marginal, and
strongly collisional), determined by a dimensionless number D*, a quantity
analogous to the Reynolds number. The marginal state is marked by a critical
number D* = D0 that is preserved in time. Turbulence initialized above this
value become increasingly inertial in time, evolving toward larger and larger
D*; turbulence initialized below D0 become more and more collisional, decaying
to progressively smaller D*.Comment: 12 pages, 12 figures; replaced to match published versio
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