584 research outputs found
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
Resolving velocity space dynamics in continuum gyrokinetics
Many plasmas of interest to the astrophysical and fusion communities are
weakly collisional. In such plasmas, small scales can develop in the
distribution of particle velocities, potentially affecting observable
quantities such as turbulent fluxes. Consequently, it is necessary to monitor
velocity space resolution in gyrokinetic simulations. In this paper, we present
a set of computationally efficient diagnostics for measuring velocity space
resolution in gyrokinetic simulations and apply them to a range of plasma
physics phenomena using the continuum gyrokinetic code GS2. For the cases
considered here, it is found that the use of a collisionality at or below
experimental values allows for the resolution of plasma dynamics with
relatively few velocity space grid points. Additionally, we describe
implementation of an adaptive collision frequency which can be used to improve
velocity space resolution in the collisionless regime, where results are
expected to be independent of collision frequency.Comment: 20 pages, 11 figures, submitted to Phys. Plasma
Neuro-flow Dynamics and the Learning Processes
A new description of the neural activity is introduced by the neuro-flow
dynamics and the extended Hebb rule. The remarkable characteristics of the
neuro-flow dynamics, such as the primacy and the recency effect during
awakeness or sleep, are pointed out.Comment: 8 pages ,10 Postscript figures, LaTeX file, to appear in Chaos,
Solitons and Fractal
Free energy cascade in gyrokinetic turbulence
In gyrokinetic theory, the quadratic nonlinearity is known to play an
important role in the dynamics by redistributing (in a conservative fashion)
the free energy between the various active scales. In the present study, the
free energy transfer is analyzed for the case of ion temperature gradient
driven turbulence. It is shown that it shares many properties with the energy
transfer in fluid turbulence. In particular, one finds a forward (from large to
small scales), extremely local, and self-similar cascade of free energy in the
plane perpendicular to the background magnetic field. These findings shed light
on some fundamental properties of plasma turbulence, and encourage the
development of large eddy simulation techniques for gyrokinetics.Comment: 4 pages, 2 Postscript figure
Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence
Electrostatic turbulence in weakly collisional, magnetized plasma can be
interpreted as a cascade of entropy in phase space, which is proposed as a
universal mechanism for dissipation of energy in magnetized plasma turbulence.
When the nonlinear decorrelation time at the scale of the thermal Larmor radius
is shorter than the collision time, a broad spectrum of fluctuations at
sub-Larmor scales is numerically found in velocity and position space, with
theoretically predicted scalings. The results are important because they
identify what is probably a universal Kolmogorov-like regime for kinetic
turbulence; and because any physical process that produces fluctuations of the
gyrophase-independent part of the distribution function may, via the entropy
cascade, result in turbulent heating at a rate that increases with the
fluctuation amplitude, but is independent of the collision frequency.Comment: Revtex, 4 pages, 3 figures; replaced to match published versio
Gyrokinetic Simulations of Solar Wind Turbulence from Ion to Electron Scales
The first three-dimensional, nonlinear gyrokinetic simulation of plasma
turbulence resolving scales from the ion to electron gyroradius with a
realistic mass ratio is presented, where all damping is provided by resolved
physical mechanisms. The resulting energy spectra are quantitatively consistent
with a magnetic power spectrum scaling of as observed in \emph{in
situ} spacecraft measurements of the "dissipation range" of solar wind
turbulence. Despite the strongly nonlinear nature of the turbulence, the linear
kinetic \Alfven wave mode quantitatively describes the polarization of the
turbulent fluctuations. The collisional ion heating is measured at
sub-ion-Larmor radius scales, which provides the first evidence of the ion
entropy cascade in an electromagnetic turbulence simulation.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let
Considering Fluctuation Energy as a Measure of Gyrokinetic Turbulence
In gyrokinetic theory there are two quadratic measures of fluctuation energy,
left invariant under nonlinear interactions, that constrain the turbulence. The
recent work of Plunk and Tatsuno [Phys. Rev. Lett. 106, 165003 (2011)] reported
on the novel consequences that this constraint has on the direction and
locality of spectral energy transfer. This paper builds on that work. We
provide detailed analysis in support of the results of Plunk and Tatsuno but
also significantly broaden the scope and use additional methods to address the
problem of energy transfer. The perspective taken here is that the fluctuation
energies are not merely formal invariants of an idealized model
(two-dimensional gyrokinetics) but are general measures of gyrokinetic
turbulence, i.e. quantities that can be used to predict the behavior of the
turbulence. Though many open questions remain, this paper collects evidence in
favor of this perspective by demonstrating in several contexts that constrained
spectral energy transfer governs the dynamics.Comment: Final version as published. Some cosmetic changes and update of
reference
Gyrokinetic simulation of entropy cascade in two-dimensional electrostatic turbulence
Two-dimensional electrostatic turbulence in magnetized weakly-collisional
plasmas exhibits a cascade of entropy in phase space [Phys. Rev. Lett. 103,
015003 (2009)]. At scales smaller than the gyroradius, this cascade is
characterized by the dimensionless ratio D of the collision time to the eddy
turnover time measured at the scale of the thermal Larmor radius. When D >> 1,
a broad spectrum of fluctuations at sub-Larmor scales is found in both position
and velocity space. The distribution function develops structure as a function
of v_{perp}, the velocity coordinate perpendicular to the local magnetic field.
The cascade shows a local-scale nonlinear interaction in both position and
velocity spaces, and Kolmogorov's scaling theory can be extended into phase
space.Comment: 8 pages, 10 figures, Conference paper presented at 2009 Asia-Pacific
Plasma Theory Conference. Ver.2 includes corrected typos & updated reference
Mott transition in the -flux SU() Hubbard model on a square lattice
We employ the projector quantum Monte Carlo simulations to study the
ground-state properties of the square-lattice SU(4) Hubbard model with a
flux per plaquette. In the weak coupling regime, its ground state is in the
gapless Dirac semi-metal phase. With increasing repulsive interaction, we show
that, a Mott transition occurs from the semimetal to the valence bond solid,
accompanied by the discrete symmetry breaking. Our simulations
demonstrate the existence of a second-order phase transition, which confirms
the Ginzburg-Landau analysis. The phase transition point and the critical
exponent are also estimated. To account for the effect of a flux
on the ordering in the strong coupling regime, we analytically derive by the
perturbation theory the ring-exchange term which describes the leading-order
difference between the -flux and zero-flux SU(4) Hubbard models.Comment: 8 pages, 9 figure
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