25 research outputs found
Invariants and Labels in Lie-Poisson Systems
Reduction is a process that uses symmetry to lower the order of a Hamiltonian
system. The new variables in the reduced picture are often not canonical: there
are no clear variables representing positions and momenta, and the Poisson
bracket obtained is not of the canonical type. Specifically, we give two
examples that give rise to brackets of the noncanonical Lie-Poisson form: the
rigid body and the two-dimensional ideal fluid. From these simple cases, we
then use the semidirect product extension of algebras to describe more complex
physical systems. The Casimir invariants in these systems are examined, and
some are shown to be linked to the recovery of information about the
configuration of the system. We discuss a case in which the extension is not a
semidirect product, namely compressible reduced MHD, and find for this case
that the Casimir invariants lend partial information about the configuration of
the system.Comment: 11 pages, RevTeX. To appear in Proceedings of the 13th Florida
Workshop in Astronomy and Physic
Magnetic Phase transitions in Plasmas and Transport Barriers
A model of magnetic phase transitions in plasmas is presented: plasma blobs
with pressure excess or defect are dia- or para-magnets and move radially under
the influence of the background plasma magnetisation. It is found that magnetic
phase separation could be the underlying mechanism of L to H transitions and
drive transport barrier formation. Magnetic phase separation and associated
pedestal build up, as described here, can be explained by the well known
interchange mechanism, now reinterpreted as a magnetisation interchange which
remains relevant even when stable or saturated. A testable necessary criterion
for the L to H transition is presented.Comment: 3 figures, 9 pages, equations created with MathType To be published
in Nuclear Fusion, accepted August 201
Markov Properties of Electrical Discharge Current Fluctuations in Plasma
Using the Markovian method, we study the stochastic nature of electrical
discharge current fluctuations in the Helium plasma. Sinusoidal trends are
extracted from the data set by the Fourier-Detrended Fluctuation analysis and
consequently cleaned data is retrieved. We determine the Markov time scale of
the detrended data set by using likelihood analysis. We also estimate the
Kramers-Moyal's coefficients of the discharge current fluctuations and derive
the corresponding Fokker-Planck equation. In addition, the obtained Langevin
equation enables us to reconstruct discharge time series with similar
statistical properties compared with the observed in the experiment. We also
provide an exact decomposition of temporal correlation function by using
Kramers-Moyal's coefficients. We show that for the stationary time series, the
two point temporal correlation function has an exponential decaying behavior
with a characteristic correlation time scale. Our results confirm that, there
is no definite relation between correlation and Markov time scales. However
both of them behave as monotonic increasing function of discharge current
intensity. Finally to complete our analysis, the multifractal behavior of
reconstructed time series using its Keramers-Moyal's coefficients and original
data set are investigated. Extended self similarity analysis demonstrates that
fluctuations in our experimental setup deviates from Kolmogorov (K41) theory
for fully developed turbulence regime.Comment: 25 pages, 9 figures and 4 tables. V3: Added comments, references,
figures and major correction
DIFFRACTION RADIATION BY A LINE CHARGE MOVING PAST A COMB: A MODEL OF RADIATION LOSSES IN AN ELECTRON RING ACCELERATOR
Symmetries of a reduced fluid-gyrokinetic system
Symmetries of a fluid-gyrokinetic model are investigated using Lie group techniques. Specifically, the nonlinear system constructed by Zocco & Schekochihin (Phys. Plasmas, vol. 18, 2011, 102309), which combines nonlinear fluid equations with a drift-kinetic description of parallel electron dynamics, is studied. Significantly, this model is fully gyrokinetic, allowing for arbitrary kρi, where k is the perpendicular wave vector of the fluctuations and ρi the ion gyroradius. The model includes integral operators corresponding to gyroaveraging as well as the moment equations relating fluid variables to the kinetic distribution function. A large variety of exact symmetries is uncovered, some of which have unexpected form. Using these results, new nonlinear solutions are constructed, including a helical generalization of the Chapman-Kendall solution for a collapsing current sheet.United States. Department of Energy (grant DE-FG02-91ER54109
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