148 research outputs found
Impact of energetic particle orbits on long range frequency chirping of BGK modes
Long range frequency chirping of Bernstein-Greene-Kruskal modes, whose
existence is determined by the fast particles, is investigated in cases where
these particles do not move freely and their motion is bounded to restricted
orbits. An equilibrium oscillating potential, which creates different orbit
topologies of energetic particles, is included into the bump-on-tail
instability problem of a plasma wave. With respect to fast particles dynamics,
the extended model captures the range of particles motion (trapped/passing)
with energy and thus represents a more realistic 1D picture of the long range
sweeping events observed for weakly damped modes, e.g. global Alfven
eigenmodes, in tokamaks. The Poisson equation is solved numerically along with
bounce averaging the Vlasov equation in the adiabatic regime. We demonstrate
that the shape and the saturation amplitude of the nonlinear mode structure
depends not only on the amount of deviation from the initial eigenfrequency but
also on the initial energy of the resonant electrons in the equilibrium
potential. Similarly, the results reveal that the resonant electrons following
different equilibrium orbits in the electrostatic potential lead to different
rates of frequency evolution. As compared to the previous model [Breizman B.N.
2010 Nucl. Fusion 50 084014], it is shown that the frequency sweeps with lower
rates. The additional physics included in the model enables a more complete 1D
description of the range of phenomena observed in experiments.Comment: Submitted to Nuclear Fusion 25/01/201
Chaotic and integrable magnetic fields in one-dimensional hybrid Vlasov-Maxwell equilibria
In this paper, we develop a one-dimensional, quasineutral, hybrid
Vlasov-Maxwell equilibrium model with kinetic ions and massless fluid electrons
and derive associated solutions. The model allows for an electrostatic
potential that is expressed in terms of the vector potential components through
the quasineutrality condition. The equilibrium states are calculated upon
solving an inhomogeneous Beltrami equation that determines the magnetic field,
where the inhomogeneous term is the current density of the kinetic ions and the
homogeneous term represents the electron current density. We show that the
corresponding one-dimensional system is Hamiltonian, with position playing the
role of time, and its trajectories have a regular, periodic behavior for ion
distribution functions that are symmetric in the two conserved particle
canonical momenta. For asymmetric distribution functions, the system is
nonintegrable, resulting in irregular and chaotic behavior of the fields. The
electron current density can modify the magnetic field phase space structure,
inducing orbit trapping and the organization of orbits into large islands of
stability. Thus the electron contribution can be responsible for the emergence
of localized electric field structures that induce ion trapping. We also
provide a paradigm for the analytical construction of hybrid equilibria using a
rotating two-dimensional harmonic oscillator Hamiltonian, enabling the
calculation of analytic magnetic fields and the construction of the
corresponding distribution functions in terms of Hermite polynomials
A discontinuous Galerkin method for the Vlasov-Poisson system
A discontinuous Galerkin method for approximating the Vlasov-Poisson system
of equations describing the time evolution of a collisionless plasma is
proposed. The method is mass conservative and, in the case that piecewise
constant functions are used as a basis, the method preserves the positivity of
the electron distribution function and weakly enforces continuity of the
electric field through mesh interfaces and boundary conditions. The performance
of the method is investigated by computing several examples and error estimates
associated system's approximation are stated. In particular, computed results
are benchmarked against established theoretical results for linear advection
and the phenomenon of linear Landau damping for both the Maxwell and Lorentz
distributions. Moreover, two nonlinear problems are considered: nonlinear
Landau damping and a version of the two-stream instability are computed. For
the latter, fine scale details of the resulting long-time BGK-like state are
presented. Conservation laws are examined and various comparisons to theory are
made. The results obtained demonstrate that the discontinuous Galerkin method
is a viable option for integrating the Vlasov-Poisson system.Comment: To appear in Journal for Computational Physics, 2011. 63 pages, 86
figure
The Abelianization of QCD Plasma Instabilities
QCD plasma instabilities appear to play an important role in the
equilibration of quark-gluon plasmas in heavy-ion collisions in the theoretical
limit of weak coupling (i.e. asymptotically high energy). It is important to
understand what non-linear physics eventually stops the exponential growth of
unstable modes. It is already known that the initial growth of plasma
instabilities in QCD closely parallels that in QED. However, once the unstable
modes of the gauge-fields grow large enough for non-Abelian interactions
between them to become important, one might guess that the dynamics of QCD
plasma instabilities and QED plasma instabilities become very different. In
this paper, we give suggestive arguments that non-Abelian self-interactions
between the unstable modes are ineffective at stopping instability growth, and
that the growing non-Abelian gauge fields become approximately Abelian after a
certain stage in their growth. This in turn suggests that understanding the
development of QCD plasma instabilities in the non-linear regime may have close
parallels to similar processes in traditional plasma physics. We conjecture
that the physics of collisionless plasma instabilities in SU(2) and SU(3) gauge
theory becomes equivalent, respectively, to (i) traditional plasma physics,
which is U(1) gauge theory, and (ii) plasma physics of U(1)x U(1) gauge theory.Comment: 36 pages; 15 figures [minor changes made to text, and new figure
added, to reflect published version
Self-consistent Langmuir waves in resonantly driven thermal plasmas
The longitudinal dynamics of a resonantly driven Langmuir wave are analyzed
in the limit that the growth of the electrostatic wave is slow compared to the
bounce frequency. Using simple physical arguments, the nonlinear distribution
function is shown to be nearly gaussian in the canonical particle action, with
a slowly evolving mean and fixed variance. Self-consistency with the
electrostatic potential provide the basic properties of the nonlinear
distribution function including a frequency shift that agrees well with driven,
electrostatic particle simulations. This extends earlier work on nonlinear
Langmuir waves by Morales and O'Neil [G. J. Morales and T. M. O'Neil, Phys.
Rev. Lett. 28, 417 (1972)], and could form the basis of a reduced kinetic
treatment of Raman backscatter in a plasma.Comment: 11 pages, 4 figures, submitted to Physics of Plasma
Phase transition in the collisionless regime for wave-particle interaction
Gibbs statistical mechanics is derived for the Hamiltonian system coupling
self-consistently a wave to N particles. This identifies Landau damping with a
regime where a second order phase transition occurs. For nonequilibrium initial
data with warm particles, a critical initial wave intensity is found: above it,
thermodynamics predicts a finite wave amplitude in the limit of infinite N;
below it, the equilibrium amplitude vanishes. Simulations support these
predictions providing new insight on the long-time nonlinear fate of the wave
due to Landau damping in plasmas.Comment: 12 pages (RevTeX), 2 figures (PostScript
A sharp stability criterion for the Vlasov-Maxwell system
We consider the linear stability problem for a 3D cylindrically symmetric
equilibrium of the relativistic Vlasov-Maxwell system that describes a
collisionless plasma. For an equilibrium whose distribution function decreases
monotonically with the particle energy, we obtained a linear stability
criterion in our previous paper. Here we prove that this criterion is sharp;
that is, there would otherwise be an exponentially growing solution to the
linearized system. Therefore for the class of symmetric Vlasov-Maxwell
equilibria, we establish an energy principle for linear stability. We also
treat the considerably simpler periodic 1.5D case. The new formulation
introduced here is applicable as well to the nonrelativistic case, to other
symmetries, and to general equilibria
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