Comment on: Thermostatistics of Overdamped Motion of Interacting Particles [arXiv:1008.1421]

In a recent paper, Phys. Rev. Lett. 105 260601 (2010) [arXiv:1008.1421], Andrade et al., argued that classical particles confined in a parabolic trap at T=0 distribute themselves in accordance with the Tsallis statistics. To prove their point the authors performed molecular dynamics simulations. Here we show that the model of Andrade et al. can be solved exactly. The distribution of particles at T=0 has nothing to do with the Tsallis entropy and is determined simply by the force balance

Non-equilibrium Statistical Mechanics of Two-dimensional Vortices

It has been observed empirically that two dimensional vortices tend to cluster forming a giant vortex. To account for this observation Onsager introduced a concept of negative absolute temperature in equilibrium statistical mechanics. In this Letter we will show that in the thermodynamic limit a system of interacting vortices does not relax to the thermodynamic equilibrium, but becomes trapped in a non-equilibrium stationary state. We will show that the vortex distribution in this non-equilibrium stationary state has a characteristic core-halo structure, which can be predicted {\it a priori}. All the theoretical results are compared with explicit molecular dynamics simulations

Symmetry Breaking in d-Dimensional Self-gravitating Systems

Systems with long-range interactions, such as self-gravitating clusters and magnetically confined plasmas, do not relax to the usual Boltzmann-Gibbs thermodynamic equilibrium, but become trapped in quasi-stationary states (QSS) the life time of which diverges with the number of particles. The QSS are characterized by the lack of ergodicity which can result in a symmetry broken QSS starting from a spherically symmetric particle distribution. We will present a theory which allows us to quantitatively predict the instability threshold for spontaneous symmetry breaking for a class of d-dimensional self-gravitating systems.Comment: 5 pages, 4 figures. Accepted for publication in Physical Review Letter

Nonlinear dynamics of electromagnetic pulses in cold relativistic plasmas

In the present analysis we study the self consistent propagation of nonlinear electromagnetic pulses in a one dimensional relativistic electron-ion plasma, from the perspective of nonlinear dynamics. We show how a series of Hamiltonian bifurcations give rise to the electric fields which are of relevance in the subject of particle acceleration. Connections between these bifurcated solutions and results of earlier analysis are made.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

Relaxation and Emittance Growth of a Thermal Charged-Particle Beam

We present a theory that allows us to accurately calculate the distribution functions and the emittance growth of a thermal charged-particle beam after it relaxes to equilibrium. The theory can be used to obtain the fraction of particles, which will evaporate from the beam to form a halo. The calculated emittance growth is found to be in excellent agreement with the simulations.Comment: 3 pages, 3 figure

Collisionless relaxation in non-neutral plasmas

A theoretical framework is presented which allows to quantitatively predict the final stationary state achieved by a non-neutral plasma during a process of collisionless relaxation. As a specific application, the theory is used to study relaxation of charged-particles beams. It is shown that a fully matched beam relaxes to the Lynden-Bell distribution. However, when a mismatch is present and the beam oscillates, parametric resonances lead to a core-halo phase separation. The approach developed accounts for both the density and the velocity distributions in the final stationary state.Comment: Accepted in Phys. Rev. Let

Wave breaking and particle jets in intense inhomogeneous charged beams

This work analyzes the dynamics of inhomogeneous, magnetically focused high-intensity beams of charged particles. While for homogeneous beams the whole system oscillates with a single frequency, any inhomogeneity leads to propagating transverse density waves which eventually result in a singular density build up, causing wave breaking and jet formation. The theory presented in this paper allows to analytically calculate the time at which the wave breaking takes place. It also gives a good estimate of the time necessary for the beam to relax into the final stationary state consisting of a cold core surrounded by a halo of highly energetic particles.Comment: Accepted in Physics of Plasma Letter