arXiv subjects

Renato Pakter

Publications and source records attributed to Renato Pakter.

28 records · Page 2Linked to original sources

arXiv2011

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.

cond-mat.stat-mech↗

arXiv2010

Statistical Mechanics of Unbound Two Dimensional Self-Gravitating Systems

We study, using both theory and molecular dynamics simulations, the relaxation dynamics of a microcanonical two dimensional self-gravitating system. After a sufficiently large time, a gravitational cluster of N particles relaxes to the Maxwell-Boltzmann distribution. The time to reach the thermodynamic equilibrium, however, scales with the number of particles. In the thermodynamic limit, $N\to\infty$ at fixed total mass, equilibrium state is never reached and the system becomes trapped in a non-ergodic stationary state. An analytical theory is presented which allows us to quantitatively described this final stationary state, without any adjustable parameters.

cond-mat.stat-mech↗

arXiv2009

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.

physics.acc-ph↗

arXiv2009

Thermodynamics of driven collisionless systems

A statistical theory is presented which allows to calculate the stationary state achieved by a driven system after a process of collisionless relaxation. The theory is applied to study an electron beam driven by an external electric field. The Vlasov equation with appropriate boundary conditions is solved analytically and compared with the molecular dynamics simulation. A perfect agreement is found between the theory and the simulations. The full current-voltage phase diagram is constructed.

cond-mat.stat-mech↗

arXiv2008

Collisionless relaxation in gravitational systems: From violent relaxation to gravothermal collapse

Theory and simulations are used to study collisionless relaxation of a gravitational $N$-body system. It is shown that when the initial one particle distribution function satisfies the virial condition -- potential energy is minus twice the kinetic energy -- the system quickly relaxes to a metastable state described {\it quantitatively} by the Lynden-Bell distribution with a cutoff. If the initial distribution function does not meet the virial requirement, the system undergoes violent oscillations, resulting in a partial evaporation of mass. The leftover particles phase separate into a core-halo structure. The theory presented allows us to quantitatively predict the amount and the distribution of mass left in the central core, without any adjustable parameters. On a longer time scale $τ_G \sim N$ collisionless relaxation leads to a gravothermal collapse.

cond-mat.stat-mech↗

arXiv2007

Image Effects on the Transport of Intense Nonaxisymmetric Charged Beams

The effect of conducting pipes on the equilibrium of intense nonaxisymmetric continuous beams of charged particles is investigated. For a cylindrical pipe and an elliptical beam, we obtain an exact closed form analytical expression for the electrostatic potential. Using a variational principle, we then explore the distortions that equilibrium beams suffer due to the conducting channel. Finally, we present an exact proof that despite the nonlinear forces acting on beams of arbitrary cross section inside conducting pipes of arbitrary shape, the density of these beams remains homogeneous and their cross sectional area remains the sa me as the one in free-space.

physics.plasm-ph↗

arXiv2007

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.

cond-mat.stat-mech↗

arXiv2007

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.

physics.plasm-ph↗

arXiv2004

Stability of off-axis motion for intense particle beams in periodically focusing channels

A general equation for the centroid motion of free, continuous, intense beams propagating off-axis in solenoidal periodic focusing fields is derived. The centroid equation is found to be independent of the specific beam distribution and may exhibit unstable solutions. A new Vlasov equilibrium for off-axis beam propagation is also obtained. Properties of the equilibrium and the relevance of centroid motion to beam confinement are discussed.

physics.plasm-ph↗

arXiv2004

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.

physics.plasm-ph↗