Felipe Barbedo Rizzato

Weak nonlinear electromagnetic waves and low-frequency magnetic-field generation in electron-positron-ion plasmas

The weakly nonlinear localization of obliquely modulated high-frequency electromagnetic waves in an electron-positron-ion plasma is considered. It is shown that the amplitude of the wave turns out to be a strongly dependent function of the angle between the slow modulations and the fast spatial variations and that the possibility appears of spontaneous generation of low-frequency magnetic fields. These magnetic fields are also functions of this angle and of the high-frequency wave polarization. The analysis of colinear modulation in electron-positron plasmas shows that some restriction must be made regarding the validity of previous calculations.

Nonequilibrium statistical mechanics of systems with long-range interactions

Abstract Systems with long-range (LR) forces, for which the interaction potential decays with the interparticle distance with an exponent smaller than the dimensionality of the embedding space, remain an outstanding challenge to statistical physics. The internal energy of such systems lacks extensivity and additivity. Although the extensivity can be restored by scaling the interaction potential with the number of particles, the non-additivity still remains. Lack of additivity leads to inequivalence of statistical ensembles. Before relaxing to thermodynamic equilibrium, isolated systems with LR forces become trapped in out-of-equilibrium quasi-stationary states (qSSs), the lifetime of which diverges with the number of particles. Therefore, in the thermodynamic limit LR systems will not relax to equilibrium. The qSSs are attained through the process of collisionless relaxation. Density oscillations lead to particle–wave interactions and excitation of parametric resonances. The resonant particles escape from the main cluster to form a tenuous halo. Simultaneously, this cools down the core of the distribution and dampens out the oscillations. When all the oscillations die out the ergodicity is broken and a qSS is born. In this report, we will review a theory which allows us to quantitatively predict the particle distribution in the qSS. The theory is applied to various LR interacting systems, ranging from plasmas to self-gravitating clusters and kinetic spin models.

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 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 tauG-N , collisionless relaxation leads to a gravothermal collapse.

Electromagnetic braking: A simple quantitative model

A calculation is presented that quantitatively accounts for the terminal velocity of a cylindrical magnet falling through a long copper or aluminum pipe. The experiment and the theory are a dramatic illustration of Faraday’s and Lenz’s laws.

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 taken to reach the thermodynamic equilibrium, however, scales with the number of particles. In the thermodynamic limit, at fixed total mass, an 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 describe this final stationary state, without any adjustable parameters.

Manifold reconnection in chaotic regimes

In this paper we extend the concept of separatrix reconnection into chaotic regimes. We show that even under chaotic conditions one can still understand abrupt jumps of diffusive-like processes in the relevant phase-space in terms of relatively smooth realignments of stable and unstable manifolds of unstable fixed points.

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 us 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.

Combined centroid-envelope dynamics of intense, magnetically focused charged beams surrounded by conducting walls

In this paper we analyze the combined envelope-centroid dynamics of magnetically focused high-intensity charged beams surrounded by conducting walls. Similar to the case where conducting walls are absent, it is shown that the envelope and centroid dynamics decouple from each other. Mismatched envelopes still decay into equilibrium with simultaneous emittance growth, but the centroid keeps oscillating with no appreciable energy loss. Some estimates are performed to analytically obtain characteristics of halo formation seen in the full simulations.

Nonintegrable three mode interaction in the Zakharov equations

Abstract In this paper we investigate the behavior of an interacting wave triplet in the context of the Zakharov equations. As the amplitude of the carrier modes grows, the nonlinear modulational frequency with which they exchange energy becomes comparable to their linear high frequencies — in this situation adiabatic approximations can no longer be used. In fact, we find that while for small amplitudes the triplet is approximately integrable and yields almost periodic solutions, for larger amplitudes it develops fully nonintegrable features characteristic of strong chaotic regimes. An appropriate Hamiltonian formalism is developed to describe the dynamics.

Temperature effects on ion acoustic solitons in plasmas with near critical density of negative ions

The authors establish a Korteweg-de Vries type equation to describe ion acoustic solitons in a plasma made up of electrons, positive and negative ions near the critical density. It is shown that the amplitudes and widths of compressive and rarefactive solitons are dependent on the ion temperatures and that this dependence is strongly asymmetric when the positive and negative ion temperatures are unequal. As an application, they analyse results of an experiment.