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

Superconducting pipes and levitating magnets

Motivated by a beautiful demonstration of the Faraday's and Lenz's law in which a small neodymium magnet falls slowly through a conducting non-ferromagnetic tube, we consider the dynamics of a magnet falling through a superconducting pipe. Unlike the case of normal conducting pipes, in which the magnet quickly reaches the terminal velocity, inside a superconducting tube the magnet falls freely. On the other hand, to enter the pipe the magnet must overcome a large electromagnetic energy barrier. For sufficiently strong magnets, the barrier is so large that the magnet will not be able to penetrate it and will be suspended over the front edge. We calculate the work that must done to force the magnet to enter a superconducting tube. The calculations show that superconducting pipes are very efficient at screening magnetic fields. For example, the magnetic field of a dipole at the center of a short pipe of radius $a$ and length $L \approx a$ decays, in the axial direction, with a characteristic length $\xi \approx 0.26 a$. The efficient screening of the magnetic field might be useful for shielding highly sensitive superconducting quantum interference devices, SQUIDs. Finally, the motion of the magnet through a superconducting pipe is compared and contrasted to the flow of ions through a trans-membrane channel

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 $\tau_G \sim N$ collisionless relaxation leads to a gravothermal collapse

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

A frenagem eletromagnética de um ímã que cai

A model is presented which allows to analytically calculate the terminal velocity of cylindrical magnets falling through nonferromagnetic pipes. Experimental results are presented for various magnets associated in series. The results are found to agree very well with the theoretical predictions. The experiments and the theory provide a very instructive demonstration of the Faraday- Lenz law.É apresentado um modelo para calcular a velocidade terminal de queda de magnetos cilíndricos em um tubo condutor nãoferromagnético. Resultados experimentais para diversos magnetos associados em série são relatados, corroborando as previsões teóricas. Os experimentos e o modelo teórico desenvolvido fornecem uma interessante ilustração da Lei de Faraday-Lenz