18 research outputs found
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
and length decays, in the axial direction, with a
characteristic length . 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 -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 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, 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 eletromagnĂ©tica de um ĂmĂŁ 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.Ă apresentado um modelo para calcular a velocidade terminal de
queda de magnetos cilĂndricos em um tubo condutor nĂŁoferromagnĂ©tico.
Resultados experimentais para diversos magnetos
associados em série são relatados, corroborando as previsÔes teóricas.
Os experimentos e o modelo teĂłrico desenvolvido fornecem
uma interessante ilustração da Lei de Faraday-Lenz