Alternate islands of multiple isochronous chains in wave-particle interactions.
We analyze the dynamics of a relativistic particle moving in a uniform magnetic field and perturbed by a standing electrostatic wave. We show that a pulsed wave produces an infinite number of perturbative terms with the same winding number, which may generate islands in the same region of phase space. As a consequence, the number of isochronous island chains varies as a function of the wave parameters. We observe that in all the resonances, the number of chains is related to the amplitude of the various resonant terms. We determine analytically the position of the periodic points and the number of island chains as a function of the wave number and wave period. Such information is very important when one is concerned with regular particle acceleration, since it is necessary to adjust the initial conditions of the particle to obtain the maximum acceleration.
Instituto de Física, Universidade de São Paulo, São Paulo, Brazil.
M C
MC
de Sousa
Instituto de Física, Universidade de São Paulo, São Paulo, Brazil.
I L
IL
Caldas
Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brazil.
A M
AM
Ozorio de Almeida
Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil.
F B
FB
Rizzato
Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil.
R
R
Pakter