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A promising configuration for laser acceleration is the cyclotron-resonance laser accelerator (CRLA) [1], where a coherent electromagnetic wave may transfer a large amount of energy to a beam of electrons gyrating in a guide magnetic field. This large amount of transferred energy takes place because of the autoresonance mechanism [2,3] where, under soine ideal conditions, an initial wave-particle synchronism is self-sustained throughout the accelerating period. It has been observed, however, that one of these CRLA ideal conditions is hardly obtained in feasible experimental schemes. This particular condition is the one requiring the laser field to be dispersionless [4], a very restrictive condition if one takes into account dispersive effects arising from the confining wave guides [5]. The analysis of dispersive CRLA's has been recently carried out both analytically (in a perturbative fashion) [6] and numerically [4], where it was shown that a typically small degree of dispersion may create some severe limits to the accelerating efficiency. On the other hand, for the unlikely situation of extremely small dispersion and equally small wave amplitudes, the accelerating efficiency was shown to be larger than in the previous case, turning out to be critically dependent on the total amount of free electromagnetic energy. In this latter case, one cannot simply solve the relativistic particle equations under the influence of a given electromagnetic wave; one has to consider the selfconsistent dynamics of particle plus waves. In the present work we intend to investigate further the mentioned self-consistent wave-particle interaction. To this end, we develop a general formalism where under the maeroparticle approximation, both particle and wave dynamics can be canonically obtained from one generalized Hamiltonian. The formalism is general in two basic senses: it is not perturbative in wave amplitudes [7], and it allows for the inclusion of a frequency mismatch fi=m —(co,o/y+kv, ) (&co, where co is the wave frequency, k is the wave vector, co,o is the nonrelativistic cyclotron frequency, v, o is the initial longitudinal velocity, and yo is the initial value of the relativistic factor (henceforth, subindex "0" denotes initia1 value). Magnetic field tape ring is not included, but by varying the mismatch, we shall show how to compensate and even partially eliminate the limiting effects due to dispersion on acceleration processes. The formalism will be applied in the microwave range (frequencies on the order of GHz), where we shall see that even if one considers dispersive systems, wave dynamics may be an important factor to take into consideration in view of the fact that careful choices of the mismatch can cause the particles to absorb an amount of energy comparable to that contained in the initial laser field. This paper is organized as follows. In Sec. II we introduce the model and briefly derive the complete set of wave-particle dynamical equations; in Sec. III, using the macroparticle approximation, we obtain a self-consistent Hamiltonian formalism governing the dynamics; in Sec. IV we perform a numerical investigation on the analytical results along with a simulation analysis to check the validity of the macroparticle approach, and in Sec. V we conclude the work.

physical review. e, statistical physics, plasmas, fluids, and related interdisciplinary topics

Effects of frequency mismatch and wave dispersion on a self-consistent Hamiltonian model for an arbitrary-amplitude cyclotron-resonance laser accelerator