Conditions at which the charged particles can be accelerated to the significant energies under interaction with the laser or maser radiation and the static magnetic field have been studied. The studies have been performed on the basis of the derived by the author's analytical solutions. With the example of an electron, the trajectory, velocity and kinetic energy as a function of the acceleration time have been shown. We have defined the maximal static magnetic field which was found to be appropriate to achieve the resonance condition in the acceleration process. At certain values of the magnetic field, the projections of the 3-dimensional trajectory onto the plane perpendicular to the axis show quite regular curves in the shape of epicycloids or hypocycloids with convex and concave bows, respectively. In the resonance region, there appears an increase in effectiveness of the energy transfer from the electromagnetic field to the accelerated particle and it can be realized simply through a very small increase of magnetic induction. The significant gain of the energy by the accelerated electron occurs only in the case of inversely directed laser beam velocity and the static magnetic field. The maximal energy can be increased by rising the laser beam or the magnetic field intensities. The energy gained by an electron depends on the acceleration time and it increases until the maximum energy is reached. The distance the electron covers to gain the maximal energy, depends on the intensities of the laser beam and the static magnetic field, and on the acceleration time. The analysis of acceleration process in the maser beam shows many advantages arising from the longer wavelength radiation emitted. The essential advantage is connected with the reduction of the static axial magnetic field intensity.
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