Laser-driven acceleration with Bessel beams

The possibility of enhancing the energy gain in laser-driven accelerators by using Bessel laser beams is examined. A formalism based on Huygens' principle is developed to describe the diffraction of finite power (bounded) Bessel beams. An analytical expression for the maximum propagation distance is derived and found to be in excellent agreement with numerical calculations. Scaling laws are derived for the propagation length, acceleration gradient, and energy gain in various accelerators. Assuming that the energy gain is limited only by diffraction (i.e., in the absence of phase velocity slippage), a comparison is made between Gaussian and Bessel beam drivers. For equal beam powers, the energy gain can be increased by a factor of ${\mathrm{N}}^{1\mathrm{/}2}$ by utilizing a Bessel beam with N lobes, provided that the acceleration gradient is linearly proportional to the laser field. This is the case in the inverse free electron laser and the inverse Cherenkov accelerators. If the acceleration gradient is proportional to the square of the laser field (e.g., the laser wakefield, plasma beat wave, and vacuum beat wave accelerators), the energy gain is comparable with either beam profile.