Particle acceleration with the axial electric field of a TEM10 mode laser beam

Abstract

Due to their finite spot size, optical beams have small axial field components. For a Gaussian TEM₁₀ mode, the axial electric field has a maximum on the optical axis while the transverse field vanishes there. The possible use of this axial field for the acceleration of highly relativistic particles has been studied.

The ratio of the axial to the maximum transverse electric field is inverse proportional to the spot size radius; for a spot size radius of ω ₀ ≈ 100 λ, it is in the order of 4 10⁻³. But the transverse field components seen by the highly relativistic particles are significantly reduced by the Lorentz transformation, thus the axial field components become important.

Finite spot size and axial field are inevitably connected to a phase velocity along the axis which is by approximately a factor of (1 − π/(kw ₀)²)⁻¹ above c. Consequently synchronism between wave and particle beam cannot be sustained for more than half a RF period. But due to the relativistic Doppler shift, particles can travel approximately the confocal length, kw ²₀ , before the field reverses sign. The particle energy increase is proportional to the square root of the laser power, and lies in the order of 10 MeV for laser powers of 10¹² W.¹