Direct laser-driven electron acceleration and energy gain in helical beams

A detailed study of direct laser-driven electron acceleration in paraxial Laguerre-Gaussian modes corresponding to helical beams $\text{LG}_{0m}$ with azimuthal modes $m=\left\{1,2,3,4,5\right\}$ is presented. Due to the difference between the ponderomotive force of the fundamental Gaussian beam $\text{LG}_{00}$ and helical beams $\text{LG}_{0m}$ we found that the optimal beam waist leading to the most energetic electrons at full width at half maximum is more than twice smaller for the latter and corresponds to a few wavelengths $\Delta w_0=\left\{6,11,19\right\}\lambda_0$ for laser powers of $P_0 = \left\{0.1,1,10\right\}$ PW. We also found that for azimuthal modes $m\geq 3$ the optimal waist should be smaller than $\Delta w_0 < 19 \lambda_0$. Using these optimal values we have observed that the average kinetic energy gain of electrons is about an order of magnitude larger in helical beams compared to the fundamental Gaussian beam. This average energy gain increases with the azimuthal index $m$ leading to collimated electrons of a few $100$ MeV energy in the direction of the laser propagation.