  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. 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.
