We demonstrate that hybrid laser wakefield and direct acceleration (LWDA) canbe significantly improved by using two laser pulses with differentpolarizations or frequencies. The improvement entails higher energy and chargeof the accelerated electrons, as well as weaker sensitivity to the time delaybetween the leading (pump) pulse responsible for generating the wakefield, andthe trailing laser pulse responsible for direct laser acceleration (DLA). Whenthe two laser pulses have the same frequency, it is shown that it isadvantageous to have their polarization states orthogonal to each other. Aspecific scenario of a frequency-doubled ($\lambda_{\rm DLA}=\lambda_{\rmpump}/2$) DLA laser pulse is also considered, and found to be an improvementover the single-frequency ($\lambda_{\rm DLA} = \lambda_{\rm pump}$) scenario.
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