  Direct laser acceleration of electrons is considered in a strongly magnetized
plasmoid with the magnetic field strength allowing for reaching the
auto-resonance. The plasmoid may be optically created by irradiation of
specially designed targets with an auxiliary intense laser beam at the previous
stage of interaction in a possible all-optical setup. Specifics of the strongly
magnetized plasma solenoid may be critically important for the resonant
processes where a small deviation of the parameters destroys the matching
conditions. The process of the autoresonant electron acceleration is analyzed
for different configurations inherent in the possible realizations of the
setup, estimates for the efficiency of acceleration and resonance magnetic
fields are proposed. Despite the modifications of the autoresonance conditions
and the presence of collective effects, generation of energetic electron
bunches in a realistic setup may be possible and effective.
