  To maximize the charge of a high-energy electron beam accelerated by an
ultra-intense laser pulse propagating in a subcritical plasma, the pulse length
should be longer than both the plasma wavelength and the laser pulse width,
which is quite different from the standard bubble regime. In addition, the
laser--plasma parameters should be chosen to produce the self-trapping regime
of relativistic channeling, where the diffraction divergence is balanced by the
relativistic nonlinearity such that the laser beam radius is unchanged during
pulse propagation in a plasma over many Rayleigh lengths. The condition for
such a self-trapping regime is the same as what was empirically found in
several previous simulation studies in the form of the pulse width matching
condition. Here, we prove these findings for a subcritical plasma, where the
total charge of high-energy electrons reaches the multi-nC level, by
optimization in a 3D PIC simulation study and compare the results with an
analytic theory of relativistic self-focusing. A very efficient explicitly
demonstrated generation of high-charge electron beams opens a way to a
high-yield production of gammas, positrons, and photonuclear particles.
