  The direct laser acceleration (DLA) of electrons in underdense plasmas can
provide 100s of nC of electrons accelerated to near-GeV energies using
currently available lasers. Here we demonstrate the key role of electron
transverse displacement in the acceleration and use it to analytically predict
the expected maximum electron energies. The energy scaling is shown to be in
agreement with full-scale quasi-3D particle-in-cell (PIC) simulations of a
laser pulse propagating through a preformed guiding channel and can be directly
used for optimizing DLA in near-future laser facilities. The strategy towards
optimizing DLA through matched laser focusing is presented for a wide range of
plasma densities paired with current and near-future laser technology. Electron
energies in excess of 10 GeV are accessible for lasers at $I\sim
10^{21}~\mathrm{W/cm^2}$.
