A new hot electron kinetic equation based on the use of real space Airy functions is discussed. The electron-phonon scattering vertex in the Airy function basis is localised in real space, and when the resonant width extends to the band tail region, a field dependent suppression of scattering at low kinetic energy results. The kinetic equation is only equivalent to the Boltzmann equation for homogeneous situations, when field dependence of the scattering is neglected. A variational technique for solving the kinetic equation has been developed which allows very rapid numerical evaluation and consequently should assist in studying more complex phenomena in very small devices, or devices operating at very high electric fields.