A high power millimeter (mm) wave, in the presence of a magnetic wiggler, p
roduces a large Longitudinal ponderomotive force that can accelerate electr
ons. When a plasma of density n similar to n(cr), where n(cr) is critical d
ensity, is introduced in the interaction region, the ponderomotive force re
sonantly drives a plasma wave that accelerates electrons to higher energies
. However, propagation of the mm wave requires a guide magnetic held; O-mod
e requiring less field than the X-mode, The plasma wave in this situation g
oes over to the upper hybrid (UH) mode. A parabolic plasma density profile
with minimum on axis provides guiding for the mm wave as well as the UH wav
e, the latter being more strongly localized than the former. The UH wave, f
or typical parameters, can accelerate electrons to several tens of megaelec
tronvolts.