  We show that a short relativistic electron beam propagating in a plasma with
a density gradient perpendicular to the direction of motion generates a
wakefield in which a witness bunch experiences a transverse force. A density
gradient oscillating along the beam path would create a periodically varying
force---an undulator, with an estimated strength of the equivalent magnetic
field more than ten Tesla. This opens an avenue for creation of a
high-strength, short-period undulators, which eventually may lead to
all-plasma, free electron lasers where a plasma wakefield acceleration is
naturally combined with a plasma undulator in a unifying, compact setup.
