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

Generation of a wakefield undulator in plasma with transverse density gradient