[en] In the presence of a magnetic wiggler, a high power millimetre (mm) wave propagating through a magnetized plasma of density close to critical, excites a large amplitude Langmuir wave. The amplitude of the Langmuir wave shows resonant enhancement around cyclotron resonance, however, the wiggler period required to produce large phase velocity Langmuir waves approaches to impractically small values near resonance. As a compromise, one could choose ω_L/ω_c = 0.7 for optimal excitation of Langmuir waves where ω_L and ω_c are the mm wave and electron cyclotron frequencies respectively. The amplitude of the Langmuir wave attains saturation by relativistic effects. For a 36 GHz wave with 1 MW/cm² power density, the field of the Langmuir wave for optimum parameters turns out to be > 30 MV /m. The Langmuir wave can be employed to accelerate electrons. The acceleration length however, scales inversely with the frequency of the mm wave. (author)