Magnetized plasma can be made transparent at the cyclotron frequency by addition of a helical undulator. The purpose of the undulator is to couple the transverse (propagating) and longitudinal (non-propagating) electromagnetic waves in the plasma. The coupling is particularly strong when the electron cyclotron and plasma frequencies are equal. It is demonstrated that this coupling gives rise to ultra-slow electromagnetic waves with group velocity v_gc (where c is the speed of light in vacuum), resulting in the extreme energy compression in the plasma. A linear propagation equation for the electromagnetic wave envelope is derived, and its group velocity and group velocity dispersion are calculated. Relativistic corrections to the plasma electron motion are included to derive the nonlinear propagation equation. It is shown that, in comparison with unmagnetized plasma, an enhancement of nonlinearities of order is expected. Implications for relativistic self-focusing in the plasma are discussed.
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