This chapter discusses the technique of solving the problem of longitudinal propagation in a magnetized time-varying plasma. It considers the wave propagation in a magnetized transient plasma for the case of a rise time comparable to the period of the source wave. The chapter focuses on a perturbation technique for the computation of the scattering coefficients. A causal Green's function is developed as the basis for the perturbation. The method gives a closed-form expression for the scattering coefficients for a general temporal profile for which an exact solution is not available. The development of the Green's function and perturbation series provides a unique approach in giving the analytical insights. Using this new approach, the variation of the scattering coefficients of the frequency-shifted waves due to a finite rise time of the transient magnetized plasma can be computed individually. The linear profile, which has no analytical solution, illustrates the superiority of the approach.