Abstract
A formalism is developed to describe the propagation along a slowly varying magnetic field of purely transverse cyclotron waves. By an expansion of the coupled set of Vlasov-Maxwell equations, a one-dimensional wave equation is derived, which is applied to the case where the field configuration is a magnetic mirror with small field variation which includes points of cyclotron resonance where the local gyrofrequency is equal to the wave frequency. An investigation is made of the processes whereby particles trapped in the mirror field can cause anomalous transmission and reflection of the wave by a nonlocal mechanism. It is found that the nonlocal processes are most significant when the function which gives the total phase difference observed by a trapped particle on its orbit between the point of damping of the incident wave and that of excitation of the transmitted or reflected wave is stationary with respect to both the energy and magnetic moment of the particle.
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