Satellite and ground-based studies have demonstrated that coherent VLF signals propagating in the terrestrial magnetosphere can trigger diffuse and structured emission bursts. A triggering mechanism for diffuse emissions which may operate when the coherent signal propagates parallel to the geomagnetic field is investigated in this note. The theory is based on the concept that trapping of energetic particles in the potential wells of the coherent signal alters the gradient of the particle distribution function with respect to parallel velocity. If, as a result of trapping, the gradient becomes sufficiently steep, broad band wave growth takes place as predicted by established theory. The resulting pitch angle diffusion of particles produces a more stable configuration in which the steep gradient is reduced towards that corresponding to the marginally stable distribution. For initially positive gradients in the energetic electron distribution function with respect to parallel velocity, wave growth takes place above the frequency of the causative coherent signal. The theory predicts that the bandwidth of emissions triggered in this way should rapidly increase with time and may reach maximum widths of several hundred hertz.