Since its discovery in 1996, the source of the bright H-alpha emission (up to 750 mR) along the Magellanic Stream has remained a mystery. There is no evidence of ionising stars within the HI stream, and the extended hot halo is far too tenuous to drive strong shocks into the clouds. We now present a hydrodynamical model that explains the known properties of the H-alpha emission and provides new insights on the lifetime of the Stream clouds. The upstream clouds are gradually disrupted due to their interaction with the hot halo gas. The clouds that follow plough into gas ablated from the upstream clouds, leading to shock ionisation at the leading edges of the downstream clouds. Since the following clouds also experience ablation, and weaker H-alpha (100-200 mR) is quite extensive, a disruptive cascade must be operating along much of the Stream. In our model, the clouds are evolving on timescales of 100-200 Myr, such that the Stream must be replenished by the Magellanic Clouds at a fairly constant rate. The ablated material falls onto the Galaxy as a warm drizzle which suggests that diffuse ionized gas at 10**4 K may be an important constituent of galactic accretion. The observed HI emission provides a new constraint on the rate of disruption of the Stream and, consequently, the infall rate of metal-poor gas onto the Galaxy. When the ionized component of the Stream is fully accounted for, the rate of gas accretion is 0.4 Msun/yr, roughly twice the rate deduced from HI observations alone.