Ion cyclotron emission (ICE) offers a unique promise as a diagnostic of the fusion born alpha-particle population in magnetically confined plasmas. Pioneering observations from JET and TFTR found that ICE intensity P_{ICE} scales approximately linearly with the measured neutron flux from fusion reactions, and with the inferred concentration, n_{α}/n_{i}, of fusion born alpha particles confined within the plasma. We present fully nonlinear self-consistent kinetic simulations that reproduce this scaling for the first time. This resolves a long-standing question in the physics of fusion alpha-particle confinement and stability in magnetic confinement fusion plasmas. It confirms the magnetoacoustic cyclotron instability as the likely emission mechanism and greatly strengthens the basis for diagnostic exploitation of ICE in future burning plasmas.