The path of radioactivity through the missile facility would point at the facility with the beam, because the showers of induced particles would be along the sa

The path of radioactivity through the missile facility would point at the facility with the beam, because the showers of induced particles would be along the same axis. You then nuke that country out of existence, as is standard policy if governments fear an attack on their strategic capability. You could also, eg, track the facility ingesting that incredible amount of power — whose signature would be basically impossible to hide from satellites.