The advantage of muons as the medium with which to sustain a chain reaction is that, unlike neutrons in fission, they are charged and can thus have freedom of movement constrained (by magnetic field or electrostatics). The downside is short lifetime.
From: Bob Cook I think the rate of reaction is influenced by a stimulus of some sort—probably electric or magnetic to create proper resonances. Multiple coherent systems are required, each to be stimulated in turn to reach a lower energy state… As Jones recently noted, it is hard to maintain a chain reaction in a coherent system.
