Overview of the muon catalyzed fusion cycle

  

Figure 1.1: Greatly simplified cycle of muon catalyzed fusion in D/T mixture.

Figure 1.1 illustrates a greatly simplified scheme of the muon catalyzed fusion ($\mu$CF) cycle in a D/T mixture. The system has attracted the greatest interest because of its most favorable efficiency for fusion catalysis (see for a review [1,2,3,4]). Note that a homogeneous mixture, of mostly gas or liquid, has been used traditionally, as opposed to the inhomogeneous targets used in this thesis.

A muon injected into the hydrogen target will slow down and form a small atomic system, muonic deuterium ($\mu d$) or muonic tritium ($\mu t$), by replacing the electron in the atom. If a $\mu d$ is formed, the muon will be transferred to a triton forming a more tightly bound $\mu t$. The $\mu t$ will then collide with a deuterium molecule and form the muonic molecule $d\mu t$. Molecular formation occurs predominantly via a resonant mechanism, in which the energy released from the formation of the $d\mu t$ molecule is absorbed by the rotational and vibrational excitation of the molecular complex $[(d\mu t)dee]$ where the compact object $d\mu t$ acts as a pseudonucleus. Muonic molecule formation can also occur by releasing the energy via the Auger process (non-resonant formation), but this rate is much smaller than resonant formation. Because the size of the muonic molecule is smaller than ordinary molecules by its mass ratio ( $m_{\mu}/m_{e}$) in zeroth order, the internuclear distance in $d\mu t$ is small enough that fusion takes place within 10^-12 s. After fusion, the muon is released more than 99% of the time, but a small probability exists for a process known as sticking in which the muon becomes attached to the charged fusion product, in this case an $\alpha$ particle. If sticking occurs, the muon is lost from the cycle, and this indeed limits the ultimate number of fusions that one muon can catalyze. In the following sections, we will discuss each process involved in some detail.