Applied General & Particle Physics, Hydrogen Energy and Renewable Power Research
As in any form of nuclear fusion, the energy release is the difference in nuclear mass between the initial and final fusion states. For the case of deuterium plus tritium fusion into Helium and a neutron: \( d + t \rightarrow \alpha + n \) the sum of the masses of the initial state free Hydrogen nuclei (the deuteron mass \( m_d = 1.88 \) GeV and triton mass \( m_t = 2.81 \) GeV) are together greater than the mass of the Helium nucleus (the \( \alpha \) particle mass \(m_\alpha = 3.73\) GeV) and neutron (\(m_n = 0.939\) GeV). By Einstein energy-mass equivalence $$E=mc^2$$ the mass difference between \( (m_d + m_t) - ( m_\alpha + m_n ) = 17.58\) MeV = \(X\) kWh is the nuclear energy release per fusion and since this is miniscule, then the number of fusion reactions per hour must be gargantuan (\( Y \)) to achieve 1 GW of power.
If there are then \(10^{15}\) muons per bunch, \(500\) bunches per second then there are \(1.8 \times 10^{21}\) muons per hour in the μCF accelerator-reactor and since there are more than 100 fusions per muon then this implies \(1.8 \times 10^{23}\) fusions per hour. If this could be comparable to \( Y \), then this μCF accelerator-reactor could compete at annual energy production levels with current nuclear fission reactors while yet generating only a miniscule fraction of the hazardous nuclear waste materials inevitably and unavoidably produced by them. (Compare Maine Yankee -- a 900 MW facility at 61% annual duty cycle delivering \( E_{out} \simeq 4,800 \) GWh, decommissioned 1995 yet still hazarding 86,040 spent-fuel-rod assemblies in 60 nuclear waste cannisters under 24/7/365 military guard in on-site pools. There are no spent-fuel-rod assemblies -- none, zero -- produced by μCF accelerator-reactors.)
The question of course is whether the condition is met to exceed breakeven \( E_{out} > E_{in} \). The \( E_{in} \) needed to drive this μCF accelerator-reactor has so far been greater than this output energy \( E_{out} \). Accordingly, all prior μCF programs shut down a decade or more ago, although I maintain & strongly advocate that μCF ought to continue to be pursued as the demonstrable neutron source that it is and has been for the last half century.
(Were requisite financial resources available, I would vigorously conduct my own μCF program not for energy but rather neutron production directed toward nuclear waste elimination which I denote mATW. To be sure, there would be energy production \( E_{out} \) that would certainly reduce Opex but of course not enough to exceed \( E_{in} \). Determining just how much Opex can be reduced is a matter for experimental observation. If significant, however, this could perhaps render such a μCF accelerator-reactor economically viable.)
Discovery of Muon Catalyzed Fusion (1957) took place when Luis Alvarez was analyzing the results of experimental observations which were unexplained. To explain particle tracks which had electric charge of +2 (more curvature than charge +1 particles) and mass of α particles (Helium nuclei) in the observations, Alvarez theorized that the muon was binding together hydrogen isotopes (deuterons and tritons) into muon-molecules -- as opposed to the familiar electron-molecules of everyday experience. Since the muon binding orbit in such a hydrogenic muo-molecule was 200 times smaller than the eqivalent electron orbits, Alvarez theorized that the deuteron and triton spatially extended wave functions overlapped sufficiently for the quantum mechanics effect of tunneling to occur result in the nuclear fusion reaction of d + t -> α + n. Since the final state neutron is neutral it is not bent by a magnetic field as would be the α particle.
Discovery of Muon Catalyzed Fusion (1957) followed by identification of the Vesman Mechanism (1967) and as a talk I once attended emphasized something significant in 1977, 1987.....it seemed always following that pattern! A complete description of muCF