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| 1 | +.. Copyright Celeritas contributors: see top-level COPYRIGHT file for details |
| 2 | +.. SPDX-License-Identifier: CC-BY-4.0 |
| 3 | +
|
| 4 | +.. _api_mucf_physics: |
| 5 | + |
| 6 | +************ |
| 7 | +MuCF Physics |
| 8 | +************ |
| 9 | + |
| 10 | +The muon-catalyzed fusion physics in Celeritas is derived from custom |
| 11 | +implementations written by Ara Knaian (Acceleron Fusion), Kevin Lynch |
| 12 | +(Fermilab), and Sridhar Tripathy (UC Davis), not available in the standard |
| 13 | +Geant4 source code. |
| 14 | + |
| 15 | +Currently, the physics is managed by a single ``Executor`` that is responsible |
| 16 | +for the full cycle, from atom formation to generating the outgoing secondaries |
| 17 | +after fusion occurred. |
| 18 | + |
| 19 | +Physics overview |
| 20 | +================ |
| 21 | + |
| 22 | +Muons can be used to fuse deuterium-tritium mixtures at low temperatures |
| 23 | +:cite:`kamimura-mucf-2023`. This is caused by the fact that molecular orbital |
| 24 | +radii are inversely proportional to the mass of the lepton: the muon, with a |
| 25 | +mass approximately 207 times larger than the electron's, leads to an orbital |
| 26 | +radius about 207 times smaller. The reduced molecular orbital leads to a higher |
| 27 | +nuclear wavefunction overlap, which in turn leads to a fusion reaction that does |
| 28 | +not require high-temperature, magnetic-confined plasma to happen. |
| 29 | + |
| 30 | +The full cycle time is a few orders of magnitude smaller than the average decay |
| 31 | +time of the muon (:math:`2.2 \times 10^{-6}` s). Muonic atom formation takes |
| 32 | +about :math:`10^{-12}-10^{-13}` s, muonic molecule formation takes |
| 33 | +:math:`10^{-8}-10^{-10}` s, and the fusion process itself is at the order of |
| 34 | +:math:`10^{-12}` s. In most instances, the muon is free after the fusion |
| 35 | +process, leading to another cycle and giving the muon-catalyzed fusion its name. |
| 36 | +The possible channels for all deuterium-tritium molecules are outlined below: |
| 37 | + |
| 38 | +- :math:`(dd)_\mu` |
| 39 | + |
| 40 | + - :math:`\longrightarrow ^3\text{He} + \mu + n + 3.27 \ \text{MeV}` |
| 41 | + |
| 42 | + - :math:`\longrightarrow (^3\text{He})_\mu + n + 3.27 \ \text{MeV}` |
| 43 | + |
| 44 | + - :math:`\longrightarrow t + \mu + p + 4.03 \ \text{MeV}` |
| 45 | + |
| 46 | + - :math:`\longrightarrow (t)_\mu + p + 4.03 \ \text{MeV}` |
| 47 | + |
| 48 | +- :math:`(dt)_\mu` |
| 49 | + |
| 50 | + - :math:`\longrightarrow \alpha + \mu + n + 17.6 \ \text{MeV}` |
| 51 | + |
| 52 | + - :math:`\longrightarrow (\alpha)_\mu + n + 17.6 \ \text{MeV}` |
| 53 | + |
| 54 | +- :math:`(tt)_\mu` |
| 55 | + |
| 56 | + - :math:`\longrightarrow \alpha + \mu + 2n + 11.33 \ \text{MeV}` |
| 57 | + |
| 58 | + - :math:`\longrightarrow (\alpha)_\mu + 2n + 11.33 \ \text{MeV}` |
| 59 | + |
| 60 | +In the cases where the muon sticks to an outgoing nucleus, e.g. generating a |
| 61 | +:math:`(\alpha)_\mu`, the catalysis is halted. This happens at a fraction of a |
| 62 | +percent to a few percent level, and the number that represents the fraction of |
| 63 | +times this happens, with respect to the case where the muon is free, is called |
| 64 | +the sticking factor. |
| 65 | + |
| 66 | +A single muon can repeat this fusion cycle somewhat between 100 to 400 times. |
| 67 | +The total number of fusion cycles produced by a single muon defines how much |
| 68 | +energy can be extracted from it, in the effort of reaching a break-even |
| 69 | +scenario. This is the threshold point where the energy required to generate the |
| 70 | +muon is equal to the energy produced by said muon through the muCF cycles. The |
| 71 | +sticking factor and the fusion cycle time are the main conditions that define |
| 72 | +how many fusion cycles a muon can undergo. The fusion cycle time depends on the |
| 73 | +d-t mixture, its temperature, and on the final spin of the molecule. Only muonic |
| 74 | +molecules where the total spin :math:`F = I_N \pm 1/2` is on, or has a |
| 75 | +projection onto the total angular momentum J = 1 are reactive. The spin states |
| 76 | +of the three possible muonic molecules are summarized in table |
| 77 | +:numref:`muon_spin_states`. |
| 78 | + |
| 79 | + |
| 80 | +.. _muon_spin_states: |
| 81 | + |
| 82 | +.. table:: Spin states of dt muonic molecules |
| 83 | + |
| 84 | + +------------------+-----------+--------------+-------------------------+---------------------+ |
| 85 | + | Molecule | Nuclei | :math:`I_N` | :math:`F = I_N \pm 1/2` | Reactive states (F) | |
| 86 | + +==================+===========+==============+=========================+=====================+ |
| 87 | + | :math:`(dd)_\mu` | 1, 1 | 0, 1, 2 | 1/2, 3/2, 5/2 | 1/2, 3/2 | |
| 88 | + +------------------+-----------+--------------+-------------------------+---------------------+ |
| 89 | + | :math:`(dt)_\mu` | 1, 1/2 | 1/2, 3/2 | 0, 1, 2 | 0, 1 | |
| 90 | + +------------------+-----------+--------------+-------------------------+---------------------+ |
| 91 | + | :math:`(tt)_\mu` | 1/2, 1/2 | 0, 1 | 1/2 | 1/2 | |
| 92 | + +------------------+-----------+--------------+-------------------------+---------------------+ |
| 93 | + |
| 94 | +Input |
| 95 | +===== |
| 96 | + |
| 97 | +The input data is currently hardcoded in the |
| 98 | +:cpp:class:`celeritas::inp::MucfPhysics` structure, which includes |
| 99 | +temperature-dependent rates for mean cycle time, muonic atom transfer, and |
| 100 | +muonic atom spin flip. The muon-catalyzed fusion process is activated by |
| 101 | +enabling the ``mucf_physics`` option in |
| 102 | +:cpp:class:`celeritas::ext::GeantPhysicsOptions`. |
| 103 | + |
| 104 | +.. doxygenclass:: celeritas::inp::MucfPhysics |
| 105 | + |
| 106 | +.. todo:: Expand description when hardcoded data is finalized. |
| 107 | + |
| 108 | +Geant4 integration |
| 109 | +------------------ |
| 110 | + |
| 111 | +For integration interfaces, if ``mucf_physics`` option in |
| 112 | +:cpp:class:`celeritas::ext::GeantPhysicsOptions` is enabled, the muon-catalyzed |
| 113 | +fusion data is constructed when the ``G4MuonMinusAtomicCapture`` process is |
| 114 | +registered. |
| 115 | + |
| 116 | +.. todo:: Add process/model/executor details |
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