Meson-catalyzed fusion in ultradense plasmas

We first argue that negative muons in the MeV energy range can be fully stopped in warm-dense-matter and fast ignition scenario ultradense plasmas on a picosecond time scale by taking into account the slowing down of partially degenerate electrons and charged hydrogen isotope ions taken as classical. Atomic and molecular recombinations within these plasmas on the lowest available exoatom bound states are then demonstrated. The very existence of in situ produced exoatoms can be proved with x-ray line Stark broadening. Finally, a former conjecture about the negligibility of meson sticking on fusion-produced particles is reinforced. Mesonic catalysis of deuterium-tritium fusion reactions is then shown to be possible in short-lived plasma targets with rates that are orders of magnitude above cold deuterium reactions. The dipole exoatom orientations clearly favor the cold and long-lived warm-dense-matter option.

Figure 1

(a) Electron-electron covariant Möller diagram. (b) D-electron-disintegration and (c) T-electron-disintegration. In (b) and (c) ${\pi }^{-}$ appears when REB energy $E_b\ge 150\mathrm{MeV}$.

Figure 2

X-ray (Stark) line profiles emitted by D/T $\mu$ exoatoms in FIS plasmas ($N_e={10}^{26}/{\mathrm{cm}}^3, T=1$ keV). Energies are in Ry = 2812.35 eV (muon a.u.). Lyman-$\alpha$ with unperturbed $\lambda =6.146\AA$.

Figure 3

Three-body $\mathrm{D}/\mathrm{T}-\mu -\mathrm{D}/{\mathrm{T}}^{+}$ recombination rates $\overline{K}({\text{cm}}^3/\text{ps})$ in terms of target plasma temperature $T$ (eV) parametrized with dipole contribution for $n=2$. $c=0.1$ (blue) qualifies a rotating dipole and $c=1$ (orange) a fixed one. $c=0$ (light green) advocates only a polarizable dipole. (a) Geometry of D/T ion interacting with exoatom $\mathrm{D}/\mathrm{T}\mu$, (b) WDM target ($N=5.64\times {10}^{23}/{\text{cm}}^3,T=1.75\text{eV}$), (c) FIS target ($N={10}^{26}/{\text{cm}}^3,T=1\text{keV})$.

Figure 4

Solutions $N_{\mu }\left(t\right)$ (blue) and $N_{\text{D/T}\mu }\left(t\right)$ (orange) from Eqs. (27a) and (27b) in terms of time (ps) for exoatom main quantum number $n$ and dipole contribution $c$ [Eq. (16)] in a WDM plasma with $N_e=5.64\times {10}^{23}{\mathrm{cm}}^{-3}, T=1.75\text{eV}$, and 500 ps duration.

Figure 5

Same as Fig. 4 for fast ignition plasmas (FIS) with $N_e={10}^{26}{\mathrm{cm}}^{-3}, T=100$ eV, and 1 ps duration.

Figure 6

Same as Fig. 5 for FIS plasmas with $T=1$ keV.