The most feasible nuclear reaction for a "first-generation" fusion reaction is the one involving deuterium (D) and tritium (T): $$ \mathrm{D} + \mathrm{T} \rightarrow \alpha (3.5\;\mathrm{MeV}) + n (14.1\;\mathrm{MeV}) $$ Tritium is not a primary fuel and does not exist in significant quantities naturally since it decays with a half life of 12.3 years. It therefore has to be "bred" from a separate nuclear reaction. Most fusion reactor design concepts employ a lithium "blanket" surrounding the reaction vessel which absorbs the energetic fusion neutrons to produce tritium in such a reaction.

There are two stable isotopes of lithium, $\mathrm{^6Li}$ (7.59 % abundance) and $\mathrm{^7Li}$ (92.41 %). Both absorb neutrons to produce tritium:

\begin{align*}
\mathrm{^6Li} + \mathrm{n} & \rightarrow \mathrm{T} + \alpha + 4.8\;\mathrm{MeV}\\
\mathrm{^7Li} + \mathrm{n} & \rightarrow \mathrm{T} + \alpha + \mathrm{n} - 2.466\;\mathrm{MeV}
\end{align*}

Unfortunately, only the reaction with the less-abundant isotope has a significant cross section for thermal neutrons, and even then a neutron multiplier is required because of unavoidable neutron losses and incomplete geometric coverage of the blanket (endothermic nuclear reactions involving $\mathrm{^9Be}$ or $\mathrm{Pb}$ have been suggested). Enrichment of lithium is currently a messy and expensive activity involving large quantities of mercury: a viable method will need to be developed before a nuclear fusion reactor can become a reality.

The following code uses the ENDF data files Li-6(n,T)He-4.endf and Li-7(n,n+T)He-4.endf to plot the cross sections for the above reactions.

import numpy as np from matplotlib import rc import matplotlib.pyplot as plt rc('font', **{'family': 'serif', 'serif': ['Computer Modern'], 'size': 14}) rc('text', usetex=True) def read_xsec(filename): """Read in the energy grid and cross section from filename.""" E, xs = np.genfromtxt(filename, comments='#', unpack=True, usecols=(0,1)) return E, xs # Read in the data files: # 6Li + n -> T + 4He + 4.8 MeV E_Li6, Li6_xs = read_xsec('Li-6(n,T)He-4.endf') # 7Li + n -> T + 4HE + n' - 2.466 MeV E_Li7, Li7_xs = read_xsec('Li-7(n,n+T)He-4.endf') fig, ax = plt.subplots() ax.loglog(E_Li6, Li6_xs, lw=2, label='$\mathrm{^6Li-n}$') ax.loglog(E_Li7, Li7_xs, lw=2, label='$\mathrm{^7Li-n}$') # Prettify, set the axis limits and labels ax.grid(True, which='both', ls='-') ax.set_xlim(10, 1.e8) ax.set_xlabel('E /eV') ax.set_ylim(0.001, 100) ax.set_ylabel('$\sigma\;/\mathrm{barn}$') ax.legend() plt.savefig('lithium-xsecs.png') plt.show()

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