Thermonuclear Fusion: The Basic Process — Question 2

Question 2

Fusion product recoil places most deuterium-tritium energy in the neutron

For a D-T reaction with negligible initial center-of-mass kinetic energy, take Q=17.6 MeV and approximate final masses by $m_\alpha=4m_n$. Treat product motion as nonrelativistic.

1. Derive the neutron and alpha kinetic energies.

2. Find the fraction immediately available in the charged product and its speed relative to the neutron.

Question 2 - Solution

Fusion product recoil places most deuterium-tritium energy in the neutron

(a) Method and calculation

$$p_\alpha=p_n,\quad K_\alpha/K_n=m_n/m_\alpha=1/4.$$$$\boxed{K_\alpha=Q/5=3.52\,\mathrm{MeV},\quad K_n=4Q/5=14.08\,\mathrm{MeV}}.$$

(b) Interpretation and further calculation

$$\boxed{f_{\mathrm{charged}}=K_\alpha/Q=.200}.$$$$m_\alpha v_\alpha=m_nv_n\Rightarrow\boxed{v_\alpha/v_n=1/4}.$$

Physical check

The charged alpha can transfer energy to a plasma through electromagnetic interactions. The neutron is not magnetically confined. Relativistic corrections are neglected.