Fusion Power Density

The deuterium-tritium (D-T) reaction is the most promising fusion fuel cycle for near-term reactors:

$\text{D} + \text{T} \rightarrow {}^4\text{He} (3.5\,\text{MeV}) + n (14.1\,\text{MeV})$

Total energy release: 17.59 MeV (= 2.818 \times 10^{-12}) J per reaction.

Fusion Power Density

The volumetric power density is:

$P_{\text{fus}} = n_D \cdot n_T \cdot \langle \sigma v \rangle \cdot E_{\text{fus}}$

For an equimolar D-T plasma: (n_D = n_T = n/2).

D-T Reactivity ⟨σv⟩

The Lawson approximation gives the D-T reactivity as a function of temperature (valid ~5–100 keV):

$\langle \sigma v \rangle \approx \frac{3.68 \times 10^{-18}}{T_{\text{keV}}^{2/3}} \exp\!\left(\frac{-19.94}{T_{\text{keV}}^{1/3}}\right) \quad [\text{m}^3/\text{s}]$

The reactivity peaks around T ≈ 70 keV but is already substantial at 20 keV, which is the target operating temperature for tokamak reactors.

Lawson Criterion

The Lawson criterion states that for ignition (fusion power ≥ heating power), the plasma must satisfy:

$n \cdot \tau_E > 10^{20} \text{ m}^{-3}\text{s}$

at (T \approx 20) keV, where (\tau_E) is the energy confinement time. This triple product (n T \tau_E) is the key figure of merit for fusion devices.