Description
Inertial electrostatic confinement (IEC) plasmas support non-Maxwellian fuel-ion velocity distribution functions (VDFs) due to electrostatic acceleration, orbit topology, charge-exchange and Coulomb collision processes. In deuterium-tritium (D-T) operation, the $ \mathrm{D(T,n)}^{4}\mathrm{He} $ reaction produces nominal 14.1 MeV neutrons whose birth energy-angle distribution is a direct functional of the reactant VDFs and of the energy-dependent differential fusion cross section.
We present a forward model that maps parameterised deuteron and triton VDFs $f_d(\mathbf{r},\mathbf{v})$ and $f_t(\mathbf{r},\mathbf{v})$ to the doubly differential neutron birth source $S_n(\mathbf{r},E_n,\Omega)$ and to angle-resolved detector observables. The local reaction rate density is evaluated without Maxwellian assumptions by
$ R_{dt}(\mathbf{r}) = n_d(\mathbf{r}),n_t(\mathbf{r}) \iint f_d(\mathbf{r},\mathbf{v}_d), f_t(\mathbf{r},\mathbf{v}_t), \sigma_{dt}(v_{rel}), v_{rel}, d^3 v_d, d^3 v_t, $
with $ v_{rel}=|\mathbf{v}_d-\mathbf{v}_t| $ and $ \sigma_{dt}(E_{cm}) $ taken from Bosch-Hale parameterisations.
The neutron birth source term is
$ S_n(\mathbf{r},E_n,\Omega)= n_d n_t \iint f_d f_t, v_{rel}, \frac{d^2\sigma_{dt}}{dE_n, d\Omega}, d^3 v_d, d^3 v_t, $
where the center-of-mass angular distribution is represented by Legendre expansions using evaluated coefficients for $\mathrm{T(d,n)}^{4}\mathrm{He}$.
Neutron kinematics are computed using fully relativistic two-body transforms via Monte Carlo sampling consistent with the DRESS framework for arbitrary reactant distributions.
The deuteron VDF includes an accelerated component derived from an incident deuteron energy distribution $g_d(E)$ set by the effective IEC potential drop and collisional broadening, enabling inference of $g_d(E)$ moments from directional neutron spectral moments and relative yields. The inverse problem is posed as a Bayesian fit of VDF parameters (effective potential drop, fast-ion fraction, anisotropy, collisional width) to measured pulse-height spectra across multiple lines of sight, providing posterior constraints on D-T ion kinetics in IEC plasmas.