Radiation transport simulations were used to analyse neutron imaging with the current-biased kinetic inductance detector (CB-KID). The PHITS Monte Carlo code was applied for simulating neutron, $^{4}$He, $^{7}$Li, photon and electron transport, $^{10}$B(n,$alpha$)$^{7}$Li reactions, and energy deposition by particles within CB-KID. Slight blurring in simulated CB-KID images originated $^{4}$He and $^{7}$Li ions spreading out in random directions from the $^{10}$B conversion layer in the detector prior to causing signals in the $X$ and $Y$ superconducting Nb nanowire meander lines. 478 keV prompt gamma rays emitted by $^{7}$Li nuclei from neutron-$^{10}$B reactions had negligible contribution to the simulated CB-KID images. Simulated neutron images of $^{10}$B dot arrays indicate that sub 10 $mu$m resolution imaging should be feasible with the current CB-KID design. The effect of the geometrical structure of CB-KID on the intrinsic detection efficiency was calculated from the simulations. An analytical equation was then developed to approximate this contribution to the detection efficiency. Detection efficiencies calculated in this study are upper bounds for the reality as the effects of detector temperature, the bias current, signal processing and dead-time losses were not taken into account. The modelling strategies employed in this study could be used to evaluate modifications to the CB-KID design prior to actual fabrication and testing, conveying a time and cost saving.
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