A method of calculating spatiotemporal distribution of ion temperature in hot spots of one-dimensional implosions based on multi-diagnostic parameter analysis

<sec>In inertial confinement fusion (ICF), the ion temperature of hot spots is a critical parameter determining fusion gain, and its spatiotemporal distribution provides insights into energy deposition and dissipation processes. However, directly diagnosing such a distribution remains challenging due to the extreme spatiotemporal scales of hot spots (~100 ps, ~100 μm). To cope with this challenge, a computational method of reconstructing the spatiotemporal ion temperature distribution in one-dimensional implosion hot spots through multi-diagnostic parameter analysis is proposed in this work.</sec><sec>Taking shock-compressed implosions for example, the physical process is simulated via the one-dimensional (1D) radiation-hydrodynamics code Multi1D. The analysis shows two key mechanisms. One is that the propagation of reflected shock waves governs the rapid temperature rise and spatiotemporal differences in peak temperatures, and the other is that ion-ion conduction and ion-electron thermal conduction dominate the slow temperature decline. These mechanisms are found to be universal under different initial conditions. Based on these characteristics, a mathematical model with 10 parameters is developed to describe the spatiotemporal ion temperature distribution. The relationships between this distribution and experimental diagnostic quantities, including neutron yield, average ion temperature, time-dependent fusion reaction rate, and neutron imaging profile, are rigorously derived.</sec><sec>Using computational cases as simulated experiments, key diagnostic parameters related to ion temperature are generated as constraints. Genetic algorithm is employed to optimize the model parameters, and the resulting ion temperature distributions show excellent agreement with simulation results in the fusion phase, thus validating the effectiveness of the method.</sec><sec>This approach provides a way to reconstruct the ion temperature distribution in near-one-dimensional ICF experiments by using traditional neutron diagnostics, thus bypassing the limitations of spatiotemporally resolved measurement techniques. Although theoretically extensible to 2D/3D scenarios, challenges such as increased model complexity and insufficient multidimensional diagnostic data must be addressed. This method provides a valuable experimental way for understanding formation and evolution of hot spots, calibrating radiation-hydrodynamics codes, and optimizing implosion designs, which is of great significance for achieving fusion ignition.</sec>