Not yet reviewed by Pith; the record is open.

The detonation behaviors during thermonuclear burning indicate a state of robust hot spot burning and are widely present in astronomical phenomena, such as supernovae. In this work, we propose an analytical model including alpha-particle deposition at the shock front, which significantly lowers the detonation threshold. The new temperature threshold is 13.4 keV for the isochoric ignition and 25.1 keV for the isobaric ignition, both of which are more accessible experimentally. When a shock wave is present, alpha-particle deposition occurs at the high-density shock front instead of the cold fuel, accelerating the burning wave by approximately 20%. To further validate these findings, we conducted a series of 3D radiation hydrodynamics simulations using finite isochoric hot spots with different fast electron energy. The results reveal a rise in burn-up fraction caused by the detonation wave with a deposited fast electron energy about 8.5 kJ. This work can provide a reference for the realization of fusion energy via fast ignition schemes, such as the double-cone ignition scheme. This work also shows the possibility of studying the detonation in astrophysics with laser driven fast ignition.