The formation and evolution of hotspots is important for achieving ignition and high energy gain in inertial fusion process.However,most of relevant studies are carried out on pre-compressed plasmas with an isobaric configuration,the evolution of the hotspot in a plasma with an isochoric configuration is rarely studied.In this paper,a semi-analytical model is developed to describe the evolution of the hotspot boundary and propagation of fusion burning waves for a high-density pre-compressed plasma with an isochoric configuration in the double-cone ignition scheme.For the shock wave,the strong shock wave approximation and the quasi-isobaric approximation are reasonable.The quasi-isobaric approximation shows that as the plasma density behind the shock wave increases,the plasma temperature decreases.Because of these,the range of-α particles decreases rapidly behind the shock wave,forming an-α particle absorption peak.Therefore,considering that the hotspot is the main region whereα-particles are produced and deposited,the position of the shock peak can be used to identify the boundary of the hotspot in a high-density plasma with an isochoric configuration.It also shows that a"self-regulating burning process"exists in the burning process of the isochoric hotspot,most of α-particles are deposited in the stable region and behind the shock,and finally,transport through the shock peak and heat the cold fuel,resulting in the temperature rising.In the high-density hotspots of plasma with an isochoric configuration,the deposition of α-particles behaves as an obvious non-uniform distribution effect.By analyzing the non-uniform deposition of α-particles,the deposition rate of α-particles at the edge of spherical uniform hotspot is calculated,then the temperature and density evolution of the isochoric hotspot can be well described.The model can be used to estimate the Lawson parameter of the hotspots at the end of the early stage of ignition.It is found that a lower fast electron energy is more beneficial to ignition and high gain operation of fusion plasma.It is also shown that the high density of the hotspots in the isochoric plasma will lead to a higher fusion burning rate,which can offset the negative influence of the shock wave and even achieve higher energy gain.The semi-analytical model is verified by the hydrodynamic simulations of O-SUKI-N.
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