Subsonic radiative ablation model in nonlocal thermodynamic equilibrium fusion plasmas

In indirect-drive inertial confinement fusion, the radiative ablation process is vitally important for both building up of a uniform x-ray radiation in the high- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>Z</a:mi> </a:mrow> </a:math> hohlraum and subsequently capsule implosion ablated by the x-ray radiation. For the former circumstance, various supersonic and subsonic ablation models are developed under the local thermodynamic equilibrium (LTE) assumption. However, for the latter, since the capsule plasma is of low <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>Z</b:mi> </b:mrow> </b:math> , the electron and radiation temperatures are hard to achieve equality; i.e., LTE assumption breaks. So far, how to precisely describe and simulate such a non-LTE ablation process is unknown. Here, by self-consistently including the energy exchange between radiations and electrons into the radiation hydrodynamic (RHD) equations and considering the heat wave velocity as subsonic, we derive and set up a non-LTE subsonic radiative ablation model. Different from previous models where only the Rosseland opacity <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msub> <c:mi>σ</c:mi> <c:mi>R</c:mi> </c:msub> </c:math> functions, in our non-LTE model, besides <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi>σ</d:mi> <d:mi>R</d:mi> </d:msub> </d:math> , the Planck opacity <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi>σ</e:mi> <e:mi>P</e:mi> </e:msub> </e:math> plays an important role as well. Our model shows that most characteristic physical quantities of the non-LTE ablation, such as the ablation velocity, ablation pressure, and shock velocity, depend on a combination of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:msub> <f:mi>σ</f:mi> <f:mi>P</f:mi> </f:msub> <f:mo>/</f:mo> <f:msub> <f:mi>σ</f:mi> <f:mi>R</f:mi> </f:msub> </f:mrow> </f:math> , while the damping scale length of the radiation temperature scales as <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>L</g:mi> <g:mo>∝</g:mo> <g:msup> <g:mrow> <g:mo>(</g:mo> <g:msub> <g:mi>σ</g:mi> <g:mi>P</g:mi> </g:msub> <g:msub> <g:mi>σ</g:mi> <g:mi>R</g:mi> </g:msub> <g:mo>)</g:mo> </g:mrow> <g:mrow> <g:mn>1</g:mn> <g:mo>/</g:mo> <g:mn>2</g:mn> </g:mrow> </g:msup> </g:mrow> </g:math> . Therefore, we propose using a simple single multiplier <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mi>ζ</h:mi> </h:math> on both opacities as <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mover accent="true"> <i:msub> <i:mi>σ</i:mi> <i:mi>P</i:mi> </i:msub> <i:mo>̃</i:mo> </i:mover> <i:mo>=</i:mo> <i:mi>ζ</i:mi> <i:msub> <i:mi>σ</i:mi> <i:mi>P</i:mi> </i:msub> </i:mrow> </i:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mrow> <k:mover accent="true"> <k:msub> <k:mi>σ</k:mi> <k:mi>R</k:mi> </k:msub> <k:mo>̃</k:mo> </k:mover> <k:mo>=</k:mo> <k:mi>ζ</k:mi> <k:msub> <k:mi>σ</k:mi> <k:mi>R</k:mi> </k:msub> </k:mrow> </k:math> to match the RHD simulation with experimental results, where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>L</m:mi> </m:math> , or more practically, the preheating radiation temperature <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:msub> <n:mi>T</n:mi> <n:mi>pre</n:mi> </n:msub> </n:math> , can be chosen as a proper benchmark.