A kinetic line-driven radiation operator and its application to Gyrokinetics

Abstract A velocity dependent, kinetic model for line radiation is developed for continuum kinetic codes. It has been implemented in the full- f gyrokinetic code Gkeyll. The total radiation for a charge state is modeled as an advection in velocity space with a form of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">∇</mml:mi> <mml:mi>v</mml:mi> </mml:msub> <mml:mo>⋅</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>v</mml:mi> <mml:mi>ν</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>v</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>v</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> , guaranteeing particle conservation. The velocity dependence (in the form of an effective frequency <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>ν</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>v</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> ) is found through fitting the energy loss of the operator, i.e. the second velocity moment, to the radiation data in the OpenADAS database. Therefore, each individual transition does not need to be evaluated every time step, significantly reducing the computational cost of including line radiation in a kinetic model. The dependence on velocity instead of the usual, temperature, allows the radiation to be computed from non-Maxwellian electron distribution functions: We benchmark the model against a collisional radiative model using isotropic non-Maxwellian distribution functions. A velocity dependent model of radiation can more accurately describe the radiation in the more kinetic regimes expected in reactor-scale devices. The velocity dependence qualitatively captures the quantum mechanical need for a minimum velocity before any radiation occurs.