Kinetic theory of helium ash source from distribution function of He ions and its effects on helium ash density profile

Abstract In this work, the source of helium (He) ash is explicitly defined in terms of the full energy distribution function of He ions in deuterium–tritium burning plasmas, and the He ash density profile is subsequently predicted by considering both source and radial transport. By numerically solving the Fokker–Planck equation, including the energy diffusion term, we obtain the distribution function of He ions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>He</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> in the full energy range and propose a method to quantitatively define the demarcation energy between energetic alpha ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:math> ) particles and He ash in energy space. The corresponding source of He ash is then calculated. On the one hand, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>He</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> in the low-energy region is significantly higher than the classical slowing down distribution function due to energy diffusion, which indirectly enhances the source of He ash. On the other hand, the directly introduced source term by energy diffusion makes He ions diffuse from the low-energy to the high-energy range, which reduces the source and plays the role of a sink for He ash. Combining the competition between the source and sink, the total source <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>S</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>ash</mml:mtext> </mml:mrow> <mml:mo>,</mml:mo> <mml:mrow> <mml:mtext>t</mml:mtext> </mml:mrow> </mml:mrow> <mml:mrow> <mml:mtext>F</mml:mtext> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> is increased compared to that without energy diffusion. Consequently, the corresponding He ash density profile with the total source is also higher than that without energy diffusion, and closer to that with the source defined by the density of energetic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:math> particles (Angioni et al 2009 Nucl. Fusion 49 055013). These results underscore the significance of complete kinetic calculations. Moreover, the complete kinetic calculations presented in this work show that a simple source defined by the density of energetic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:math> particles provides an accurate description, and therefore leads to a predicted density profile of He ash close to that obtained with the full kinetic calculated source.