Bremsstrahlung radiation power in fusion plasmas revisited: towards accurate analytical fitting

Abstract In fusion plasmas, where electron temperatures <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> range from keV to hundreds of keV, bremsstrahlung radiation constitutes a significant energy loss mechanism. While various thermal average fitting formulas exist in the literature, their accuracy is limited, particularly for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> <mml:mtext>⩽</mml:mtext> <mml:mn>20</mml:mn> </mml:mrow> </mml:math> keV with error <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>&gt;</mml:mo> <mml:mn>10</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:math> . Additionally, non-relativistic fitting formulas become invalid for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> <mml:mtext>⩾</mml:mtext> <mml:mn>50</mml:mn> </mml:mrow> </mml:math> keV. The accurate calculation of bremsstrahlung radiation is important for fusion gain study, especially of advanced fuels fusion. In this work, we develop new but still simple fitting formulas that are valid for electron temperatures ranging from small ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>≲</mml:mo> <mml:mn>0.1</mml:mn> </mml:mrow> </mml:math> keV) to extreme relativistic range, with errors of less than 1% even for high atomic number ions (e.g. Z = 30), which could be sufficient for fusion plasma applications. Both electron–ion (e–i) and electron–electron (e–e) bremsstrahlung radiations are considered. Both polynomial fitting with truncated ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>k</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">B</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> <mml:msup> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mtext>⩽</mml:mtext> <mml:mn>10</mml:mn> </mml:mrow> </mml:math> ) and one-fit-all formulas are provided. Additionally, we offer fitting formulas for e–i and e–e specifically for electron energies, which could prove useful in non-Maxwellian bremsstrahlung radiation studies.