Evaluation of suprathermal fusion probability through <i>α</i> -particle large-angle elastic scattering in dense p ¹¹ B plasmas

Abstract Proton-boron-11 (p 11 B) is a nearly aneutronic and naturally abundant fuel, making it a promising candidate for advanced fusion fuels. However, achieving ignition and self-sustaining burn in p 11 B fuel remains extremely challenging. In comparison to deuterium-tritium (DT) fuel, the fusion reactivity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo fence="false" stretchy="false">⟨</mml:mo> <mml:mi>σ</mml:mi> <mml:mi>v</mml:mi> <mml:mo fence="false" stretchy="false">⟩</mml:mo> </mml:mrow> </mml:math> of 11 B(p, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:math> )2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:math> reaction is significantly lower at plasma temperatures below 100 keV, while radiation losses are substantially higher. As for the additional nonthermal effects, the possibility of an avalanche reaction (or chain reaction) due to suprathermal fusion caused by energetic protons recoiled by p 11 B fusion-produced α -particles via large-angle elastic scattering has been discussed. Belloni reported that the multiplication factor of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> </mml:math> -particles G due to suprathermal fusion is at most 1% under the conditions of low ion temperature ( T i –1 keV), high electron temperature ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mtext>e</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>≤</mml:mo> <mml:mn>100</mml:mn> <mml:mrow> <mml:mtext> keV</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> ), and electron number density 10 24 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>≤</mml:mo> </mml:mrow> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>n</mml:mi> <mml:mrow> <mml:mtext>e</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>≤</mml:mo> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>28</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mrow> <mml:mtext> c</mml:mtext> </mml:mrow> <mml:mrow> <mml:msup> <mml:mrow> <mml:mtext>m</mml:mtext> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> </mml:math> (Belloni 2021 Plasma Phys. Control. Fusion 63 055020). In this study, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> </mml:math> -particle multiplication factor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> due to the suprathermal reaction at higher temperatures was evaluated under the conditions relevant to the ignition and burn processes of p 11 B fuel in inertial fusion using the latest p 11 B fusion cross section (Tentori and Belloni 2023 Nucl. Fusion 63 086001) and considering the effects of the thermal motion of the background particles. The maximum value of the multiplication factor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> was found to be only 3% at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>ρ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>50000</mml:mn> <mml:mrow> <mml:mtext> g</mml:mtext> </mml:mrow> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow> <mml:mtext>c</m