Thermal gradient effect on hydrogen transport in tungsten

Abstract One key challenge for efficiency and safety in fusion devices is the retention of tritium (T) in plasma-facing components. Tritium retention generates radioactive concerns and decreases the amount of fuel available to generate power. Hence, understanding the behavior of T in tungsten (W), as the main candidate as armor material, is critical to the deployment of fusion as a reliable energy source. In this work, we have studied the effect of a thermal gradient in the transport properties of hydrogen (as a T surrogate) in pure W. Strong thermal gradients develop in the divertor as a result of the intense energy fluxes arriving at the material. We have developed an analytical approach to compute the heat of transport ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>Q</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> ) that is parameterized from molecular dynamics (MD) simulations. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>Q</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> is a parameter needed in irreversible thermodynamics frameworks to understand mass transport in the presence of thermal gradients. We show that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>Q</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> can be written as a function of temperature, temperature gradient, a characteristic length and the ratio of the rates towards hot and cold regions. Furthermore, we describe how, to first order, the dependence of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>Q</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> on the thermal gradient vanishes, in agreement with MD results. On average, we find <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>Q</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mn>5.41</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> <mml:mi>k</mml:mi> <mml:msup> <mml:mi>T</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mrow> <mml:mi>eV</mml:mi> </mml:mrow> </mml:mrow> </mml:math> for H in pure W, with k the Boltzmann constant and T the temperature.