Classical Thermodynamic Analysis of Deuterium-Based Fusion Reactions

Abstract

The fusion reactions involving deuterium are of great interest for the exploitation of the fusion energy via magnetic-confinement devices. In classical thermodynamics, the spontaneity of a process is established through the assessment of the change in Gibbs free energy. So far, the feasibility of nuclear reactions has been characterized in terms of cross section and Q-value while the entropic term (T ΔS) has been neglected. Such an assumption is always justified for fission reactions where the term ΔS is positive. In the case of fusion reactions that operate at very high temperatures (106–107 K) and where ΔS is negative, the change in Gibbs free energy may be positive, making the reaction non-spontaneous. This paper proposes a classical thermodynamic analysis of D-based reactions of interest for the magnetic-confinement fusion applications. The entropy contribution was evaluated via the Sackur–Tetrode equation while the change in enthalpy was considered constant and as corresponding to the Q-value of the fusion reaction. The results of the thermodynamic analysis are compared with nuclear reaction feasibility criteria based on the reaction reactivity. The DT and D3He reactions show a high degree of spontaneity although the second one presents a lower reactivity. An increase in temperature could enhance the reactivity of the D3He reaction at the cost of decreasing its thermodynamic spontaneity. Both branches of the DD reaction are characterized by a much lower thermodynamic spontaneity than that of the DT and D3He reactions. Furthermore, at the temperature of their maximum cross section, the DD reactions exhibit a largely positive change in Gibbs free energy and, therefore, are not spontaneous. At the temperature of magnetic-confinement fusion machines (1.5 × 108 K), among the D-based reactions studied, the DT one exhibits the highest degrees of spontaneity and reactivity.