Fusion Gain and Triple Product for the Sheared-Flow-Stabilized Z Pinch

Fusion gain Q and triple product nTtau are derived for the sheared-flow-stabilized (SFS) Z pinch[1] by including the input power associated with driving the plasma flow and the additional advective loss of thermal energy[2], [3]. Plasma impurities contribute to radiative power losses and to thermal power losses by increasing the electron population. The presence of impurities increases the required plasma parameters, characterized by the triple product, to achieve fusion gain. The analysis is applied to deuterium-tritium (D-T) fusion, though the methodology can be extended to other reactions. Since D-T fusion produces an alpha particle, confining the alpha with sufficiently high self-generated magnetic fields is possible. Confined alpha particles can heat the D-T fusion fuel, reduce the needed input power, and thereby amplify the fusion gain. However, ignition (infinite Q) does not occur since the axial plasma flow must be externally driven. The impacts of alpha heating and impurity losses are considered on the fusion performance of the SFS Z pinch. Requirements, assumptions, and limitations are described that would justify a determination of “D-T equivalent Q = 1 conditions” in a D-D plasma. A minimum set of experimental measurements of plasma parameters are specified that can be compared to a plasma parameter map to facilitate a “Q = 1” claim, where Q is defined by instantaneous values of fusion power and input power. Corroborating measurements are also discussed that would further support extrapolation of plasma and fusion performance to D-T operation.