Enhancement of fusion reactivity under non-Maxwellian distributions: effects of drift-ring-beam, slowing-down, and kappa super-thermal distributions

Abstract

Non-Maxwellian distributions of particles are commonly observed in fusion studies, especially for magnetic confinement fusion plasmas. The particle distribution has a direct effect on fusion reactivity, which is the focus of this study. We investigate the effects of three types of non-Maxwellian distributions, namely drift-ring-beam, slowing-down, and kappa super-thermal distributions, on the fusion reactivities of D-T (Deuterium-Trillium) and p-B11 (proton-Boron) using a newly developed program, where the enhancement of fusion reactivity relative to the Maxwellian distribution is computed while keeping the total kinetic energy constant. The calculation results show that for the temperature ranges of interest to us, namely 5–50 keV for D-T and 100–500 keV for p-B11, these non-Maxwellian distributions can enhance the fusion reactivities. In the case of the drift-ring-beam distribution, the perpendicular ring beam velocity leads to decreased enhancement in low temperature range and increased enhancement in high temperature range. This effect is favorable for p-B11 fusion reaction and unfavorable for D-T fusion reaction. This is because the important temperature range for p - B 11 fusion reaction significantly overlaps with the high temperature enhancement range, while the important temperature range for D - T fusion significantly overlaps with the low temperature reduction range. In the slowing-down distribution, the birth speed plays a crucial role in both reactions, and increasing birth speed leads to a shift in the enhancement ranges towards lower temperatures, which is beneficial for both reactions. Finally, the kappa super-thermal distribution results in a relatively large enhancement in the low temperature range with a small high energy power-law index κ . Overall, this study provides insight into the effects of non-Maxwellian distributions on fusion reactivity and highlights potential opportunities for enhancing fusion efficiency.

On the upper bound of non-thermal fusion reactivity with fixed total energy

“…In our previous studies (see [9,10]), the fusion reactivity enhancement factors (defined in equation ( 11)) for several typical non-thermal distributions mainly fell within the range of 0.5-1.5. While we were able to calculate the fusion reactivity for arbitrary ion velocity distributions using a simple and fast approach (see [15]), it did not provide information about which distribution could yield the maximum fusion reactivity or what the upper limit of the enhancement factor might be.…”

“…We can utilize the Lagrange multiplier method to determine the maximum of equation ( 9) while adhering to the constraint given in equation (10). We define the Lagrangian as follows: which leads to the requirement:…”

“…For example, in the case of D-T fusion, there are only 1-2 solutions when T 2 = 0. This implies that the maximum of equation ( 9) occurs when E 1n takes on 1-3 specific values, indicating that the distribution of f 1 (E) should consist of 1-3 beams, regardless of the value of N. The actual values of the beam energies depend on equation (10). The model described above remains challenging to solve for N → ∞.…”

“…Before studying the general cases, we investigate cases with small values of N and T 2 = 0. We randomly choose E 1n to find the maximum of equation ( 9), while satisfying equation (10).…”

“…It is interesting to study non-thermal fusion reactivity, as it is common in fusion experiments (see [3]), and it offers a potentially attractive solution to enhance realistic fusion energy production with the challenges posed by advanced fuels (see [4][5][6][7][8]). Comprehensive theoretical investigations of fusion reactivities involving common drift bi-Maxwellian distributions [9], drift ring beams, slowing down, and superthermal kappa distributions [10], and velocity-space anisotropy distribution [11] in fusion plasmas have revealed potential enhancement ranges for fusion reactivity when compared to thermal Maxwellian plasmas. It has also been demonstrated that even a modest increase in proton-Boron fusion reactivity, such as 20%, can significantly impact the feasibility of proton-Boron fusion energy production (see [9,12]).…”