Erratum: Improving the feasibility of economical proton-boron-11 fusion via alpha channeling with a hybrid fast and thermal proton scheme [Phys. Rev. E 106, 055215 (2022)].

This corrects the article DOI: 10.1103/PhysRevE.106.055215.

Critical role of isopotential surfaces for magnetostatic ponderomotive forces.

By producing localized wave regions at the ends of an open-field-line magnetic confinement system, ponderomotive walls can be used to differentially confine different species in the plasma. Furthermore, if the plasma is rotating, this wall can be magnetostatic in the laboratory frame, resulting in simpler engineering and better power flow. However, recent work on such magnetostatic walls has shown qualitatively different potentials than those found in the earlier, nonrotating theory. Here, using a simple slab model of a ponderomotive wall, we resolve this discrepancy. We show that the form of the ponderomotive potential in the comoving plasma frame depends on the assumption made about the electrostatic potential in the laboratory frame. If the laboratory-frame potential is unperturbed by the magnetic oscillation, one finds a parallel-polarized wave in the comoving frame, while if each field line remains equipotential throughout the perturbation region, one finds a perpendicularly polarized wave. This in turn dramatically changes the averaged ponderomotive force experienced by a charged particle along the field line, not only its scaling, but also its direction.

Improving the feasibility of economical proton-boron-11 fusion via alpha channeling with a hybrid fast and thermal proton scheme.

The proton-boron-11 (p-B11) fusion reaction is much harder to harness for commercial power than the easiest fusion reaction, namely, the deuterium and tritium (DT) reaction. The p-B11 reaction requires much higher temperatures, and, even at those higher temperatures, the cross section is much smaller. However, as opposed to tritium, the reactants are both abundant and nonradioactive. It is also an aneutronic reaction, thus avoiding radioactivity-inducing neutrons. Economical fusion can only result, however, if the plasma is nearly ignited; in other words if the fusion power is at least nearly equal to the power lost due to radiation and thermal conduction. Because the required temperatures are so high, ignition is thought barely possible for p-B11, with fusion power exceeding the bremsstrahlung power by only around 3%. We show that there is a high upside to changing the natural flow of power in the reactor, putting more power into protons, and less into the electrons. This redirection can be done using waves, which tap the alpha particle power and redirect it into protons through alpha channeling. Using a simple power balance model, we show that such channeling could reduce the required energy confinement time for ignition by a factor of 2.6 when energy is channeled into thermal protons, and a factor of 6.9 when channeled into fast protons near the peak of the reactivity. Thus, alpha channeling could dramatically improve the feasibility of economical p-B11 fusion energy.

Nonresonant Diffusion in Alpha Channeling.

The gradient of fusion-born alpha particles that arises in a fusion reactor can be exploited to amplify waves, which cool the alpha particles while diffusively extracting them from the reactor. The corresponding extraction of the resonant alpha particle charge has been suggested as a mechanism to drive rotation. By deriving a coupled linear-quasilinear theory of alpha channeling, we show that, for a time-growing wave with a purely poloidal wave vector, a current in the nonresonant ions cancels the resonant alpha particle current, preventing the rotation drive but fueling the fusion reaction.

Favorable Collisional Demixing of Ash and Fuel in Magnetized Inertial Fusion.

Magnetized inertial fusion experiments are approaching regimes where the radial transport is dominated by collisions between magnetized ions, providing an opportunity to exploit effects usually associated with steady-state magnetic fusion. In particular, the low-density hotspot characteristic of magnetized liner inertial fusion results in diamagnetic and thermal frictions, which can demix thermalized ash from fuel, accelerating the fusion reaction. For reactor regimes in which there is a substantial burnup of the fuel, increases in the fusion energy yield on the order of 5% are possible.

The competition between simple and complex evolutionary trajectories in asexual populations.

BACKGROUND: On rugged fitness landscapes where sign epistasis is common, adaptation can often involve either individually beneficial "uphill" mutations or more complex mutational trajectories involving fitness valleys or plateaus. The dynamics of the evolutionary process determine the probability that evolution will take any specific path among a variety of competing possible trajectories. Understanding this evolutionary choice is essential if we are to understand the outcomes and predictability of adaptation on rugged landscapes. RESULTS: We present a simple model to analyze the probability that evolution will eschew immediately uphill paths in favor of crossing fitness valleys or plateaus that lead to higher fitness but less accessible genotypes. We calculate how this probability depends on the population size, mutation rates, and relevant selection pressures, and compare our analytical results to Wright-Fisher simulations. CONCLUSION: We find that the probability of valley crossing depends nonmonotonically on population size: intermediate size populations are most likely to follow a "greedy" strategy of acquiring immediately beneficial mutations even if they lead to evolutionary dead ends, while larger and smaller populations are more likely to cross fitness valleys to reach distant advantageous genotypes. We explicitly identify the boundaries between these different regimes in terms of the relevant evolutionary parameters. Above a certain threshold population size, we show that the probability that the population finds the more distant peak depends only on a single simple combination of the relevant parameters.