Calculating the charged particle stopping power exactly to leading and next-to-leading order

I will discuss a new method for calculating transport quantities, such as the charged particle stopping power, in a weakly to moderately coupled plasma. This method, called dimensional continuation, lies within the framework of convergent kinetic equations, and it is powerful enough to allow for systematic perturbative expansions in the plasma coupling constant. In particular, it provides an exact evaluation of the stopping power to leading and next-to-leading order in the plasma coupling, with the systematic error being of cubic order. Consequently, the calculation is near-exact for a weakly coupled plasma, and quite accurate for a moderately coupled plasma. The leading order term in this expansion has been known since the classic work of Spitzer. In contrast, the next-to-leading order term has been calculated only recently by Brown, Preston, and Singleton (BPS), using the aforementioned method, to account for all short- and long-distance physics accurate to second order in the plasma coupling, including an exact treatment of the quantum-to-classical scattering transition. Under conditions relevant for inertial confinement fusion, BPS find the alpha particle range in the DT plasma to be about 30% longer than typical model predictions in the literature. Preliminary numerical studies suggest that this renders the ignition threshold proportionally higher, thereby having potential adverse implications for upcoming high energy density facilities. Since the key ideas behind the BPS calculation are possibly unfamiliar to plasma physicists, and the implications might be important, I will use this opportunity to explain the method in a pedagogical fashion.