Session YI3: BPP Invited III: Gyrokinetic Modeling, Basic Shocks, EOS, and Laboratory Astrophysics

Current Singularity Formation in Line-tied Magnetic Fields: the Parker Problem

Coronal heating has been a long-standing problem in solar physics. Parker’s conjecture that the current density in the corona is distributed in the form of singular current sheets that produce the required heating has been controversial. In ideal MHD, can genuine current singularities emerge from a smooth 3D line-tied magnetic field? To resolve this issue computationally, the numerical scheme must preserve magnetic topology exactly to avoid artificial reconnection. We develop a novel variational integrator for ideal MHD by discretizing Newcomb’s ideal MHD Lagrangian on a moving mesh using discrete exterior calculus (Zhou et al. 2014, PoP 21, 102109). The motion of the mesh advects the discrete magnetic flux exactly, such that the scheme is free of artificial reconnection. With this method, we confirm that the nonlinear solution to the ideal Hahm-Kulsrud-Taylor (HKT) problem in 2D yields a singular current sheet (Zhou et al. 2016, PRE 93, 023205), agreeing well with an analytical solution we obtain using the boundary layer approach developed by Rosenbluth et al. (1973) for the m=1 internal kink problem. We then extend the ideal HKT problem to 3D line-tied geometry (Zhou et al. 2018, ApJ 852, 3), the effect of which is crucial in the controversy over Parker's conjecture. The linear solution, which is singular in 2D, is found to be smooth. However, with finite amplitude, it can become pathological when the system is sufficiently long. The nonlinear solution turns out to be smooth for short systems. Nonetheless, the scaling of peak current density vs. system length suggests that the nonlinear solution may become singular at a finite length. Albeit not yet a conclusive resolution, our results contribute to our understanding of the Parker problem by exemplifying how the line-tied geometry influences the formation of current singularities.   

The Barkas Effect in Plasma Transport

Molecular dynamics simulations reveal that a fundamental symmetry of plasma kinetic theory is broken at moderate to strong Coulomb coupling: the collision rate depends on the signs of the colliding charges. This breaking of charge-sign symmetry is analogous to the ``Barkas effect'' observed in charged-particle stopping experiments. It gives rise to significantly enhanced electron-ion collision rates and is expected to affect any neutral plasma with moderate to strong Coulomb coupling such as ultracold neutral plasmas (UNP) and the dense plasmas of ICF and laser-matter interaction experiments. The physical mechanism responsible for the Barkas effect is screening of binary collisions by the correlated plasma medium. By including screening directly in the interaction potential governing collisions, it is shown that the Barkas effect arises in the close interactions that lead to large-angle scattering.  Because the effect hinges on how screening affects close -- not distant -- interactions, it is a phenomenon beyond what is predicted by traditional transport models based on cut-off Coulomb collisions or mean-field dielectric response. A model for the effective screened interaction potential is presented that is suitable for the coupling strengths achieved in UNP experiments. Transport calculations using this potential agree with simulated relaxation rates and predict that the Barkas effect can cause up to a 70\% increase in the electron-ion collision rate at the conditions of present UNP experiments, where the electron coupling parameter can range from $\Gamma_e\approx0.1$ to $0.5$. The influence of the Barkas effect in other transport processes is also considered.