Power-law index and cutoff of particles accelerated by reconnection
In plain words
Reconnection in strongly magnetized astrophysical plasmas makes particles with a power-law energy distribution, few particles at high energy but many more than a thermal gas has. How steep that power law is and how high it extends is not settled.
Precise statement
For relativistic pair-plasma or electron-ion reconnection with magnetization $\sigma = B^2/(4 \pi w)$ ($w$ = relativistic enthalpy density) from 1 to 1e3, determine the index $p$ of dN/dgamma ~ gamma^-p and the high-energy cutoff $\gamma_{\max}$ as functions of $\sigma$, guide field and system size $L/d_e$ in 3D, in the limit $L/d_e$ going to infinity. An answer is $p(\sigma, B_g)$ and the scaling of $\gamma_{\max}$ with $L$, converged in system size.
What would settle it
3D particle-in-cell simulations converged in system size, with an analytic acceleration model reproducing $p\ \text{and}\ \gamma_{\mathrm{max}}$.
Status in the literature
Unverified note
Particle-in-cell work through 2025 finds $p$ approaching $1 \text{ to } 2$ at $\sigma$ much larger than 1, but convergence with system size and the role of 3D effects are disputed.