strongly-tangled and turbulent magnetic field. The radial thickness of such regions is $\sim 5$ stellar radii close to the star and broadens with increasing radial distance. This likely continues out to large distances from the star ($10$ AU or greater) where particles can be copiously advected and diffused by the turbulent wind.'
author:
- 'F. Fraschetti'
- 'J. J. Drake'
- 'O. Cohen'
- 'C. Garraffo'
bibliography:
- 'ffraschetti.bib'
title: 'Mottled protoplanetary disk ionization by Magnetically-channeled T Tauri star energetic particles'
---

Introduction {#sec:intro}
============

Angular momentum transport within a protoplanetary disk governs the flow of material toward and away from the star and is one of the primary drivers of disk evolution affecting the formation and migration of planets within the disk [e.g. @Bodenheimer:95; @Coleman.Nelson:16; @Bai:17]. The important transport processes are thought to be the turbulence resulting from the magneto-rotational instability (MRI; @Balbus.Hawley:98), stresses due to large-scale magnetic fields driving an outflow [@Wardle.Koenigl:93; @Koenigl.etal:10; @Bai.Stone:13; @Bai:17] and shearing within the disk [@Turner.Sano:08]. All these magnetic angular momentum transport processes require that the gas be sufficiently ionized to couple to magnetic fields. However, models of protoplanetary disks heated by the UV-IR spectral energy distributions of their host stars are too 