# Local semi-analytic models of magnetic flux transport in protoplanetary discs

## TL;DR

This paper develops semi-analytic models to study magnetic flux transport in protoplanetary discs, revealing how non-ideal MHD effects influence flux movement and the role of Hall drift in different regimes.

## Contribution

It introduces two one-dimensional semi-analytic models for flux transport in discs, analyzing the impact of various non-ideal MHD effects and disc magnetizations.

## Key findings

- Ohmic and ambipolar diffusivities cause outward flux transport.
- Wind outflows promote inward flux transport, enhanced by Hall drift.
- Hall effect can reduce or drive flux transport depending on conditions.

## Abstract

The evolution of a large-scale poloidal magnetic field in an accretion disc is an important problem because it determines the launching of winds and the feasibility of the magnetorotational instability to generate turbulence or channel flows. Recent studies, both semi-analytical calculations and numerical simulations, have highlighted the crucial role non-ideal MHD effects (Ohmic resistivity, Hall drift and ambipolar diffusion), relevant in the protoplanetary disc context, might play in magnetic flux evolution in the disc. We investigate the flux transport in discs through the use of two one-dimensional semi-analytic models in the vertical direction, exploring regimes where different physical source terms and effects dominate. The governing equations for both models are derived by performing an asymptotic expansion in the limit of a thin disc, with the different regimes isolated through setting the relative order of the leading terms between variables. Flux transport rates and vertical structure profiles are calculated for a range of diffusivities and disc magnetisations. We found that Ohmic and ambipolar diffusivities drive radially outward flux transport with an outwardly inclined field. A wind outflow drives inward flux transport, which is significantly enhanced in the presence of Hall drift in the positive polarity case, $\eta_H (\boldsymbol{B}_z \cdot \boldsymbol{\Omega}) > 0$, an effect which has only been briefly noted before. Coupled only with outward inclination, the Hall effect reduces the flux transport given by a background Ohmic and/or ambipolar diffusivity, but drives no flux transport when it is the only non-ideal effect present.