# Magnetohydrodynamics in a Cylindrical Shearing Box

## TL;DR

This paper extends the Cartesian shearing box model to cylindrical coordinates for MHD simulations, enabling the study of quasi-steady mass accretion and magnetic turbulence in a more realistic local disk environment.

## Contribution

It introduces a new cylindrical shearing box framework with boundary conditions based on conservation laws, allowing for more accurate MHD simulations of accretion processes.

## Key findings

- Demonstrated quasi-steady mass accretion in cylindrical shearing box
- Compared magnetic field properties with Cartesian shearing box results
- Showed inward mass flux balancing angular momentum transport

## Abstract

We develop a framework for magnetohydrodynamical (MHD) simulations in a local cylindrical shearing box by extending the formulation of the Cartesian shearing box. We construct shearing-periodic conditions at the radial boundaries of a simulation box from the conservation relations of the basic MHD equations, taking into account the explicit radial dependence of physical quantities. We demonstrate quasi-steady mass accretion, which cannot be handled by the standard Cartesian shearing box model, with an ideal MHD simulation in a vertically unstratified cylindrical shearing box up to 200 rotations. In this demonstrative run we set up (i) net vertical magnetic flux, (ii) a locally isothermal equation of state, and (iii) a sub-Keplerian equilibrium rotation, whereas the sound velocity and the initial Alfven velocity have the same radial dependence as that of the Keplerian velocity. Inward mass accretion is induced to balance with the outward angular momentum flux of the MHD turbulence triggered by the magnetorotational instability in a self-consistent manner. We discuss detailed physical properties of the saturated magnetic field, in comparison to the results of a Cartesian shearing box simulation.