  Polarisation measurements by the Event Horizon Telescope from M87$^{\ast}$
and Sgr A$^\ast$ suggest that there is a dynamically strong, ordered magnetic
field, typical of what is expected of a magnetically arrested accretion disk
(MAD). In such disks the strong poloidal magnetic field can suppress the
accretion flow and cause episodic flux eruptions. Recent work shows that
General Relativistic Magnetohydrodynamic (GRMHD) MAD simulations feature
dynamics of turbulence and mixing instabilities that are becoming resolved at
higher resolutions. We perform a convergence study of MAD states exceeding the
status quo by an order of magnitude in resolution. We use existing 3D
simulations performed with the H-AMR code, up to resolution of 5376 x 2304 x
2304 in a logarithmic spherical-polar grid. We find consistent time-averaged
disk properties across all resolutions. However, higher resolutions reveal
signs of inward angular momentum transport attributed to turbulent convection,
particularly evident when mixing instabilities occur at the surfaces of flux
tubes during flux eruptions. Additionally, we see wave-like features in the jet
sheath, which become more prominent at higher resolutions, that may induce
mixing between jet and disk. At higher resolutions, we observe the sheath to be
thinner, resulting in increased temperature, reduced magnetisation, and greater
variability. Those differences could affect the dissipation of energy, that
would eventually result in distinct observable radiative emission from
high-resolution simulations. With higher resolutions, we can delve into crucial
questions about horizon-scale physics and its impact on the dynamics and
emission properties of larger-scale jets.
