**Organisers:**

- Chris Jones (University of Leeds)
- Peter Davidson (University of Cambridge)
- Steve Tobias (University of Leeds)
- Mike Proctor (University of Cambridge)
- Jon Aurnou (UCLA)
- Ulrich Christensen (Max Planck Institute for Solar System Research)

This workshop will take place at the University of Leeds, 19th-23rd October 2020. It is aimed at scientists interested in theoretical, numerical and experimental aspects of dynamo theory, and will include work on rotating and MHD turbulence and convection.

The main issues comprise (i) the role of small-scale helical turbulence, structured large-scale convection and differential rotation in generating magnetic field at small and large scales, (ii) the force balance in natural MHD flows and how well dynamo simulations get this balance right, and (iii) flow driven by tides, precession or nutation and its ability to drive a dynamo.

While direct numerical simulations of dynamos in planets and stars have had many successes, they do not capture processes at small scales, which are potentially important. Whereas most time-dependent high magnetic Reynolds number flows are dynamos, sometimes the generated magnetic fields remain small-scale and sometimes they develop strong large-scale fields. We currently have limited understanding of how the transition between small and large scale fields works. Since it is mainly large-scale fields that can be observed, this is a major obstacle to progress. A first point is to better understand the mechanisms that generate magnetic field at a fundamental level, so that we can predict when large-scale fields will emerge. How important is rotation, and if it is, what measure of the rotation governs the transition? Are large-scale flows such as differential rotation important to generate large-scale field? Is inverse cascading of small-scale helical flow to large-scale vortices important? Can the magnetic energy directly cascade upwards from small to large scales? Different dynamo modes probably differ in the relative importance of the various field-generating mechanisms and one goal would be to better identify and characterize them at the fundamental level. Here, scientists who develop dynamo models for stars or planets will benefit from the interaction with researchers who study hydrodynamic or MHD turbulence in general.

A second issue is the understanding of the magnetostrophic limit, relevant to natural dynamos. For example, flow in the Earth’s core is thought to be governed by a balance of Coriolis force, Lorentz force and buoyancy force, with very subordinate roles for viscous and inertial forces. A dynamo working in this limit is said to be in a Taylor state. While the equations for the asymptotic limit and the methodology to solve these have been introduced over 50 years ago, numerical attempts to the full problem have so far been unsuccessful. From a mathematical point of view the regularity of the solution of this reduced set of PDEs is very hard to achieve (though recently progress has been made). In the magnetostrophic limit, the dynamo branch is expected to bifurcate subcritically, and its connection with current numerical models is unclear. What are the requirements for a dynamo simulation to satisfy such a balance to a sufficient degree? In slowly rotating stars such as the Sun, inertial forces can be expected to play a significant role, which may be essential for the different dynamo mode found there, but is inertia also crucial for rapidly rotating stars? The motivation is to assess under which conditions (e.g. combination of control parameter values) planetary and stellar dynamo simulations are approaching an appropriate asymptotic regime, i.e., what is needed for capturing the essential physics of the dynamo process despite the tremendous mismatch in control parameters.

Laboratory experiments on rotating and/or MHD flow are an important complement to numerical simulations because they can reach higher degrees of turbulence and/or stronger influence of rotational forces. Some experiments that used liquid sodium as working fluid, such as the VKS-experiment in Cadarache, have demonstrated self-sustained dynamo action. Experiments on rotating convection, with or without an (imposed) magnetic field, can map out in parameter space the different flow regimes and help to understand under which conditions the asymptotic limit thought to apply in cosmic objects is approached. A key objective will be to foster exchanges between experimentalists, applied mathematicians and numerical modellers. In particular we want to prompt new analytical developments by having a direct exchange of ideas between these communities.

While convection-driven dynamos have been studied extensively, forcing of the flow by tides, precession or nutation is also a possible mechanism for some planetary cores. A prerequisite for dynamo action is that basically laminar flow becomes unstable and leads to sufficiently vigorous turbulent motion. While the conditions for instability have been studied, the character of MHD flow excited in this way and its ability to generate magnetic fields in agreement with observed fields needs to be explored. Laboratory experiments play an essential role also in this context. In particular, the DRESDYN experiment, which uses liquid sodium in a large rotating and precessing cylinder and which could potentially become a self-sustained dynamo, will probably be fully operational by 2020.