Title and Abstract

Title:   Modeling the Solar Dynamo: Past, Present and Future

Abstract:   The solar dynamo is the mechanism generating and amplifying the magnetic field that we observe at the solar surface in the form of sunspots and a large-scale dipolar field. It is responsible for the 11-year solar activity cycle.  Despite being a problem in physics for more than a hundred years now,  some important properties of the dynamo still remain mysterious, hidden somewhere beneath the solar photosphere.  The mathematical framework used to describe this process is called mean-field dynamo  theory (Parker 1950, Steinbeck, Krause & Radler 1966).  It has been used along the past decades with various modifications and approaches to explain the main properties of the solar cycle.  However, until now there is not a complete model able to explain these characteristics.  In this talk I will present in a comprehensive form the fundamentals of the mean-field theory and the results obtained with the most successful models of the Sun's dynamo.  I will also present the recent modeling attempts using first-principles, three dimensional, spherical simulations, indicating their achievements, advantages and caveats, and giving a perspective of what will be the future steps to evolve in our understanding of this process.