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.