Physics Colloquium 29th January 2016 delivered by Professor Per Helender The Princeton astrophysicist Lyman Spitzer famously figured out how a magnetic field can be used to confine a fully ionised plasma in steady state. His solution, the so-called stellarator, involves a counter-intuitive twisting of the field without employing an electric current, and is mathematically related to the Berry phase in quantum mechanics. Six decades later, Spitzer’s idea is put to a billion-euro test in the Wendelstein 7-X experiment of the Max Planck Society. This talk will describe some basic physics and mathematics underpinning stellarators, including the use of “hidden symmetries” to improve plasma confinement. An overview will also be given of Wendelstein 7-X, which after a decade of construction has just started operation. If successful, it should produce steady-state plasmas under conditions suitable for extrapolation to a fusion reactor.