So this is an alternating current, but with a cycle time of 22 years instead of a fraction of a second?
Whether the sun is chaotic in the technical sense (i.e. the butterfly effect) is still open to question [1]. The solar magnetic field is poorly understood. In the 1980s, everybody thought that a particular model (mean-field dynamos IIRC) had it all figured out, but new observations from helioseismology showed them wrong. Wikipedia has a good article on the solar cycle: https://en.wikipedia.org/wiki/Solar_cycle My advisor wrote a more technical overview: http://solarphysics.livingreviews.org/Articles/lrsp-2010-3/a...
[1] See: https://en.wikipedia.org/wiki/Chaos_theory#Distinguishing_ra...