Resonance Maps for 3D Alfven Waves in a Compressed Dipole Field

Resonance Maps depict the possible locations and polarizations of resonant Alfven waves (Field Line Resonances - FLRs) for a given equilibrium and driving frequency. Previously the use of Resonance Maps has been developed for gaining insight into the behavior of Alfven waves in basic potential magnetic fields that allow the use of an orthogonal field aligned coordinate system. In more general magnetic fields these coordinates do not exist. In this paper we explore the application of Resonance Maps to such equilibria. A number of simulations of resonant Alfven waves are presented and interpreted using the Maps. We find that Resonance Maps remain useful when some of the constructions used previously are generalised to accommodate the properties of more general magnetic fields. For example, Resonance Maps are able to predict the location and polarisation of Alfven waves which are driven strongly by fast mode waves using a "tangential alignment condition". Unusual properties, such as Alfven waves crossing flux surfaces persist in the more general magnetic fields we consider.