I am not an expert in this subject, so please take what I say with a grain of salt:<br /><br />As far as I know, there is a class of white dwarfs known as "magnetic white dwarfs" that have magnetic fields on the order of a million gauss (the solar magnetic field strength near the surface is about a single gauss). But these are quite rare, it seems that for most white dwarfs we only have upper limits of ~10000 gauss on the field strengths. However, if you were to shut off the Sun's dynamo, it would take on the order of 10 billion years for the magnetic field to diffuse out, so it's reasonable to think that the magnetic field may persist in the white dwarf sun even though convection has ceased. If it does persist through the collapse to the white dwarf stage you can estimate that the field strength should be about 10000 gauss (for a plasma the magnetic flux is conserved, so the field strength times the surface area of the object is basically constant). However, it is possible that the planetary nebula stage carries away the field, I don't know that we really know. (I don't know anything about whether white dwarfs have "internal motion" of some sort or what its effects might be).<br /><br />As for red giants, there are models that do suggest that dynamo action can generate magnetic fields in giants. These stars do have surface convection, so I don't know that it's surprising that they would have a dynamo. They also do have a wind, but it's not like the super-hot, super-tenuous solar corona. Instead the wind seems to be slower but involve more mass. Stars may end up losing as much as 20% of their mass while they are red giants, and then even more through the thermal pulses as an asymptotic giant.<br /><br />I think the late stages of a star's life (RGB and AGB phases) is really a fascinating subject, and there's a pretty accessible paper dealing with the winds from these stars at
http://xxx.lanl.gov/pdf/astro- <div class="Discussion_UserSignature"> </div>