I believe that a solar physicist is, above all, a Physicist. Therefore, you should try to gain the best physical and mathematical background that you can. Subjects like Atomic Physics and Spectroscopy, Radiation and Transport phenomena, and Fluid Mechanics all converge to Plasma Physics, which is the basis of a solar physicist's education. These subjects are relevant even to a space physicist and an astrophysicist. I do not know of any university with a master or a PhD programme which converges from all of these subjects to solar physics in this way. You can find parts of a complete solar physics education, however, in several universities, such as here, at La Laguna, in Frieburg and Goettingen Univ (Germany), and in St. Andrews (Ireland), and others too, in a more limited way. I am not very familiar with the US universities at this level. However, in these, and other universities, you can find very good solar physics PhD courses.
What about the actual health of solar physics nowadays?. There are great projects that are yielding a fair amount of data in many areas of solar physics. Projects such as: a) SOHO, an ESA-NASA project, which is generating data in helioseismology (interior of the Sun), in the solar atmosphere (chromosphere, transition region and corona) both in the visible, UV and extreme UV wavelengths; b) the Japanese YOHKOH project, which is generating data about the active Sun in X-rays since 1991; c) the ULYSSES spacecraft, which is studying the interplanetary medium near and above and below the sun (from the poles). Also from the ground: there are projects such as the helioseismic networks of GONG, IRIS, TON and BiSON; and projets operating at great observatories at Sac Peak, Kitt Peak, Big Bear, Hawaii, Canary Islands and others which have incorporated new instrumentation to better measure the magnetic fields on the Sun through polarimetry. These projects are yielding a huge amount of high quality data that will take at least a decade for us and others (maybe you) to study.
You may think that this will finish with the problems in solar physics and none will be left for you. Not at all, they just create new questions which will demand better instrumentation and cleverer mathematical analysis procedures and more ingenious models to make everything fit together, in order to provide a nice and complete understanding of our Sun. In fact, extensions (extended missions) of GONG (US) and SOHO (maybe?) during the next 6 years will give solar physicists impetus to try to understand the Sun's structure, the solar activity and its origins. New projects are being pushed forward such as: CLEAR (in USA), a new-generation telescope of more than 2m diameter, for solar physics to resolve problems of the interaction of the smallest magnetic flux tubes on the Sun with the non-magnetic plasma surrounding it. Another new project is a second version of YOHKOH (in Japan) to perform polarimetry from space, amongst other tasks. Also, there are new computer codes to solve the hydrodynamical equations for energy transport in the convection zone, including the interaction with magnetic fields. These new simulations need the next generation of faster computers with more memory. New technologies are also being developed in the field of infrared photopolarimetry. As you can see, there is plenty of new ideas and projects that are being developed right now, and that are on the road to receive adequate financial support.
However, my personal view about the financial picture for basic solar research for the next five or so years in Europe is not very optimistic. At the moment, in Europe, there is a shortage of money for basic research, as opposed to applied research. However, I believe that we will succeed in attracting enough funds for continuing the solar physics research as part of Sun-Earth interaction environmental studies. Such "space weather" studies show the relationships and causal effects of the Sun on the near-Earth and on the atmospheric Earth, and these studies are likely to be the sources of major investment in the near future. I believe that the situation in the US is nearly similar.
I hope that you do not get too worried and/or exultant in reading this. I, personally, believe that, when studying at a university, one has to follow ones own feelings and study the matters that makes one happy; after all, what one learns is how to solve physics-related problems. What specific problems that you will have to solve in your future is difficult to predict, at the stage that you are at now. A bit of HAKUNA MATATA, is NOT bad at this moment. However, this is a very, very personal view.
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