research topics/work to do.

I've been continuing with this effort of finding links between beam dynamics and other areas. I met with some theorists to try to explain what are some of the problems here, and see if I could find stuff in common. In general, I've been trying to find other areas of physics that could have things in common with beam dynamics and synchrotron radiation physics. But in order to do this, I need to identify what areas of beam dynamics are really research topics that could use developing. So here is my attempt to point out what I think are still somewhat hard, but maybe tractable problems to be worked on.

1. Single particle dynamics :Given a one turn map- find the long behavior. What is the stable region ? What happens when damping is added ? Can we find the right parameters from the one-turn map that effect the long term behavior ? Has this problem been solved in chaotic map literature?
2. Collective effects: Distribution with diffusion, damping, feedback. Instability due to one effect may be limited by other effects. Is there a theory in this range ?
   Want to know emittance growth, non-Gaussain distributions.
   Analysis of Fokker-Planck. Maybe more terms as in Master equation is needed sometimes?
3. Radiation from electron beam:Interface between electron beam and photons. Definition of Wigner function. Sometimes negative. Not fully understood.
   Need to define photon beam operationally based on how the photons will interact, be focussed by optics, etc.
   Radiation from spin-polarized electrons?

Now, there's certainly been work done on each of these. For the first, we have the whole theory of normal form. For the second, we have all the stuff about mode frequencies and instabilities, and covers the basics of equilibrium distributions. And the third is the basic way things are computed, but there's still some confusion. But it would be nice to point these a little more directly towards the applications in biology, chemistry and solid state physics.
On the software end, there's work to be done on the electron side and on the code side. On the electron side, we have many codes. Personally I think AT is good to develop, since its in Matlab and easier to add to. Elegant is also nice, though open and extendable in the same way. On the radiation side, we have SRW to compute the radiation in the near field, right out of the bending magnets or undulators. Then there's Shadow which tracks the radiation further down the beam line. There may be some work underway to combine these together in some way.

For myself, I just like to see this big picture. Of course I can only work on a very small amount of this. But I'd at least like to work on something within a bigger picture that makes sense to me.