space charge solver

[li.chao]

Dear Michael,
I have one question about the sc solver in Elegant.
As explained in the manual, it is the BE formula based on the Gaussian assumption; meanwhile, it is also assumed
that the beam distributions are elliptical in x-y space.

For a very strongly coupled beam near linear coupling resonance, the beam is tilted in real space (x-y).
In that case, I would say the BE formula has to be applied in the tilted frame.

Do you think it is the correct argument? And does Elegant do the frame rotation for SC kicks?

Many thanks
Chao

[michael_borland]

Chao,

Because the space charge is applied as a kick at discrete locations, which involves integrals over the beta functions up and downstream of the kick location, it isn't straightforward to properly account for x-y tilts. At present, elegant doesn't attempt to do it.

--Michael

[li.chao]

Dear Michael,

At a certain element, once the beam coordinates are available, one can get the tile angle in x-y space.
Then one can apply a rotation from (x,y) to tilte frame (x_t,y_t), then in the tilte (x_t,y_t) frame , the BE mode can be applied
to get the kick strength (delta_px_t,delta_py_t), then swith from (delta_px_t,delta_py_t) to (delta_px,delta_py).

Do you think that is the right logic, and is it easy to apply to Elegant?
Many thanks
Chao