Fringe Field descriptions

[DavidSagan]

Needed is a discussion on fringe fields and how to characterize them. Do we want to try to find a common ground or do we create a FringeP that can be customized like TrackingP?

[rdemaria]

In Xsuite we are going in the direction of using s-dependent fields derivatives as components (implementation is in progress):

where a_n,b_n,b_s are functions in s. Those components are expanded in fields as follows (h is a constant curvature in the z-x plane):

.

For now, we will stick to quartic polynomials (such that the infinite series converges) defined by the coefficients :

This allows to create an entire fringe or any slice of it with the desired accuracy easily from field maps or well-behaved guesses. High order effects emerging from higher order longitudinal derivatives of the field components are neglected in this case. A complementary interface would allow specifying polynomials of any order from their coefficients.

This expansion has a broken symmetry that makes it suitable for bent geometries, but it is easy to recover symmetries if needed. This is an example of the rotational symmetric fringe of a solenoid, following maxwell equations:

for which the fields will depend only on r^2=x^2+y^2

[cemitch99]

There are many fringe field models and/or parameterizations that could be used here. I think finding a common ground that is code-agnostic will be a difficult task. Maybe creating an open-ended and customizable FringeP is the best option. Otherwise, having options to support 1) 3D field maps and/or 2) fields specified by closed-form expressions would overlap with this capability, and those options have been discussed previously.

[ax3l]

For 1) 3D field maps we could read and slice/expand/convert from openPMD.