Change names of multipoles in a bend?

[DavidSagan]

Multipoles vertically pure and horizontally pure multipoles in a bend are functionally different from multipoles for straight line elements. See the PALS documentation for details. One thought is that the names of these types of multipoles should be different from straight multipoles to avoid confusion. A Possible naming convention is to use a b after the multipole order digit(s). Thus, for example

• Ks4 would be Ks4b,
• Bn6L would be Bn6bL
• En8 would be En8b

It would be an error to mix straight line multipole names with a bend element and vice versa. Note: multipoles in a bend, if referenced to a straight line (and not referenced to the bend arc), are straight line multipoles. The is selected by the geometry switch in MagneticMultipoleP and ElectricMultipoleP.

Thoughts?

[ax3l]

cc @cemitch99

[rdemaria]

I don't know if it was already discussed. One way out is to avoid mentioning multipoles or generalized gradients, which apply to specific conditions, but use the following definition (as MAD-X, MAD-8 do by the way):

and similarly for non scaled magnetic and electric fields.

This leads to well-defined fields in the source-free region for longitudinally constant or varying fields, straight or curved paths (in the x-s plane).

I guess different codes have taken other choices, but for a standard, I see the advantage to have one simple definition that fits several use cases.

[DavidSagan]

@rdemaria Unfortunately these equations only work for straight line elements. And for straight line elements, PALS is the same as MAD.

[rdemaria]

@rdemaria Unfortunately these equations only work for straight line elements. And for straight line elements, PALS is the same as MAD.

not sure to understand, once you define the derivates in the midplane, you can generate fields in the curved frame using the usual Laplacian recursion equations. See https://proceedings.jacow.org/ipac2024/pdf/TUPS09.pdf, but the idea comes from L. C. Teng, “Expanded form of magnetic field with median plane,” 1962. doi:10.2172/7364341 https://www.osti.gov/servlets/purl/7364341 .

The point is to have a good definition of the fields, it is up to the code to use it properly by generating the expansion in straight or curved frame.

[JosephPeterDevlin]

@DavidSagan I think using these equations essentially boils down to the horizontally pure choice, since one is viewing the usual multipole coefficients in the horizontal plane and generating a Maxwellian field from it.

[DavidSagan]

@rdemaria The way multipoles are defined, they satisfy Maxwell's equations and there is no s-dependence. This is different from generalized gradients which is essentially a Taylor expansion that is truncated and is s-dependent. A generalized gradient description can be useful and should be part of PALS (this will need a future PR) but this is different from the multipole description.

[cemitch99]

@rdemaria @DavidSagan There are also natural generalizations of multipole definitions to curved elements as in:
T. Zolkin, Phys. Rev. Accel. Beams 20, 043501 (2017) and references therein.

[cemitch99]

@DavidSagan I appreciate the concern about confusing the two cases, but as you mentioned, the distinction is already made using the geometry switch. I think adding an additional suffix to the name of the multipole parameters could cause more confusion, especially if the suffix is too brief and non-descriptive. However, if you go in that direction, I suggest something explicit like Ks4_bent.

[rdemaria]

@DavidSagan I think using these equations essentially boils down to the horizontally pure choice, since one is viewing the usual multipole coefficients in the horizontal plane and generating a Maxwellian field from it.

This is my understanding. I wanted to point out that using derivatives as definition of k, one gets one definition that works for both straight and bent elements (and generalizations when s-dependence matters).

[rdemaria]

@rdemaria @DavidSagan There are also natural generalizations of multipole definitions to curved elements as in: T. Zolkin, Phys. Rev. Accel. Beams 20, 043501 (2017) and references therein.

Thanks, I did not know about this paper!

[JosephPeterDevlin]

@rdemaria I can understand that point of view. But, the way I think of it is that since you lose so many properties, it is better to call them something entirely different. For example, a curved magnet with only nonzero k1 does not act exactly like a straight quadrupole. Another reason is to force the user to think about how magnet measurements connect to what they are putting in the code. If they are using a rotating coil, the connection to the multipole coefficients is not as straightforward as in a straight magnet, i.e., you cannot just measure a single harmonic and put that into a single k.

[DavidSagan]

@rdemaria @DavidSagan There are also natural generalizations of multipole definitions to curved elements as in:
[T. Zolkin, Phys. Rev. Accel. Beams 20, 043501 (2017)](https://journals.aps.org/prab/abstract/10.1103/PhysRevAccelBeams.20.043501) and references therein.

Yes this is exactly the vertically and horizontally pure multipoles.

[DavidSagan]

@rdemaria Note that in all cases, horizontally pure, vertically pure, and straight line elements, the value of something like Kn1 is the value of the normalized derivative dBy/dx(x = y = 0).