LEFFECTIVE in KQUAD element

[daniel.marx]

I am confused about how the LEFFECTIVE parameter works in the KQUAD element.

According to the manual:

As of version 29.2, this element incorporates the ability to have different values for the insertion
and effective lengths. This is invoked when LEFFECTIVE is positive. In this case, the L parameter is
understood to be the physical insertion length. Using LEFFECTIVE is a convenient way to incorporate
the fact that the effective length may differ from the physical length and even vary with excitation,
without having to modify the drift spaces on either side of the quadrupole element.

I would have thought that elegant makes a quadrupole with length LEFFECTIVE and then adds drift spaces on either side to make up the total length L. I would therefore expect that when LEFFECTIVE = L, this is the equivalent of having LEFFECTIVE = 0, i.e. deactivated. However, it seems this is not the case. How exactly does it work?

[michael_borland]

Daniel,

The function of the LEFFECTIVE parameter, if non-zero, is to specify the length of the active focusing region. So if LEFFECTIVE is positive, the model is

Code: Select all

Drift[(L-LEFFECTIVE)/2] Quad[LEFFECTIVE] Drift[(L-LEFFECTIVE)/2]

So if LEFFECTIVE=L, the drifts have zero length and it is as if you didn't bother to specify LEFFECTIVE at all.

As LEFFECTIVE approaches zero from above, the quadrupole part is just a thin kick with drift spaces of L/2 on either side. Note that the integrated strength of the quad is K1*LEFFECTIVE.

--Michael

[daniel.marx]

Michael,

Thanks for your explanation. This is pretty much how I thought it was implemented.

There is still something I don't understand and I've attached an example to illustrate this.
If I optimize with LEFFECTIVE set to L and then with LEFFECTIVE set to 0, my K1 values from the matching are exactly the same. However, the beta function is different when I track through this lattice. This can be easily seen by changing MQZM_LEFFECTIVE in the lattice file attached. What's going on here?

[michael_borland]

Daniel,

I'm unable to duplicate the problem. I set up a test using your input files and get the same beta functions and tunes in both cases. Please see attached.

--Michael

[daniel.marx]

Michael,

I think you're right. I'm not sure what I was doing on Friday but I tried again just now and the results agree. Thanks.