Amplitude dependent tune shift from KQUAD

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petrenko
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Amplitude dependent tune shift from KQUAD

Post by petrenko » 19 Nov 2009, 05:12

Michael,

Why does KQUAD element like this one (without nonlinearities) generate some significant amplitude dependent tune shift?
KQUAD, N_KICKS=10, L=0.3, K1=+4.00

Are there any hidden nonlinearities (like fringe fields or something) that are taken into account?
Matrix version of this quadrupole of any order do not produce tune shift.

Alexey.
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michael_borland
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Re: Amplitude dependent tune shift from KQUAD

Post by michael_borland » 19 Nov 2009, 10:31

Alexei,

This is an interesting question. The KQUAD element does not have any fringe field modeling. Given that, I agree that the behavior of KQUAD is counterintuitive. QUAD displays no such behavior, even if I increase the ORDER to 3.

I also checked against the BMAP_XY element, which does integration through a 2D field map. Although it is a completely separate and very different implementation (non-symplectic), I'd expect very similar results to KQUAD if KQUAD is right. Indeed, that's what I get as you can see in the attached figure. The files I used are also attached. Based on this, I guess I need to look more carefully at the higher-order terms in the QUAD matrix.

However, I don't understand physically why the KQUAD and BMAPXY modeling gives these results. My original thought was that it was a result of the length of the quads, but some tests showed that wasn't the case. It also doesn't matter much if I use the 2nd or 4th order integrator.

By the way, using sddsnaff allows getting accurate frequencies with far fewer turns than needed for sddsfft.

--Michael
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petrenko
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Re: Amplitude dependent tune shift from KQUAD

Post by petrenko » 19 Nov 2009, 11:52

It looks like this tune shift in KQUAD comes from the v_z * H_y term in the Lorents force.
In qaudrupole vertical magnetic field is
H_y = G * x
Then horizontal Lorentz force is
F_x = (e/c) * v_z * G * x
The motion is linear as long as we assume v_z to be constant. This is only approximately true since
(v_z)^2 = v^2 - (v_x)^2 -(v_y)^2.

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