Emittance statistics about the difference resonance

[ChongChong]

Dear all,

I changed betatron tunes to realize the difference resonance (equal fractional betatron tunes)in order to obtain a round beam(emittance x is equal to emittance y). I used "WATCH" to record the data of emittance x and emittance y for tracking particles in the elegant.

But the statistical results show that emittance x is not equal to emittance y, which is not consistent with the theory.
Could you help me solve my doubts?

Thank you,

Chongchong

[michael_borland]

Chongchong,

This is probably the result of correlations between the x and y coordinates. When there is strong coupling, the x and y planes are not the correct ones in which to analyze the beam distribution. See A. Wolski, PRSTAB 9, 024401 (2006). You can use the moments_output command in elegant to find the three actual emittances (parameters e1, e2, and e3). It will also give the projected emittances, which are not conserved (they vary around the ring).

You can also try putting in several watch elements at different locations and comparing the results. You should see that the emittances at the various locations vary.

If you continue to have problems, please post your input files.

--Michael

[ChongChong]

Dear Michael,

According to your suggestion, I used the moments_output command in elegant to find the three actual emittances.
e1 (m) = 3.420662e-11
e2 (m) = 5.694252e-17
e3 (m) = 5.261045e-06
And I put in several watch elements at different locations, the results are not all the same.

Theoretically, emittance x is equal to emittance y when fractional betatron tunes are equal(the difference resonance ). But I can not track the results with elegant. Attach is the input files, please review it.

Thank you,

Chongchong

[michael_borland]

Chongchong,

Your simulation does not appear to have any cross-plane coupling terms. In that case, even with equal x and y tunes, we do not expect the vertical emittance to be significantly different from zero. Indeed, you get e2=5.694252e-17.

You need to add some skew quadrupole or quadrupole tilt errors to the simulation.

--Michael