CEA Codes forum

Dear Didier,

I have a question about phase advance. I used a set of test lattice which consists of two periods, each containing a solenoid and a drift. My solenoids are very short, so the betax of the beam in the solenoid remains almost constant at 0.59 mm/π.mrad. The lattice is as follows

FREQ 162.5

lattice 2 1
;CELL 1
FIELD_MAP 70 20 0 20 0.64 1 0 0 sol_1 0
DRIFT 20 20 0 0 0

;CELL 2
FIELD_MAP 70 20 0 20 0.64 1 0 0 sol_1 0
DRIFT 20 20 0 0 0

end

According to the definition in tracewin, the phase advance sigma is defined as:


In the envelope, we can observe that throughout the entire period, the betax remains approximately at 0.59 mm/π.mrad.


In my lattice, the phase advance of the first period should be
phase advance =∫ 1/betax dl， The integration range is from 0 to 20 mm.

Approximately equal to
phase advance =∫1/0.59 dl = 33.9 π.mrad
Convert to angle
33.9*180/1000 = 6.1（deg）


The result given by tracewin is 0.046 degrees.


The integration length is the length of the solenoid. If integration length is the length of the first period, then the integration length is 40mm, and the result is 12 degrees.

So, my question is whether my understanding has gone wrong somewhere or if there is an issue with the setup, which is preventing me from obtaining the correct phase advance. From the above plots, it can also be deduced that if only the solenoid and drift sections are present, the phase advance in the z-direction is not calculated. However, In my mind， as long as there is a betaz, it should also be integrable. Does TRACEWIN have specific rules that govern this selection?

Best regards,
Li

Dear Li,

Firstly, I think you should upgrade your version, the plots tell me it's not recent.
One comment, be careful that you use the phase advance for the "Structure" and not for the "Beam": 'Structure' means that you're not using the beta integral but the phase advance of the transfer matrix see here : https://dacm-codes.fr/Softwares/TraceWi ... definition

OK, I've done a similar example of my own (see below) and it seems coherent to me.

The integration range is from 0 to 40 mm.
phase advance =∫1/0.6 dl = 1.66 x 0.04 = 0.064 rad
Convert to angle
0.064*(180/pi) = 3.8 deg

Regards,

Didier

Dear Didier,

Thank you very much for your response. I now understand the issue. However, I still have a question. According to the display in TraceWin, the unit of beta should be "mm/π.mrad", and after integrating the phase shift, the unit should be "π.rad". In the past, I understood this as 1π.rad being equal to 180 degrees. Therefore, I expected the integrated result to be 0.064π.rad = 0.064 * 180 = 11.52 degrees. However, in your response, the integrated result is given as 0.064 rad. So, in "mm/π.mrad," does the π merely serve as an indication that the unit is in radians, without actual numerical significance?

Dear Li,

This ∏ is actually a bit inconsistent and doesn't represent anything in particular here apart from unity. It's a bit like the ∏ in emittance unit, some people put it in or not, it's not always very clear. So from my point of view, it's to maintain a certain consistency with the emittance unit.
Sorry for confusiojn about that.

Regards,

Didier