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
