The OPAL Discussion Forum

[Huiwen Koay <koay AT rcnp.osaka-u.ac.jp>]

Hi.

I have a question regarding the sigma-matrix shown in the output file of OPAL-cycl execution.

In the manual, it is stated that the sigma-matrix computation is based on (x,x′,y,y′,z,δ) instead of (x,px,y,py,z,pz). However, when I try to convert the x' to the sigmapx as shown in the output of MatchedGauss distribution, I couldnt reproduce the same value. 

For example, the output of OPAL shows:

OPAL> * I= 2.2 (mA) E= 580 (MeV) OPAL> * EX= 1e-06* EY= 1e-06* ET= 1e-06* FMAPFN ring590_bfld.dat OPAL> * FMSYM= 8* HN= 6* PHIINIT= 0 OPAL> * ---------------------------------------------------- OPAL> * Converged (Ex, Ey, Ez) = (0.313794, 0.313794, 0.313794) pi mm mrad for E= 580 (MeV) OPAL> * Sigma-Matrix OPAL> 3.914 & -0.6486 & 0 & 0 & 0.4542 & 1.362 \\ OPAL> -0.6486 & 0.6396 & 0 & 0 & 0.7265 & -0.2685 \\ OPAL> 0 & 0 & 6.239 & 1.198 & 0 & 0 \\ OPAL> 0 & 0 & 1.198 & 0.3859 & 0 & 0 \\ OPAL> 0.4542 & 0.7265 & 0 & 0 & 2.363 & 0.1752 \\ OPAL> 1.362 & -0.2685 & 0 & 0 & 0.1752 & 0.8944 \\ OPAL> * ************* D I S T R I B U T I O N ******************************************** OPAL> * OPAL> * Distribution type: MATCHEDGAUSS OPAL> * SIGMAX = 0.001978 [m] OPAL> * SIGMAY = 0.002498 [m] OPAL> * SIGMAZ = 0.001537 [m] OPAL> * SIGMAPX = 4.129e-05 [Beta Gamma] OPAL> * SIGMAPY = 3.639e-05 [Beta Gamma] OPAL> * SIGMAPZ = 4.49e-05 [Beta Gamma] OPAL> * AVRGPZ = 0 [Beta Gamma] OPAL> * CORRX = -0.4099 OPAL> * CORRY = 0.7722 OPAL> * CORRZ = 0.1205 OPAL> * R61 = 0.7277 OPAL> * R62 = -0.355 OPAL> * R51 = 0.1493 OPAL> * R52 = 0.5909 OPAL> * CUTOFFX = 3 [units of SIGMAX] OPAL> * CUTOFFY = 3 [units of SIGMAY] OPAL> * CUTOFFZ = 3 [units of SIGMAZ] OPAL> * CUTOFFPX = 3 [units of SIGMAPX] OPAL> * CUTOFFPY = 3 [units of SIGMAPY] OPAL> * CUTOFFPZ = 3 [units of SIGMAPY] As the definition of rms-emittance is given by emittance=sqrt(sigma_11*sigma_22-sigma12*sigma21). However, if I used only the red coloured matrix, I can neither reproduce the matched emittance at 0.3137 pi mm mrad, nor the rms-px by taking sqrt(639)/1000*betagamma. I can only obtain the rms of X by taking the sqrt of 3.914.

I would appreciate if somebody could help and shed a light on this matter.

Thanks again.

Best regards,

Huiwen