Envelope Fit

About Simultaneous Multiple Envelope Fits

Envelope Fit Simultaneously fitting several sets of measured profile data is an excellent way to precisely measure the projected emittances of a given beam. In the shown sample (72 MeV proton beam at the exit of Injector I) the x- and y-beam profiles at 3 locations (MNP29/30 and MNP1-4) are measured for 5 different settings of the quadrupoles QNC1, QNC2 and QNC3. The most difficult part is to find these different settings for the quads, so that the (x,x')- and (y,y')-beam ellipses at a given location behind the triplet vary enough (beam ellipse rotation angle variation of ±120 degrees). In the Transport input file the beam line appears 5 times with the same beam and correlation cards, but with the different measured profile data and quadrupole gradients inserted. In the fit section, the vary codes of the type code 1 and 12 have to be letters (A, B, C etc.) in order to make them changing by the same amount everywhere while fitting (coupled vary codes, see Transport manual). Also here, a computer program has been used to collect the data and insert them automatically into the transport input file.

Here is the sample Transport input file: 

 /QNC-Triplet, Simultaneous Multi Envelope Fit./
 0
 15. 1.0 /MM/ .1 ;
 15. 6.0 /PM/ .1 ;

 1. 1.906 1.682 3.68 .477 .0 .0 .3735 /B1/ ;
 12. -.938 .0 .0 .0 .0 .706 .0 .0 .0 .0 .0 .0 .0 .0 .0 /C1/ ;
 3. 1.443 ;
 16. 5.0 47.5 ;
 16. 7.0 .425 ;
 20. 180.0 ;
 2. 2.0 ;
 4. .315 1.3955 .0 /ANE/ ;
 2. .0 ;
 20. -180.0 ;
 3. .69 /MP29/ ;
 -10. 1.0 1.0 2.5 .1 /F1/ ;
 -10. 3.0 3.0 4.6 .1 /F2/ ;
 3. .244 ;
 5. .252 3.02895 47.5 /QNC1/ ;
 3. .299 ;
 5. .252 -4.08463 47.5 /QNC2/ ;
 3. .299 ;
 5. .252 2.53452 47.5 /QNC3/ ;
 3. 1.529 /MNP1/ ;
 -10. 1.0 1.0 1.2 .1 /F3/ ;
 3. .189 /MNP2/ ;
 -10. 3.0 3.0 1.9 .1 /F4/ ;
 3. 1.27 /MNP4/ ;
 -10. 3.0 3.0 .7 .1 /F6/ ;
 3. .187 /MNP3/ ;
 -10. 1.0 1.0 1.9 .1 /F5/ ;
 3. .293 /S/ ;

 1. 1.906 1.682 3.68 .477 .0 .0 .3735 /B2/ ;
 12. -.938 .0 .0 .0 .0 .706 .0 .0 .0 .0 .0 .0 .0 .0 .0 /C2/ ;
 3. 1.443 ;
 16. 5.0 47.5 ;
 16. 7.0 .425 ;
 20. 180.0 ;
 2. 2.0 ;
 4. .315 1.3955 .0 /ANE/ ;
 2. .0 ;
 20. -180.0 ;
 3. .69 /MP29/ ;
 -10. 1.0 1.0 2.5 .1 /F1/ ;
 -10. 3.0 3.0 4.5 .1 /F2/ ;
 3. .244 ;
 5. .252 2.3608 47.5 /QNC1/ ;
 3. .299 ;
 5. .252 -3.81737 47.5 /QNC2/ ;
 3. .299 ;
 5. .252 2.75723 47.5 /QNC3/ ;
 3. 1.529 /MNP1/ ;
 -10. 1.0 1.0 1.7 .1 /F3/ ;
 3. .189 /MNP2/ ;
 -10. 3.0 3.0 2.1 .1 /F4/ ;
 3. 1.27 /MNP4/ ;
 -10. 3.0 3.0 1.2 .1 /F6/ ;
 3. .187 /MNP3/ ;
 -10. 1.0 1.0 1.4 .1 /F5/ ;
 3. .293 /S/ ;

 1. 1.906 1.682 3.68 .477 .0 .0 .3735 /B3/ ;
 12. -.938 .0 .0 .0 .0 .706 .0 .0 .0 .0 .0 .0 .0 .0 .0 /C3/ ;
 3. 1.443 ;
 16. 5.0 47.5 ;
 16. 7.0 .425 ;
 20. 180.0 ;
 2. 2.0 ;
 4. .315 1.3955 .0 /ANE/ ;
 2. .0 ;
 20. -180.0 ;
 3. .69 /MP29/ ;
 -10. 1.0 1.0 2.7 .1 /F1/ ;
 -10. 3.0 3.0 4.6 .1 /F2/ ;
 3. .244 ;
 5. .252 1.91536 47.5 /QNC1/ ;
 3. .299 ;
 5. .252 -3.63919 47.5 /QNC2/ ;
 3. .299 ;
 5. .252 2.53452 47.5 /QNC3/ ;
 3. 1.529 /MNP1/ ;
 -10. 1.0 1.0 2.9 .1 /F3/ ;
 3. .189 /MNP2/ ;
 -10. 3.0 3.0 1.0 .1 /F4/ ;
 3. 1.27 /MNP4/ ;
 -10. 3.0 3.0 1.8 .1 /F6/ ;
 3. .187 /MNP3/ ;
 -10. 1.0 1.0 1.6 .1 /F5/ ;
 3. .293 /S/ ;

 1. 1.906 1.682 3.68 .477 .0 .0 .3735 /B4/ ;
 12. -.938 .0 .0 .0 .0 .706 .0 .0 .0 .0 .0 .0 .0 .0 .0 /C4/ ;
 3. 1.443 ;
 16. 5.0 47.5 ;
 16. 7.0 .425 ;
 20. 180.0 ;
 2. 2.0 ;
 4. .315 1.3955 .0 /ANE/ ;
 2. .0 ;
 20. -180.0 ;
 3. .69 /MP29/ ;
 -10. 1.0 1.0 2.7 .1 /F1/ ;
 -10. 3.0 3.0 4.6 .1 /F2/ ;
 3. .244 ;
 5. .252 2.02672 47.5 /QNC1/ ;
 3. .299 ;
 5. .252 -3.75055 47.5 /QNC2/ ;
 3. .299 ;
 5. .252 2.42316 47.5 /QNC3/ ;
 3. 1.529 /MNP1/ ;
 -10. 1.0 1.0 3.2 .1 /F3/ ;
 3. .189 /MNP2/ ;
 -10. 3.0 3.0 .9 .1 /F4/ ;
 3. 1.27 /MNP4/ ;
 -10. 3.0 3.0 2.9 .1 /F6/ ;
 3. .187 /MNP3/ ;
 -10. 1.0 1.0 2.0 .1 /F5/ ;
 3. .293 /S/ ;

 1. 1.906 1.682 3.68 .477 .0 .0 .3735 /B5/ ;
 12. -.938 .0 .0 .0 .0 .706 .0 .0 .0 .0 .0 .0 .0 .0 .0 /C5/ ;
 3. 1.443 ;
 16. 5.0 47.5 ;
 16. 7.0 .425 ;
 20. 180.0 ;
 2. 2.0 ;
 4. .315 1.3955 .0 /ANE/ ;
 2. .0 ;
 20. -180.0 ;
 3. .69 /MP29/ ;
 -10. 1.0 1.0 2.8 .1 /F1/ ;
 -10. 3.0 3.0 4.6 .1 /F2/ ;
 3. .244 ;
 5. .252 2.13808 47.5 /QNC1/ ;
 3. .299 ;
 5. .252 -4.08463 47.5 /QNC2/ ;
 3. .299 ;
 5. .252 2.3118 47.5 /QNC3/ ;
 3. 1.529 /MNP1/ ;
 -10. 1.0 1.0 3.6 .1 /F3/ ;
 3. .189 /MNP2/ ;
 -10. 3.0 3.0 3.2 .1 /F4/ ;
 3. 1.27 /MNP4/ ;
 -10. 3.0 3.0 7.5 .1 /F6/ ;
 3. .187 /MNP3/ ;
 -10. 1.0 1.0 3.0 .1 /F5/ ;
 3. .293 /S/ ;

 SENTINEL
 -1
 1.ABCD /B1/ ; (coupled variation of x, x', y and y' on all 5 sections)
 1.ABCD /B2/ ;
 1.ABCD /B3/ ;
 1.ABCD /B4/ ;
 1.ABCD /B5/ ;
 10. /F1/ ;
 10. /F2/ ;
 10. /F3/ ;
 10. /F4/ ;
 10. /F5/ ;
 10. /F6/ ;

 SENTINEL
 -1
 12.E0000F /C1/ ; (coupled variation of r12 and r34 in all 5 sections)
 12.E0000F /C2/ ;
 12.E0000F /C3/ ;
 12.E0000F /C4/ ;
 12.E0000F /C5/ ;
 1. /B1/ ; (freeze x, x', y and y' in all 5 sections)
 1. /B2/ ;
 1. /B3/ ;
 1. /B4/ ;
 1. /B5/ ;

 SENTINEL
 /*PLOT*/
 -1
 1.ABCD /B1/ ; (coupled variation of x, x', y and y' in all 5 sections)
 1.ABCD /B2/ ; (r12 and r34 stay free!)
 1.ABCD /B3/ ;
 1.ABCD /B4/ ;
 1.ABCD /B5/ ;
 SENTINEL
 SENTINEL

Envelope Fit The graphical output of the above Transport input sample is shown in ( Fig.1: 17 kB ) . To visualize the special fit constraints, you have to set the two parameters 'x-Measurements' and 'y-Measurements' in the 'Display Parameters' dialog box into the "on" position (MEASX=1.0 and MEASY=1.0 in FOR004.DAT). In the Graphic Transport display these constraints then appear as little "T"s. This method to measure the emittance has first been shown in the SIN annual report 1980, page 15 (in German).

Envelope FitEnvelope Fit Back to:Envelope FitAbout Transport Envelope Fits
Envelope FitEnvelope Fit Last updated by Urs Rohrer on 31-Jan-2006