Beam Centroid Shift Fits

Transport Beam Centroid Shift FitsBeam Centroid Shift Fits

Beam Centroid Shift Fits In order to get an automatic beam-centering program working well, for a given optics one has to measure the influence matrix elements of all used steering and bending magnets along the beam line. On all profile monitors (ev. harps or beam scanners) after each of these devices the beam displacements (1st moments) in x or y for defined deviations of the magnets have to be carefully measured. Usually this cannot be done with full intensity of the beam, because at some locations along the beam line the losses may get to high causing interlocks. Even at low intensities caution has always to be taken, that the beam does not get cut off partially by apertures, because this would lead to wrong profile data. First moments are signed (in contrary to 2nd moments for envelope fits) and usually show several zero-crossings along a whole beam line. Because zero-crossings are often well detectable, this method is more accurate than measuring widths for finding out wrong parameters of the beam line under consideration.
Beam Centroid Shift Fits The indicators for the beam centroid fit constraints are (0,1) for horizontal or (0,3) for vertical displacements. The shift (type code 7) has to be placed at the location of the steering magnet or in the middle of the bending magnet. Only the second (x') or the forth (y') vary code of the shift (type code 7) has to be freed for fitting. In the sample Transport input file shown below, with a second fit run a test is made if a 're-calibration' of the 4 quads (by varying simultaneously its apertures) would lead to a better chi-squared. In this sample it does, but this doesn't mean very much, because there are only 4 data points for 2 varied parameters. To be sure you would need at least 10 data points and several measurements done with different magnets which would finally lead all to the same correction(s) of the chosen parameter(s). Being finally successful with the re-calibration of a set of quadrupoles by changing its apertures could of course also mean that its effective lengths or the calibration of its power supplies have to be modified. Simultaneous variation of the apertures by a given percentage is just much easier as for the other mentioned parameters.

Here is a Transport sample input file: 

 /Sample Beam Centroid Shift Fit/
 0
 15. 1.0 /MM/ .1 ;
 15. 6.0 /PM/ .1 ;
 1. 2.8 .5 1.6 .7 .0 .5 1.2048 /BEAM/ ;
 16. 7.0 .425 ;
 16. 5.0 15.35 ;
 2. .0 ;
 4. .41 16.9414 -.045 /AHA/ ;
 7. .0 .0 .0 .0 .0 .0 /SHIF/ ; (this bend has produced displacements)
 4. .411 16.9414 -.045 ;
 2. 2.3 ;
 3. .344 ;
 16. 7.0 .425 ;
 16. 5.0 35.0 ;
 2. .0 ;
 4. .567 18.3014 .01 /AHB/ ;
 4. .568 18.3014 .01 ;
 2. -.4 ;
 3. .828 /SA1Y/ ;
 3. .214 ;
 5. .426 -2.6135 50.0 /QHA1/ ;
 3. .284 /MHC1/ ;
 3. .435 /MHP1/ ;
 -10. .0 1.0 2.689 .1 /S1/ ; (measured displacement in x)
 3. .425 ;
 5. .426 .3736 50.0 /QHA2/ ;
 3. .283 /SA2X/ ;
 3. .754 /SA3Y/ ;
 3. .381 /MHP3/ ;
 -10. .0 1.0 5.822 .1 /S3/ ; (measured displacement in x)
 3. .298 ;
 16. 5.0 50.0 ;
 16. 7.0 .425 ;
 20. 180.0 ;
 2. .1 ;
 4. .804 16.2482 -.01 /AHC/ ;
 4. .804 16.2482 -.01 ;
 2. .0 ;
 20. -180.0 ;
 3. .393 ;
 5. .426 -1.3992 50.0 /QHA3/ ;
 3. 1.588 ;
 5. .426 .9908 50.0 /QHA4/ ;
 3. .328 /MHP5/ ;
 -10. .0 1.0 6.076 .1 /S5/ ; (measured displacement in x)
 3. 1.147 /EHT/ ;
 3. .91 /MHP7/ ;
 -10. .0 1.0 5.227 .1 /S7/ ; (measured displacement in x)
 SENTINEL
 //
 -1
 7.01 /SHIF/ ;  (x' is freed)
 10. /S1/ ;
 10. /S3/ ;
 10. /S5/ ;
 10. /S7/ ;
 SENTINEL
 /*PLOT*/
 -1
 5.00A /QHA1/ ; (all 4 quads have their aperture varied by the same amount)
 5.00A /QHA2/ ;
 5.00A /QHA3/ ;
 5.00A /QHA4/ ;
 SENTINEL
 SENTINEL

Beam Centroid Shift Fits The Transport graphical output is shown in Fig. 1 (10 kB). The white curve shows the fit without varied quadrupole apertures. The red curve shows it with the quadrupole apertures freed. (This picture demonstrates the capability to show more than one Transport output in the same frame.) To visualize the special (0,1)- or (0,3)-fit constraints, you have to set the parameters 'd-Measurements', 'x-Ray' and/or 'y-Ray' in the 'Display Parameters' dialog box into the "on" position (MEASD=1.0, RAX=1.0 and/or RAY=1.0 in FOR004.DAT). In the Graphic Transport display these constraints then appear as little "+"s. By setting the 'x/y-Ray' parameter(s) to 1, the envelope display is disabled, but the central trajectory curves are displayed instead.
Beam Centroid Shift Fits An example of how well beam centroid shift fits may work is shown in Fig. 2 (23 kB) which shows the results of a beam centroid shift fit produced by varying the currents through the bending magnet AHL and the steering magnet SHG21x of the SINQ beam line and by using the measured changements in beam position at the different profile monitor locations (+) as fit constraints.

Beam Centroid Shift Fits Note: Like with envelope fits Transport allows also to perform simultaneous multi beam centroid shift fits in order to vary quadrupole apertures and the like coherently in order to improve the testing of sets of measurements done with different steering elements on the same beam line.

Beam Centroid Shift Fits A precise and consistent definition of the influence matrix elements is vital for the good functioning of an automatic beam-centering program with profile or beam position monitors. The better one knows the influence matrix, the faster and more precise deviations from the desired beam positions at the diverse monitors may be corrected. If all beam centroid shift fits for one setting of the quadrupoles are good, then the 'steering sensitivity' in mrad / DAC unit for all involved steering and bending magnets can be computed. With a special program (MATEL) the influence and steering (= inverse of influence) matrices for almost all other desired quadrupole settings may be computed (by accumulating R12 for horizontal and R34 for vertical transfer matrix elements) afterwards at any time without re-measuring. For a scheme of the fast (up to 10 Hz) autonomous centering loops (programmed in PDP-11 Fortran-77 and Assembler) serving the 590 MeV proton beam lines between 1985 and 1995 see Fig. 3 (12 kB). The principle of an automatic beam centering is explained in Fig. 4 (9 kB) which is an example with 2 steering magnets and 2 monitors.

Beam Centroid Shift FitsBeam Centroid Shift Fits Back to:Beam Centroid Shift FitsAbout Transport Envelope Fits
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Beam Centroid Shift FitsBeam Centroid Shift Fits Last updated by Urs Rohrer on 7-Feb-2006