Asova G

Floettmann K

Holder DJ

Khodyachykh S

Krasilnikov M

Muratori B

Stephan F

English

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DESIGN CONSIDERATIONS FOR PHASE SPACE TOMOGRAPHYDIAGNOSTICS AT THE PITZ FACILITY∗G. Asova† , S. Khodyachykh, M. Krasilnikov, F. Stephan, DESY, 15738 Zeuthen, GermanyK. Floettmann, DESY, 22761 Hamburg, GermanyD.J. Holder, B. Muratori, ASTeC, STFC Daresbury Laboratory, Warrington, UKAbstractA major goal of the Photo Injector Test Facility at DESYin Zeuthen (PITZ) is to build and to optimise high bright-ness electron sources for SASE FELs where the detailedknowledge of the phase-space distribution of the electronbeam is very important.The current upgrade of the PITZ facility includes a di-agnostic section suitable for transverse phase space tomog-raphy and multiscreen emittance measurements. The de-signed module should be capable of operation over a rangeof beam momenta between 15 and 40 MV/c. It mainly con-sists of four observation screens with three FODO cellsin between them. An upstream section of a number ofquadrupoles is used to match the electron beam Twiss pa-rameters to the tomography section.The design considerations of the tomography section andresults from numerical simulations will be presented in thiscontribution.INTRODUCTIONThe Photo Injector Test Facility at DESY in Zeuthen(PITZ) will be upgraded to operate with higher beam en-ergies in early 2008. The upgrade also implies extendeddiagnostics, including a tomography section for detailedanalysis of the transverse phase-space density distributionof the electron beam. At a later stage the tomography mod-ule will be equipped with an RF deflecting cavity to studythe transverse distributions and measure emittance of lon-gitudinal slices for selected electron bunches [1].The tomography module will consist of three FODOcells and four diagnostic stations for beam size measure-ments. It has previously been shown that 45◦ phase ad-vance between the cells delivers the smallest emittancemeasurement errors using four screens [2]. Since the beamin general does not have the necessary size and slope on thefirst screen, a matching section is necessary. Both the to-mography and the matching sections have been designed ina collaboration between STFC Daresbury Laboratory andDESY. Preceding iterations of the design can be found in[3].In this paper some major aspects concerning the designof the tomography module are reviewed as follows: The∗This work has partially been supported by the European Com-munity, contracts RII3-CT-2004-506008 and 011935 (EUROFEL), andby’Impuls- und Vernetzungsfonds’ of the Helmholtz Association, contractVH-FZ-005.† galina.asova@desy.defirst section justifies the choice of the physical layout; thisis followed by general considerations of the matching sec-tion and then two different examples of matching are given,confronted with an ideal case where no space charge forcesare acting on the beam (zero current). Phase space recon-struction from ASTRA-simulated [4] distributions providesthe final results.DESIGN LAYOUT OF THETOMOGRAPHY SETUPThe proposed tomography setup is shown schematicallyin Fig. 1. It consists of a number of matching quadrupoles,which will be discussed later, and the three identical sym-metric FODO cells at the end. In a previous design itera-Figure 1: Tomography and matching setup (not to scale).Two more upstream quadrupoles are not shown.tion a quadrupole effective length of 0.06 m was assumedbut, due to stringent space restrictions, shorter quadrupoleswith an effective length of 0.04 m and a physical one of0.062 m have been chosen now. Geometrically the min-imum drift allowed between two adjacent quadupoles is0.26 m but the drifts between the quadrupoles in the firsttwo cells and the one between the quadrupoles in an identi-cal cell upstream, used for matching, have to accommodatekicker magnets for extraction of a single bunch from thebunch train. From the point of view of motion stability, thequadrupole effective length allows the use of any drift forwhich | cosµ = T11+T222 |≤ 1, where T is the transportmatrix from screen to screen and µ is the phase advance,up to a maximum 0.46 m. Thus, a cell length of 0.76 mwas chosen. As it can be seen from Fig. 2, for the idealcase of zero current phase advance, the maximum RMSsize excursion does not exceed 0.15 mm for a normalisedemittance of 0.99 mm·mrad and beam energy of 32 MeVand on a screen the Twiss parameters are βx,y = 0.99 m,αx,y = ∓1.12.Numerical simulations excluding particles’ self-repulsion, for quadrupoles with effective lengths of0.06 m, show smaller β-mismatch 1 on the screens in1∆β[%] =βdesigned−βmeasuredβdesigned· 100Proceedings of DIPAC 2007, Venice, Italy TUPB23Beam Instrumentation and Feedback FEL related117óx,y[mm]ysxsFigure 2: RMS beam size inside the FODO lattice fora beam with zero current. The abscissa coordinates areshifted with respect to the entrance of the matching sec-tion so that s = 0 corresponds to the beginning of the driftspace in front of the first matching quadrupole.comparison to the case of 0.04 m effective length. Themismatch increases when decreasing the energy whichclearly shows that the space charge term dominates overthe emittance term in the equations of motion. For beammomentum of 32 MeV/c the space charge term is 10 timesthe emittance one and decreasing the energy to 15 MeVleads to 50 times bigger space charge term. Thus, thematching procedure should be based on the equations ofmotion including space charge and emittance terms.MATCHING OF THE ELECTRON BEAMTO THE TOMOGRAPHY SECTIONMatching of space charge-dominated beams impliesminimisation of a ’cost function’ which takes into accountthe beam size X(z), Y(z) and slope X′(z), Y′(z) and gen-eralised perveance2, including the kinetic energy and thebeam peak current as a ratio between the bunch charge andlength.Initially five quadrupoles used for matching were as-sumed but they are not sufficient with the effective lengthwe are planning to use. There is a possibility to include upto a further four magnets, located in an upstream straightsection. Two independent approaches and setups wereevaluated in order to obtain a matched beam on the firstscreen in the presence of self repulsive forces.Initially ASTRA was used to track the electron beamalong the full setup shown in Fig. 1 - seven matchingquadrupoles, excluding the self-field repulsion. This wouldrepresent the ideal solution to be achieved. Including thespace charge afterwards gives an idea of what the beam sizemismatch is and where the effects have strongest influence.2K =IpeakIAlfven· 2(βγ)3The defined cost function is∆2 = (δX ′w − δX ′wo)2 + (δY ′w − δY ′wo)2+(σx,w − σx,wo)2 + (σy,w − σy,wo)2,where w denotes simulation with space charge included,wo - with space charge forces switched off, andδU ′ =σU,zstart − σU,zendzend − zstart ,with U being either X or Y for both w and wo, zstartand zend refer to the beginning and the end of the driftssurrounding the quadrupoles taken into account. The costfunction has to be minimised in a number of iterationswhere the strength of each magnet for zero current is cor-rected with a predefined valueδk =LLeff· KR2,where L is the overall length the space charge forces areacting on, Leff is the quadrupole effective length, K is theperveance and R is beam radius. δk can be changed ineach successive iteration to a value where the value of ∆is smaller. This iterative procedure has to include not lessthan two quadrupoles at a time. The process is rather timeconsuming since it requires evaluation of the results butin this way the mismatch was decreased down five timesinside the FODO lattice, while without correction no pe-riodic solution was obtained. An example of the resultsinside the FODO lattice is shown in Fig. 3 The beam wasFigure 3: βx (left) and βy (right) along the tomographysection.also matched with the help of TRACE-3D [5] for the samelayout of quadrupoles. The agreement in the resulting mis-match between the two methods is rather good. In bothcases the periodicity in one of the transverse planes is bet-ter than in the other.This can be seen as well using a different matching setup- excluding the first magnet from the previous case and in-cluding one more upstream. The result is shown in Fig. 4- here the periodic solution for one plane was very good,while for the other it was not found. Inverting the po-larity swaps the results for the two planes. Since the to-mographic reconstruction requires recording (x, y) projec-tions for both planes, the reconstruction error will dependstrongly on the mismatch for either of the transverse planesif they are coupled.TUPB23 Proceedings of DIPAC 2007, Venice, ItalyBeam Instrumentation and Feedback118FEL relatedFigure 4: βx (left) and βy (right) along the tomographysection. Inverting the quadrupoles’ gradients along the to-mography and matching sections delivers the same periodicsolution for βy .PHASE SPACE RECONSTRUCTIONFROM NUMERICAL DATAElectron beam distributions have been numerically gen-erated (using ASTRA), matched and tracked along bothsections for the two matching setups described here. Thefour (x, y) on-screen distributions obtained are used as aninput for the adopted Maximum ENTropy (MENT) [6] re-construction algorithm. Results from (x, y) reconstructiononto (y, y′) with the first setup, where the beam matchingis worse in this same plane (see Fig. 3), are presented inFig. 5. Fig. 6 shows results from the second setup, again inthe plane with stronger mismatch (see Fig. 4).Figure 5: Original (left) and reconstructed (right) phasespace in (y, y’) plane.Visually there is a good agreement with respect to theslope of the ellipses, but this is not the case for the sizewhen there is a strong mismatch. The disagreement be-tween the reconstructed and the ASTRA-generated distri-butions in terms of emittance, RMS size and the covarianceare summarised in Table 1.CONCLUSIONSThe present work reviews some basic considerationsconcerning a tomography diagnostics setup at the PITZ fa-cility, particularly with regard to space charge effects. ItFigure 6: Original (left) and reconstructed (right) phasespace in (y, y’) plane.Table 1: Disagreement between the ASTRA-simulated andthe reconstructed result (matching case 1, 2 referred to withsubscripts).Original Reconstructed Disagreement [%]σy,1 0.26 0.24 7.7σyy′,1 -0.03 -0.03 -εy,N,1 1.21 1.18 2.6σy,2 0.3 0.3 -σyy′,2 -0.12 -0.13 8.3εy,N,2 1.24 1.48 19has been shown that a space charge-dominated beam canbe successfully matched (if done separately in both planes)but work still has to be done in order to easily obtain this re-sult in both planes simultaneously. Reconstruction resultsfor two different matching cases have been presented withgood agreement in terms of phase space RMS radius, slopeand covariance between the simulated and reconstructeddistributions when the beam size mismatch is minimised.REFERENCES[1] S. Korepanov at al., “RF Deflector for the Longitudinal andTransverse Beam Phase Space Analysis at PITZ”, these pro-ceedings[2] G. Asova et al., “Phase space tomography diagnostics at thePITZ facility”, proceedings of ICAP 2006, Chamonix, France[3] D.J. Holder et al., “A phase space tomography diagnostic forPITZ”, proceedings of EPAC 2006, Edinburgh, UK.[4] ASTRA: A Space Charge Tracking Algorithm,http://www.desy.de/˜mpyflo/.[5] PBO Lab 2.0, Gillespie Associates, Inc., 2001[6] J.J. Scheins, “Tomographic Reconstruction of Tranverse andLongitudinal Phase Space Distribution using Maximum En-tropy Algorithm”, TESLA Report 2004-08Proceedings of DIPAC 2007, Venice, Italy TUPB23Beam Instrumentation and Feedback FEL related119

2.0, Gillespie Associates,

A phase space tomography diagnostic for PITZ”, proceedings of EPAC

ASTRA: A Space Charge Tracking Algorithm,

Phase space tomography diagnostics at the PITZ facility”, proceedings of ICAP

RF Deflector for the Longitudinal and Transverse Beam Phase Space Analysis at PITZ”, these proceedings

Tomographic Reconstruction of Tranverse and Longitudinal Phase Space Distribution using Maximum Entropy Algorithm”,

Design considerations for phase space tomography diagnostics at the PITZ Facility

Design considerations for phase space tomography diagnostics at the PITZ Facility

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