Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL

1. Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL L. Groening, W. Barth, W. Bayer, G. Clemente, L. Dahl, P. Forck, P. Gerhard, I. Hofmann, G. Riehl, S. Yaramyshev, GSI, Germany D. Jeon, ORNL, U.S.A. D. Uriot, CEA/Saclay, France R. Tiede, University of Frankfurt, Germany • Introduction and set-up • Data reduction • Reconstruction of initial distribution • Results of experiment and simulations • Emittance growth reduction by rms-matching • Summary & outlook We acknowledge the support of the European Community – Research Infrastructure Activity under the FP6 "Structuring the European Research Area" program (CARE, contract number RII3-CT-2003-506395).

2. UNILAC at GSI: Overview RFQ, IH1, IH2 Alvarez DTL Transfer to Synchrotron HLI: (ECR,RFQ,IH) MEVVA MUCIS 1 ≤ A/q ≤ 9.5 1 ≤ A/q ≤ 65 Alvarez DTL RFQ IH1 IH2 PIG Gas Stripper 11.4 MeV/u β = 0.16 2.2 keV/u β = 0.0022 120 keV/u β = 0.016 1.4 MeV/u β = 0.054

3. The UNILAC Alvarez DTL A1 A4 A2b A3 A2a Tank : E [MeV/u] : 1.4 3.6 4.8 5.9 8.6 11.4 54 m • 5 independent rf-tanks • 108 MHz, 192 rf-cells • DTL based on F-D-D-F focusing • DC-quads grouped to 13 families • Inter-tank focusing : F-D-F • Synchr. rf-phases -(30°,30°,30°,25°,25°)

4. 108 MHz 36 MHz Section in Front of DTL Gas Stripper

5. Experimental Set-up & Procedure rms-bunch length measurement • set beam current to 7.1 mA of 40Ar10+ (equiv. to FAIR design of 15 mA of 238U28+) • measure hor., ver., emittance and long. rms-bunch length at DTL entrance • set DTL transverse phase advance to values from 35° to 90° • tune depression varied from 21% (90°) to 43% (35°) • measure transmission, hor., and ver. rms-emittance at DTL exit

6. Data Reduction • Measurement • projection of 6-dim to 2-dim plane • matrix of pixels • pixel size 0.8 mm / 0.5 mrad • evaluation based on pixel contents • Simulations • full 6-dim information available to compare measurement and simulation adequately, the evaluation procedures must be identical

7. Data Reduction • particle coordinates from simulations are projected onto virtual meas. device • projection is evaluated as a measurement

8. Definition of Fractional rms-Emittance • rms-emittance from a fraction of p% of the total intensity • calculate sum ∑100 of all pixel contents • sort pixels from top by their contents • sum them up until the fraction p from ∑100 is reached • use the pixels included in this sum for rms-emittance evaluation benchmarking used p = 95% of the intensity

9. Re-Construction of initial rms-Parameters for Simulations horizontal vertical Start of Simulations DTL Buncher 36 MHz Buncher 108 MHz → (α, β, ε)xy check (βε)l rms-tracking backwards meas. (α, β, ε)xy bunch length measurement guessed (α, β, ε)l • Selfconsistent backtracking finding (α,β,ε)l that fit to measured bunch length • Varification wether applied machine settings would give full DTL transmission

10. Re-construction of initial type of Distribution measured in front of DTL horizontal vertical measured initial distribution inhabits different amount of halo horizontally and vertically

11. Re-construction of initial type of Distribution • Gauss, Lorentz, Waterbag distributions do not fit the measured amount of halo • Several functions tried in order to fit halo in both planes • function found as: applying different powers for different planes the amount of halo can be reproduced

12. Initial Distribution and Codes initial distribution Simulations with four different codes as used by the participating labs: DYNAMION (GSI) PARMILA (SNS) PARTRAN (CEA/Saclay) LORASR (Univ. of Frankfurt) Gaussian cut at 4σ assumed

13. Beam Transmission through DTL All codes reproduce measured full transmission. LORASR is lower by few percent

14. σo = 35° σo = 60° σo = 90° Experiment DYNAMION PARMILA PARTRAN LORASR Shapes of Final Horizontal Distributions • agreement for intermediate σo • disagreement for low/high σo • high σo: attached wings (islands)

15. σo = 35° σo = 60° σo = 90° Experiment DYNAMION PARMILA PARTRAN LORASR Shapes of Final Vertical Distributions • differences even at intermediate σo • high σo: no attached wings

16. Evolution of Simulated rms-Emittances (100%) • growth occurs mainly along first two tanks (agrees to previous measurements*) • LORASR predicts strongest growth • lowest growth at intermediate phase advances *www-dapnia.cea.fr/Phocea/file.php?class=std&&file=Doc/Care/care-report-07-030.pdf

17. Final 95%-rms Emittances as Function of Phase Advance vertical horizontal • three codes underestimate growth • LORASR predicts more growth • codes predict peak at σo=70° • three codes fit to meas. (except σo≤ 45°) • LORASR predicts more growth • codes predict peak at σo=70° (but LORASR) results do not depend on initial long. emittance within 0.1∙εl,o and 2∙εl,o

18. Final 95%-rms Emittances as Function of Phase Advance (horizontal + vertical) / 2 • codes and measurements reveal minimum growth at σo≈ 60° • LORASR predicts strongest growth • DYNAMION, PARMILA, PARTRAN fit well at σo≥ 60°, LORASR fits well at σo≤ 60° • codes predict peak at σo=70° (but LORASR)

19. Mismatch to Periodic DTL Envelopes rms-tracking algorithm for re-construction of initial distribution was used to estimate mismatch to DTL T.P. Wangler, Rf Linear Accelerators, p. 217

20. Reduction of Mismatch • algorithm used to rms-match (incl. space charge) the initial distribution to periodic DTL • test of matching by re-measuring emittance growth (one year later) • significant reduction of emittance growth by rms-matching including space charge • reduction demonstrates that algorithm to re-construct initial rms-values is valid

21. Summary • rms-emittance growth along a 5-tank DTL measured for 12 phase advances from ..35° to 90° • Measurements simulated using four codes (DYNAMION, PARMILA, PARTRAN, LORASR) • Special emphasis put on re-construction of amount of halo within initial distribution • Very good agreement found among DYNAMION, PARMILA, and PARTRAN • LORASR predicts higher growth rates with respect to other three codes • Codes describe well the behavior of measured sum of hor. and ver. emittances • Considerable differences between meas. & sim. growth within single planes • For low and high phase advances orientations and shapes of final distributions ..depend on the code • Systematic reduction of rms-mismatch to DTL under space charge conditions • rms-mismatch reduction resulted in considerable emittance growth reduction • (experimental reduction from 90% to 20% for space charge conditions equivalent to FAIR requirements)

22. Outlook • Using improved rms-matching measurements to be extended towards σo≈ 130° • Emittances to be measured after first DTL tank to avoid inter-tank-mismatch • Simulations predict a space charge driven 4th order resonance (talk by D. Jeon) • Attempt for experimental verfication at UNILAC scheduled for Dec. 2008

24. Gesellschaft für SchwerIonenforschung GSI Synchrotron, Bδ = 18 Tm p: 4 GeV Ne: 2 GeV U: 1 GeV 3 sources Fragment Separator Stor. Ring, Bδ = 10 Tm UNILAC, p – U : 3 – 12 MeV/u High Energy Physics ion species vary from pulse to pulse: simultaneous experiments using different ions

25. Construction of initial rms-Parameters for Simulations initial bunch length & transv. emittances measured at different locations !! Buncher 108 MHz Buncher 36 MHz Quadrupoles 15° 15° "A" 30° Alvarez 1st Tank transv. emitt. meas. "t" starting point of simulations "s" bunch length meas. "l" • DTL transmission is very sensitive to buncher settings, i.e. long. mismatch • applied buncher settings resulted in full DTL transmission and minimized low energy tails • -> useful in re-constructing the long. input distribution for simulations • transv. and long. emittance were measured at different locations, i.e. at "t" & "l" • distances from "l" and "s" to point "A" differ by 0.4 m • to merge transv. & long. measurements together some approximations were used

26. Re-construction of initial rms-Parameters for Simulations Buncher 108 MHz Buncher 36 MHz Quadrupoles 15° "A" 15° transv. emitt. meas. "t" 30° bunch length meas. "l" Starting point of simulations "s" • to merge measurements together some approximations were used : • "transport" from "l" to "s" approximated by drift of 0.4 m (with space charge) • at "t": combine measured x&y-rms-Twiss parameters with guessed long. rms-Twiss ..parameters • rms-tracking with space charge from "t" to "s-0.4m", using applied machine settings • if bunch length at "s-0.4m" agrees reasonably with measured one at "l": -> ok • if not: -> do different guess on long. Twiss parameters at "t" • put "s"-rms-Twiss parameters (x,y,l) into rms-matching routine • compare suggested buncher settings with those used during experiment • agreement: -> ok, rms-parameters of distribution re-constructed • no agreement: -> do different guess on long. Twiss parameters at "t"

27. Re-construction of initial type of Distribution • emittance growth is sensitive to type of initial distribution (i.e. amount of halo) • amount of halo can be visualized by plotting the fractional emittance vs. fraction no halo (KV) fractional rms-emittance some halo strong halo 0 100 fraction of particles [%]

28. Phase Advances

29. Dependence on Initial Long. rms-Emittance Value (using Gaussians cut at 2σ in each plane)