1. RFQ 3Dtree Space Charge Studies Simon Jolly 6 th June 2012

2. RFQ Space Charge Studies It’s always been an open question with RFQ simulations: how do we model space charge correctly? –Want to simulate continuous beam AND bunched beam: RFQ makes the transition. –Full 3D simulation would require MASSIVE bunch train to simulate small number of particles. –Alan wrote 3Dtree code using Barnes & Hut tree model: Gives N logN simulation time vs. N 2 for full 3D simulation. Includes effects of bunched beams by adding “ghost” bunches fore and aft of actual bunch for space charge calculation. 2 questions really need answering for 3Dtree simulations: –How many “ghost” bunches do we need to accurately model? –How do we get input/output beam dynamics right? I have looked at the first of these questions… 06/06/12Simon Jolly, University College London2

3. Adding “Ghost” Bunches (1) 06/06/12Simon Jolly, University College London3 H - Bunch 1 RF period long

4. Adding “Ghost” Bunches (2) 06/06/12Simon Jolly, University College London4 H - Bunch 1 RF period long If the simulation only contained 1 RF period’s worth of particles, space charge would force the bunch to elongate significantly… Transverse space charge matched by E- field of RFQ, but nothing similar for longitudinal field.

5. Adding “Ghost” Bunches (2) 06/06/12Simon Jolly, University College London5 H - Bunch 1 RF period long For N particles in the tracking bunch and M ghost bunches, GPT makes N tracking calculations rather than N*(1 + 2M) and N log N*(1 + 2M) space charge calculations rather than (N*(1 + 2M)) 2. But how many extra bunches do we need…? Add extra bunches in front and behind to balance space charge and approximate continuous beam.

6. RFQ Space Charge Studies: Extra Bunches Current simulations have all used 1 ghost bunch: –Is this enough? –If not, what is the optimum number of ghost bunches? Too few means longitudinal beam dynamics are incorrect: still looks like a bunched beam. Too many means simulations take too long due to extra space charge calculations. Ran 11 sets of simulations, with 0-10 ghost bunches, to investigate the “threshold”. Simulation parameters the same as before: –Still starting 10.9 mm long bunch at start of matching section. –0.25 pi mm mrad waterbag emittance. –Finely grained loss map takes care of losses. All previous simulations have used a single ghost bunch. 06/06/12Simon Jolly, University College London6

7. 0 Ghost Space Charge Bunches 06/06/12Simon Jolly, University College London7

8. 1 Ghost Space Charge Bunch (Standard) 06/06/12Simon Jolly, University College London8

9. 2 Ghost Space Charge Bunches 06/06/12Simon Jolly, University College London9

10. 3 Ghost Space Charge Bunches 06/06/12Simon Jolly, University College London10

11. 4 Ghost Space Charge Bunches 06/06/12Simon Jolly, University College London11

12. 5 Ghost Space Charge Bunches 06/06/12Simon Jolly, University College London12

13. 6 Ghost Space Charge Bunches 06/06/12Simon Jolly, University College London13

14. 7 Ghost Space Charge Bunches 06/06/12Simon Jolly, University College London14

15. 8 Ghost Space Charge Bunches 06/06/12Simon Jolly, University College London15

16. 9 Ghost Space Charge Bunches 06/06/12Simon Jolly, University College London16

17. 10 Ghost Space Charge Bunches 06/06/12Simon Jolly, University College London17

18. Ghost Bunches: 60 mA Transmission 06/06/12Simon Jolly, University College London18

19. 3 MeV ParticlesAll Particles Ghost Bunches: Full Transmission 06/06/12Simon Jolly, University College London19

20. Conclusions A single ghost bunch isn’t enough! Fractionally overestimating our transmission for all particles. Clearly underestimating our 3 MeV transmission. Too few ghost bunches meant longitudinal space charge not high enough, so a few percent too many particles not captured by RF. Optimal simulation looks to be 5-6 ghost bunches: any preferences…? And now, some home movies… 06/06/12Simon Jolly, University College London20

21. 0-3 Ghost Bunches, z-E 06/06/12Simon Jolly, University College London21

22. 0-3 Ghost Bunches, z-y 06/06/12Simon Jolly, University College London22

23. 1,4,7,10 Ghost Bunches, z-E 06/06/12Simon Jolly, University College London23

24. 1,4,7,10 Ghost Bunches, z-y 06/06/12Simon Jolly, University College London24

25. Paper 1: RFQ Integrated Design Paper will cover modelling background for our integrated RFQ design method. This is mainly RFQSIM -> Inventor -> Comsol -> GPT -> Matlab, but also includes sections on bulk CAD design and electromagnetic/thermal simulations. Half written: just waiting for other people to fill in some sections: –Introduction –*Vane Modulation Parameter Generation (APL – RFQSIM) –*RFQ Mechanical Design (PJS) –Vane Tip Modulation CAD Design (SJ) –*Electromagnetic Cavity Simulations (SL) –*Thermal Modelling (SL) –Beam Dynamics Simulations (SJ) Field Mapping (SJ - Comsol) Particle Tracking in GPT (SJ) –Conclusions (SJ) 06/06/12Simon Jolly, University College London25

26. Paper 2: FETS RFQ Design Paper will cover all steps we went through to design FETS RFQ. Will refer to previous integrated design paper, so no need to describe methods again, but needs to include all information showing how much work we’ve done on the various aspects of the design. I will take as much as I can from the conference papers, but will need help filling in gaps as there are several things that have been presented at FETS meetings I couldn’t find in PAC/EPAC papers. Outline will be similar: –Initial parameter generation and design limitations (APL + RF/klystron) –Basic CAD design (PJS) –Cold model construction and bead pull (SJ/PJS) –Electromagnetic cavity simulations (SL) –Thermal simulations and squirt nozzle/cooling design (SL/PJS) –Vane tip CAD modelling (SJ) –Beam dynamics simulations, inc RFQSIM/CAD modelling comparison (SJ) –Final CAD design, including tuner design, RF feedthroughs etc and final RFQ parameter comparison (SJ/PJS/APL) –Anything else… As Juergen suggested, this paper should include everything but also refer to conference papers… 06/06/12Simon Jolly, University College London26

27. Paper 3: Fringe Fields/Tolerances Paper will cover all the “edge effects” that have come largely from the CAD modelling. Try to show how really starts to interfere on some of the “optimised” areas of the RFQ design. Juergen’s work on the effect on the beam energy spread from the matching section fringe field: I will run some simulations (suggestions please…). All the simulations I’ve done recently checking the alignment and machining tolerances. 06/06/12Simon Jolly, University College London27