RFQ 3Dtree Space Charge Studies

Simon Jolly6th June 2012

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. N2 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…06/06/12 Simon Jolly, University College

London2

Adding “Ghost” Bunches (1)

06/06/12 Simon Jolly, University College London

3

H- Bunch

1 RF period long

Adding “Ghost” Bunches (2)

06/06/12 Simon Jolly, University College London

4

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.

Adding “Ghost” Bunches (2)

06/06/12 Simon Jolly, University College London

5

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.

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.

06/06/12 Simon Jolly, University College London

6

0 Ghost Space Charge Bunches

06/06/12 Simon Jolly, University College London

7

1 Ghost Space Charge Bunch (Standard)

06/06/12 Simon Jolly, University College London

8

2 Ghost Space Charge Bunches

06/06/12 Simon Jolly, University College London

9

3 Ghost Space Charge Bunches

06/06/12 Simon Jolly, University College London

10

4 Ghost Space Charge Bunches

06/06/12 Simon Jolly, University College London

11

5 Ghost Space Charge Bunches

06/06/12 Simon Jolly, University College London

12

6 Ghost Space Charge Bunches

06/06/12 Simon Jolly, University College London

13

7 Ghost Space Charge Bunches

06/06/12 Simon Jolly, University College London

14

8 Ghost Space Charge Bunches

06/06/12 Simon Jolly, University College London

15

9 Ghost Space Charge Bunches

06/06/12 Simon Jolly, University College London

16

10 Ghost Space Charge Bunches

06/06/12 Simon Jolly, University College London

17

Ghost Bunches: 60 mA Transmission

06/06/12 Simon Jolly, University College London

18

3 MeV Particles All Particles

Ghost Bunches: Full Transmission

06/06/12 Simon Jolly, University College London

19

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…06/06/12 Simon Jolly, University College

London20

0-3 Ghost Bunches, z-E

06/06/12 Simon Jolly, University College London

21

0-3 Ghost Bunches, z-y

06/06/12 Simon Jolly, University College London

22

1,4,7,10 Ghost Bunches, z-E

06/06/12 Simon Jolly, University College London

23

1,4,7,10 Ghost Bunches, z-y

06/06/12 Simon Jolly, University College London

24

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)06/06/12 Simon Jolly, University College

London25

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…

06/06/12 Simon Jolly, University College London

26

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.

06/06/12 Simon Jolly, University College London

27