RFQ Exit Bunch Modelling Simon Jolly 25 th July 2012

RFQ Exit Bunches To correctly model MEBT, need a single, discrete exit bunch from RFQ. Problem: single “injected” bunch (simulation of 1 RF period of DC input beam) separates into several “exit” bunches. Solution: recombine several bunches into single exit bunch. Problem: how do we do the recombination… 27/06/12Simon Jolly, University College London2

Exit Bunch Recombination There are 4 methods we could use to recombine our multiple exit bunches into a single bunch for the MEBT simulation: –Select a single timeslice and move bunches in space by N RF periods in space to overlap bunches. –Select bunches from several timeslices, each separated by 1 RF period, and select the bunch at the same point in space. –Select all bunches from a single screen, reconstructing the spatial positions from the time distribution. –Only select a single bunch with the most particles in it. 27/06/12Simon Jolly, University College London3

1: Single Time Step In a single simulation timestep, all bunches are present but at different points in space. To recombine them into a single bunch, move the fast/slow bunches by N RF periods so all the bunches overlapp. Good: –All data present in single data slice. –Gets space charge right using SCtree3D. Bad: –Particle dynamics changes along beam path. –Not overlapping “same” bunch but bunches that have undergone more/less dynamics. 27/06/12Simon Jolly, University College London4 1 RF Period

2: Single Region in Space Select a region of space that you wish to extract the exit bunch from. Choose a timestep where the first bunch is exactly centred in this region. 27/06/12Simon Jolly, University College London5

2: Single Region in Space Add the particles in this bunch to the “exit” bunch. 27/06/12Simon Jolly, University College London6

2: Single Region in Space Move on N timeslices, where N  t = 1 RF period. 27/06/12Simon Jolly, University College London7

2: Single Region in Space Add the particles in the next bunch to the “exit” bunch. 27/06/12Simon Jolly, University College London8

2: Single Region in Space Repeat for all bunches with particles above threshold energy (2.8 MeV). Good: –Gets beam dynamics exactly right. Bad: –Computationally intense: need all simulation data. –Have to select exit bunch by hand (only need to do this once though). –Space charge not quite right: need to select sub-region to avoid unphysical distortions in particle density. 27/06/12Simon Jolly, University College London9

3: Single Screen Screen contains all particle data at a single position in space. To reconstruct beam distribution, create longitudinal distribution in time. 27/06/12Simon Jolly, University College London10

3: Single Screen Add/subtract N RF periods from each particle time to create single bunch. Use  x,  y and  z values for each particle to reconstruct single bunch eg. z = ct  z. Good: –All data present in single screen. –Much more economical to extract data: only output screens. Bad: –Particle dynamics changes along beam path due to space charge. –Distortions more pronounced due to evolving space charge. –Greater need to select particle subset: requires more simulated particles. 27/06/12Simon Jolly, University College London11 1 RF Period

4: Single Bunch Only select single bunch containing the most particles for exit bunch. 27/06/12Simon Jolly, University College London12 Good: –Simplest! No reconstruction required. Bad: –Still have to select time slice by hand. –Space charge wrong: parts of distribution are missing, so need large particle numbers. –Missing parts may contain different dynamics.

Results Ran single simulation with 100k particles. Extract 3 sets of data: –Several bunches in single timeslice 1571 with central bunch outside RFQ exit datum (method 1). –One bunch after RFQ exit datum from several timeslices 10 steps apart (1 timestep = 0.1 RF period) and overlap (method 2). –Several bunches from single screen at RFQ exit datum (method 3). RFQ Exit Datum fixed at outer face of main exit flange, NOT insert. 27/06/12Simon Jolly, University College London13 Output plane for RFQ GPT simulations

Single Timestep: X-Y 27/06/12Simon Jolly, University College London14

Multiple Timesteps: X-Y 27/06/12Simon Jolly, University College London15

Single Timestep: X-X’ 27/06/12Simon Jolly, University College London16

Multiple Timesteps: X-X’ 27/06/12Simon Jolly, University College London17

Single Timestep: Y-Y’ 27/06/12Simon Jolly, University College London18

Multiple Timesteps: Y-Y’ 27/06/12Simon Jolly, University College London19

Single Timestep: Z-Y 27/06/12Simon Jolly, University College London20

Multiple Timesteps: Z-Y 27/06/12Simon Jolly, University College London21

Single Timestep: Z-E 27/06/12Simon Jolly, University College London22

Multiple Timesteps: Z-E 27/06/12Simon Jolly, University College London23

Preliminary Conclusions Difference between several bunches at single timeslice and single bunch from several timeslices clear. Bunches from single timestep don’t overlap: difference from drift too great. “Fast” bunches have different dynamics (hollow z-E distribution): –Need to include this data (about 2% of transmitted beam). –Single bunch not good enough. 27/06/12Simon Jolly, University College London24

Multiple Timesteps: X-Y 27/06/12Simon Jolly, University College London25

Single Screen: X-Y 27/06/12Simon Jolly, University College London26

Multiple Timesteps: X-X’ 27/06/12Simon Jolly, University College London27

Single Screen: X-X’ 27/06/12Simon Jolly, University College London28

Multiple Timesteps: Y-Y’ 27/06/12Simon Jolly, University College London29

Single Screen: Y-Y’ 27/06/12Simon Jolly, University College London30

Multiple Timesteps: Z-Y 27/06/12Simon Jolly, University College London31

Single Screen: Z-Y 27/06/12Simon Jolly, University College London32

Multiple Timesteps: Z-E 27/06/12Simon Jolly, University College London33

Single Screen: Z-E 27/06/12Simon Jolly, University College London34

Conclusions Whatever method is chosen, we need to include multiple bunches at the same point in space. This leaves 2 options: –Multiple timeslices with manual selection of single bunch from each. –Automatic selection of bunches from single screen. Both methods give broadly similar results: –Former has slightly more accurate distribution since latter doesn’t (and can’t) use space charge in extrapolating particle positions. –Latter requires much smaller output file, less computing to extract data and no manual intervention. I will still need to run simulations with all timesteps for particle dynamics/losses, so take your pick… 27/06/12Simon Jolly, University College London35