1. Simulation of Multiturn Injection into SIS-18
Seminar Beam Physics for FAIR
13. Mai 2019
Stefan Paret - Beschleunigerphysik

2. Stefan Paret - Beschleunigerphysik
Outline
Motivation
Linear multiturn-injection scheme
Old and new PATRIC
First result
Advanced injection schemes
Summary
Outlook
13. Mai 2019
Stefan Paret - Beschleunigerphysik

3. Stefan Paret - Beschleunigerphysik
Motivation
Increase of beam intensity for FAIR
Increase of number of particles per beamlett
As many injections as possible
Low loss budget for U28+ due to dynamic vacuum
 Impact of space charge within and between beamletts needs to be studied
 Optimization of injection parameters for high intensity
 Investigation of other injection schemes
13. Mai 2019
Stefan Paret - Beschleunigerphysik

4. Single turn injection
Trajectory merged into closed orbit by means of a local orbit bump
4 degrees of freedom: x, x’ at end of bump  close orbit xinj, x’inj  match bump to incoming beamlett
Generated by 4 kickers
Kickers switched off within one turn
trajectory from transfer channel (TK)
collimator
beamlett
local orbit bump
dsep
septum
injection kicker
nominal orbit without bump
13. Mai 2019
Stefan Paret - Beschleunigerphysik

5. Multiturn injection (MTI)
Singleturn injection  beam intensity limited to intensity in injector
Increase of intensity in synchrotron by accumulation of beamletts  multiturn injection
Problem:
Fundamental theorem of beam injection
Equal beamletts cannot be injected into the same phase-space volume.
13. Mai 2019
Stefan Paret - Beschleunigerphysik

6. Stefan Paret - Beschleunigerphysik
MTI using stacking
Solution:
Stacking or phase-space painting
Filling of different
phase-space volumes
Consequences:
Off-centered beamletts  Deflection by quadrupoles
Emittance growth: εMTI > Ninj εbeamlett
SIS-18:
Horizontal stacking  time-dependent horizontal orbit bump
Parameters optimized empirically y
acceptance x
ε of full beam
Idealized transverse stacking
13. Mai 2019
Stefan Paret - Beschleunigerphysik

7. Stefan Paret - Beschleunigerphysik
Simple linear Ramp
Simplest approach
Reduction of bump height by two beam radii 2a + thicksep per revolution
Drawback: inefficient use of acceptance x’ x
13. Mai 2019
Stefan Paret - Beschleunigerphysik

8. Stefan Paret - Beschleunigerphysik
Improved linear ramp
Use of quadrupolar deflection
For fractional tune Qf = 0.33 beamlett returns to septum after 3 turns
Sufficient reduction of bump height: 2a within 3 turns
 Ramp rate determined by a and Qf
septum x’
turn 2
shifted orbit x
turn 1
injection x x’ x x’ x x’ x x’
shifted orbit
13. Mai 2019
Stefan Paret - Beschleunigerphysik

9. Beginning of Injection
Bump must be smaller than displacement of first beamlett otherwise:
Minimal offset depends on ε, beta function β, Q
Estimated limit: 1.5a
 Beginning roughly determined by a x x’ x x’ x’ x x’ x
13. Mai 2019
Stefan Paret - Beschleunigerphysik

10. Stefan Paret - Beschleunigerphysik
Ending of Injection
Last injection: bump height = 2a
3 Turns later: bump height = 0
(for Qf = 0.33)
 Ending determined by a
13. Mai 2019
Stefan Paret - Beschleunigerphysik

11. Stefan Paret - Beschleunigerphysik
PATRIC
Developed at GSI
Particle in cell tracking
Space charge and other collective effects
Lattice: Constant focusing or input from MADX
Only stationary beams
 Not suitable for injection
PATRIC
beam initialization
sector map Ki, Rij, Tijk
lattice parameters α, β, μ, Δμ(Δp),…
particle motion
1. order lattice
space charge
MADX
beam optics file
emittance, losses, offset,…
13. Mai 2019
Stefan Paret - Beschleunigerphysik

12. Stefan Paret - Beschleunigerphysik
Extension of PATRIC
Turn by turn generation and addition of beamletts
Time dependent local orbit bump for injection
Parameterization
Modification of sector map from MADX
Accounting of chromaticity
PATRIC
beamlett initialization
addition to beam
bump adjustment
particle motion
1. order lattice
space charge
chromaticity
sector map Ki, Rij, Tijk
lattice parameters α, β, μ, Δμ(Δp),…
MADX
beam optics file
without bump
emittance, losses, offset,…
13. Mai 2019
Stefan Paret - Beschleunigerphysik

13. Stefan Paret - Beschleunigerphysik
First Results
13. Mai 2019
Stefan Paret - Beschleunigerphysik

14. More advanced injection schemes I
Skew quadrupole Emittance transfer to vertical plane by linear coupling horizontal phase space freed
(formerly) used at CERN and RHIC
Studied for SIS-18 (G. Franchetti, W. Daqa) but not finished
β-mismatch smaller βTK  smaller a at injection  more injections possible consequence: mismatched beam proposed by C. Carli y x y d1
d2<d1 x d2
13. Mai 2019
Stefan Paret - Beschleunigerphysik

15. More advanced injection schemes II
Emittance transfer before injection decrease of εhor at cost of εver UNILAC  smaller a  more injections possible proposed by L. Groening x x’ y y x x’ x x
εver * 4
εhor / 4
Possible with space charge?
Non-linear ramps PhD work of Y. El-Hayek (GSI)
13. Mai 2019
Stefan Paret - Beschleunigerphysik

16. Stefan Paret - Beschleunigerphysik
Summary
Model of injection with time-linear local orbit bump
Implementation in PATRIC
Demonstration of first results
Possible improvements of injection scheme
Linear coupling
β-mismatch
Emittance transfer
Non-linear ramps
13. Mai 2019
Stefan Paret - Beschleunigerphysik

17. Stefan Paret - Beschleunigerphysik
Outlook
Introduction of chromaticity
Verification of new code
Investigate impact of space charge
Inclusion of field errors in MADX
Consider simulations in 2.5D
Simulate more advanced injection schemes
Measurements in SIS-18
13. Mai 2019
Stefan Paret - Beschleunigerphysik