Simulation of Multiturn Injection into SIS18 Seminar Beam

Simulation of Multiturn Injection into SIS-18 Seminar Beam Physics for FAIR 13 Juni 2021 Stefan Paret - Beschleunigerphysik

Outline • Motivation • Linear multiturn-injection scheme • Old and new PATRIC • First result • Advanced injection schemes • Summary • Outlook 13 Juni 2021 Stefan Paret - Beschleunigerphysik 2

Motivation Increase of beam intensity for FAIR • Increase of number of particles per beamlett • As many injections as possible • Low loss budget for U 28+ 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 Juni 2021 Stefan Paret - Beschleunigerphysik 3

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 trajectory from transfer channel (TK) collimator beamlett local orbit bump septum dsep injection kicker nominal orbit without bump • Kickers switched off within one turn 13 Juni 2021 Stefan Paret - Beschleunigerphysik 4

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 Juni 2021 Stefan Paret - Beschleunigerphysik 5

MTI using stacking Solution: Stacking or phase-space painting Filling of different phase-space volumes Consequences: • Off-centered beamletts Deflection by quadrupoles • Emittance growth: y acceptance x ε of full beam Idealized transverse stacking εMTI > Ninj εbeamlett SIS-18: Horizontal stacking time-dependent horizontal orbit bump Parameters optimized empirically 13 Juni 2021 Stefan Paret - Beschleunigerphysik 6

Simple linear Ramp Simplest approach Reduction of bump height by two beam radii 2 a + thicksep per revolution Drawback: inefficient use of acceptance x’ x 13 Juni 2021 Stefan Paret - Beschleunigerphysik 7

Improved linear ramp Use of quadrupolar deflection For fractional tune Qf = 0. 33 beamlett returns to septum after 3 turns x’ turn 2 shifted orbit x turn 1 ➔ Sufficient reduction of bump height: 2 a within 3 turns septum injection x’ shifted orbit x Ramp rate determined by a and Qf 13 Juni 2021 Stefan Paret - Beschleunigerphysik 8

Beginning of Injection • Bump must be smaller than displacement of first beamlett otherwise: x’ x • Minimal offset depends on ε, beta function β, Q • Estimated limit: 1. 5 a x’ x Beginning roughly determined by a 13 Juni 2021 Stefan Paret - Beschleunigerphysik 9

Ending of Injection Last injection: bump height = 2 a 3 Turns later: bump height = 0 (for Qf = 0. 33) Ending determined by a 13 Juni 2021 Stefan Paret - Beschleunigerphysik 10

PATRIC • • • Developed at GSI Particle in cell tracking Space charge and other collective effects Lattice: Constant focusing or input from MADX PATRIC Only stationary beams beam initialization Not suitable for injection MADX • sector map Ki, Rij, Tijk • lattice parameters α, β, μ, Δμ(Δp), … particle motion • 1. order lattice • space charge beam optics file emittance, losses, offset, … 13 Juni 2021 Stefan Paret - Beschleunigerphysik 11

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 MADX beam optics file without bump 13 Juni 2021 • sector map Ki, Rij, Tijk • lattice parameters α, β, μ, Δμ(Δp), … PATRIC • beamlett initialization • addition to beam • bump adjustment particle motion • 1. order lattice • space charge • chromaticity emittance, losses, offset, … Stefan Paret - Beschleunigerphysik 12

First Results 13 Juni 2021 Stefan Paret - Beschleunigerphysik 13

More advanced injection schemes I • Skew quadrupole Emittance transfer to vertical plane by linear coupling horizontal phase space freed y (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 x y proposed by C. Carli 13 Juni 2021 Stefan Paret - Beschleunigerphysik d 1 x d 2<d 1 d 2 14

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 y x’ y x x x’ x εver * 4 εhor / 4 x Possible with space charge? • Non-linear ramps Ph. D work of Y. El-Hayek (GSI) 13 Juni 2021 Stefan Paret - Beschleunigerphysik 15

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 Juni 2021 Stefan Paret - Beschleunigerphysik 16

Outlook • Introduction of chromaticity • Verification of new code • Investigate impact of space charge • Inclusion of field errors in MADX • Consider simulations in 2. 5 D • Simulate more advanced injection schemes • Measurements in SIS-18 13 Juni 2021 Stefan Paret - Beschleunigerphysik 17