Hollow Bunches for Space Charge Mitigation Adrian Oeftiger Space - PowerPoint PPT Presentation

Hollow Bunches for Space Charge Mitigation Adrian Oeftiger Space Charge 2017, GSI, Germany October 5, 2017

Motivation Motivation In the context of strong space charge regime with LHC Injectors Upgrade (LIU) beam parameters: mitigate detrimental space charge impact due to integer resonance at PS injection plateau Content of this talk: proof of principle (2015) 1 establish hollow bunch production procedure SC mitigation with hollow bunches recent advances for reliable production (2016) 2 1 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

Situation at PS 6.3 6.2 6.1 Qy 6.0 5.9 5.8 5.9 6.0 6.1 6.2 6.3 Qx Figure: Gaussian footprint with ∆ Q SC ≈ 0.31 . Figure: (old) PS cycle structure y LHC-type beams: 1 . 2 s injection plateau in PS waiting for 2 nd batch LIU upgrade: 2 × higher N, same ǫ x , y ⇒ higher space charge (SC) tune spread = → resonances: upper limit 8 Q y = 50 vs. lower limit Q y = 6 − 2 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

How-To: Mitigate Space Charge detuning from transverse direct space charge � r p λ ( z ) β x , y ( s ) (1) ∆ Q x , y ( z ) = − ds � � 2 πβ 2 γ 3 σ x , y ( s ) σ x ( s ) + σ y ( s ) with beam sizes � � ǫ y β x ( s ) ǫ x βγ + D x ( s ) 2 δ rms 2 , (2) σ x ( s ) = σ y ( s ) = β y ( s ) βγ 3 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

How-To: Mitigate Space Charge detuning from transverse direct space charge � r p λ ( z ) β x , y ( s ) (1) ∆ Q x , y ( z ) = − ds � � 2 πβ 2 γ 3 σ x , y ( s ) σ x ( s ) + σ y ( s ) with beam sizes � � ǫ y β x ( s ) ǫ x βγ + D x ( s ) 2 δ rms 2 , (2) σ x ( s ) = σ y ( s ) = β y ( s ) βγ = ⇒ mitigate space charge (lower max ∆ Q x , y ) by increasing injection energy ( ⇒ LIU baseline: Linac4 & PS) 3 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

How-To: Mitigate Space Charge detuning from transverse direct space charge � r p λ ( z ) β x , y ( s ) (1) ∆ Q x , y ( z ) = − ds � � 2 πβ 2 γ 3 σ x , y ( s ) σ x ( s ) + σ y ( s ) with beam sizes � � ǫ y β x ( s ) ǫ x βγ + D x ( s ) 2 δ rms 2 , (2) σ x ( s ) = σ y ( s ) = β y ( s ) βγ = ⇒ mitigate space charge (lower max ∆ Q x , y ) by increasing injection energy ( ⇒ LIU baseline: Linac4 & PS) line charge density depression λ max ∼ λ ( z centre ) 3 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

How-To: Mitigate Space Charge detuning from transverse direct space charge � r p λ ( z ) β x , y ( s ) (1) ∆ Q x , y ( z ) = − ds � � 2 πβ 2 γ 3 σ x , y ( s ) σ x ( s ) + σ y ( s ) with beam sizes � � ǫ y β x ( s ) ǫ x βγ + D x ( s ) 2 δ rms 2 , (2) σ x ( s ) = σ y ( s ) = β y ( s ) βγ = ⇒ mitigate space charge (lower max ∆ Q x , y ) by increasing injection energy ( ⇒ LIU baseline: Linac4 & PS) line charge density depression λ max ∼ λ ( z centre ) enlarging momentum spread δ rms 3 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

Hollow Bunches mitigate space charge via flat beam profile : standard approach: double harmonic RF systems 1 novel approach: hollow phase space distribution 2 1. double-harmonic RF bucket 2. hollow distribution 0 . 8 [10 12 p / m] 3 0 . 8 [10 12 p / m] [10 9 p / m] 3 [10 9 p / m] 2 2 0 . 4 0 . 4 1 1 0 0 0 0 3 3 2 2 δp/p 0 [10 − 3 ] δp/p 0 [10 − 3 ] 1 1 0 0 − 1 − 1 − 2 − 2 − 3 − 3 0 0 0 0 0 0 5 3 0 0 0 0 0 0 1 2 3 4 2 2 4 . 4 2 2 4 − − 1 − − [10 13 p] [10 13 p] z [m] z [m] 4 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

Hollow Bunches mitigate space charge via flat beam profile : standard approach: double harmonic RF systems 1 novel approach: hollow phase space distribution 2 1. double-harmonic RF bucket 2. hollow distribution − additional RF systems + single-harmonic RF − precise phase alignment across − creation reportedly often suffers machines from instabilities 4 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

Hollow Bunches mitigate space charge via flat beam profile : standard approach: double harmonic RF systems 1 novel approach: hollow phase space distribution 2 1. double-harmonic RF bucket 2. hollow distribution − additional RF systems + single-harmonic RF − precise phase alignment across − creation reportedly often suffers machines from instabilities + lower λ max + lower λ max + larger momentum spread δ rms ⇒ larger horizontal beam size � β x ǫ x /( βγ ) + D 2 x δ 2 σ x = rms 4 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

Creation in CERN’s PS Booster (PSB) kinetic energy programme (PSB) kinetic energy programme (CPS) kinetic energy [GeV] kinetic energy [GeV] 25 1.4 1.2 20 1.0 15 0.8 inj@C275 extr@C805 0.6 10 0.4 inj@C170 extr@C2850 5 0.2 0.0 0 300 400 500 600 700 800 500 1000 1500 2000 2500 ctime [ms] ctime [ms] Strategy: start from usual LHC beam production cycle 1 add hollowing process during PSB ramp 2 → enables creation without instabilities! − → solidly reproducible results! − excite dipolar parametric resonance to deplete distribution 3 transfer hollow bunches to PS 4 ⇒ mitigate space charge during PS injection plateau = 5 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

Method: Excitation of Parametric Resonance Exploit phase feedback loop to make bucket phase reference oscillate: φ re f ( t ) = φ s + ˆ (3) φ dr ive sin( ω dr ive t ) � �� � driven oscillation phase loop offset (PSB) 20 LHC1A offset [deg] 10 hollow 0 10 20 575 580 585 590 ctime [ms] ! parametric resonance: m ω dr ive = n ω s ,0 → excite m = 1, n = 1 dipolar resonance = ⇒ only one filament − → use ω dr ive ≈ 0.9 ω s ,0 to excite slightly outside centre, − � � RF bucket non-linearity + space charge = ⇒ ω s = ω s J long . 6 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

Prediction vs. Reality 8 10 [10 12 p / m] [10 12 p / m] [10 9 p / m] [10 9 p / m] 30 30 4 4 15 15 PyHEADTAIL Simulations Incl. Space Charge 0 0 0 0 3 3 rel. momentum δ rel. momentum δ 2 2 1 1 δ [10 − 3 ] δ [10 − 3 ] 0 0 − 1 − 1 − 2 − 2 − 3 − 3 10 10 position z position z 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 6 4 2 [10 12 p / m] 8 6 4 2 [10 12 p / m] [10 9 p / m] 30 2 4 [10 9 p / m] 2 30 4 2 4 2 4 − − − − − − − − [10 13 p] [10 13 p] 4 4 15 15 z [m] z [m] (a) start from Gaussian (b) excitation for 3.5 T S 0 0 0 0 3 3 rel. momentum δ rel. momentum δ 2 2 1 1 δ [10 − 3 ] δ [10 − 3 ] 0 0 − 1 − 1 − 2 − 2 − 3 − 3 position z position z 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 6 4 2 2 4 2 8 4 6 4 2 2 4 2 4 − − − − − − − − [10 13 p] [10 13 p] z [m] z [m] (c) after 6 T S excitation (d) filamenting 7 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

Prediction vs. Reality 8 10 [10 12 p / m] [10 12 p / m] [10 9 p / m] [10 9 p / m] 30 30 4 4 15 15 PyHEADTAIL Simulations Incl. Space Charge PSB Measurements 0 0 0 0 3 3 rel. momentum δ rel. momentum δ rel. momentum δ 2 2 1 1 δ [10 − 3 ] δ [10 − 3 ] 0 0 − 1 − 1 − 2 − 2 − 3 − 3 10 10 position z position z position z 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 6 4 2 [10 12 p / m] 8 6 4 2 [10 12 p / m] [10 9 p / m] 30 2 4 [10 9 p / m] 2 30 4 2 4 2 4 − − − − − − − − [10 13 p] [10 13 p] 4 4 15 15 z [m] z [m] (a) start from Gaussian (b) excitation for 3.5 T S (a) start from Gauss. 0 0 0 0 3 3 rel. momentum δ rel. momentum δ rel. momentum δ 2 2 1 1 δ [10 − 3 ] δ [10 − 3 ] 0 0 − 1 − 1 − 2 − 2 − 3 − 3 position z position z position z 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 6 4 2 2 4 2 8 4 6 4 2 2 4 2 4 − − − − − − − − [10 13 p] [10 13 p] z [m] z [m] (b) filamenting (c) after 6 T S excitation (d) filamenting 7 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

Reproducibility in PSB Some consecutive shots: 8 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

PS Experiment Overview → single bunch (ring 3), LHC25 type, minimalistic changes − parameter symbol value long. 100% emittance hollow ǫ z ,100% 1.43 ± 0.15 eVs long. 100% emittance Gauss ǫ z ,100% 1.47 ± 0.11 eVs PSB horizontal r.m.s. emittance ǫ x ≈ 2 . 23mmmrad PSB vertical r.m.s. emittance ≈ 2 . 12mmmrad ǫ y (1.661 ± 0.053) × 10 12 intensity hollow N (1.835 ± 0.034) × 10 12 intensity Gauss N injection plateau energy E kin 1 . 4 GeV horizontal coh. dip. tune Q x 6.23 vertical coh. dip. tune 6.22 Q y Q − 1 synchrotron period ( V = 25kV) 725 turns S ,0 Table: relevant PS beam specifications at injection. 9 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017