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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

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SLIDE 1

Hollow Bunches for Space Charge Mitigation

Adrian Oeftiger Space Charge 2017, GSI, Germany October 5, 2017

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SLIDE 2

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:

1

proof of principle (2015)

establish hollow bunch production procedure SC mitigation with hollow bunches

2

recent advances for reliable production (2016)

1 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 3

Situation at PS

Figure: (old) PS cycle structure

5.9 6.0 6.1 6.2 6.3 5.8 5.9 6.0 6.1 6.2 6.3 Qx Qy

Figure: Gaussian footprint with ∆QSC

y

≈ 0.31.

LHC-type beams: 1.2 s injection plateau in PS waiting for 2nd batch LIU upgrade: 2× higher N, same ǫx,y

= ⇒ higher space charge (SC) tune spread − → resonances: upper limit 8Qy = 50 vs. lower limit Qy = 6

2 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 4

How-To: Mitigate Space Charge

detuning from transverse direct space charge

∆Qx,y(z) = − rpλ(z) 2πβ2γ3

  • ds

βx,y(s) σx,y(s)

  • σx(s)+σy(s)
  • (1)

with beam sizes

σx(s) =

  • βx(s) ǫx

βγ +Dx(s)2δrms2, σy(s) =

  • βy(s)

ǫy βγ

(2)

3 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 5

How-To: Mitigate Space Charge

detuning from transverse direct space charge

∆Qx,y(z) = − rpλ(z) 2πβ2γ3

  • ds

βx,y(s) σx,y(s)

  • σx(s)+σy(s)
  • (1)

with beam sizes

σx(s) =

  • βx(s) ǫx

βγ +Dx(s)2δrms2, σy(s) =

  • βy(s)

ǫy βγ

(2)

= ⇒ mitigate space charge (lower max ∆Qx,y) by increasing injection energy (⇒ LIU baseline: Linac4 & PS)

3 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 6

How-To: Mitigate Space Charge

detuning from transverse direct space charge

∆Qx,y(z) = − rpλ(z) 2πβ2γ3

  • ds

βx,y(s) σx,y(s)

  • σx(s)+σy(s)
  • (1)

with beam sizes

σx(s) =

  • βx(s) ǫx

βγ +Dx(s)2δrms2, σy(s) =

  • βy(s)

ǫy βγ

(2)

= ⇒ mitigate space charge (lower max ∆Qx,y) by increasing injection energy (⇒ LIU baseline: Linac4 & PS) line charge density depression λmax ∼ λ(zcentre)

3 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 7

How-To: Mitigate Space Charge

detuning from transverse direct space charge

∆Qx,y(z) = − rpλ(z) 2πβ2γ3

  • ds

βx,y(s) σx,y(s)

  • σx(s)+σy(s)
  • (1)

with beam sizes

σx(s) =

  • βx(s) ǫx

βγ +Dx(s)2δrms2, σy(s) =

  • βy(s)

ǫy βγ

(2)

= ⇒ mitigate space charge (lower max ∆Qx,y) by increasing injection energy (⇒ LIU baseline: Linac4 & PS) line charge density depression λmax ∼ λ(zcentre) enlarging momentum spread δrms

3 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 8

Hollow Bunches

mitigate space charge via flat beam profile:

1

standard approach: double harmonic RF systems

2

novel approach: hollow phase space distribution

  • 1. double-harmonic RF bucket
  • 0. 4
  • 0. 8

[1012 p/m] − 4 − 2 2 4 z [m] −3 −2 −1 1 2 3 δp/p0 [10−3] 1 2 3 [109 p/m] 1 . 5 3 [1013 p]

  • 2. hollow distribution
  • 0. 4
  • 0. 8

[1012 p/m] − 4 − 2 2 4 z [m] −3 −2 −1 1 2 3 δp/p0 [10−3] 1 2 3 [109 p/m] 1 2 3 [1013 p]

4 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 9

Hollow Bunches

mitigate space charge via flat beam profile:

1

standard approach: double harmonic RF systems

2

novel approach: hollow phase space distribution

  • 1. double-harmonic RF bucket

− additional RF systems − precise phase alignment across

machines

  • 2. hollow distribution

+ single-harmonic RF − creation reportedly often suffers

from instabilities

4 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 10

Hollow Bunches

mitigate space charge via flat beam profile:

1

standard approach: double harmonic RF systems

2

novel approach: hollow phase space distribution

  • 1. double-harmonic RF bucket

− additional RF systems − precise phase alignment across

machines

+ lower λmax

  • 2. hollow distribution

+ single-harmonic RF − creation reportedly often suffers

from instabilities

+ lower λmax + larger momentum spread δrms ⇒ larger horizontal beam size σx =

  • βxǫx/(βγ)+D2

xδ2

rms

4 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 11

Creation in CERN’s PS Booster (PSB)

300 400 500 600 700 800

ctime [ms]

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

kinetic energy [GeV]

inj@C275 extr@C805

kinetic energy programme (PSB)

500 1000 1500 2000 2500

ctime [ms]

5 10 15 20 25

kinetic energy [GeV]

inj@C170 extr@C2850

kinetic energy programme (CPS)

Strategy:

1

start from usual LHC beam production cycle

2

add hollowing process during PSB ramp

− → enables creation without instabilities! − → solidly reproducible results!

3

excite dipolar parametric resonance to deplete distribution

4

transfer hollow bunches to PS

= ⇒ mitigate space charge during PS injection plateau

5 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 12

Method: Excitation of Parametric Resonance

Exploit phase feedback loop to make bucket phase reference oscillate:

φre f (t) = φs + ˆ φdr ive sin(ωdr ivet)

  • driven oscillation

(3)

575 580 585 590

ctime [ms]

20 10 10 20

  • ffset [deg]

LHC1A hollow phase loop offset (PSB)

parametric resonance:

mωdr ive

!

= nωs,0 − → excite m = 1,n = 1 dipolar resonance = ⇒ only one filament − → use ωdr ive ≈ 0.9ωs,0 to excite slightly outside centre,

RF bucket non-linearity + space charge =

⇒ ωs = ωs

  • Jlong.
  • 6 of 16

Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 13

Prediction vs. Reality

PyHEADTAIL Simulations Incl. Space Charge

  • rel. momentum δ

4 8 [1012 p/m] − 8 − 6 − 4 − 2 2 4 z [m] −3 −2 −1 1 2 3 δ [10−3] 15 30 [109 p/m] 2 4 [1013 p]

position z (a) start from Gaussian

  • rel. momentum δ

4 10 [1012 p/m] − 8 − 6 − 4 − 2 2 4 z [m] −3 −2 −1 1 2 3 δ [10−3] 15 30 [109 p/m] 2 4 [1013 p]

position z (b) excitation for 3.5TS

  • rel. momentum δ

4 10 [1012 p/m] − 8 − 6 − 4 − 2 2 4 z [m] −3 −2 −1 1 2 3 δ [10−3] 15 30 [109 p/m] 2 4 [1013 p]

position z (c) after 6TS excitation

  • rel. momentum δ

4 10 [1012 p/m] − 8 − 6 − 4 − 2 2 4 z [m] −3 −2 −1 1 2 3 δ [10−3] 15 30 [109 p/m] 2 4 [1013 p]

position z (d) filamenting

7 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 14

Prediction vs. Reality

PyHEADTAIL Simulations Incl. Space Charge

  • rel. momentum δ

4 8 [1012 p/m] − 8 − 6 − 4 − 2 2 4 z [m] −3 −2 −1 1 2 3 δ [10−3] 15 30 [109 p/m] 2 4 [1013 p]

position z (a) start from Gaussian

  • rel. momentum δ

4 10 [1012 p/m] − 8 − 6 − 4 − 2 2 4 z [m] −3 −2 −1 1 2 3 δ [10−3] 15 30 [109 p/m] 2 4 [1013 p]

position z (b) excitation for 3.5TS

  • rel. momentum δ

4 10 [1012 p/m] − 8 − 6 − 4 − 2 2 4 z [m] −3 −2 −1 1 2 3 δ [10−3] 15 30 [109 p/m] 2 4 [1013 p]

position z (c) after 6TS excitation

  • rel. momentum δ

4 10 [1012 p/m] − 8 − 6 − 4 − 2 2 4 z [m] −3 −2 −1 1 2 3 δ [10−3] 15 30 [109 p/m] 2 4 [1013 p]

position z (d) filamenting

PSB Measurements

  • rel. momentum δ

position z (a) start from Gauss.

  • rel. momentum δ

position z (b) filamenting

7 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 15

Reproducibility in PSB

Some consecutive shots:

8 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 16

PS Experiment Overview

− → single bunch (ring 3), LHC25 type, minimalistic changes

parameter symbol value

  • long. 100% emittance hollow

ǫz,100% 1.43±0.15eVs

  • long. 100% emittance Gauss

ǫz,100% 1.47±0.11eVs

PSB horizontal r.m.s. emittance

ǫx ≈ 2.23mmmrad

PSB vertical r.m.s. emittance

ǫy ≈ 2.12mmmrad

intensity hollow

N (1.661 ± 0.053)×1012

intensity Gauss

N (1.835 ± 0.034)×1012

injection plateau energy

Ekin

1.4 GeV horizontal coh. dip. tune

Qx

6.23 vertical coh. dip. tune

Qy

6.22 synchrotron period (V = 25kV)

Q−1

S,0

725 turns

Table: relevant PS beam specifications at injection.

9 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 17

Compared Distributions in PS @C185

heavily flattened parabolic (“Gauss”)

150 100 50 50 100 150 ns 7.5 5 2.5 2.5 5 7.5 MeV 0.5 1 1.5 2 A 3E5 2.5E5 2E5 1.5E5 1E5 5E4 eeV 5 10 15 20 Iterations

Nov 15 16:07:08 2015 MD7, C185

1.81E12 eeVs

RMS Emitt. 0.293 eVs BF 0.396 90 Emitt. 1.12 eVs Ne 1.9E12 Mtchd Area 1.41 eVs Duration 200 ns RMS dpp 1.09E3 fs0;1 611;471 Hz

hollow

100 50 50 100 150 ns 7.5 5 2.5 2.5 5 7.5 MeV 0.25 0.5 0.75 1 1.25 1.5 1.75 A 2E5 1.5E5 1E5 5E4 eeV 5 10 15 20 Iterations

Nov 15 21:03:53 2015 MD7, C185

1.69E12 eeVs

RMS Emitt. 0.318 eVs BF 0.446 90 Emitt. 1.13 eVs Ne 1.7E12 Mtchd Area 1.36 eVs Duration 195 ns RMS dpp 1.12E3 fs0;1 611;477 Hz

same longitudinal matched 100% emittances (equal BL)

= ⇒ ∼ 9% larger r.m.s. emittances in hollow case

10 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 18

Transfer to PS: Bunch Length Scan

scan bunch length BL to vary space charge ∆Qx,y ∝ λmax ∝ 1/BL: compare hollow to standard parabolic (Gaussian-type) bunches

120 140 160 180 200 220

BL [ns]

2.0 2.5 3.0 3.5 4.0

λmax/N [10−2/m]

40 30 20 10 0 10 20 30 40

z [m] (1m ≈ 3.6ns)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

λmax/N [10−2/m]

maximal bunch length restricted by PSB recombination kicker window (PSB has 4 rings whose h = 1 bunches need to be enchained for PS)

= ⇒ reduce maximal line density by factor 0.9 for hollow bunches

(unrealistic rectangular extreme case gives factor

  • 2π/4 ≈ 0.63)

11 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 19

Transfer to PS: Bunch Length Scan

scan bunch length BL to vary space charge ∆Qx,y ∝ λmax ∝ 1/BL: compare hollow to standard parabolic (Gaussian-type) bunches

120 140 160 180 200 220

BL [ns]

2.0 2.5 3.0 3.5 4.0

λmax/N [10−2/m]

40 30 20 10 0 10 20 30 40

z [m] (1m ≈ 3.6ns)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

λmax/N [10−2/m]

maximal bunch length restricted by PSB recombination kicker window (PSB has 4 rings whose h = 1 bunches need to be enchained for PS)

= ⇒ reduce maximal line density by factor 0.9 for hollow bunches

(unrealistic rectangular extreme case gives factor

  • 2π/4 ≈ 0.63)

11 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 20

Hollow Bunches vs. Parabolic Bunches

0.20 0.24 0.28 0.32

∆Qy

2.0 2.5 3.0 3.5 4.0

ǫfin

y [mm mrad]

high vertical SC tune spreads lead to blow-up from integer resonance

= ⇒ final core emittance for reference Gaussian space charge shift

(computed using injection values for each shot in formulae (1), (2))

− → read this plot as “to what extent does the longitudinal distribution

improve PS transmission compared to a Gaussian distribution?”

12 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 21

2016 Results: “Nominal-like” Hollow Bunches

Produced hollow bunches with longitudinal matched area of ∼ 1.4eVs at ∼ 0.32eVs RMS emittance (nominal 0.25 eVs): minimalistic changes to operational LHC cycle

1

adiabatic change from h = 2 to h = 1 (after nominal C16 blow-up)

2

sinusoidal phase loop offset excites dipolar parametric resonance

3

second C16 blow-up to flatten / smoothen phase space distribution

13 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 22

Tomograms Over Process

300 400 500 600 700 800

ctime [ms]

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

kinetic energy [GeV]

inj@C275 extr@C805

kinetic energy programme (PSB)

PSB C573 before excitation

14 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 23

Tomograms Over Process

300 400 500 600 700 800

ctime [ms]

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

kinetic energy [GeV]

inj@C275 extr@C805

kinetic energy programme (PSB)

PSB C573 before excitation PSB C591 after excitation

14 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 24

Tomograms Over Process

300 400 500 600 700 800

ctime [ms]

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

kinetic energy [GeV]

inj@C275 extr@C805

kinetic energy programme (PSB)

PSB C573 before excitation PSB C591 after excitation PSB C800 after synchro, before extraction

14 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 25

Tomograms Over Process

300 400 500 600 700 800

ctime [ms]

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

kinetic energy [GeV]

inj@C275 extr@C805

kinetic energy programme (PSB)

PSB C573 before excitation PSB C591 after excitation PSB C800 after synchro, before extraction CPS C171 after transfer

14 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 26

2016 Results: Large Emittance Hollow Bunches

How to achieve large longitudinal emittances (towards LIU goal 3 eVs)? later times in PSB cycle: more available RF bucket area

∆E E0

  • max

∝ 1 −η

for

φs = const

and

η < 0 → increasing

(4)

− → move parametric resonance from C575 to C675 (extraction: C805) = ⇒ easily obtain 0.5 eVs RMS longitudinal emittance (2 eVs matched

area) after excitation (double RMS emittance compared to nominal)

15 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 27

Summary and Outlook

We have seen hollow bunches mitigating space charge impact of integer resonance

− → lower ǫy transmitted through PS injection plateau (compared to

nominal parabolic bunches) for same injected ǫx,y, N and BL

continuous and reliable hollow bunch production possible Next steps: PSB: finalise large ǫz hollow bunches (towards LIU goal)

− → improve resonance excitation to even larger synchrotron amplitudes − → investigate high-harmonic phase modulation settings for smoothing

PS: space charge study

now much cleaner hollow bunch production: narrower error bars

− → more accurate figure of improvement over parabolic bunches = ⇒ demonstrate higher intensity reach at same extracted emittance

16 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 28

Thank you for your attention!

Acknowledgements: Maria-Elena Angoletta, Hannes Bartosik, Michael Betz, Christian Carli, Heiko Damerau, Alan Findlay, Simone Gilardoni, Cedric Hernalsteens, Alexander Huschauer, Michael Jaussi, Kevin Li, Giovanni Rumolo, Guido Sterbini, Raymond Wasef special thanks to PSB / CPS OP teams for their support and kind patience!! ;-)

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SLIDE 29

Space Charge Tune Spreads

Figure: Tune footprints for both a Gaussian and a hollow distribution in the PS with the same beam characteristics (intensities, transverse emittances etc.)

5.9 6.0 6.1 6.2 6.3 5.8 5.9 6.0 6.1 6.2 6.3 Qx Qy

(a) Gaussian footprint with

∆QSC

y

≈ 0.31.

(b) Hollow footprint for the same

parameters.

17 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 30

1 : 2 Parametric Resonance Creates 2 Filaments

18 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 31

Waterfall Plot During 1 : 1 Parametric Resonance

19 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 32

Lessons Learned

1

as we need consecutive C16 blow-ups: make C16 transparent in between active times via non-integer harmonic values (e.g.

h = 9.5) to minimise induced

voltage (Alan Findlay)

2

need to minimise cross-dependency of radial and phase loop feedback systems (to cleanly excite dipolar resonance):

− → bad idea: switching off radial loop entirely during hollowing

procedure (⇒ persistent beam loss afterwards)

− → per default, PSB radial loop at unnecessarily strong gain − → low radial loop gain allows to reliably excite to 0.5 eVs RMS emittance − → on top, low biquad corrector gain for (i.) weaker immediate radial

loop reaction and (ii.) overall less noisy radial position

20 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 33

Horizontal Emittance Determination

assume betatron distribution fβ to be Gaussian get momentum distribution fδ via tomography / Abel transform from bunch shape monitor dispersive distribution fdisp(x) = fδ(Dxδ)

|Dx|

convolute Gaussian with fdisp to fit wire scan

= ⇒ find Gaussian σxβ in least squares approach

sum of independent random variables

x = xβ +Dxδ

xβ,δ indep.

= ⇒ fx(x) =

  • dx′ fβ(x′)fdisp(x − x′)
  • convolution of profiles

fx → wire scan profile, fdisp → dispersive distribution

21 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 34

Horizontal Emittance Determination

assume betatron distribution fβ to be Gaussian get momentum distribution fδ via tomography / Abel transform from bunch shape monitor dispersive distribution fdisp(x) = fδ(Dxδ)

|Dx|

convolute Gaussian with fdisp to fit wire scan

= ⇒ find Gaussian σxβ in least squares approach

20 15 10 5 5 10 15 20

horizontal position [mm]

20 40 60 80 100 120

horizontal distribution measured: Dxδ distribution input: Gaussian xβ distribution

21 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 35

Horizontal Emittance Determination

assume betatron distribution fβ to be Gaussian get momentum distribution fδ via tomography / Abel transform from bunch shape monitor dispersive distribution fdisp(x) = fδ(Dxδ)

|Dx|

convolute Gaussian with fdisp to fit wire scan

= ⇒ find Gaussian σxβ in least squares approach

20 15 10 5 5 10 15 20

horizontal position [mm]

20 40 60 80 100 120

horizontal distribution measured: Dxδ distribution input: Gaussian xβ distribution measured: horizontal wire scan

  • utput: convolution of xβ with Dxδ

21 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017

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SLIDE 36

PS: Tripple Splitting of Hollow Distribution

central bunch slightly hollow, others flat Mountain diagram from C1830 to C1890, period of 185 turns

= ⇒ any PS blow-ups before C1900 switched off – otherwise hollow

distribution disrupted (cf. PSMD logbook 04.11.) ր

22 of 16 Adrian Oeftiger Hollow Bunches – October 5, 2017