Beam-beam simulations for IT PC tolerances - PowerPoint Presentation

Slide1

Beam-beam simulations for IT PC tolerances

M. Fitterer, R. De Maria, S. Fartoukh, M. GiovannozziAcknowledgments: G. Arduini, A. Ballarino, R. Bruce, J.-P. Burnet, E. McIntosh, F. Schmidt, H. Thiesen, E. Todesco and the LHC@Home volunteersSlide2

2

OutlinePowering scheme ITA bit of theory:effect of a tune modulationdefinition of dynamic apertureSimulation setup

Ripple

tolerances and dynamic aperture

studies

Conclusion

Further studiesSlide3

3

Proposed powering scheme HL-LHCproposed by WP3 (HL-LHC perliminary

Design report)

and presented by

A.

Ballarino

,

4

th

LHC Parameter and Layout Committee

preferred option

from

hardware sideSlide4

T

VtoI,load: LHC magnets modeled as RL circuit => the higher the magnet inductance the stronger the

attenuation

of the

higher

frequencies (

R

tot

negligible)

Note: powering scheme is nottaken into account (singlemagnet inductance is used

for simulations)

TItoB: assume B=const.*I => Inoise/Imax=Bnoise/BmaxTVacuum: additional attenuation for frequencies >50 Hz, nottaken into account

4

Expected spectrum of the magnetic field

Note:

50 Hz already attenuated by x8 in respect of 1HzSlide5

5

Effect of a tune modulationIn addition to the tune shift the tune modulation (ripple) introducesresonance side bands [5,6]:

[5]

O. S.

Brüning

, F.

Willeke

, Phys. Rev.

Lett

. 76,

No.

20 (1995), [6] O. S. Brüning, Part. Acc. 41, pp. 133-151 (1993)slow modulation (e.g. 50 Hz): distances between the sidebands are small but amplitudes decrease only slowly with increasing order

fast modulation (e.g. 600 Hz): distances

between the sideband are large and amplitudes decrease rapidly with increasing order

slow+fast modulation: the sidebands of the fast modulation form the seeds for the sidebands of the slow modulation (“seeding resonances”)

7

th

order resonancesSlide6

6

Dynamic aperture (1)The influence of non-linearities and the stability and diffusion of particles can be studied analytically or more pragmatic by tracking particles with certain amplitudes and phases in order to obtain:dynamic aperturesurvival plots

frequency map analysis …

[7] M.

Giovannozzi

, W.

Scandale

, E.

Todesco

, Phys. Rev. E 57, No. 3 (1998)

one of the most common approaches to determine the dynamic aperture is the

Lyapunov

exponent

, which distinguishes regular from chaotic motion:

I

n case of

tune modulation

the particle losses can be

extremely slow

and chaotic regions can be stable for a sufficiently long time resulting in an underestimate of the DA with the

Lyapunov

exponent (DA larger than the DA predicted by

Lyapunov

) [7].

slow losses can be detected with

survival plots

. As survival plots are in general very irregular, they are difficult to interpret and extrapolate

no modulation

threshold

with modulation

lost after 10

7

turns

stable after 10

7

turnsSlide7

7

Dynamic aperture (2)following the approach taken in [8] a more regular pattern can be obtained from the survival plots by averaging over the angles. The dynamic aperture is then defined as a function of the number of turns – “DA vs turns”:

the integral can be calculated in different ways and the error estimated.

The DA can then be interpolated by:

where “A” is the dynamic aperture for an infinite number of turns.

-> In general, obtaining a stable fit is not so trivial, therefore only visual comparison at the moment

[8] E.

Todesco

, M.

Giovannozzi

, Phys. Rev. E 53, No. 4067 (1996)Slide8

8

Dynamic aperture (3)Example of LHC lattice [8]:[8] E. Todesco, M. Giovannozzi, Phys. Rev. E 53, No. 4067 (1996)

no modulation

with modulation

extrapolation to infinity

prediction through

Lyapunov

exponentSlide9

9

DA studies: simulation setup (1)latticesLHCV3.1btracked beamBeam 1

beam parameters

E

beam

= 7

TeV

,

N

b=2.2e+11 (mask,

sixtrack

)εN,x/y=2.5 μm (mask) -> “bb kicks”εN,x/y=3.75 μm (sixtrack) -> normalisation DAbunch spacing: 25 nsσE=1.1e-4 (mask) , σt=7.5 cm (mask) -> head-on bb slicingΔp/p=2.7e-04 (sixtrack) -> initial momentum offset trackingopticsIR1/5

IR2/8

β*=15 cm

β*=10 m

x-schemeIR1/5IR2IR8

no separation

x-angle:

±295

μ

rad,

hor.

xing

in IR5, vert.

xing

in IR1

no

separation

, but halo

collission at 5 sigma -> ±144.72 μm separation (vert.)x-angle: ±240 μrad (hor.), ±0.2919 μrad (vert.)no separationx-angle: ±305 μrad (hor.), ±1.8 μrad (vert.)tune

Q

x/Qy

=62.31/60.32Slide10

10

DA studies: simulation setup (2)beam-beamIR1/5IR2/85 head-on slices, 18

+1

long-range interactions

crab

cavities at 0% or 100%

5 head-on slices, 15 +1 long-range interactions

(4D beam-beam + crab

cavities)

errors

no a

1/b1 from all magnets, no b2s from quadrupoles, errors up to a15/b15note: b2 errors of dipole -> approx. 3% beta-beatcorrectionsincluded:- no orbit correction (as no a1/b1

errors)- MB field errors

- IT/D1 field errors- rematch x-scheme using orbit

correctors at Q4/Q5/Q6

- rematch spurious dispersion with DS orbit correctors- coupling correction- rematch tune using trim quadrupoles- rematch linear chromaticity using first sextupoles

, then

sextupoles

and trim

sextupoles

not included:

correction

of

residual

Q’’

by

octupoles

simulation parameters60 seeds2-14σ with 30 particles for 2σ, 59 angles106 turnsSlide11

11

DA studies: simulation setup (3)Analysis methods:calculation of minimum, maximum and average DA over the seeds using the particles lost criterion = largest amplitude for which all particles with smaller amplitudes are not lost after the number of turns trackedcalculation of the DA as a function of the number of turns (“DA

vs

turns

”) (see backup slides) which is more suited for detecting slow long term effects [7]

->

criterion for effect of ripple:

DA changes in respect to reference cases without ripple

[7] M.

Giovannozzi

, W.

Scandale, E. Todesco, Phys. Rev. E 57, No. 3 (1998)Slide12

12

Dynamic aperture studiesDynamic aperture studies to asses the influence of the ripple on the long term stability:in this talk only beam-beam simulations:without crab cavities

with crab cavities at 100%

two different scenarios:

determination

of the dangerous frequencies:

50 Hz, 100 Hz (main grid)

300 Hz, 600 Hz (diode rectifier)

high frequency

9kHz,

20 kHz (ITPT converters

)simulation parameters:same amplitude (δkl) for all quadrupoles taking the polarity and baseline powering scheme into account (no trims - negligible)choose amplitude to obtain ΔQx/y= ±10-4 (±10-3, ±10-5, ±10

-6)

frequency spectrum provided by

EPC group (slide 6) (“real spec”)

taking the polarity and baseline powering scheme into account (no trims)+ 50 Hz harmonics until 1kHz (“real spec 1k”)Slide13

13

beam-beam, no crab cavitiesSlide14

14

Dangerous frequencies, bb (1) no crab cavities and ΔQ=10-4, particle lost criterion

decrease of DA for

ΔQ

=10

-

4

300 Hz and 600 HzSlide15

15

Dangerous frequencies, bb (2) no crab cavities and ΔQ=10-3, particle lost criterion

decrease of DA for

ΔQ=10

-3

and 50 Hz, 100 Hz and 9 kHzSlide16

16

Dangerous frequencies, bb (3) no crab cavities and ΔQ=10-5, particle lost criterion

decrease of DA for

ΔQ=10

-5

and 300 HzSlide17

17

Dangerous frequencies, bb (4) no crab cavities and ΔQ=10-6, particle lost criterion

no decrease of DA for

ΔQ=10

-6Slide18

18

Real frequency spectrum – bb (1)no crab cavities and real frequency spectrum, particle lost criterionSlide19

19

Real frequency spectrum – bb (2)no crab cavities and real frequency spectrum, particle lost criterion

effect on DA for an amplification larger than

x10

old: slightly wrong frequency for 300

Hz (37.43333333333334 -> 37.483333333333334) and the

amplitude smaller amplitude for

the 10 MHz (

2.5246x10

-16->5.0492x10-16)

-> no considerable effect on DA expectedSlide20

20

beam-beam, crab cavitiesSlide21

21

Dangerous frequencies, bb (1) with crab cavities (100%) and ΔQ=10-4, particle lost criterion

decrease of DA for

ΔQ

=10

-

4

300 Hz and 600 HzSlide22

22

Real frequency spectrum – bb (1)with crab cavities (100%) and real frequency spectrum, particle lost criterionSlide23

23

Real frequency spectrum – bb (2)with crab cavities (100%) and real frequency spectrum, particle lost criterion

visible effect on DA for a larger amplification than

x100Slide24

24

Summary: dangerous frequencieswith beam-beam - without crab cavities: simulation for ΔQ=10-6-10-2 to determine tolerance on modulation amplitude

frequency

maximum

tune shift

limit on

δkl

50 Hz

no effect for ΔQ=10

-4

,

visible effect for ΔQ=10-3 2.1x10

-8<

δkl < 2.1x10

-7100 Hz

no effect for ΔQ=10-4, visible effect for ΔQ=10-3

2.1x10

-8

<

δkl

< 2.1x10

-7

300 Hz

no effect for ΔQ=10

-6

,

small effect for ΔQ=10

-5

,

visible effect for ΔQ=10-42.1x10-10 <δkl < 2.1x10-9600 Hzno effect for ΔQ=10-6, very small effect for ΔQ=10

-5,

visible effect for ΔQ=10-4

2.1x10

-9 < δkl

< 2.1x10-89 kHz

no effect for ΔQ=10

-4,

visible effect for ΔQ=10

-3

2.1x10-8 <

δkl < 2.1x10

-720 kHz

no effect for ΔQ=10

-4

,

2.1x10

-8

<

δkl

with beam-beam – with crab cavities:

for

ΔQ=10

-4

decrease of DA for 300 Hz and 600 Hz Slide25

25

Summary: real frequency spectrumwith beam-beam: real frequency spectrum real frequency spectrum +1k (x10 and x100)with beam-

beam +cc:

real

frequency spectrum

real

frequency spectrum +1k (x10 and x100)

case

amplification

limit on largest

δklwith bb - no crab cavitiesvery small effect for spec 1k x10 (ΔQ≈10-5), visible effect for spec 1k x100 (ΔQ≈10-4)3.2x10-10 < δ

kl < 3.2x10

-8with bb +

crab cavitiesSlide26

26

ConclusionRipple tolerances obtained with dynamic aperture studies:no effect of the real frequency spectrum on the dynamic aperture for the cases with beam-beam w/o crab. A very small effect

is seen if the spectrum is amplified by

x10

and a

visible effect

if amplified by

x100

.

sensitivity to 300 Hz and 600 Hz in all cases.

Tolerances for individual frequencies in terms of tune shift

(with beam-beam, no crab-cavities):300 Hz: 10-6 < ΔQ < 10-5 (same order of magnitude as largest amplitude for real frequency spectrum)600 Hz: 10-6 < ΔQ < 10-450 Hz, 100 Hz and 9 kHz: 10-4 < ΔQ < 10-320 kHz: 10-4 < ΔQSlide27

27

Further studiesTolerances for different frequencies also for with beam-beam and crab cavitiesEffect of slow modulation and white noise (<1Hz)

Tune scans

to investigate the dependence of the simulation on the chosen WP

Similar analysis for

alternative powering

schemes

Similar

analysis also for the

matching section quadrupoles

strong-strong simulations to study the effect on the

emittance?Slide28

Questions?Slide29

29

Experiments in the pastExperiments were done at the SPS [1,2,3] and HERA [4]:in case of the SPS a tune ripple of 10

-4

is acceptable while experiences at

HERA

show that for

low frequencies

even a tune ripple of

10

-5 and for high frequencies 10-4 can lead to significant particle diffusion.

several

ripple frequencies are much more harmful than a single one [1,2][1] X. Altuna et al., CERN SL/91-43 (AP)[2] W. Fischer, M. Giovannozzi, F. Schmidt, Phys. Rev. E 55, Nr. 3 (1996)[3] P. Burla, D. Cornuet, K. Fischer, P. Leclere, F. Schmidt, CERN SL/94-11 (1996)[4] O. S. Brüning, F. Willeke, Phys. Rev. Lett. 76, Nr. 20 (1995)Slide30

30

Spectrum of the magnetic fieldParameters used for HL-LHC (TVtoI, load, TItoB):R

PC1

,PC2

= 1.144

m

Ω

(same as for PC1 of nominal LHC

)lengthQ1,Q3 = 8.0 m, length

Q2

= 6.8 mLQ1,Q2,Q3 = 10.8 mH/mLtot=LQ1/Q2/Q3= single magnet inductance Imax,PC1,PC2 = 17.5 kAkmax,Q1,Q2,Q3 = 0.5996 x 10-2 1/m2Slide31

31

SixTrack simulation parameterslattice: sLHCV3.1boptics: β*=15 cm in IR1/5, β*=10 m in IR2/8 (opt_0150_0150thin.madx)

x-

scheme

(

opticss

):

IR1/5

: ±0.75

mm separation, ±295 μrad x-angle, IR1: hor. sep., vert. x-angle, IR5: vert. sep., hor. x-

angle

IR2: ±2.0 mm separation (hor.), ±0.2919 μrad x-angle (hor.), ±239.9994 μrad x-angle (vert.)IR8: ±2.0 mm separation (vert.), ±304.9879 μrad x-angle (hor.), ±1.8097 μrad x-angle (vert.)x-scheme (simultions):IR1/5: on_x1/5=1, on_sep1/5=0: no separation, ±295 μrad x-angle, IR1: hor. sep., vert. x-angle, IR5: vert. sep., hor. x-angle

IR2: on_alice

=1, on_x2=1, on_sep2=0.072 (5 sigma halo collision):

: separation: ±144.72 μm separation

(hor.) , ±239.9994 μrad x-angle (vert.), ±0.2919 μrad x-angle (hor.)IR8: on_lhcb

=-1, on_x8=1, on_sep8=0:

no separation

,

x-

angle

:

±305

μ

rad

(hor.), ±1.8

μ

rad (vert.)tune: Qx/Qy=62.31/60.32tracked beam: Beam 1beam parameters: Ebeam = 7 TeV, bunch spacing: 25 ns, εN,x/y=2.5 μm (mask), εN,x/y=3.75 μm (sixtrack), σE=1.1e-4 (mask) , σt=7.5 cm (mask), Δp/p=2.7e-04 (

sixtrack), N

b=2.2e+11 (mask, sixtrack)

beam-beam:-

number of head-on collisions

in IR1/2/5/8: 5 (nho_IR*=5), 5 sigma halo collissions in IR2 (on_collission=1)

-

number of long-range interactions: IR1/5 - 18 + 1 (n_insideD1 =1), IR2/8 - 15 + 1 (n_insideD1 =1

)- crab

cavities: 0% or 100% (fraction_crab = 0 or fraction_crab = 1)Slide32

32

SixTrack simulation parameterssixtrack simulation parameters:60 seeds, 2-14σ with 30 particles for 2σ ≃ 0.07

σ

steps,

10

6

turns,

59 angels

error tables: - no a1/b1 from

all

magnets, no b2s from quadrupoles, errors up to a15/b15- LHC measured errors (collision_errors-emfqcs-*.tfs), target error tables for IT (IT_errortable_v66), D1 (D1_errortable_v1), D2 (D2_errortable_v4), and Q4 (Q4_errortable_v1) and Q5 (Q5_errortable_v0) in IR1/5corrections:included: - no orbit correction (as no a1/b1 errors)- MB field errors- IT/D1 field errors- rematch x-scheme using orbit corrector at Q4/Q5/Q6

- rematch spurious dispersion with DS orbit correctors

- coupling correction- rematch tune using trim quadrupoles

- rematch linear chromaticity using first sextupoles

, then sextupoles and trim sextupolesnot included: correction of residual Q’’ by

octupoles