M Fitterer R De Maria S Fartoukh M Giovannozzi Acknowledgments G Arduini A Ballarino R Bruce JP Burnet E McIntosh F Schmidt H Thiesen E Todesco ID: 499900
Download Presentation The PPT/PDF document "Beam-beam simulations for IT PC toleranc..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
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