The LHC dynamic aperture saga: overview, ideas and recent developments Massimo Giovannozzi CERN –...
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The LHC dynamic aperture saga: overview, ideas and recent developments Massimo Giovannozzi CERN – Beams Department Definition and physics/computational
The LHC dynamic aperture saga: overview, ideas and recent
developments Massimo Giovannozzi CERN Beams Department Definition
and physics/computational issues DA studies for LHC DA vs. time:
models Benchmarking with real data Extensions Luminosity evolution
model DA measurements Outlook Acknowledgements: A. Bazzani, S.
Fartoukh, E. Laface, F. Lang, E. MacLean, W. Scandale, F. Schmidt,
E. Todesco, R. Toms, G. Turchetti, C. Yu
Slide 2
Fermilab APT seminar 5/11/2013 Definition and issues - I
Massimo Giovannozzi - CERN2 The dynamic aperture is the region in
phase in which bounded motion occurs. So far only tracking allows
computing the DA of a given system. From a numerical point of view:
A volume should be evaluated. This entails a scan over the phase
space variables. An appropriate choice of the steps in the
variables is required. NB: I will deal with protons ->
symplectic dynamics! The tracking has to be long-term
Slide 3
Fermilab APT seminar 5/11/2013 Definition and issues - II
Massimo Giovannozzi - CERN3 DA computations are CPU intensive. Fast
tracking tools are required: Optimised codes (e.g., kick codes)
Parallel approach (this is only possible over the initial
conditions). As an alternative (maybe a dream): find a dynamical
quantity with a good correlation with DA, but less expensive in
terms of CPU. A trade-off between number of turns and number of
initial conditions might be possible (e.g., use a dense set of
initial conditions iterated a small number of turns). Do not forget
stable chaos and intermittency!
Slide 4
Fermilab APT seminar 5/11/2013 Definition and issues - III
Massimo Giovannozzi - CERN4 Here are some examples of indicators:
Lyapunov exponent Tune difference (this indicator triggered several
studies on accurate computation of tunes in numerical
simulations).
Slide 5
Fermilab APT seminar 5/11/2013 DA studies for LHC - I Massimo
Giovannozzi - CERN5 The dynamic aperture studies for the LHC
absorbed a lot of resources for about two decades in terms of:
Theoretical studies in non-linear beam dynamics Software and
analysis tools Specification magnetic field quality tables (with
iterations with the magnet builders) The large amount of
information gathered during the measurement stage of the magnets
(warm and cold conditions) Special tools developed (e.g., WISE)
This allows: Estimating the DA of the LHC as-built Estimating the
impact of sorting on DA of the LHC as-built Generate realistic
realisations of the magnetic field errors, based on Actual slot
allocationActual slot allocation Actual field qualityActual field
quality
Slide 6
Fermilab APT seminar 5/11/2013 DA studies for LHC - II
Possibility to evaluate the DA for the machine as-built Possibility
to evaluate impact of sorting on DA Massimo Giovannozzi - CERN6
Summary of DA at injection energy. The error bars represent the
effect of 60 seeds Summary of DA at injection energy. The error
bars represent the effect of 60 seeds
Slide 7
Fermilab APT seminar 5/11/2013 DA studies for LHC - III
Possibility to evaluate the DA for the machine as-built Possibility
to evaluate impact of sorting on DA Massimo Giovannozzi - CERN7
Summary of minimum DA for several running configurations.
Slide 8
Fermilab APT seminar 5/11/2013 DA studies for LHC - IV
Possibility to evaluate the DA for the machine as-built Possibility
to evaluate impact of sorting on DA Massimo Giovannozzi - CERN8
Impact of sorting. Selected generic seedsSelected generic seeds
Each sequence of errors is re-ordered.Each sequence of errors is
re-ordered. The various dynamical quantities are computed.The
various dynamical quantities are computed. Yellow: all seeds
(initial and re-ordered) Blue: selected seeds. Impact of sorting.
Selected generic seedsSelected generic seeds Each sequence of
errors is re-ordered.Each sequence of errors is re-ordered. The
various dynamical quantities are computed.The various dynamical
quantities are computed. Yellow: all seeds (initial and re-ordered)
Blue: selected seeds.
Slide 9
Fermilab APT seminar 5/11/2013 DA studies for LHC - V
Possibility to evaluate the DA for the machine as-built Possibility
to evaluate impact of sorting on DA Massimo Giovannozzi - CERN9
Impact of sorting. Selected generic seedsSelected generic seeds
Each sequence of errors is re-ordered.Each sequence of errors is
re-ordered. The various dynamical quantities are computed.The
various dynamical quantities are computed. Yellow: all seeds
(initial and re-ordered) Blue: selected seeds. Red: average DA for
as- built machine. Impact of sorting. Selected generic
seedsSelected generic seeds Each sequence of errors is
re-ordered.Each sequence of errors is re-ordered. The various
dynamical quantities are computed.The various dynamical quantities
are computed. Yellow: all seeds (initial and re-ordered) Blue:
selected seeds. Red: average DA for as- built machine.
Slide 10
Fermilab APT seminar 5/11/2013 DA vs. time: models - I Massimo
Giovannozzi - CERN10 Another strategy could be: is there a model to
describe DA vs. time? In mathematical sense DA does not depend on
time. Numerical simulations are performed with a specific maximum
number of turns (N max ): the computed DA does depend on N max How
does DA depend on N max in numerical simulations? ). Studies have
been performed recently to review the functional dependence on of
fit model
Slide 11
Fermilab APT seminar 5/11/2013 Definition and issues - VII
Massimo Giovannozzi - CERN11 Dynamic aperture of a model of the LHC
ring (left) in physical space: The red points represent the initial
conditions stable up to 10 5 turns The blue points represent
unstable conditions and their size is proportional to the number of
turns by which their motion is still bounded. The time-evolution of
the DA is shown on the right. The markers represent the numerical
results The continuous line shows the fitted inverse logarithmic
law. The dotted line represents D
Slide 12
Fermilab APT seminar 5/11/2013 DA vs. time: models - III
Massimo Giovannozzi - CERN12 Is this a purely phenomenological fit?
In fact not quite. The physical picture is: For r < D The motion
is governed by KAM theorem. Fully stable region (only Arnold
diffusion for a set of initial conditions of small measure ->
irrelevant from the physical point of view). For r > D The
motion follows Nekhoroshev theorem, i.e., the stability time N(r)
of a particle at radius r is given by This provides a
pseudo-diffusion.
Slide 13
Fermilab APT seminar 5/11/2013 DA vs. time: models - IV Massimo
Giovannozzi - CERN13 Two regimes found in 4D simulations: D , b,
are always positive. This implies a stable region for arbitrary
times. In 4D simulations with tune ripple or 6D simulations: There
could be situations in which no stable region for arbitrary times
exists. This corresponds to
Slide 14
Fermilab APT seminar 5/11/2013 DA vs. time: models - V Massimo
Giovannozzi - CERN14 Fit of DA vs. time can lead to a number of
extensions: Losses in hadron machines due to non-linear effects
(single particle).
Slide 15
Fermilab APT seminar 5/11/2013 Benchmarking with real data I
Tevatron data: proton bunch at injection Estimates from purely
diffusive model included. Estimates from purely diffusive model
included. Massimo Giovannozzi - CERN 15 Nice agreement for all
models! Experimental data from: T. Sen et al. Beam Losses at
Injection Energy and During Acceleration in the Tevatron, IPAC03,
p. 1754.
Slide 16
Fermilab APT seminar 5/11/2013 Benchmarking with real data II
SPS data: proton bunch at 55 GeV in coast Estimates from purely
diffusive model included. Estimates from purely diffusive model
included. Massimo Giovannozzi - CERN 16 Negative second order
derivative cannot be reproduced by diffusive models!
Slide 17
Fermilab APT seminar 5/11/2013 Extensions - I Massimo
Giovannozzi - CERN17 Evolution of DA in presence of beam-beam
effects. N b =0.1010 11 N b =1.1510 11 N b =1.7010 11 The proposed
model holds for: -Non-linear single particle dynamics -Weak-strong
beam-beam It is then tested on luminosity data from LHC.
Slide 18
Fermilab APT seminar 5/11/2013 Extensions II Intensity and
luminosity evolution during physics fills Massimo Giovannozzi -
CERN18 LHC Tevatron
Slide 19
Fermilab APT seminar 5/11/2013 Luminosity evolution models - I
The inverse logarithm model seems to fit well al data considered so
far (LHC and other circular accelerators/colliders). For luminosity
evolution: No consideration of, e.g., burn off effect: an effective
fit has been considered and proved to work well, but the fit
parameters might have little physical content. A correct approach
would require disentangling pseudo- diffusive effects (inverse
logarithm) from the rest. The boundary conditions: try to find a
relatively simple model to allow analytical considerations. LHC Run
I provided lots of data to probe new models Massimo Giovannozzi -
CERN19
Slide 20
Fermilab APT seminar 5/11/2013 Luminosity evolution models - II
What do we know from the LHC Run I Massimo Giovannozzi - CERN20
2011 LHC data. The two curves refer to the change of * occurred
during the year.
Slide 21
Fermilab APT seminar 5/11/2013 Luminosity evolution models -
III Is it possible to factor out the contribution of the
pseudo-diffusive effects? Is it possible to normalise the data to
find a sort of universal (at least for LHC) curve? The answer is
positive: For the time being only the plain proton burn off has
been included. Emittance evolution (e.g., radiation or rest gas
interaction) can be included. Massimo Giovannozzi - CERN21
Slide 22
Fermilab APT seminar 5/11/2013 Luminosity evolution models - IV
Massimo Giovannozzi - CERN22 2011 and 2012 LHC data. Dashed line:
burn off only Blue squares: proposed model.
Slide 23
Fermilab APT seminar 5/11/2013 DA measurements - I What is the
DA of the real machine? No lifetime problems or slow losses at
injection. During aperture measurements (with beams probing high
amplitudes) no sign of slow losses was found. This observation
indicates that DA should be of the same order of mechanical
aperture, i.e., about 10 . Measurement campaign launched: Two MD
sessions organised (2011, 2012). Objective: benchmark numerical
simulations against measurements (e.g., for HERA a factor of two
was found). Massimo Giovannozzi - CERN23
Slide 24
Fermilab APT seminar 5/11/2013 DA measurements - II Two
strategies applied: Beam 1: Blow up the beam until slow losses are
observed. Record evolution of beam intensity. Fit beam intensity
with proposed models. Compare with fit parameters from numerical
simulations of DA. Beam 2: Kick the beam in order to push it
towards high amplitudes until large losses are obtained (standard
method). Requires rather strong kick (aperture kicker). Compare
amplitude of beam losses with numerical simulations of DA. Massimo
Giovannozzi - CERN
Slide 25
Fermilab APT seminar 5/11/2013 DA measurements: Beam 1 - III
Two MD sessions: 2011 Almost half of the time lost Q-kicker used to
blow up the beam emittance: not easy to induce a symmetric blow up.
Performed scans over the strength of MCOs using the same polarity
in all sectors. 2012 Much more efficient MD Transverse damper used
to blow up the beam emittance: easy and reproducible blow-up.
Performed scans over MCOs and MCDs. Used different alternating
signs schemes (suggested by Stephane). Massimo Giovannozzi - CERN
Strong chromatic effects Almost cancelled chromatic effects (but
symmetry broken
Slide 26
Fermilab APT seminar 5/11/2013 DA measurements: Beam 1 IV 2011
MD Massimo Giovannozzi - CERN 26
Slide 27
Fermilab APT seminar 5/11/2013 DA measurements: Beam 1 V MD
2011 Massimo Giovannozzi - CERN 27 Effect of Q- kicker: large tails
instead of a Gaussian beam Beam size evolution during the MD
Slide 28
Fermilab APT seminar 5/11/2013 DA measurements: Beam 1 - VI MD
2011 Massimo Giovannozzi - CERN I MCO =-40 A Another confirmation
of the scaling law of intensity vs. time
Slide 29
Fermilab APT seminar 5/11/2013 Digression: simulations for Beam
1 DA measurements in 2011 Massimo Giovannozzi - CERN 29
Slide 30
Fermilab APT seminar 5/11/2013 DA measurement: Beam 1 VII MD
2012 Massimo Giovannozzi - CERN 30 Same configuration as 2011 Scan
MCDs Scan MCOs (alternating signs)
Slide 31
Fermilab APT seminar 5/11/2013 Digression: simulations for Beam
1 DA measurements in 2012 Massimo Giovannozzi - CERN 31 Negative
Dinf found: all phase space unstable! MCO circuit in sector 1-2 was
not available: simulations to be repeated and broken symmetry.
Slide 32
Fermilab APT seminar 5/11/2013 DA measurements: Beam 2 - VIII
MD 2011-12 Massimo Giovannozzi - CERN Courtesy R. Toms et al.
Slide 33
Fermilab APT seminar 5/11/2013 Conclusions - I Massimo
Giovannozzi - CERN33 The LHC project has triggered several studies
in non- linear beam dynamics. Several tools and techniques have
been devised to achieve the goal of estimating the dynamic
aperture. Latest proposals based on DA vs. time models Intensity
vs. time Luminosity vs. time Luminosity models Next step: try to
find a diffusive model providing an equivalent behaviour of the DA
vs. time All confirmed by the analysis of available measured
data.
Slide 34
Fermilab APT seminar 5/11/2013 Conclusions - II Massimo
Giovannozzi - CERN34 The work done seems to have been fruitful: the
LHC does not suffer from any single-particle non-linear effects. DA
measurements have been performed and data analysis is in progress.
HL-LHC will require even more sophisticated tools in view of new
physics challenges!
Slide 35
Fermilab APT seminar 5/11/2013 Thank you for your attention
Massimo Giovannozzi - CERN35