Introduction to Beam-Beam Effects at
the LHC
Tatiana Pieloni
…with a lot of contributions/help from W. Herr
What are beam-beam effects?
They occur when two beams collide
Two types
High energy collisions between two
particles (wanted)
Distortions of beam by
electromagnetic forces (unwanted)
Unfortunately: usually both go
together…
What are beam-beam effects?
Beams are made of relativistic charged particles represent an
electromagnetic potential for other charges
Typically:
 0.001% (or less) of particles collide
 99.999% (or more) of particles are distorted
Beam-beam effects
At LHC interactions happen at the IP1
IP2, IP5 and IP8
Many different effects and problems
Try to understand some of them
Two main questions:
1. What happens to a single particle?
2. What happens to the whole beam?
Beam-beam effects
Beam is a collection of charges
Represent electromagnetic potential for other charges
Force on itself (space charge) and opposing beam (beam-beam
effects)
Main limit in past, present and future colliders
Important for high density beams i.e. high intensity and/or
small beams: high luminosity
Luminosity
Beam-beam Force
Particle&beam motion distorted
Focusing quadrupole
Opposite Beam
Single particle motion and whole bunch motion
• Strongest non linearity when beams collide
• Complex time dependent force
• LHC number of bunches/crossing angles create new situation
Beam-Beam Force
Lattice defocusing quadrupole
Beam-beam force
STRONG AND COMPLEX NON LINEAR FORCE NOT AVOIDABLE
Particle distributions
Static BB force
Self-consistent
Beam-beam force time dependent force
Perturbative approach is not possible for the LHC,
LHC Complications
MANY INTERACTIONS
Num. of bunches
:
3.7 m
Long range
Head-On
For 25ns case 124 BBIs per turn: 4 HO and 120 LR
LHC Complications
PACMAN and SUPER PACMAN bunches
72 bunches
….
Pacman:
miss long range BBI
(120-40 LR interactions)
Super Pacman:
miss head-on BBI
IP2 and IP8 depending on filling scheme
Different bunch families: Pacman and Super Pacman
PACMAN and SUPER PACMAN bunches
SppS
Tevatron
RHIC
LHC
Number Bunches
6
36
109
2808
LR interactions
9
70
0
120/40
Head-on interactions
3
2
2
4
Pacman bunches complexity
*
**
*
***
These effects are
already visible in the
LHC and single bunch
diagnostic is essential
to understand the full
picture!
Beam-beam effects
Mathematical derivations
Single Particle effects:
Detuning with amplitude
Dynamic Aperture reduction
Multiparticle effects:
Orbit Effects
Emittance effects
Coherent oscillations
1) Intuitive Explanation
2) Observations
3) Cures (…where possible)
N.B. All effects occur together with Pacman effects
…and with any other noise effect in the collider…
Short Beam-beam Mathematics
General approach in electromagnetic problems Reference[5] already applied to beam-beam
interactions in Reference[3, 4, 1]
Derive potential from Poisson equation for beam
with distribution r
Solution of Poisson equation
Then compute the fields
From Lorentz force one calculates the force acting on
test particle with charge q
Assuming round Gaussian distribution
and integrating we have radial force
Beam-beam Force
Linear beam-beam parameter x
A test particle will receive a radial kick:
Linear beam-beam parameter
Quantifies the strength of the force
but does NOT reflect the nonlinear
nature of the force
Beam-beam effects
Single Particle effects:
Detuning with amplitude
Dynamic Aperture reduction
Multiparticle effects:
Orbit Effects
Emittance effects
Coherent oscillations
Detuning with Amplitude for head-on
Instantaneous tune shift of test particle when it crosses the other beam
is related to the derivative of the force with respect to the amplitude
For small amplitude test particle
linear tune shift
Detuning with Amplitude for head-on
Beam with many particles this results in a tune spread
Mathematical derivation in Reference [3] using Hamiltonian formalism and in
Reference [4] using Lie Algebra
Head-on detuning with amplitude and footprints
1-D plot of detuning with amplitude
And in the other plane?
THE SAME DERIVATION
same tune spread
FOOTPRINT
2-D mapping of the detuning with
amplitude of particles
And for long-range interactions?
Second beam centered at d (i.e. 6s)
•Small amplitude particles positive tune shifts
•Large amplitude can go to negative tune shifts
Long range tune shift scaling for
distances
Long-range footprints
DQy
The picture is more complicated
now the LARGE amplitude
particles see the second beam and
have larger tune shift
Separation in vertical plane!
And in horizontal plane?
The test particle is centered with
the opposite beam
tune spread more like for head-on
at large amplitudes
Beam-beam tune shift HO + LR
IP5 Head-on + LR with HORIZONTAL separation
HO tune footprint +
In the horizontal plane long range tune shift
In the vertical plane head-on tune shift
IP1 Head-on + VERTICAL separation
The opposite of IP5
PASSIVE COMPENSATION
Qy
Qx
Footprints Pacman bunches and passive compensation with HV
crossing
75 ns spacing
25 ns spacing
Reference [7]
PASSIVE COMPENSATION to reduce space on tune diagram and avoid
resonances
When long-range effects become important footprint wings appear and
alternating crossing important
Tune shift passive compensation HV crossing IP1 and IP5
Reference [7]
PASSIVE COMPENSATION reduces Pacman effect
Alternating crossing of IP1 and IP5 is a trick to compensate beam-beam
long range tune shifts
Tevatron Footprints
Antiproton bunches footprint (blue)
Proton bunches footprint (orange)
Working point optimization 15-20% reduced emittance growth over first
15min HEP stores in Tevatron RUN II away from 5th and 12th order resonance
Beam-beam effects
Single Particle effects:
Detuning with amplitude
Dynamic Aperture reduction
Multiparticle effects:
Orbit Effects
Emittance effects
Coherent oscillations
Dynamic Aperture
Dynamic Aperture: area in amplitude space with stable motion
Reference [6]
Stable area reduced by beam-beam resulting in losses and bad
lifetime
Dynamic Aperture
Dynamic Aperture depends on beam intensity and crossing angle
Reference [6]
Stable area depends on beam-beam parameters choice of parameters
is the result of careful study of different effects
Dynamic Aperture
Dynamic Aperture depends on beta at the IP
Reference [6]
Interplay of different parameters to reduce losses as for not reducing DA
e
b
a
Np
As small as possible
Not too small
As large as possible
Defined
Dynamic aperture reduction vs tune
Dynamic Aperture depends on the working point
Reference [8]
Working point optimization can help reducing effects
Beam-beam effects
Single Particle effects:
Detuning with amplitude
Dynamic Aperture reduction
Multiparticle effects:
Orbit Effects
Emittance effects
Coherent oscillations
Orbit Effects
Long Range Beam-beam interactions lead to orbit effects
Long range kick
For well separated beams
The force has an amplitude independent contribution: ORBIT KICK
Orbit can be corrected but we should remember PACMAN effects
LHC orbit effects
d = 0 - 0.4 units of beam size
Orbit effects different due to pacman effects and the many long-range
add up giving a non negligible effect
Can be measured and calculated very well
Reference [7]
Moreover can lead to emittance growths
HV crossing as passive compensation
IP1 and IP5 alternating crossing is a passive compensation for pacman effects
VER offset IP5
Reference [7]
HV crossing
passive
compensation
•Two low beta experiments (LR effects stronger)
•Opposite Azimuth (same pairs colliding)
•Bunch to bunch fluctuations small
•Similar Optics (strength depends on sep)
Tevatron orbit effects
Beam-beam single bunch orbit
can be well reproduced and
measured also in LEP
Effects can become important
(1 s offset not impossible)
LUMINOSITY Deterioration
Reference [2]
Passive compensations reduces effects and equal beam
parameters helps keeping compensation effective
Beam-beam effects
Single Particle effects:
Detuning with amplitude
Dynamic Aperture reduction
Multiparticle effects:
Orbit Effects
Emittance effects
Coherent oscillations
Emittance effects/growth?
Emittance growth occurs when small amplitude particles move to
larger values (the core of a bunch) and one observes bad lifetimes
and bad luminosity lifetime
Driving mechanisms
BAD Working Point
Offset in collision
Bad Working point
Emittance growth due to small amplitude particles crossing resonances
Tevatron experienced some bunches with 15-20% emittance increase over first 15
minutes of HEP stores during RUN II due to some bunches crossing 5th and 12th order
Emittance growth due to offsets in collision
Offsets at collision
Maximum
LHC expects 0.4 s
offsets at IPs due to
long-rang
A clear dependency on the offset amplitude has been
demonstrated
Emittance growth due to offset
LHC nominal
Intense beams have stronger effect
(a.u.)
LHC nominal
(a.u.)
Smaller beams have stronger effect
And strong tune dependency stay away from 3rd order resonance
Emittance growth vs cures
Emittance growth occurs when small amplitude particles move to
larger values (the core of a bunch) and one observes reduction of
luminosity and bad lifetimes
Driving mechanisms
Cures:
BAD Working Point
WP optimization stay away from
13th and 16th order resonance in
LHC
Reduce LR orbit effects (large d
and HV crossing) and WP
optimization (away from 3rd order)
Try to reduce at minimum any
transverse excitation when beams
in collision (reduced damper gains)
Offset in collision
Transverse Noise
Beam-beam effects
Single Particle effects:
Detuning with amplitude
Dynamic Aperture reduction
Multiparticle effects:
Orbit Effects
Emittance effects
Coherent modes
Coherent dipolar beam-beam modes
Coherent beam-beam effects arise from the forces which an exciting bunch
exerts on a whole test bunch during collision
We study the collective behaviour of all particles of a bunch
Coherent motion requires an organized behaviour of all particles of the bunch
Coherent beam-beam force
•Beam distributions Y1 and Y2 mutually changed by interaction
•Interaction depends on distributions
•Beam 1 Y1 solution depends on beam 2 Y2
•Beam 2 Y2 solution depends on beam 1 Y1
•Need a self-consistent solution
Coherent beam-beam effects
•Whole bunch sees a kick as an entity (coherent kick)
• Coherent kick seen by full bunch different from single particle kick
•Requires integration of individual kick over particle distribution
•Coherent kick of separated beams can excite coherent dipolar
oscillations
•All bunches couple because each bunch “sees” many opposing
bunches(LR): many coherent modes possible!
Simple case:
one bunch per beam
0-mode
p-mode
0-mode
p-mode
Turn n
Turn n+1
0-mode at unperturbed tune Q0
Tune spread
p-mode is shifted at Qp =1.1-1.3 xbb
Incoherent tune spread range [0,-x]
Qp
xbb
Q0
Tune
• Coherent mode: two bunches are “locked” in a coherent oscillation
• 0-mode is stable (mode with NO tune shift)
• p-mode can become unstable (mode with largest tune shift)
Simple case: one bunch per beam and
Landau damping
0-mode
p-mode
Tune spread
Qp
xbb
Q0
Tune
Incoherent tune spread is the Landau damping region any mode
with frequency laying in this range should not develop
• p-mode has frequency out of tune spread
• No Landau damping possible
Coherent modes at RHIC
Tune spectra before collision and in collision two modes visible
If we have 2 Head-on collisions?
4bch vs 4 bch, 2 Head-on collisions IP1 and IP2
Rigid Bunch Simulation
Q
Multi Particle Simulation
Q
Q
Q
Q
Q
Q
Q
Many modes appear not all
are Landau damped!
Modes out of Landau damping range can become unstable
And if we add long-range interactions?
5bch train 1Head-on and 1 long-range
All possible modes
Qp
Qs
Bunch 1
• Long-range introduce sidebands to main head-on modes
• NO Landau damping of LR modes
And Pacman effects?
Bunch 1
Bunch 3
•Each bunch will have different
number of modes and tune
spectra
Single bunch diagnostic so important
What can we done to avoid problems?
• Coherent motion requires organized motion of many particles
• This possible with high degree of symmetry (avoid equal parameters
for two beams)
• Possible countermeasures: symmetry breaking
Different tunes for two beams
Different bunch Intensities
 Many collisions and coupling with different bunches
 Different emittances, longitudinal motion…
Different Tunes
p-mode
0-mode
Q-Q0/x
Tune split breaks symmetry and coherent modes disappear
Analytical calculations in Reference [8]
Different bunch intensities
For two bunches colliding
head-on in one IP the
coherent mode disappears
if intensity ratio between
bunches is 55%
Reference[8]
We assumed:
• equal emittances
• equal tunes
• NO PACMAN effects
(bunches will have different tunes)
The LHC will be a very “dirty” collider at nominal configuration!
Coherent modes can be visible for few bunches in symmetric
configurations!!
LHC example
8 fold symmetry
Nominal bunch
8 fold symmetry
Superpacman bunch
For a simplified LHC case:
•4 head-on collisions at IP1, IP2, IP5 and IP8
• 4 long-range interactions per IP
• Full 8-fold symmetry to enhance coherent modes
We should not expect coherent modes for the LHC full configuration!
An example: RHIC running with mirrored tunes
Proton-Proton Configuration
 2 Experiments (IPs 6 and 8)
 111 bch/beam with abort gap 9 empty slots (2 different bunch families)
 9 SuperPacman bunches (1HO collision)
 102 Nominal bunches (2 HO collisions)
2 Bunch Families
2 Frequency spectra
What should we expect ?
RHIC working points are mirrored respect to diagonal:
Beam 1 (Q1,Q2)
Beam 2 (Q2,Q1)
Same effect than a tune split but both beams have same space on tune diagram
Beam Loss and Bad Lifetime:
Beam Losses and background:
Why?
•DA reduction due to beam-beam
•Long-range effects
•Noise to the beam
•Unmatched beams Reference[10]
Bad lifetime and Lumi reduction:
•Bad working point
•Offsets in collision
•Transverse noise
Beam-beam Limits
Beam-beam effects come from two different type of interactions!
Pushing the collider performances means reaching beam-beam limits.
Limits can come from Head-on interaction or from Long-range and the
cures to apply are different and could make worse one or the other!
Parameter
Head-on
Long-range
Emittances
Larger
Smaller
Intensity
Smaller
Smaller
b*
-
Larger
WP optimization
Find the best
Find the best
Summary I
Single Particle effects:
Cures?!
Detuning with amplitude
WP optimization and HV crossing,
beam parameters as equal as
possible and filling schemes to
equalize collisions
Dynamic Aperture reduction
Increase LR d, bigger crossing angle,
Intensity moderation and careful
choice of WP
Multiparticle effects:
Orbit Effects
HV crossing, parameters equal, filling
schemes, increase LR separations
Emittance effects
Avoid bad tunes, increase LR
separations, reduce transverse noise
Coherent modes
Many tricks, but filling schemes
many collisions, parameter
fluctuations
…some comments
 Beam-beam effects are very important for a collider
 Past experience and studies explain many features and
observations but the LHC will still reserve some surprises
(PACMAN effects)
 Single bunch diagnostic is at the basis of a correct
interpretation of the collider performances
 Beam-beam has many effects and they depend on different
parameters. Improving one can make others worse. That’s
way a one solution to the problem does NOT always exist!
 Careful choice of beam parameters if we know the limits will
define the best operating scenario
 Optimization of the machine working point is a first step to
control many beam-beam effects
Some references:
[1] http://cern.ch/Werner.Herr/CAS2009/proceedings/bb_proc.pdf
[2]V. Shiltsev et al, “Beam beam effects in the Tevatron”, Phys. Rev. ST Accel. Beams 8,
101001 (2005)
[3] Lyn Evans “The beam-beam interaction”, CERN 84-15 (1984)
[4] Alex Chao “Lie Algebra Techniques for Nonlinear Dynamics” SLAC-PUB-9574 (2002)
[5] J. D. Jackson, “Classical Electrodynamics”, John Wiley & Sons, NY, 1962.
[6] H. Grote, F. Schmidt, L. H. A. Leunissen,”LHC Dynamic Aperture at Collision”, LHCProject-Note 197, (1999).
[7] W. Herr,”Features and implications of different LHC crossing schemes”, LHC-Project-Note
628, (2003).
[8] A. Hofmann,”Beam-beam modes for two beams with unequal tunes”, CERN-SL-99-039
(AP) (1999) p. 56.
[9]Y. Alexahin,”On the Landau damping and decoherence of transverse dipole oscillations in
colliding beams ”, Part. Acc. 59, 43 (1996).
[10] K. Cornelis BB workshop 1999
[11] D. Kaltchev and W. Herr, Dynamic Aperture studies
[12] Beam-beam webpage http://lhc-beam-beam.web.cern.ch/lhc-beam-beam/