Electron beam for LHC

1
Electron beam for LHC

• M.W. Krasny
• LPNHE, University Pierre et Marie Curie, Paris
• krasny_at_lpnhep.in2p3.fr

• This talk
• why electrons and at what energy?
• acceleration, storage and collisions
• of partially stripped ion beams
• PIE (Parasitic Ion-Electron collider)
• PIE versus HERA and eRHIC
• an example of physics highlights
• outlook and conclusions

e
CERN HI-forum 11.05.2004
2
High energy electron beam

• LHC-LEP scenario (1995)
• Electron beam parameters
• Energy 60 GeV
• Npart/bunch 6.4 1010
• N bunches 1016
• Emittances x,y 9.5/2.9 nm
• Collisions with standard LHC proton bunches
• b-functions x,y 0.85/0.26 m
• tune shift 0.03

not discussed in this talk
Luminosity 2.4 1032 s-1 cm-2
3
eP colliders versus ee and pp colliders high
energy frontier
4
eP(A) colliders as diagnostic tools of high
energy wide-band partonic beams

• Inclusive partonic momentum structure of nucleons
  and nuclei (x,Q2,s,A,b - maps)
• Partonic emittances and their energy dependence
• Precisely-normalized luminosities of partonic
  WBBs
• Unfolding medium effects from hard interaction
  effects
• Unfolding higher-twists
• Space structure of nucleons
• Unfolding relation between jets and coloured
  partons
• Precise detector calibration down to low energies

How Luminous the electron beam should be? What
should be the energy of the electron beam to
achieve most precise measurements using the LHC
beams and the present LHC detectors?
5
Wide-Band Partonic Beams space-time picture
q
6
Wide-Band Partonic Beams space-time picture
Nuclear WBB
7
examples of missing WBB diagnostics gluons
Need to measure variable partonic density WBBs
(e.g A 1/3 modulated) to check validity of
interpreting logQ2 slopes of the structure
function F2 at low x in terms of Gluon
distribution
?
8
examples of missing WBB diagnosticsb-dependent
partonic distribution in nuclei
but only q(x,A) measured over small range of
Q2 and for couple of A
NA-50
for full control of theoretical
prediction measurement of G(x,Q2,A,b)/q(x,Q2,A,b)
indispensable
9
examples of missing WBB diagnosticsenergy
dependence of jet quenching
10
What is the critical region where electron-beam
diagnostic of the LHC WBBs is indispensable ?

• High x region
• Precise Data exists for protons and nuclei
• DGLAP-evolution of partonic densities tested
• to high precision
• Effects due to partonic emittance are small
• Resolution of measuring partonic distributions
• using QCD hard-processes approaches
• the resolution of the electromagnetic probes

• Small x region
• Data exists for protons only at fixed energy
• Applicability of DGLAP-evolution of partonic
• densities cannot be taken for granted (low x
• resumations, higher twists, saturation, etc)
• A-dependent extrapolation highly uncertain
• Effects due to partonic emittance are large
• Resolution of measuring partonic distributions
• using QCD hard-processes inferior to
• that using the electromagnetic probes

11
What is the optimal energy of the electron beam
to cover low x region (for LHC hadronic beams and
LHC detectors)?
Collisions of low-x partons
with high energy electron beam
with low-energy electron beam
electron
electron
electron
electron
parton
parton
quark-jet
quark-jet
In z-symmetric detectors, optimized in barrel
region, the optimal energy is defined by the
condition e-parton Centre-Of-Mass System
Detector Rest System
for 10 3 gt x gt 10 4 optimal electron
energy range Ee 0.88 GeV
12
Cheap low-energy electrons

• Partially stripped ions
• Coulomb electrons
• External electron beam

EemeEA/mA
e
Z
E eGeV
1.5
Z
e
Target rest frame
Z
e
K.Hencken, in preparation not discussed in this
talk
E MeV
e
bebp
LHC bunch
E eGeV
3.5
Link to CLICK RD not discussed in this talk
13
Ion striping sequence at BNL
CERN
Lead acceleration at CERN
208Pb82
208Pb54
208Pb28 From ECR
14
Survival of partially stripped ions
the LHC lattice
LHC-Frame
Ion rest-frame
E 1011 V/cm
LHC-Dipole
e-
?
Or
B8.4 Tesla
Z
Lorenz Transformation
Binding energy of Rydberg-like atoms
Ionization of Rydberg-like atoms
Bethe-Salpeter,Quantum mechanics Of One- and
Two- Electron Atoms
B7.3 T,g2964,b1
nmax
E0
k10
nmax
nk
LOW-Z ions cannot survive!
n2
Pb80
preliminary
n1
tunneling effects
Z
E1Ry Z2/n2
15
Survival of bunches of partially stripped ions
Not in scale
Direction of motion
LAB frame
Bunch co-moving frame
Thermal motion of the ions ( governed by to beam
acceleration and focusing lattice and by the
bunch space charge). Note an analogy to the
Feynman partonic-gas-model Lorenz freeze-out
Stretched-Pancake bunch-shape dynamic
confinement within a bunch, etc
16
Survival of bunches of partially stripped ions
temperatures

• Longitudinal temperature kT mionc2b2(
  s(p)/p) 2
• Transverse temperature kTh,v
  mionc2b2(eN/ltsh,vgt)2
• Where eN is the normalized emittance and ltsh,vgt
  is the average horizontal (vertical) beam size
  ltsh,v2gt e h,v R/Q, Q horizontal and vertical
  tune and R radius of the machine
• Temperatures of the LHC bunches
• k T 2 keV, kTh,v 1 MeV (at the LHC
  injection energy and growing with g)

Kinetic energy of the transverse thermic motion
larger than binding energy of the electron on
the K-shell !!!
Can ions survive
intra-beam scattering???
17
Stabilizing bunch temperatures physics picture
Intra-beam scattering at temperatures
kT lt E1 - E2
Elastic scattering
Intra-beam scattering at temperatures
E1 E n max lt kT lt E1 - E2
Atomic excitation
photon
Followed by heat evacuation
hnk E1 - Ek
Intra-beam scattering at temperatures
kT gt E1
Atomic ionization
Stripped ion
Followed by a beam particle loss!
electron
18
Proposed recipe for accelerating partially
stripped ions in high density bunches

• (in analogy to successful
  transporting loosely -packed, fresh! eggs in
  Paris-Dakar race)

Fully stripped ions
kT
E 0
Ionization temperatures
E1
adiabatic boiling of the bunches
E1 - Enmax
Excitation temperatures
E1 - E3
iso-thermal heat evaporation by atomic
de-excitation photons
E1 - E2
g2
g1
g
Iso-thermal heat evaporation tlab ltlt t(g2)
t(g1)
Adiabatic boiling of the bunches tlab gtgt t(g2)
t(g1)
19
Numerical exercise

• An example
• accelerating of bunches of partially
  stripped ions in an accelerator specified in
  terms of the following parameters Nions/bunch
  107 eN 1.5 x 10-6 m,s(p)/p 10-4
  ltbgtcircumference 67 m sexcit 10-18 cm2 at
• T 1 MeV bunch-length 7.5 cm (the
  standard parameters for fully stripped lead ions
  at the LHC note a simplification of the full
  acceleration chain)
• Preliminary results for fully stripped ions
• Th,v(g gPS) 36 KeV , Th,v(g g SPS)
  1000 KeV
• Preliminary results for partially stripped ions
• g1(E1 - E2 ) 10 - the acceleration phase in
  which the bunch temperature should stabilizes at
  68 keV , provided that d g/dt (ggtg1) gt 0.8
  1/min

The onset of this effect may be seen in AGS at
BNL ...
20
Survival of partially stripped ions
Ionization losses

• A dominant process leading to losses of partially
  stripped ions is the ionization process in
  beam-beam and beam-gas collisions (note a quantum
  jump in magnetic rigidity of the beam particles)

K.Hencken directed my attention to these
processes
Ionization cross-sections
Experimental cross-check
Anholt and Becker, Phys.Rev.A36(1987)
Krause et al., Phys.Rev.A63(2001)
Coulomb contribution sCoul s(Zt,Zp) (Zt/Zc)2
104 barn/electron Transverse
contribution sTran t(Zt,Zp) (Zt/Zc)2 104 ln(g2)
barn/electron Where s(Zt,Zp), t(Zt,Zp) are
slowly (logarithmically) varying functions
of the electron carrier Z c and target Z t, and
g is the Lorenz factor Note - spin-flip
contribution is neglected - coherent bunch
contribution is neglected
Krause Fig 3.
Pb81(1s) ions at 158GeV/A
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Survival of partially stripped ions
beam-gas collisions

• Collisions of Pb81(1s) ions with the
  residual gas in the LHC beam pipe how long can
  they survive?
• Calculate maximal allowed concentration of
  molecules to achieve the 10 hour lifetime of the
  beam
• t -1 s i x r i x c
• Compare with the estimated densities for the gas
  molecules in the interaction regions by Rossi and
  Hilleret, LHC project rapport 674 (2003).

Preliminary result the required densities found
to be larger than estimated. The safety factor
varies between 30 (for the H2 molecules) and 2
(for the CO2 molecules). Better vacuum in arcs?
22
Survival of partially stripped ions
beam-beam collisions

• Evolution of the number of ions
• Where N number of ions/bunch, k number of
  bunches, nIR number of interaction points L
  total luminosity, sion ionization
  cross-section
• Solution for symmetric beams (equal species)
• Example Pb81(1s)-Pb81(1s) collisions N 9 x
  107 L 1027 1/cm2s k 608, nIR 2

• -1/N dN/dt nIRLsion/kN l

L(t) L(0) 1/(1 lt)2 t½ 0.41/l
impossible to collide Pb81(1s) ions at LHC
is is really hopeless to provide stable
e-beam ?
not really
t½ 1 min
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Survival of partially stripped ions
beam-beam collisions

• I propose the following recipe collide Pb81(1s)
  ions with fully stripped light ions maximize
  the Pb81(1s) survival probability

Calculation Neglect at LHC energies Coulomb,
and spin-flip contribution Approximate
t(Zt,Zp)1 Define a as the luminosity of
colliding beams in units of 1027 cm-2s-1
Plot t1/2 216h/ (azt2) Fot z 1, 4, 8
Log10(t1/2)
Beam life-time
Pb81(1s)-p
Beam-beam collisions
Pb81(1s)-He2
Pb81(1s)-O8
preliminary
Log10(a)
Allowed collision schemes e.g. Pb81(1s)-p,
Pb81(1s)-He2, Pb81(1s)-O8 Achievable
luminosities (e.g. for Pb81(1s)-p -
0.4 x 1029 cm-2s-1 )
24
PIE collider Pb81(1s)-p example

• CM energy (ep collisions) 205 GeV
• b at IP 0.5 m
• Transverse normalized emittance 1.5 m m
• Number of ions/bunch 10 8
• Number of protons/bunch 4 x 10 9
• Number of bunches 608
• Luminosity 0.4 x 10 29 cm-2 s-1

25
PIE collider Pb81(1s)-p example
Basic merit pp, pA, AA, ep, eA observed in the
same detector Precise relative
Measurements Note luminosity sufficient for
inclusive measurements at small x
eRHIC
PIE
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PIE versus eRHIC

• Specific merits of eRHIC (not accessible for
  PIE )

M.W. Krasny, Snowmass 2001 rapport.

• Tunability of the type of colliding particles
  (almost any collision
• combination of e, g, p A)
• Broad band of tagged collision energies available
• A 4p detector with the IP optics integrated into
  detector design
• (in my view the highest energy where
  no-compromise design
• can be made)
• Small emittance, high intensity beams allowing
  to use nucleus as
• femto-detector and to study rigidity oh hadronic
  matter exposed
• to point-like perturbations
• Polarization of electrons and protons (comment on
  PIE)

27
Kinematical region of the PIE collider
Comment on trigger
Note The ep luminosity used in the first
measurement of the Structure Function F2 at
HERA could be collected in two 10 hour-long Pb
80 - p collision runs at LHC
28
Selected physics highlights

• ep and eA program in parasitic mode
• diagnostic of partonic distributions and
  emittance and for pp, pA and AA collisions
• pA Luminosity measurement to 1 precision and
  easy transport of the Lumi measurement to the
  pp running
• Continuous, high precision beam diagnostics (
  beam divergence, beam position, etc
• High precision relative measurements (within the
  same detector) of hard processes of colored and
  uncolored partons (note that longitudinal
  Heisenberg-delocalisation of a quark carrying a
  fraction of 5x10-4 of the nucleon is the same as
  for the K-shell electron)
• Precise detector calibration down to low energies
  
• Etc

29
An example absolute ep luminosity

Elastic e p e p g scattering at
small angles
At HERA
At LHC?
Photon detector
30
An example absolute ep luminosity(detection of
low energy photons in the real machine operation
environment courtesy F.Moreau)
LHC energy regime
Bethe-Heitler spectrum photons depend only on
the proton charge insensitive to its structure
ep
e-gas
1 precision can be achieved
p-gas
Empty bunches
Eg arbitrary scale
Eg arbitrary scale
31
An example and its transport to pA and pp in 4
steps
L ep L pPb (If
one attached electrons)
S T E P S
Determine absolutely normalized quark
distribution in the proton (using
deep-inelastic ep collisions) and, subsequently,
in the lead nucleus using W and W- production in
pPb collisions (W-rate 1/sec) fqPb (x,pt),
fqp (x,pt), q d, d_bar, u, u_bar
Use absolutely normalized fqp (x,pt), for the
absolute normalization of the pp luminosity using
W production
For arbitrary A use interpolated fqA (x,pt),
for absolute normalization
32
Summary and outlook

• The proposed method of getting cheap electrons in
  the LHC interaction points is promising (tests at
  BNL could be decisive)
• The proposed stripping sequence may have
  important impact on running fully stripped heavy
  ion collisions - if the proposed cooling method
  is experimentally confirmed (low emittance beams)
• Remaining worries vacuum in the LHC ring,
  Touschek effect, ???
• Not discussed in this talk external electron
  beams in the context of the CLIC RD