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Tests of beam-beam effects with
strong field QED experiments in
crystals
Ulrik I. Uggerhøj
Department of Physics and Astronomy
Aarhus University, Denmark
Beamstrahlung
Beam-beam interaction
Electric field from one bunch boosted by 22 as seen by
particles in the other bunch
Small beams, high Lorentz factors =>
Strong electromagnetic fields =>
Beam focusing
Increase of luminosity
Beamstrahlung
Synchrotron radiation
’Typical’ fraction of energy radiated classically
B
photons
electrons
Beamstrahlung
High energy, high luminosity
’Typical’ fraction of energy radiated classically
For high energy and high luminosity (unless
’ribbon pulses’ are used):
Classical
synchrotron-radiation
Classical synchrotron radiation
10
Incident energy,
Ee=10 GeV
dN/d
1
Critical energy
0.1
0.01
Standard magnet, B = 1 T, 1m
Si <110>max , Bequiv = 25.000 T, 0.1 mm
0.001
0.001
0.01
0.1
1
10
100
Photon energy [MeV]
1000
10000
100000
D. Schulte
Strong, but partial,
suppression compared to
classical beamstrahlung
From the ’locals’
But do we know
(i.e. do experiments show)
that these formulas are
correct?
Strong fields
Other kinds of
motivation…
heavy ion collisions
Superstrong field,
but of short
duration
E1s/E0 = 3Z3
Extended nucleus:
Z  172
Coherent pair production
“The total capture cross sections are dominated by electron capture from pair production ...”
Strong lasers (-collisions )
-collision scheme
(Telnov et al.)
Laser wavelength (and
 energy) limited
by non-linear Compton
scattering
χ (or )  1
Plasma
wakefields
Transverse focusing forces:
Lead to values
for realistic parameters:
Magnetars
• Magnetars
• B  1010 T
• relativistic gyration:
ħ/mc2
= B/B0
• Electrosphere of
strange stars:
 ≈ 5-100
T=0.01 MeV
T=15 MeV
The strong magnetic field of the Earth
1,0
0,9
a
Conversion probability
0,8
0,7
0,6
0,5
0,4
0,3
0.53 G
0.25 G
0,2
0,1
0,0
10
100
Photon energy [EeV]
1000
Hawking radiation as a strong field effect
Gravitatonal acceleration at Schwarzschild
radius:
g(RS)=c4/4GM
RS=2GM/c2
Set equal to critical field acc.:
g0=eE0/m=c2/c
Light (small) black holes are
hotter:
c=2RS
Beamstrahlung
|
V
Crystals
?
What are the invariants?
Motion perpendicular to an electric field:
Recall:
Synchrotron-radiation in a critical field
Classical synchrotron radiation
1.0
10
Incident energy,
Ee=10 GeV
0.8
dN/d
1
0.6
Critical energy
0.1
0.01
0.4
Standard magnet, B = 1 T, 1m
Si <110>max , Bequiv = 25.000 T, 0.1 mm
0.001
0.001
0.2
0.01
0.1
1
10
100
Photon energy [MeV]
I/Icl
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1
0.1
0.01
1E-3
0.01
0.1
1
10
100

J. Schwinger, 1954
See, e.g. Berestetskii, Pitaevskii, Lifshitz – Quantum electrodynamics
1000
10000
100000
Similar situations ?
Blankenbecler, Drell (PRD 36, 277 (1987), Quantum treatment of beamstrahlung:
”Pulse transforms into a very long narrow ’string’ of N charges.”
ILC / CLIC
Bunch-size: 3000.60.006 μm3, 2·1010 particles
Density: 0.005 Å-3, 0.6 Å-3 (at IP)
Si
crystal
Density: 0.05 Å-3, of Z = 14
Strong fields in
crystals
Experiments on strong field QED
in crystals
(CERN NA43 and NA63)
J.U. Andersen, H. Knudsen, S.P. Møller, A.H. Sørensen, E. Uggerhøj, U.I. Uggerhøj
Department of Physics and Astronomy, Aarhus University, Denmark
P. Sona
Dipartimento di Fisica, Universitá degli Studi di Firenze,
Polo Scientifico, Sesto F.no, Italy
S. Connell, S. Ballestrero
Schonland Research Institute, Johannesburg, South Africa
T. Ketel
NIKHEF, Amsterdam, Holland
S. Kartal, A. Dizdar
Department of Physics, Istanbul University, Turkey
A. Mangiarotti
Laboratório de Instrumentação e Física Experimental de Partículas,
Coimbra, Portugal
Strong
crystalline
fields
Crystals
Extremely strong
electric fields
1010-1011 V/cm
Channeling transverse potential
50 V / 0.1 Å
=
5·1010 V/cm
’Super-critical’ fields
9
Electric field in units of =E/Ec
Relativistic invariant:
Ge <110> at 100 K
8
7
6
5
4
3
2
16
Ec=mc /eC=1.3*10 V/cm
2
1
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Distance from atomic string [A]
0.8
0.9
1.0
Formation length
High particle energy, low photon energy:
Long formation length
250 GeV e-, 1 GeV γ: 0.1 mm
NA63 experiment
Crystal on goniometer
Total length of setup: 65 m => good angular resolution (few μrad)
Strong crystalline fields
• Critical fields can
be simulated in a
crystal.
• Example:
Radiation
emission in
diamond
(CERN NA43)
One of the complications Setting up within a few days: Electronics, hardware, crystal target….
Strong crystalline fields
• Critical fields can
be simulated in a
crystal.
• Example: Pair
production in Ge
(CERN NA43)
Similar results
obtained in W and Ir
Quantum
synchrotron
χ << 1
Synchrotron-radiation
1.0
0.8
0.6
0.4
0.2
I/Icl
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1
0.1
0.01
1E-3
0.01
0.1
1
10
100

Schwinger, Proc. Nat. Acad. Sci. 1954; Berestetskii, Lifshitz, Pitaevskii
Beamstrahlung – synchr.rad.
Quantum suppression of intensity
1.0
Synchrotron radiation
Blankenbecler & Drell, eq. (7.5)
0.8
0.6
0.4
0.2
0.0
-4
Classical: -> 0
=>
Cb -> infty
-2
0
log10(1/), log10(C)
2
4
Quantum-synchrotron
(CERN NA43)
Classical = linear
Beamstrahlung,
D. Schroeder
Spin-flip
Spin-flip
Spin-flip
’Polarization time’
Similar situations
Blankenbecler, Drell (PRD 36, 277 (1987), Quantum treatment of beamstrahlung:
”Pulse transforms into a very long narrow ’string’ of N charges.”
ILC / CLIC
Bunch-size: 3000.60.006 μm3, 2·1010 particles
Density: 0.005 Å-3, 0.6 Å-3 (at IP)
Si
crystal
Density: 0.05 Å-3, of Z = 14
Spin contr. to beamstrahlung
Blankenbecler and Drell, ”Quantum treatment of
beamstrahlung”, PRD 36, 277 (1987)
Radiation from crystal
1.0
0.9
=100
0.8
Total
pure spin
no spin
C ≈ 1/χ
dN/d [Arb.]
0.7
0.6
0.5
0.4
0.3
0.2
Spin-flip contribution:
0.1
0.0
0.0
0.2
0.4
0.6
Fractional photon energy, =h/Ee
0.8
1.0
Spin contr. to beamstrahlung
35 GeV, =1.0
no spin
w/ spin
2.0
1.8
1.6
Power, dN/d
1.4
Blankenbecler and Drell, ”Quantum treatment of
beamstrahlung”, PRD 36, 277 (1987)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
Fractional photon energy, =h/Ee
0.8
1.0
Trident production
(electroproduction)
’Coherent pairs’
’Landau-Lifshitz process’
Electroproduction
“The probability of photon radiation during
beam-beam collision in linear colliders
turns out to be of the order of unity and the
density of accompanying photons becomes
comparable to the density of the charged
particles in the colliding beams. At
these photons are converted with
high probability in electron-positron pairs in
the field of the counter-moving beam.”
Amorphous case
Electroproduction of
electron-positron
pair in a medium
Authors: V. N. Baier,
V. M. Katkov
arXiv:0805.0456v1
[hep-ph]
Direct
Sequential
Direct
process
dominates
below 30
GeV
Non-aligned crystal
0.035
170 m Ge <110>
Experiment
Theory
Photons
Sum
a)
0.030
E0dN/dE+
0.025
Geometric
acceptance
0.020
0.015
Small multihit capability
0.010
0.005
0.000
1
2
3
Positron momentum [GeV/c]
JETP Lett.88:80-84,2008
4
5
Aligned crystal
enhancement
10
1
180 GeV, 170 m
Theory
Experiment, positrons
Experiment, electrons
a)
1
2
p [GeV/c]
Phys. Lett. A, accepted
3
4
5
Summary
• Experiments in crystals may address
today:
– Coherent pairs
– Electroproduction
– Beamstrahlung (radiation)
• Quantum reduction
• Spin-flip processes
in the >> 1 regime relevant for
beamstrahlung in future linear colliders.
More about these and related effects in:
•H.D. Hansen, U.I. Uggerhøj, C. Biino, S. Ballestrero, A. Mangiarotti, P. Sona, T. Ketel and Z.Z. Vilakazi: Is
the electron radiation length constant at high energies?, Phys. Rev. Lett. vol. 91, 014801 (2003)
•H.D. Hansen, U.I. Uggerhøj, C. Biino, S. Ballestrero, A. Mangiarotti, P. Sona, T. Ketel and Z.Z. Vilakazi:
The LPM effect for multi-hundred GeV electrons, Phys. Rev. D vol. 69, 032001 (2004)
•U.I. Uggerhøj, H. Knudsen, S. Ballestrero, A. Mangiarotti, P. Sona, T.J. Ketel, A. Dizdar, S. Kartal and C.
Pagliarone: Formation length effects in very thin targets, Phys. Rev. D vol. 72, 112001 (2005)
•H.D. Thomsen, K. Kirsebom, H. Knudsen, E. Uggerhøj, U.I. Uggerhøj, P. Sona, A. Mangiarotti, T.J. Ketel,
A. Dizdar, M. Dalton, S. Ballestrero and S. Connell: On the macroscopic formation length for GeV photons,
subm. to Phys. Lett. B (2008)
•T. Virkus, U.I. Uggerhøj, H. Knudsen, S. Ballestrero, A. Mangiarotti, P. Sona, T.J. Ketel, A. Dizdar, S.
Kartal and C. Pagliarone (CERN NA63): Direct measurement of the Chudakov effect, Phys. Rev. Lett. vol.
100, 164802 (2008)
•J. Esberg, K. Kirsebom, H. Knudsen, H.D. Thomsen, E. Uggerhøj, U.I. Uggerhøj, P. Sona, A. Mangiarotti,,
T.J. Ketel, A. Dizdar, M. Dalton, S. Ballestrero, S. Connell (CERN NA63): Addressing the Klein paradox by
trident production in strong crystalline fields, in preparation (2008)
Thank you for your attention!