Theoretical models and simulations of high energy electron ... · Crystal field strength Diversity...
Transcript of Theoretical models and simulations of high energy electron ... · Crystal field strength Diversity...
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Theoretical models and simulations of high
energy electron radiation in oriented crystals
Victor V. Tikhomirov Institute for Nuclear Problems,
Belarusian State University, Minsk, Belarus
March 30, 2018 Orsay LAL
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PlanIntoduction. Crystal field strength
Diversity of orientation effects in crystals- synchrotron type radiation and pair production, intensity growth and
saturation. Shift to zero incidence angle
- polarization and spin effects, charm and beauty hyperon magnetic and
electric dipole moments
- gamma-telescopes, gamma-background suppression (CLEVER)
- crystal undulators (PEARL), Ferrara experiments in u-short bent crystals
Crystal assisted collimation Crustal cut. Multiple volume reflection.
Miscut problem. Scattering by atomic strings.
Simulation of high-energy electron radiation in crystals. − the need of detailed simulations (CFA insufficiency)
− incoherent processes in crystals
− radiation under multiple volume reflection
− crystalline scintillator performance (PRIN)
− medium energy electron radiation in W <111>
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Moving in oriented crystals, particles come under the action
of the practically inter-atomic-scale effective crystal field
The uniqueness of crystal field
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Planar channeling
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Scattering by atomic strings
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When channeling radiation becomes
synchrotron-like radiation:
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Synchrotron-like radiation
Dipole radiation
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Field amplification in the particle rest frame
Lorentz amplification of field can exceed γ ~ 105 times
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Synchrotron-like radiation quantum parameter χ
2
3 2 3 2
0 0
.( / )
v
e comF k
m m c e mc
Invariant parameter:
2 316
0 1.32 10m c
eVe
Critical field:
“Quantum” synchrotron-like radiation
is observable in crystals:
2/3 e
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Channeling radiation
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Channeling radiation
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A virtual pair conversion to a real onein electric field E ~ E0
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Electron-positron pair production
by gamma-quanta in the uniform field
2
3 2 3 2
0 0
.( / )
v
comF k
m m c e mc
Invariant parameter:
2 316
0 1.32 10m c
eVe
Critical electric field:
2
0
2 21
1expe e
n com
dP
dr n
PP in vacuum
(Schwinger)
this process is also observable in crystals:
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Critical electron and photon energies
Baryshevsky, Tikhomirov UFN, 1989
ele-
mentZ plane / axis
Emax(GV/cm)
Heff
(kilotesla)
ħωcr= εcr(GeV)
Si 14 plane (110) 5.7 1.9 1200
Ge 32 axis ‹110›100K 144 48 47
W 74 axis ‹111› 500 167 13.6
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Typical angle V0/m for synchrotron-like
radiation and PP processes in crystals
01 1( ) ( )
p Vd me z dz e z
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At high energies both radiation and PP processes
acquire synchrotron nature
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25/14-time increase of radiative energy losses
of 150 GeV electrons in 0.4/1.4 mm Ge<110> 100K
A. Belkacem, PRL 1985
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Electron radiative cooling
Baryshevskii V. G., Dubovskaya I. Ya. // Phys. Lett. 1977. Vol. A62. P. 45.
Belkacem A. et al. // Phys. Lett. 1986. Vol. B177. P. 211.
Tikhomirov V. V. // Phys. Lett. 1987. Vol. A125. P. 411.
Tikhomirov V. V. // Nucl. Instr. Meth. 1989. Vol. B36. P. 282.
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All plans for PeV energies and higher
are based on radiative cooling in crystlas
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8-time increase of PP probability
in Ge<110> 100K at 150 GeV
A. Belkacem, PRL 1987
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Crystal dichroism and birefringence
For visible light
For - quanta
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Spin effects in bent crystalV. G. Baryshevsky. Pis'ma Zh. Tekh. Fiz. 5(1979)182; 5(1979)1529.
Channeled е+ and е move or are produced by gamma-quanta in
bent crystals in the regions with dominating direction of the planar
electric field. which represents itself an origin of a numberof spin effects.
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Spin effects in bent crystal
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Spin rotation in bent crystals and
magnetic and electric moment measurement
B
S
g BB
E761 Collaboration, FERMILAB
”First observation of spin precession
of polarized hyperons channeled
in bent crystals”, LNPI Research
Reports (1990-1991) 129.
Energy of : 200 – 300 GeVBP
BP
BP
BP
E
*B
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D. Chen ”First Observation of Magnetic Moment Precession of
Channeled Particles in Bent Crystals”, Phys. Rev. Lett. 69 (1992) 3286.
Baryshevsky V.G., The possibility to measure the magnetic
moments of short-lived particles (charm and beauty baryons) at
LHC and FCC energies using the phenomenon of spin rotation in
crystals, Physics Letters B, V. 757, 2016, pp 426–429.
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Circularly
polarized SOS
radiation of
channeling
positrons
/1.0
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Crystal-based
angular-sensitive
gamma-telescope
V.A. Baskov, V.A. Khablo, V.V. Kim et al., NIM B 122(1997)194.
V.N. Baier, V.M. Katkov, V.M. Strakhovenko, Electromagnetic
Processes at High Energies in Oriented Single Crystals, World
Scientific, Singapore, 1998.
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CsI scintillators
in the Fermi Large Aperture Telescope
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The GAMMA-400 project
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Crystals in the GAMMA-400 telescope
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Pair production probability by 300Gev. 1 Tev and 3 TeV gamma-quanta
vs the angles of incidence w.r.t. <110> Si axis.
The probability is measured in units of Beth-Heitler PP probability WBH ≈ 0.083/cm.
To the crystal gamma-telescope development
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Any (Eγ ≥ 10 TeV) energy
can be measured
with the same
detector thickness
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Magnetic undulator (Ginzburg, 1947; Motz, 1953)
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Crystal Undulators
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855 MeV electron rechanneling
in “Backe CU”
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A “fortunate” 500 MeV positron
trajectory
0 20 40 60 80 100
-0.4
-0.2
0.0
0.2
0.4
z, m
x,
A
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“Principles” of construction of the
“optimal” positron CU
• Maximal undulator radiation energy
• Minimal CU radiation spectral width
• LCU ≈ Ldech
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Spectral distribution of the radiation emitted by a 1.5 GeV positron:
Solid line − in the “optimal” Si (110) CU
Dotted line − in a plane 0.48 mm Si (110) crystal
Positron beam incidence angle equals zero,
incident beam angular divergence is Δθe = 10 μrad
and collimation semi-apex angle is θγ = 1/8γ = 42.6 μrad.
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Crystal
assisted
collimation
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Orientational effects in crystals allow to facilitate collimation
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channeling − limited efficiency
volume reflection − small deflection angle
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Channeling efficiency can
be increased by crystal cut
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beam
cut
crystalz1
z2
z3
0
x
y z
The capture probability increase by crystal cut
V.V.Tikhomirov, JINST, 2(2007)P08006
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V, , eVe
x, A
e
x1x2
V(x )2
V(x )1
. . ..
Vmax
d
v1
v2
v0
e
x0
Transverse energy reduction by the cut
The cut diminishes the potential energy
preserving the transverse kinetic one
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Protons cease to reach the
high nuclear density regions
plane crystal
crystal with cut
z1
z2
0
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-0,5
0,0
0,5
1,0a
0,5 1,0 1,5
b
c
0,0 0,5 1,0 1,5
-1,0
-0,5
0,0
0,5
1,0
dd
dx, Å
0,0 0,5 1,0 1,5
-1,0
-0,5
0,0
0,5
1,0
x, Åx, Å
e
ch
/
ch
/
ch
/
ch
/
Phase space transformation by the cut
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Channeling efficiency increase by crystal cut
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Deflection of nonchanneled
particles can be increased
by multiple volume
reflection in one crystal
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Volume Reflection prediction
A.M.Taratin and .A.Vorobiev
Phys. Lett. A119 (1987) 425, NIM B26 (1987) 512
Large acceptance, however
small deflection angles
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Multiple Volume Reflection in One Crystal (MVROC)V.V. Tikhomirov, PLB 655(2007)217
Axes form many inclined reflecting planes
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In this talk only and just for short
MVR = multiple volume reflection
in one crystal/”axial VR”
VR = “one plane VR”/”planar VR”
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Protons are reflected from many
different crystal plane sets in one crystal
Proton motion
in comoving reference plane
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Reflection from different crystal planes
increases VR angle about 5 times
Reflection angles from planes of
one crystal vs bending radius
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First MVROC observationW. Scandale et al, PLB 682(2009)274
MVROC indeed increases reflection angle 5 times
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multiple volume reflection
in one crystal can be
combined with planar
channeling
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-20 -10 0 10 20 30 40 50
-40
-30
-20
-10
0
10
20
30
MVR + Channeling
y,
mra
d
x,
mrad
-20 -10 0 10 20 30 40 50
-40
-30
-20
-10
0
10
20
30
nearly pure MVR
y,
mra
d
x, rad
-20 0 20 400.00
0.03
0.06
0.09
drastic MVR angular divergion increase by channeling
(1
/N)
dN
/d
y,
rad
-1
x, rad
X = 3.56 --> 13.5 rad
Enhanced beam
angular dispersion
by MVR can be
combined
with channeling
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-20 0 20 400.00
0.02
0.04
0.06
2
(1/N
) d
N/d
y,
rad
-1
x, rad
lcr=5mm,
X0=4rad
MRV R=70m,
x,y
=30,17.3rad
AxCh R=700m,
x/y
=0rad
X=13.5/3.71
X
MVR+channeling in comparison with axial
channeling of 7 TeV protons
-20 -10 0 10 20 30 40 50
-40
-30
-20
-10
0
10
20
30
MVR + Planar Channeling vs Axial Channeling
y,
mra
d
x,
mrad
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Uncorrelated scattering
by atomic strings
will enhance random
scattering practically
at any alignment
requirements
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Particle scattering
by the atoms
constituting a string
are correlated (coherent)
coherent effects
in particle scattering
by the atomic string
will increase
the “scattering power”
by nearly 1000 times
Particle scattering by atoms constituting a string
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Multiple uncorrelated scattering by atomic strings
7~10 , ~ 0.01string stringl cm l cm
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-15 -10 -5 0 5 10 150.00
0.05
0.10
0.15
x10
(1/N
)dN
/d
X,
rad
-1
X, rad
axes
amorph
Uncorrelated scattering amplification
by atomic strings in 1 cm W target
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The “miscut problem”
V.V. Tikhomirov, A.I. Sytov, The miscut angle influence on the future
LHC crystal based collimation system. Problems of Atomic Science
and Technology № 1 2012. 88-92. arXiv:1109.5051.
No big difference in fact!
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Need of
comprehensive simulations
of high-energy electron
radiation in crystals
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Electron radiative cooling
Baryshevskii V. G., Dubovskaya I. Ya. // Phys. Lett. 1977. Vol. A62. P. 45.
Belkacem A. et al. // Phys. Lett. 1986. Vol. B177. P. 211.
Tikhomirov V. V. // Phys. Lett. 1987. Vol. A125. P. 411.
Tikhomirov V. V. // Nucl. Instr. Meth. 1989. Vol. B36. P. 282.
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General
simulation
method
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Key simulation points:
Trajectory simulations in most
realistic potentials
Simulation of incoherent scattering on
both nuclei and electrons
Separate simulation of single
and multiple scattering
Direct integration of
Baier-Katkov formula
Infinite trajectories, density effect…
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Radiation process simulations
from the “First Principles”
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Radiation at sharp change of particle trajectory
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Single scattering effects are treated separately
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Simulation of radiation
accompanying
multiple volume reflection
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Radiation amplification under Multiple Volume
Reflection in One Crystal (120 GeV e-, 2 mm Si ‹111›)
• soft radiation amplification by reflection
by different planes
• hard radiation amplification
by axial field
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120 GeV electron radiation
in <001> PWO
(Dr. L. Bandiera PRIN project)
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120 GeV electron energy losses on 4 mm of amorphous PbWO4 (1),
crystalline PbWO4 with (3) and without (2) PP by radiated photons
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Electromagnetic shower development
acceleration in PWO at Ee =120 GeV
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First simulations of shower
development in ECAL CMS
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Electromagnetic shower acceleration
in PWO at 50, 100 and 1000 GeV
50 GeV
em shower maximum shifts
by 2 ÷ 5
radiation lengths
1000 GeV
100 GeV
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Electromagnetic shower acceleration in PWO
can influence H boson mass measurements
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Thickness of the CMS ECAL calorimeters
can be made smaller
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A first step to positron
source simulations:
electron radiation
in 1 mm W <111>
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0.0000 0.0001 0.0002 0.0003 0.0004
600
700
800
vx
vx, v
y, ra
d
z, cm
vy
A 20 GeV in <110> W field trajectory
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550 600 650700
750
800
850v
y, ra
d
vx, rad
Transverse
velocity
component
evolution
Mind single
scattering!
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0 5 10 15 200
1
2
3
E , GeV
(E/N
)dN
/dE
Radiation amplification in <110> W at 20 GeV(photon spectra thin crystal limit)
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20 GeV electron trajectory in W<111> 1 mm
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20 GeV electron trajectory in W<111> 1 mm
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A part of electron trajectory in W<111>
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0 5 10 15 200.0
0.5
1.0
1.5
2.0
2.5
(E/N
)dN
/dE
E, GeV
20 GeV e-- radiation amplification in <110> W 1 mm
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20 GeV electron spectrum behind 1 mm <110> W
0 5 10 15 200.00
0.05
0.10
0.15
Ee, GeV
(1/N
e)d
N/d
Ee
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as a conclusion
Possible cooperation directions
− positron source
− crystal assisted collimation
− crystal undulators
− crystal scintillators
− gamma-telescopes
− radiation pair production at high energies,
polarization and spin effects
− charm and beauty hyperon magnetic and
electric dipole moments
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Thank you for attention!