Suppression of Ultra Relativistic Electron RadiationSuppression of Ultra Relativistic Electron Radiation
in a Thin Layer of Matter: in a Thin Layer of Matter:
Direct Manifestation of “Half-Bare” Particle InteractionDirect Manifestation of “Half-Bare” Particle Interaction
SS.P..P. Fomin Fomin,, A.S. Fomin and N.F. Shul’gaA.S. Fomin and N.F. Shul’ga
Akhiezer Institute for Theoretical Physics Akhiezer Institute for Theoretical Physics
National Science Center “Kharkov Institute of Physics & Technology”National Science Center “Kharkov Institute of Physics & Technology”
KharkovKharkov 61108 61108, Ukraine, Ukraine (e-mail: [email protected])(e-mail: [email protected])
IC New Trends in HEP 23-29 Sept 2013 BITP, Alushta, Crimea
Overview:Overview:
• Introduction and motivation: Bremssrahlung at ultra high energy
• Multiple scattering effect on radiation: LPM effect
• Radiation in a thin layer of matter (SLAC exp E-146)
• TSF effect: theory and CERN experiment NA63
• Spectral-angular distribution and polarization of γ-quanta
at the non-dipole regime of radiation
• Future experiment suggestions
3
Coherence length (Ter-Mikaelian, 1953)Coherence length (Ter-Mikaelian, 1953)
22
cl m
22 '
cl m
R
min
222
2 q
q
qd d q dq U
q
1
22 '
eff eff cr q lm
1eff
effr Rq
, p p k q 2
min / 2 'effq q m
k q
p 'p
100 GeV = 10 MeV 1 mmcl r
RZ e
U r er
2 /: 2cl
/ m
1934:1934: Bethe Bethe--Heitler theory ofHeitler theory of Bremsstrahlung Bremsstrahlung H. Bethe and W. Heitler, Proc. Roy. Soc. A 146 (1934) 83.
BHms
dET
d
2
BHdE
d
2
2 2
2 20
21
3BHdE T
d X
: 0
E 4( )
3ВHd T
fd X
12 6
0 2
4ln
Z e nX mR
m
,
and if
where is the Radiation length = f(Z,n), but not !!!
2
minmax
1
2 '
mq
r
max 2
2 'cohr l
m
screening effect
R
maxr R
maxeffr r effr R
rR
Z ee
rZ e
r
Coherence LengthCoherence Length
amorphous media
dE
d
dE
d
B H
LPM
22cl
crystal
6
sФd
d
d
dM
BHLPM
EE
42sin2
0
224 ststetcthdtssMФ
0
E 4
3ВHd T
d X
LPMs
22
1
4 22LPM q ~
2
20
1sqX
LPME
~d
d
Cosmic ray M.Miesowicz, O.Stanisz, W.Wolther. Novo Cimento 5 (1957) 513.experiments: A.Varfolomeev et al. Sov. Phys. JETP 11 (1960) 23.
Multiple Scattering Effect on Radiation in Amorphous Multiple Scattering Effect on Radiation in Amorphous MediumMedium
L. Landau and Ya. Pomeranchuk Dokl. Akad. Nauk SSSR 92 (1953) 735.A.B. Migdal, Dokl. Akad. Nauk SSSR 96 (1954) 49; JETP 32 (1957) 633.
1
7
LPM effect for very high energyLPM effect for very high energyF(x) = E’LPM / E’BH
x = ω/ ε
Increasing of Radiation length !!! GEANT, …Detector design and Radiation shielding calculation …
LPM ~ 2
8
1994:1994: SLAC experiment E-146 SLAC experiment E-146
9
SLAC experiment E-146SLAC experiment E-146
2 2 1 2 2 1 2 2 1
Anthony P.L. et al., Phys. Rev. Lett. 75 (1995) 1949.Klein S., Rev. Mod. Phys. 71 (1999) 1501.
Bethe-Heitler ? ? ? LPM effect
, but T < lc and T > lc
F.F. Ternovskii. JETP 12 (1961) 123. lnsms
T
X
T
X
2
0
22
0
11
9
10
cl T
22
222
4In
e
dd
Ed
vk
v
dt
dedtiI )t(rkti
vk
v
vk
viI
dE e
ln( ) ,d
2 22
2
2 2 11 1
1
12
e, ,
dE
d eln( ), .
22 2
22 2
31
24 1
T, ,dE
d lnT, .
2
2
1
1
V
T
lcoh
V /
z
x
θs
0
γ
θk
Radiation in a thin layer of matter :Radiation in a thin layer of matter :
Shul’ga N.F. and Fomin S.P., JETP Lett. 27 (19781978)126; Fomin S.P. and Shul’ga N.F., Phys. Lett. A114 (19861986)148.
;
dE
d
2 2 1
BH
suppression of radiation
L
2
24 e r r t
t
2 2
, , 0ve
r t tz vt
1
1
1
3
20
1 1, Re
2
, ,
i k kv tikv tikr ikt
rett
v v
e d k er t e e e
k kv k kv
t r r t r t r t
1 21 2 ct k kv l
E.Feinberg, JETP 50 (1966) 202. S.P. Fomin, N.F. Shul’ga, Phys. Let. A 114 (1986) 148 A.I. Akhiezer, N.F. Shul’ga, Sov.Phys.Usp. 30 (1987) 197
Electromagnetic field of electron at scattering
For 25 GeV, 10 MeV, 0.1 mmcl
- retarded Liénard–Wiechert potential
dE
d
2 2 1
'BHE L
L
lnT S FE L
2 2 1
0
0
2
3LPdE L
d X E
2 1
13
Quantitative theory of radiation in a thin layer of matterQuantitative theory of radiation in a thin layer of matterShul'ga N.F., Fomin S.P., JETP Lett. 63 (1996) 873; JETP 86 (1998) 32; NIM B145 (1998) 73.
s s
dE dEd f ( ) ,
d d
B M cf ( ) d J ( )exp d q J ( )2 40 0
0 0
12 1
2
2 2 1 2
2SF2 2
dE 2e 2 2 Cln a C 1 1
d a a B
2 2 2a
2 2c B
2 2 2cB ln B ln( R ) 1 2C
2 2 4 2c 4 nLZ e /
0,577C
:
,
14
Other publications on this subject:
R. Blankenbacler, S.D. Drell. The Landau-Pomeranchuk-Migdal effect for finite targets.Phys.Rev. 1996, v. D53, p. 6265-6281.
R. Blankenbacler. Structured targets and Landau-Pomeranchuk-Migdal Effect.Phys. Rev. 1997, v. D55, p. 190-195.
B.G. Zhakharov. Structured targets and Landau-Pomeranchuk-Migdal effect for finite-size targets. JETP Lett. 1996, v. 64, p. 781-787.
B.G. Zhakharov. Light-cone path integral approach to the Landau-Pomeranchuk-Migdal effect. Yadernaya Fiz. 1998, v. 61, p. 924-940.
R.Baier, Yu.L.Dokshitser, A.H.Mueller, S.Peigne, D.Schiff. The Landau-Pomeranchuk-Migdal effect in QED. Nucl. Phys. 1996, v. B478, p. 577-597.
V.N. Baier, V.M. Katkov. Landau-Pomeranchuk-Migdal effect and transition radiation in structured targets. Phys. Rev. 1999, v. D60, 076001, 12 p.. . . . . . . .
15
20052005
A.I. Akhiezer, N.F. Shul'ga, S.P. Fomin.
The Landau-Pomeranchuk-Migdal Effect.
Cambridge Scientific Publishers,
Cambridge, UK, 2005, 215 p.
16
CERN NA63 experiment 2005CERN NA63 experiment 2005SPS secondarySPS secondary positron beam E = 178 GeV, target thickness: 2, 10, 20 positron beam E = 178 GeV, target thickness: 2, 10, 20 μμmm
CERN NA63 experiment 2008CERN NA63 experiment 2008SPS secondarySPS secondary electron beam E = 206 & 234 GeV, target thickness: 5-10 electron beam E = 206 & 234 GeV, target thickness: 5-10 μμmm
18
CERN NA63 experiment 2008CERN NA63 experiment 2008
19
Thickness dependence !!!Thickness dependence !!!N. Shul'ga, S. Fomin: JETP Lett. 27(1978)126. Phys.Let.A 114(1986)148; JETP 86(1998)32
1 = 800 MeV
2 = 350 MeV
3 = 150 MeV
1 /TFSTSF
TSF = m2t / 2 ≈ 6.6 PeV ∙ t (сm)
TSF ≈ 22/t
If << TSF :
t ≈ lc()
June 5, 2009Dear Nikolai and Serguei,
It is a pleasure for me to tell you that in the CERN experiment we are running these days, we have confirmed the logarithmic thickness we have confirmed the logarithmic thickness dependence that your theory for thin targets has predicteddependence that your theory for thin targets has predicted, …
… we are certain that the effect is there, and we thought we would let you know that we have 'seen' the 'half-bare' electronwe have 'seen' the 'half-bare' electron :-) :-)
Best regards from all of us at NA63,
Ulrik Uggerhoj
Spokesman of CERN NA63 collaborationProfessor, Aarhus University, Denmark
CERN experiment NA63 - June 2009CERN experiment NA63 - June 2009
21
TSF Theory & CERN experiment NA63 June 2009TSF Theory & CERN experiment NA63 June 2009
A.S.Fomin, S.P.Fomin, N.F.Sul’ga, Nuovo Cimento 34C (2011) 45.
H.D.Thomsen et al., Phys. Rev. D 81 (2010) 052003
BH, LPM and TSF theories applicability rangesBH, LPM and TSF theories applicability ranges
Thickness dependence of radiation spectral density
2
02
el X
( ) 1ms l
The cover picture
from H.Thomsen
PhD thesises
22
cl m
23
cosd E e
d d G G
2 2 2 2 2 2
22 2
1 2 1
1
k e
V
T
lc
V /
z
x
θs
0
γ
θk
Angular Dirtribution of Radiation in Non-Dipole CaseAngular Dirtribution of Radiation in Non-Dipole Case
cosG 2 21 2
,d E e
n Id d
2 2 2
2
24 ( )i t kr t d v v v
I i dt e idt kv kv kv
cl T
e 10
S.P. Fomin, N.F. Shul’ga, S.N. Shul’ga, Phys. Atom. Nucl. 66 (2003) 421
24
Fomin S.P., Shul’ga N.F., Shul’ga S.N., Yad.Fiz. 66 (2003) 421
k
e
Angular Dirtribution of Radiation in Non-Dipole CaseAngular Dirtribution of Radiation in Non-Dipole Case
cl T
-5 0 5 10 150.0
0.2
0.4
0.6
0.8
1.0
1086
4
3
1
0.5
s=2
2 /(e2 2 )
d2 E
/(dd)
22 2 2
2 2 21 1
d E e
d d
22 2 2
2 22
2 2
2 2
1 , ,1
, .1
1
1
d E e
d d
θy = 0 :
,
Spectral-angular distribution of radiationSpectral-angular distribution of radiation in a thin amorphous target in a thin amorphous target
Fomin S.P., Shul'ga N.F. and Shul'ga S.N., Phys. of Atomic Nuclei 66 (2003) 396.
dd
,,dET,fdd
dd
dE ssss MB
2
0 0
2 40 0
0 0
1( )exp 2 1 ( )
2B M cf d J d q J
2
24
42
22
2
1 ,1
1dE e
d d
2 2 2
22 21
dE e
d d
2 2
2 1
Angular distribution of radiation in Angular distribution of radiation in a thin amorphous targeta thin amorphous target
0 2 4 6 8 100,0
0,1
0,2
0,3
(< e
2>)1/2 = 105210.5
(/e
)2 d2 E
/dd
o
27
ik i k
eJ e I e I ,
2 2
24 i,k i k ike n , e e . 0
J JP
J J
11 22
11 22
J JP
J J
12 21c
11 22
ik kcoh ciat l T 0: J J P
Polarization matrix:
Linear polarization:
Circular polarization:
for all observation angles !
where
Polarization of Radiation at Non-Dipole RegimeA.S. Fomin, S.P. Fomin, N.F. Shul'ga, Proc. SPIE, 5974 (2005) 177; 6634 (2007) 663406.
a
ψ
N ~ 2 R / ψ a
p
ψ p
p ̀
x
y
z
θ
φ
Multiple Scattering in Aligned CrystalMultiple Scattering in Aligned Crystal
Ee = 200 GeV W <111> T = 20 μm ψ = ψL L = 35
Pc ~ 80%
Electrons
Polarization
Polarization at Strong Non-Dipole Regime of Radiation Polarization at Strong Non-Dipole Regime of Radiation
A.S. Fomin, S.P. Fomin, N.F. Shul'ga, Proc. SPIE, 5974 (2005) 177; 6634 (2007) 663406.
Polarization in Crystalline and Amorphous TargetsPolarization in Crystalline and Amorphous Targets
Thank you for attention!Thank you for attention!
ConclusionConclusion
1. The effect of suppression of ultrarelativistic electron radiation due to a multiple
scattering on atoms in a thin amorphous target (TSF effect) was finally
confirmed in the CERN experiment NA63 by observation of logarithmic
dependence of the radiation spectral density on the target thickness.
2. It is theoretically shown that this effect leads to essential changing not only
spectral density of radiation, but also its angular distribution and polarization,
that can be verified by future experiments in SLAC and CERN.
3. The TSF effect takes place also in a thin crystal at the coherent multiple
scattering of an electron on the crystal atomic chains. This effect is planed for
experimental study in CERN after SPS restart.
4. The analogous of the LPM and TSF effects have to take place in QCD
at quark-gluon interaction.
CERN experiment NA63 (2005)CERN experiment NA63 (2005)Results of our calculations:
2 10 180.0
0.1
0.2
0.3
0.4
0.5
t = lc LPM
TSF
BH
Au t = 10 m E = 178 GeV
dN Xod t
, GeV 2 10 180.0
0.1
0.2
0.3
0.4
0.5
BH
LPM
W t = 20 m E = 178 GeV
dN Xod t
, GeV
5 10 15 200.4
0.6
0.8
1.0
1.2
1.4
1.6
TSF/LPM
BH
TSF
LPM
Ta E = 206 GeV
dE Xod t
, GeV
34
LPM and TSF effects in a crystalShul’ga N., Fomin S., JETP Letters 27 (1978)126; Phys. Lett. A114 (1986)148.Laskin N., Mazmanishvili A., Shul’ga N., Phys. Lett. A112 (1985) 240.
Multiple scattering on crystal atomic strings
Shul’ga N., Truten’ V., Fomin S., J. Techn. Phys. 52 (1982) 2279.
a
ψ
N ~ 2 R / ψ a
p
ψ p
p ̀
x
y
z
θ
φ
35
CERN experiment: Bak J.F. et al. Nucl. Phys., B302 (1988) 525.
Theory: Laskin N., Shul’ga N., Phys.Lett. A135 (1989) 147.
e- : E=10 GeV
e+: E=20 GeV
Lapko V.P., Nasonov N.N., NIM B 84 (1994) 48.
Circular Polarization of Radiation in Non-Dipole Case
How relativistic electron emits photonHow relativistic electron emits photon? ?
Force lines at rest and uniformly moving electric charge
B.Bolotovsky and A. Serov, Sov. Phys. Usp. 179 (2009) 517.
B.Bolotovsky and A. Serov, Sov. Phys. Usp. 179 (2009) 517.R.Y. Tsien, AJP 40 (1972) 46
How relativistic electron emits photonHow relativistic electron emits photon? ?
The own Coulomb fields of instantly started and immediately stopped charge
Как излучает релятивистский электрон?Как излучает релятивистский электрон?
Поле вращающегося заряда с тангенсиальной скоростью
= 0.5 и = 0.9
R.Y. Tsien, AJP 40 (1972) 46
Как излучает релятивистский электрон?Как излучает релятивистский электрон?
Поле вращающегося заряда с тангенсиальной скоростью
= 0.95 и поле рассеянного на угол 5° заряда с = 0.943
R.Y. Tsien, AJP 40 (1972) 46
Как излучает релятивистский электрон?Как излучает релятивистский электрон? Поле дважды рассеянного заряда
42
CERN experiment NA63 June 2009CERN experiment NA63 June 2009
H.D.Thomsen et al.,“The distorted Coulomb field of the scattered electron”
Phys. Rev. D 81 (2010) 052003
SPS secondarySPS secondary electron beam E = 149 GeV, electron beam E = 149 GeV, Ta target thickness: 2 - 200 Ta target thickness: 2 - 200 μμm; m; hω = 0.2 – 3 GeV
43
TSF Theory & CERN experiment NA63 June 2009TSF Theory & CERN experiment NA63 June 2009
Thickness dependence of radiation spectral densityThickness dependence of radiation spectral density
Coherence Length (informal introduction)Coherence Length (informal introduction)
22cohl
relv c v 22c cc v t t
c
v
pre-wave zone wave zone
2 2 2/ 1 /mc v c 2 2 2/ 1/ 1 /mc v c
1/
100 GeV = 10 MeV 1 mmcl
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