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: sfomin@kipt.kharkov.ua)(e-mail: sfomin@kipt.kharkov.ua)

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