N. M. Naumova-Radiation Back-reaction on Electrons in Relativistically Strong and QED-Strong Fields

8/4/2019 N. M. Naumova-Radiation Back-reaction on Electrons in Relativistically Strong and QED-Strong Fields

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N. M. Naumova,1 I. V. Sokolov,2 J.A. Nees3,

V.P.Yanovsky3, G.A. Mourou4

Radiation back-reaction on

electrons in relativistically strongand QED-strong fields

ELI - Beamlines Scientific Challenges Workshop

April 26-27, 2010, Prague, Czech Republic

1Laboratoire d'Optique Applique, ENSTA, Ecole Polytechnique, CNRS, France

2Space Physics Research Laboratory, University of Michigan, USA

3Center for Ultrafast Optical Science and FOCUS Center, University of Michigan, USA

4Institut de la Lumire Extrme, ENSTA, Ecole Polytechnique, CNRS, France


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Motivation

Laser intensity gradually increased

during 20 years from 1018 to 1022 W/cm2.

The next challenge with ELI is coming in

the next decade.

Laser-plasma interaction in the new

intensity range up to 1025

W/cm2

neednew models to be developed. QED

effects become an inevitable part of

these models.

Particle-In-Cell (PIC) codes, being of

great help in studying collective

phenomena during 50 years, traditionally

use classical electrodynamics as a basis.

Incorporation of QED effects is on the

way.


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There is a pronounced similarity betweenprocesses in strong electromagnetic fields, in

different environments.

Particularly, for a relativistic electron interactingwith the magnetic field of a neutron star, and forinteractions of counter-propagating electrons withrelativistically strong laser pulses the same

dimensionless parameter,

is essential, which is the ratio of the electric field,experienced by an electron, in the frame ofreference, co-moving with the electron,

to the Schwinger field,

e

-

cpddA

mcBpE

/)(|/|

/

||

0

CeS ecmE /2

SEE /~ 0

Introduction


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e-

In the astrophysical environments, >1

occurs in relation to:(1) the high-field limit of gyro-synchrotronemission,(2) possible pair creation,(3) significant electron recoil while emitting.

>1 can be achieved when 600MeVelectron interacts with a counter-propagatinglaser pulse of intensity 2x1022W/cm2. QEDeffects including radiation back-reaction onthe particle motion come to power.

Introduction

e-

Before the interaction

After the interaction


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At >1 the following inequalities hold:

(1) Electric field acting on the particle in the co-moving frame exceedsThat is, this field is QED-strong.

(2) While formally calculated within the classical theory, the typical energy

of emitted photons exceeds the electron energy so that:

That is, the electron recoil should be accounted for; and

(3) The radiation loss rate, calculated in the classical theory exceeds the

"Comptonian radiation loss rate:

If >1 the actual radiation loss rate differs from

It should be re-calculatedself-consistently

(see Figure : below).

,3/2 SE

Ccl II

2mcc

Introduction

2

2

27

8

C

C

ceI

CeS ecmE /2

3

2 SclC

EII)3/(2)( 3220

4

0cmEeEI ecl

C

cl

I

I

clI

)( clQED II


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QED is not compatible with the traditional approach to the radiation force inclassical electrodynamics (LAD equation and its known approximations).

An alternative equation of motion for a radiating electron with respect to propertimehas been suggested:

The derivation of these equations is given: by re-normalizing the mass operator [1];

from the conservation law for a single-photon emission: for the electron to

acquire the extra energy from the classical field, an extra classical current mustbe generated [2];

from QED in the classical limit, for 1D wave [3].

Equation of motion for a radiated electron

2mc

pI

d

dxFc

e

d

dpi

QEDkiki

cm

peF

I

I

m

p

d

dx kik

cl

QEDii

20

[1] I.V. Sokolov, JETP 109, 207 (2009);

[2] I.V. Sokolov, et al, PoP 16, 093115 (2009);

[3] I.V. Sokolov, et al, PRE 81, 036412 (2010).


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The suggested equation of motion conserves:

Total energy-momentum in the system including the externalfield, the radiating electron and the emitted radiation;

Generalized momentum of an emitting electron in symmetric

fields;

Maintains the relativistic identity, ;

This set of properties seems to be unique :(1) in the LAD equation the conserving momentum does not

satisfy the relativistic identity,

(2) the LL equation does not care on the generalized

momentum;

Probably, the simplicity of the transition to QED-strong fields isalso unique for this equation only.

This equation is easy to implement in numerical modeling.

Equation of motion for a radiated electron

22cmpp


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Emission spectra

0

2

000

2

00

0

)(K)(K

)(K)(K

),(

32

35

32

35

r

r

rrrdyyrdr

rrrdyyr

rQ

Cc c /

2

2

27

8

C

C

ceI

C

cl

II

0

0

1 r

r

r

c

r0

For >0.1 emission spectrum significantly differs from classical

)/(log10 c

)/(log10 CII

01.02

1.02

12


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Emitted radiated power

0

2

000 )(K)(K8

39

32

35

rcl

QEDrrrdyyrdr

I

I

,0

0

rQI

I

p

pI

drd

dI

cl

QED

cl

Interpolation formula(dashed line):

3/4

/04.11 Ccl

clQED

II

II

)/(log10 CQED II

)/(log10 Ccl II

0.1 1 10


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Frequency and angular distribution

of the radiation

mcpmcpTafinalxinitialx 130;300

pol.circular;100;15,,

0

12

d

dI

Photon energy (MeV)

1 - Radiation energy spectrum

2 - Distribution by the dominant frequency c

Such an experiment could manifest the effect of radiation

back-reaction and would allow us to measure it.

dd

dI


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dd

dI

A signature of the radiated photonsin the polarization plane

~1%, or 0.26J is in backwardscattered high-frequency radiation;above 150keV 0.24J (shown here).

3D PIC simulation parameters:

Laser pulse: 30-fs linearly polarized

Plasma:

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00mceAa

crnn 30

222/10 cWI m8.0

linear polarization

10L

For super-high-intensity circular polarized laser pulses (a=100-1000) andelectron beams of ~1 GeV the radiation angular distribution can be wide: ~a/ .

Linear polarization can restrict the radiation in space.


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Validating QED effects in the model

Validation of QED effects inthe model can be done for :

=[0.1, 1].

In the example is shownemission spectrum for :

600 MeV electrons interactingwith 30-fs laser pulse ofintensity 2x1022 W/cm2.

We see that physically absurdprediction (dashed curve) thatthe maximum photon energy

exceeds 1 GeV is eliminatedby the QED effects. )/(log 010 c

)/(log10 ddI

1.1 MeV 1.1 GeV

QEDclassical


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QED-strong fields vslaser intensity & electron energy

Values of parameter forcounter-propagating laserand electron beams are

between [0.01,10] for ELIfacilities.

This range of laser-plasma interaction can be

simulated using :quasi-classical modeltaking into account QEDeffects.

223

3

/10107.2

cmW

I

MeV

Eel

~ Limit of the validity of classical approach

of taking into account the radiation losses


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charge

separation

layer

Counter-propagating electrons aregenerated in laser-plasma interaction

Counter-propagating electronsappear when laser pulse interactswith the plasma layer.

Due to lower speed of ions thecharge separation field is formed,which, accelerating ions in theforward direction, can accelerateelectrons toward the laser pulse.

The charge separation layer isoscillating, allowing electrons topenetrate there.

Electrons, accelerating toward thelaser pulse, in the same timegenerate photons, losing energy.

Radiated photons can bescattered coherently in UV rangeor incoherently in -range.

Schlegel et al., PoP (2009)

Nees et al., JMO (2005)


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Conclusions

For laser intensities of 1023 - 1024 W/cm2 gamma-photons

dominate (as the loss mechanism, as the most abundant sort ofparticles, as the main effect in the electron motion).

Electrons are driven by QED-strong field.

All reactions with incoming or outgoing electrons have modifiedprobabilities.

Intensities 1023 W/cm2 combined with the oppositely propagating

1GeV electron beam could allow us to foresee what will occur at

1024 W/cm2.

Diagnostics for >100 MeV gamma-photons are required.

Challenges in modeling: Gamma-emission spectrum, radiation back-reaction, QED

corrections

Radiation transport, gamma-to-pair absorption.

N. M. Naumova-Radiation Back-reaction on Electrons in Relativistically Strong and QED-Strong Fields

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