Yuelin Li and Stephen V. Milton Advanced Photon Source, Argonne National Laboratory

2002 CLEO, Long Beach, California, May 19-24, 2002, Session CWA

Intensity and pulse shape effect on the Intensity and pulse shape effect on the spectral and angular distribution of spectral and angular distribution of

nonlinear Thomson scattering*nonlinear Thomson scattering*

Yuelin Li and Stephen V. Milton

Advanced Photon Source, Argonne National Laboratory

Argonne, IL 60565

*Supported by the U. S. Department of Energy, Office of Basic Energy Sciences

Contract No. W-31-109-ENG-38


Electron dynamics and radiation in high intensity laser fieldsPonderomotive scatteringViolent accelerationHarmonic and broadband radiation….

Laser acceleration of electronsMeV and GeV electron acceleration…..

Ultrafast X-ray radiation generationNonliear Thomson scattering into X-rayBremsstrahlung X-ray ….

Background and relatedBackground and related


GeometryGeometry

Y.I. Salamin et al

Only electrons initially at rest and on axis are considered, x0=0, 0=0, =0.8 m, w0=10 m, Zr=400 m.


FormulaFormulaField: angular spectrum representation

,4

,24

,4

420

23030

20

32

2

230

22

120

Ir

xEE

IrIkrk

xyEE

Ir

yI

rk

yxI

EE

z

y

x

420

32

2

230

22

120

4

,4

,

Ir

y

c

EB

Ir

xI

rk

xyI

c

EB

c

EB

z

y

yx

,)()cos()

1

11(

,)(1

)sin(

,)(1

)sin(

,)()sin()11(

2012

1

0

4/4

3002

1

0

4/3

2012

1

0

4/2

0021

0

4/1

22

22

22

22

dbbrbkJb

eI

dbbrbkJb

eI

dbbrbkJb

eI

dbbrbkJbeI

bb

bb

bb

bb

.

,1

,1

22

00

200

yxr

wk

bzktb


FormulaFormula

Energy spectrum calculation by Lienard-Wiechert potentials

).(,,0

0

0

Bm

pEepdtpppdt

pr

The dynamics is solved numerically

.)(4

2)/(

2

222

dtennc

e

dd

Id crnti


Single electron caseSingle electron caseMomentum and spectra

0 10 20 30 40 50

0.0

0.5

1.0

0.0

0.5

1.0

0.0

0.5

1.0

a0=0.01, =/2

h (eV)

a0=1, =1.

a0=3, =0.5

d2 I/d

dE

(a.

u. )

-1

0

1

-20 0 20 40 60

-0.01

0.00

0.01

-3

0

3

6

a0=1

px,

pz/m

c

a0=0.01

Time (fs)

pz a

0=3


Single electron trajectory, R-Single electron trajectory, R-frameframe

-0.075 -0.050 -0.025 0.000 0.025 0.050 0.075-0.625

-0.500

-0.375

-0.250

-0.125

0.000

0.125

0.250

0.375

0.500

x/ 0

z/0


Single electron: Spectrum Single electron: Spectrum details details

1 2 3 4 5

0

1

2

3

4

5

e

d

c

b

a

dE

/dd

(a

.u.)

h (eV)Fig. 1. Spectra of single electron irradiated by (a)-(d) 20-fs laser pulse with a0=3 for =40 at

=0, 30, 60, and 90, and (e) with quasi-flat-top 80-fs pulse with a0=3 for =40 at = 90.


Single electron: Angular Single electron: Angular distribution distribution

0

30

6090

120

150

180 0

30

6090

120

150

180

0

30

6090

120

150

180 0

30

6090

120

150

180

0

30

6090

120

150

180 0

30

6090

120

150

180

(b)

(c) (d)

(e) (f)

(a)

Fig. 2. Radiation pattern of the second (solid) and third (dashed) harmonics at =90 (left panels) and 60 (right panels) for (a)-(b) 80-fs quasi-flat-top pulse a0=3, (c)-(d) 20-fs pulse with a0=3 and (e-f) 20-fs pulse with a0=2.


Single electron: conclusion Single electron: conclusion

1 2 3 4 5

0

1

2

3

4

5

e

d

c

b

a

dE

/dd

(a

.u.)

h (eV)

Observations

1. Red shift with intensity and polar angle, explained by theory

)cos1()2/(1 20

a

nn

2. Spectral broadening, modulation, and over lapping are pulse- shape and intensity- dependent and not discussed previously.

3. Angular distribution is also intensity-and pulse shape-dependent

0

30

6090

120

150

180 0

30

6090

120

150

180

0

30

6090

120

150

180 0

30

6090

120

150

180

0

30

6090

120

150

180 0

30

6090

120

150

180

(b)

(c) (d)

(e) (f)

(a)


Collective effects Collective effects

For a collection of electrons, the radiation is calculated as

.)(4

2

)/(

2

222

dtennc

e

dd

Id

j

crntij

jj

.)(4

2)/(

2

222

j

crntij dtenn

c

e

dd

Idjj

When the positions of the electrons are totally random, the only terms survive the integration are the individual terms of each electrons, hence the radiation for a collection of electrons can be approximated as


Z-dependence: Spectra Z-dependence: Spectra

0 1 2 3 4 5 h (eV)

4ZR

3ZR

2ZR

ZR

0

-ZR

-2ZR

-3ZR

h0=1.55 eV

w0=10 m

zr=400 m

a0=3

=90°=42°

-4ZR


Target thickness dependence Target thickness dependence

0 1 2 3 4 5

h (eV)

3ZR

5ZR

7ZR

h0=1.55 eV

w0=10 m

zr=400 m

a0=3

=90°=42°

9ZR


Target thickness: angular Target thickness: angular distribution distribution

0.00

0.25

0.50

0.75

1.00

0

30

60

90

120

150

180

210

240270

300

330

0.00

0.25

0.50

0.75

1.00

0.00

0.25

0.50

0.75

1.00

0

30

60

90

120

150

180

210

240270

300

330

0.00

0.25

0.50

0.75

1.00

0.00

0.25

0.50

0.75

1.00

0

30

60

90

120

150

180

210

240270

300

330

0.00

0.25

0.50

0.75

1.00

0.00

0.25

0.50

0.75

1.00

0

30

60

90

120

150

180

210

240270

300

330

0.00

0.25

0.50

0.75

1.00

3zr

2nd 3rd

5zr

7zr 9z

r


Conclusion Conclusion

Nonlinear Thomson scattering emission spectra and angular distribution are sensitive to the laser intensity, pulse shape and target configuration both on the microscopic and macroscopic level, showing spectral shift, broadening and mixing between harmonics.


References References

1. E. S. Sarachik and G.T. Schappert, “Classical theory of the scattering of intense laser radiation by free electrons,” Phys. Rev. D 1, 2738-2753 (1970).

2. S. K. Ride, E. Esarey, and M. Baine, “Nonlinear Thomson scattering of intense laser pulses from beams and plasmas,” Phys. Rev. E 48, 3003-3021 (1993).

3. S-Y Chen, A. Maksimchuk, and D. Umstadter, “Experimental observation of relativistic nonlinear Thomson scattering,” Nature 396, 653-655 (1998).

4. K. Ta Phus et al., “Synchrotron-like radiation produced from an intense femtosecond laser system,” OSA Conference on Applications of High Field and Short Wavelength Sources IX, October 21–24, 2001, Palm Springs, California.

5. B. Quesnel and P. Mora, “Theory and simulation of the interaction of ultraintense laser pulses with electrons in vacuum,” Phys. Rev. E 58, 3719-3732 (1998), and references therein.

6. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1976).7. Y. Ueshima, Y. Kishimoto, A. Sasaki and T. Tajima, “Laser Larmor X-ray radiation

from low-Z matter,” Laser Part. Beams 17, 45-58 (1999).

Yuelin Li and Stephen V. Milton Advanced Photon Source, Argonne National Laboratory

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