Nonlinear Optics in Plasmas

What is relativistic self-guiding?

Ponderomotive self-channelingresulting from expulsion of electrons on axis

Relativistic self-focusingresulting from relativistic modification of electron mass

20( , ) 1 ( , ) / 2r t a r t

1210 2

0 ( , ) 8.5 10 [ ] [ / ]a r t m I W cm

What is relativistic self-guiding?

the combinational effect of relativistic self-focusing and ponderomotive self-channeling overcomes the natural diffraction, leading to the self-guiding of the laser pulse.

At

What is Raman forward scattering in a plasma?

What is Raman forward scattering in a plasma?

Setup for characterizing relativistic self-guiding and Raman forward scattering

Setup for characterizing relativistic self-guiding and Raman forward scattering

Side imaging of Thomson scattering for various laser powers

Transverse profiles of the self-guided laser beam

Channel length vs. laser pulse duration and chirp

A longer self-guiding channel is observed for longer pulse duration. Chirp has no effect.

pulse duration

(fs)

linear chirp

(10 fs )(magnitude)

-5 -2

negative chirp positive chirp

55

400

1000

6.2

2.5

Breakup of the laser pulse due to a lower contrast

contrast at -1 ns <5x105

Low contrast produces a longitudinal plasma density gradient which results in bifurcation of the laser beam.

Ne = 1.3x1019 cm-3, E = 310 mJ

Raman spectra for various plasma densities

The frequency shift is equal to plasma frequency

Raman spectra for various laser powers

The frequency shift is independent of laser power.

We can conclude that the frequency shift is due to RFS.

Dependence of RFS on the chirp of a laser pulse

Raman forward scattering is expected to be assisted by a positively chirped pulse and suppressed by a negatively chirped pulse.

Raman intensity vs. laser pulse duration and chirp

0 100 200 300 400 500 600 700

pulse duration (fs)

inte

nsity

(a.

u.)

10

0

20

30

40

1 .0 2 .0

group-delay dispersion ( x10 fs )4 2

positive chirp negative chirp

The intensity of the Raman Stokes satellite is observed to be stronger for positively chirped pulse in comparison to negatively chirped pulse.

Raman spectra vs. laser pulse duration and chirp

inte

nsity

(lo

g sc

ale)

0 -1 -2 -3 -4 -5 -6 -7

55

76 [-0.2]

76 [0.2]

120 [-0.4]

120 [0.4]

170 [-0.6]

170 [0.6]

220 [-0.8]

220 [0.8]

430 [-1.7]

430 [1.7]

640 [-2.5]

pulse duration (fs) [GDD (10 fs )]4 2

640 [2 .5]

negativechirp

positivechirp

( 10 rad/s)14

The narrowing and spread of the Stokes satellite spectrum for positively and negatively chirped pulses respectively confirms that Raman forward scattering is enhanced by positive chirp and inhibited by negative chirp.

Setup for producing a collinearly-propagating second-harmonic probe pulse

Setup for time-resolving the phase modulation

Blue shift of the probe pulse wavelength versus delay

High contrast results in a significant ionization at within 1 ps prior to the peak of the pulse. Such an ionization front excites a plasma wave to seed the growth of Raman forward scattering.

when strong Raman satellite is observed when no Raman satellite is observed.

contrast at -1 ps = 104

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

-1.5

-1

-0.5

0

delay (ps)

(nm

)

contrast at -1 ps = 103

-1.5

-1

-0.5

0

delay (ps)-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

(nm

)

Blue shift of the probe occurs due to the rapid change of plasma density at the ionization front.

Summary

Relativistic self-guiding can be enhanced by increasing pulse duration.

Raman forward scattering is enhanced by positive chirp and suppressed by negative chirp.

Channel bifurcation of relativistic self-guiding can be suppressed by raising the nanosecond-scale temporal contrast.

Raman forward scattering is suppressed when the picosecond-scale temporal contrast falls below a threshold of 10⁴.

Laser-Plasma-Based Electron Accelerator

Acceleration of electrons by an electron plasma wave

+-

+-

+-

+-

+-

pump pulse

plasma wave driven by Raman forward scattering instability

electrons injected by Raman backscattering instability

Raman forward scattering instability can drive an electron plasma wave with a phase velocity close to c. Electrons with initial energy higher than a threshold can be trapped and accelerated by the plasma wave.

pump pulseprobe pulse

plasma wave envelope

Probe delay

Use collective Thomson scattering to measure an electron plasma wave

k 0 k p

k p

k A S

k S

A n ti-S tokes

k 0

S tokes

Scattering efficiency of the probe into the first Stokes and anti-Stokes satellites is

2

2 2 2 20 0 2

0

1 sin ( )

4s

e

P kLn r L

P kL

Scanning the probe delay maps out the the temporal evolution of the electron plasma wave.

2×1019 cm-3

1.8×1019 cm-3

1.5×1019 cm-3

1.3×1019 cm-3

pump pulse: 260 mJ, 275 fs (-)t = 0

Thomson satellites vs. plasma density

The frequency shift is equal to plasma frequency

Thomson satellites vs. probe delay

pump pulse: 260 mJ, 275 fs (-)Ne = 2×1019 cm-3

Temporal evolution of the amplitude of the plasma wave

pump pulse: 260 mJ, 275 fs (-)Ne = 2×1019 cm-3

The decay rate of the electron plasma wave driven by Raman forward scattering is measured to be about 1 ps-1. Since the plasma wave lasts for only 1 ps, the macro-bunch duration of the accelerated electrons should be less than 1 ps.

Acceleration of electrons by an electron plasma wave

The same dependence of the electron number and Raman satellite energy on laser pulse duration and chirp proves that the electrons are accelerated by the plasma wave driven by Raman forward scattering instability.

Ram

an S

toke

s energ

y (a

.u.)

ele

ctro

n n

umbe

r (a

.u.)

Raman satellite

electron number

laser focus at the center of the gas jet

-4 -3 -2 -1 0 1 2 3 4

+chirp -chirp

grating position (mm)

1

10

10-2

102

104

106

8

250 mJ, 55 fs3x1019 cm-3

Total number of electrons accelerated vs. plasma density and laser peak power

scintillator

10

10

10

electron density ( 10 cm ) 19 -3

6

7

5

108

109

1010

1.0 1.5 2.0 2.5 3.0 3.5104

ele

ctro

n n

um

be

r

small divergence angle electron beamlarge divergence angle electron beam

Above an appearance threshold the total number of electrons accelerated increases exponentially with plasma density and laser peak power, and saturates at >1x109.

ele

ctro

n n

um

be

r

10

10

10

6

7

5

108

109

1041.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

laser power (TW)

3.3x1019 cm-3250 mJ

55 fslaser focus at the front edge of the gas jet

Divergence of the electron beam

-4 -3 0 1 2 3 4

angle (degrees)

0

1

2

3

4

inte

nsi

ty (

a.u

.)-2 -1

1.8

Since the source size should be smaller than the laser channel size (10 m), the transverse emittance is lower than 0.1 -mm-mrad, better than that of a state-of-the-art electron gun.

mirror

CCD

color filter

laser

electron beam

gas jet nozzle

Kodak LANEX

vacuum chamber

Al foil

calibratedscintillator-PMT

Low-energy electron spectrum

ele

ctr

on n

um

be

r (a

.u.)

2 4 6 8 100.01

0.1

1

10

e le c t r o n k in e t ic e n e r g y ( M e V )

T=1.8 MeV

mirror

CCD

color filter

laser

electron beam

lead collimator

gas jet nozzle

permanent dipole magnet

Kodak LANEX

vacuum chamber

Al foil

B0

The dispersion of the image on the LANEX under magnetic field identifies that it is indeed from electrons. The electron energy spectrum can be fitted into an exponetial decay with a characteristic temperature of 1.8 MeV

250 mJ, 55 fs3.3x1019 cm-3

focus at front edge

High-energy electron spectrometer

vacuum chamber

dipole

lead collimator

scintillating fiber & PMT array

vir tual source point

electron beammylar window

vacuum chamber

lead collimator

gas jet nozzleQ1 Q2 Q3

quadrupoles

{ dipole

scintillating fiber & PMT array

scintillator & PMT

laser

0 5 10 15 20 25 30 350

50

100

150

200

250

300

350

ele

ctro

n n

um

ber

(a.u

)electron energy: 40 MeV

position (fiber number)

The existence of electrons of a certain energy can be confirmed by checking if they indeed move in the path expected.

High-energy electron spectrum

20 25 30 35 40 4510

electron energy (MeV)

T=28 MeV

T=8.5 MeV

ele

ctro

n n

um

be

r (a

.u.)

102

103

Electrons with kinetic energy up to 45 MeV was observed. The energy spectrum can be fitted into an exponetial decay with a characteristic temperature of 8.5 MeV, a flat region, and a high-energy cut-off.

250 mJ, 55 fs3.3x1019 cm-3

focus at front edge

gas jet position ( m)

50

150

200

250

300

350

450

550

600

250 mJ, 55 fs

Laser channel and electron beam profile vs. gas jet position

0: laser focus at the center of the gas jet

400: laser focus at the front edge of the gas jet

The electron beam with smaller divergence angle is produced when the laser focus is positioned at near the front edge of the gas jet. It is correlated with the onset of relativistic self-guiding.

3.3x1019 cm-3

Laser channel and electron beam profile vs. plasma density and laser peak power

0.27 TW

electron density:

0.27 TW

0.26 TW

0.24 TW

0.2 TW

0.22 TW

0.23 TW

3.4

19c m

-3electron density( 10 )

3.4 1019

c m-3

2.8

2.4

2.1

1.7

1.4

1.0

100 m 10 55 fslaser focus at the front edge of the gas jet

Once the small-divergence electron beam appears, its divergence angle shows little variation with increasing plasma density and laser peak power.

Laser channel and electron beam profile vs. laser pulse duration and chirp

The large-divergence electron beam is stronger for positive chirp, while the small-divergence electron beam is stronger for negative chirp. The onset of the small-divergence electron beam does not correspond to a sudden decrease of the large-divergence electron beam.

100 fs

100 fs

270 fs

270 fs

340 fs

340 fs

75 fs

75 fs

positive

ch

irpn

eg

ative ch

irp

transform limited

55 fs

laser focus at the front edge of the gas jet

250 mJ, 55 fs3.1x1019 cm-3

Summary

The decay rate of the electron plasma wave driven by Raman forward scattering instability is measured to be about 1 ps-1 using probing collective Thomson scattering.

The generated electron beam has a total electron number of >109, a divergence angle of 1.8º, and a maximum electron energy exceeding 40 MeV.

The same dependence of the electron number of the large-divergence electron beam and Raman satellite energy on laser pulse duration and chirp proves that these electrons are accelerated by the plasma wave driven by Raman forward scattering instability.

The appearance of an electron beam with small divergence angle is correlated with the onset of relativistic self-guiding, possibly resulting from a direct laser acceleration mechanism.