Post on 05-Jan-2016
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.