Direct observation of ultrafast surface transport of laser-driven fast electrons in a solid
target
Prashant Kumar Singh, Y. Q. Cui, Gourab Chatterjee, Amitava Adak, W. M. Wang, Saima Ahmed, Amit D. Lad,
Z. M. Sheng, and G. Ravindra Kumar
Citation: Physics of Plasmas (1994-present) 20, 110701 (2013); doi: 10.1063/1.4830101
View online: http://dx.doi.org/10.1063/1.4830101
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PHYSICS OF PLASMAS 20, 110701 (2013)
Direct observation of ultrafast surface transport of laser-driven fast
electrons in a solid target
Prashant Kumar Singh,1 Y. Q. Cui,2 Gourab Chatterjee,1 Amitava Adak,1 W. M. Wang,2
Saima Ahmed,1 Amit D. Lad,1 Z. M. Sheng,2,3,a) and G. Ravindra Kumar1,b)
1
Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Mumbai 400005, India
Beijing National Laboratory of Condensed Matter Physics, Institute of Physics, CAS, Beijing 100190, China
3
Key Laboratory for Laser Plasmas (MoE), Department of Physics and Astronomy,
Shanghai Jiao Tong University, Shanghai 200240, China
2
(Received 24 July 2013; accepted 26 September 2013; published online 7 November 2013)
We demonstrate rapid spread of surface ionization on a glass target excited by an intense,
ultrashort laser pulse at an intensity of 3 1017 W cm2. Time- and space-resolved reflectivity of
the target surface indicates that the initial plasma region created by the pump pulse expands at c/7.
The measured quasi-static megagauss magnetic field is found to expand in a manner very similar to
that of surface ionization. Two-dimensional particle-in-cell simulations reproduce measurements
of surface ionization and magnetic fields. Both the experiment and simulation convincingly
demonstrate the role of self-induced electric and magnetic fields in confining fast electrons along
C 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4830101]
the target-vacuum interface. V
The gigantic strides in the development of tabletop
intense ultrashort lasers provide a great impetus to study
diverse areas such as relativistic optics,1 high-energy-density
science,2 laboratory astrophysics,3 and novel compact highenergy charged4 or neutral particle accelerators.5 All these
applications are basically driven by the laser-generated fast
electron beams, which are facilitated by several collisionless
absorption mechanisms.6 The transport of fast electrons is
governed both by the self-generated azimuthal magnetic field
(B)7 and the longitudinal electric field (E) present at the
target-vacuum interface.8 These self-induced fields can redirect most of the energy far away from the laser focal spot by
the well-known E B drift,9 causing significant surface
transport. Self-induced magnetic fields can originate from
hot electron streams and target return current,3,7,10 thermomagnetic phenomena,11 etc. Surface spreading of hot electrons can (a) critically compromise the efficacy of the laser
plasma as a point x-ray source, (b) hinder energy-coupling
into the bulk by deleterious transverse dissipation, and (c)
prevent longitudinal transport by confining hot electrons at
interfaces. Surface transport is therefore a crucial part of the
overall transport process. Some previous experiments10,12,13
and numerical studies9,14 have investigated the role of selfgenerated magnetic fields in surface transport of fast electrons. Most previous measurements focused on the transport
of fast electrons created by long laser pulses10,12,13,15 and/or
used time-integrated methods such as the surface spread of
Ka x-ray and ion emission16 for inferring the lateral transport. A recent study17 has probed surface heat transport in an
aluminum target in the ultrashort pulse regime using optical
reflectometry. However, there were no measurements of the
self-induced fields at the surface. To clearly establish the
role of self-induced electric and magnetic fields in the confinement of electrons along the surface, it is crucial to have
a)
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b)
1070-664X/2013/20(11)/110701/4/$30.00
simultaneous measurements of the spatial extent of the fields
and the ionization spots away from the laser-irradiated
region.
In this letter, we address the crucial physics of fast electron surface transport by a confluence of (i) time- and spaceresolved surface ionization measurement by pump-probe
reflectometry, (ii) time- and space-resolved surface magnetic
field measurements via polarimetry, (iii) surface electric field
measurements via the energy of protons accelerated by the
sheath field at the target front and finally, (iv) two-dimensional
particle-in-cell (2D-PIC) simulations and their comparison
with the experiments. Our temporal resolution on the femtosecond scale and spatial resolution on the micrometer scale
enable clear delineation of the surface transport process. We
observe the non-local nature of this surface ionization process
attributable to the E B drift of the fast electrons. This multipronged approach establishes the physics of the ultrafast laserdriven electron transport correctly and unambiguously.
The experiment was performed at the Tata Institute of
Fundamental Research, Mumbai using a Ti:sapphire chirped
pulse amplification laser system with a laser pulse (800 nm,
30 fs) depositing 32 mJ on target, focused by an f/4 off-axis
parabola to a spot size of 20 lm. A p-polarized laser pulse,
incident on a 5 mm thick BK7 glass target at 40 , was used
to excite the target at a peak intensity of 3 1017 W cm2
(nanosecond contrast 3 106). A pump-probe reflectometry set-up was used to map the temporal and spatial evolution
of the hot dense plasma at the target surface. A small fraction
extracted from the main pulse and frequency-doubled
(400 nm) served as a probe. The time-delayed probe was
focused on target front to a spot of 60 lm of intensity of
1011 W cm2. The reflected signal was fed into a CCD to
capture time- and space-resolved information.
To understand the surface transport, it is essential to
map out the time evolution of electron density in the transverse plane. We address this by capturing spatially resolved
snapshots of the reflected probe at different time delays
20, 110701-1
C 2013 AIP Publishing LLC
V
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Singh et al.
FIG. 1. Space-resolved snapshots of reflected probe at different time delays.
R(a.u.): Reflected signal in arbitrary units.
(Fig. 1). At early time (t ¼ 0.1 ps), we see a bright blob of
size similar to that of the pump spot, the spatial overlapped
region of pump and probe. Soon after, the highly reflecting
area spreads rapidly, indicating a massive and ultrafast ionization of the area well beyond the initially irradiated region.
For a quantitative measure of the extent of surface ionization, an integrated line-out is plotted in the inset of Fig. 2. At
t ¼ 0.1 ps, the signal level is nearly flat across the probe
dimensions. At 0.1 ps a high-reflectivity peak appears at
position of 22 lm, indicated by leftmost vertical yellow line.
After 0.4 ps a second peak appears 18 lm away from the initially excited area (shown by middle yellow line), an indication of non-local nature of surface transport. Close to 0.7 ps,
the entire probe region is excited to high reflectivity, indicating that hot electrons have expanded to a region thrice the
originally excited region. The speed of this surface ionization was calculated to be 4.5 109 cm/s (c/7).
Measurements performed (Fig. 2) with much bigger probe,
FIG. 2. Temporal evolution of the surface excitation captured with much
bigger probe (snapshots not shown here). Inset shows line profile of reflected
probe of Fig. 1, along the vertical direction after averaging pixels along horizontal axis, at different time delays. Each normalized to its peak value.
Phys. Plasmas 20, 110701 (2013)
FIG. 3. Temporal evolution of front side reflectivity from experiment (green
square) and simulation (red circle), compared with (1–A), (blue star), where
A denotes the resonance absorptivity. Inset: temporal evolution of simulated
y-averaged electron density profile. L: electron-density scale length.
of sampling size of 300 lm, show similar expansion speed of
c/7 up to 0.6 ps after which it saturates.
To see the entire transition of this ultrafast plasma dynamics, the temporal evolution of the spatially integrated
reflectivity signal is presented in Fig. 3. Consistent with
Fig. 1, there is a sharp rise in the reflectivity just after the
pump arrival followed by a decay which lasts up to 6 ps.
The reflectivity drops at later times due to absorption in
the evolving plasma. To simulate the observation, a 2D-PIC
simulation was performed using our PIC code KLAPS
(Refs. 18 and 19) with ionization module and binary collisions included.20 The simulation parameters were similar to
that of the experiment, with the exception of hydrogen
atoms being used as the target material instead of BK7 glass
for reducing the requirement of computation resources.
Different materials can result in different target density and
atom species, which may change the electron transport
processes. Obviously, the higher the target density, the
slower the electron transport rate. In this sense, our simulation model with high density hydrogen instead of glass provides a qualitative picture of electron transport. From the
view point of laser interaction including ionization in the
simulation, it is adequate to use hydrogen instead of glass.
In the simulation, the target was comprised of a slab of homogeneous neutral hydrogen atoms of 10nc with a thickness
of 9.6 lm (between x ¼ 12 lm and 21.6 lm) and low density
preplasma with a thickness of 3.2 lm in front of the slab
(Fig. 5). Absorption boundary conditions are used for all
sides of the simulation box, i.e., particles reaching the
boundaries will escape from the simulation box. Moreover,
there is no vacuum region in the target rear side to avoid
possible refluxing effects in our relatively thin target. The
simulated temporal evolution of the reflectivity of the probe
pulse is shown in Fig. 3. The inset of Fig. 3 shows the simulated density profiles at different times, with the measured
scale length L ¼ dx=dðln ne Þ at ne ¼ 4nc (nc and 4nc denote
the critical density for 800 nm and 400 nm, respectively).
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110701-3
Singh et al.
Phys. Plasmas 20, 110701 (2013)
FIG. 4. Snapshot of reflectivity (a) and magnetic field (b) at 0.4 ps time
delay. (c) Temporal evolution of experimental and simulated magnetic field,
(d) proton energy spectrum at front side of the target.
Using the formula in Ref. 21, we calculated the resonance
absorptivity, A with the scale lengths given in the inset,
and found that the value (1–A) is in good agreement with
the reflectivity. We have estimated the plasma expansion
towards the vacuum by the temporal evolution of the
simulated density profile (inset of Fig. 3), which is
3 107 cm/s. Even if we assume a similar speed for the
plasma flow along the surface, it is still two orders of magnitude smaller than the speed of observed surface ionization
(Figs. 1 and 2). This rules out any possible role of bulk
plasma motion in the observed surface transport. The rapid
spread of surface excitation is therefore clearly due to the
lateral transport of the fast electrons.
To ascertain the role of magnetic field, we have carried
out time- and space-resolved surface magnetic field measurements using a two-pulse Cotton-Mouton polarimetry method
(details described elsewhere3,22) simultaneous with the
reflectivity measurements. Except the probe wavelength
(800 nm), all other parameters were similar to the reflectivity
experiment discussed earlier. For illustration, measurements
of reflectivity and magnetic field at a time delay of 0.4 ps are
shown in Figs. 4(a) and 4(b), respectively. Consistent with
the rapid spread of the high reflectivity zone (which indicates
ultrafast electron transport), the magnetic field shows a similar rapid transverse spread. At the same time, the magnetic
field shows similar spatial features in form and extent.
Furthermore, we also present temporal evolution of the spatially integrated magnetic field (Fig. 4(c)). The magnetic
field rises in nearly 200 fs to its peak value of 8 MG and
decreases exponentially with a decay constant of s 0.4 ps.
The temporal evolution of simulated magnetic field is also
shown in the same figure, matching very well with the
measurements.
The spatial extent of the surface ionization driven by the
self-induced fields can be estimated by a simple E B drift
picture.9 The drift speed (vd) is given23 as vd ¼ 108 (E/B),
where vd, E, and B are in units of cm/s, V/cm, and Gauss,
respectively. For an estimation of the target surface electric
FIG. 5. Snapshots of electron density (a), electric field strength (b) at
t ¼ 0.1 ps, 0.3 ps, 0.4 ps, and 1.3 ps. and magnetic field (c) from PIC simulation at t ¼ 0.15 ps, 0.4 ps, 0.58 ps, and 0.95 ps. The laser coming from left to
right as marked by the white arrow in (a), excites the 9.6 lm thick target
kept at x ¼ 12 lm.
field, we carried out ion measurements at the target front
under similar conditions. A high-resolution Thomson parabola spectrometer24 was used to measure the proton energy
spectra (Fig. 4(d)). The maximum energy of the protons
accelerated by the electric field at the target front was found
to be nearly 20 keV. The maximum proton energy25 is given
¼ eELn , where e is the electron charge, E is
as Eproton
max
the front side electric field and Ln is the plasma scale
length. By taking a scale length of 0.5 lm at a delay of
around 1 ps (Fig. 3 inset), we infer a maximum surface electric field of 0.4 GV/cm. With E ¼ 0.4 GV/cm and B ¼ 107 G
(corresponding to 0.95 ps snapshot of Fig. 5(c)), the drift
velocity vd comes to nearly 4 109 cm/s. Interestingly, this
E B drift speed agrees very well with surface ionization
expansion speed calculated in reflectivity measurements
(Fig. 2).
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110701-4
Singh et al.
We now confirm all the above observations by 2D
PIC simulations (computational details described earlier).
Figure 5 shows snapshots of the spatial distributions of electron density, electric field and magnetic field at the same
instant. The electric field at t ¼ 0.1 ps and magnetic field at
t ¼ 0.15 ps are the components of the reflected laser pulse.
The laser massively ionizes the target material within its
penetration region of several micrometers, producing a high
density plasma which reflects the laser. During the laser irradiation, a large flux of hot electrons is produced and they can
penetrate into the neutral background. When the hot electrons move into the target, local charge separation fields and
quasi-static magnetic fields are produced on both sides of the
target. These fields tend to confine the hot electrons within
the target so that they can only transport within the target
along the surface. During the transport process, strong electric fields at the boundary and inside the target are generated,
which are as large GV/cm. These fields continue to ionize
the background media and produce more electrons, resulting
in a much larger ionized area compared to the laser focal
spot. The transverse expanding speed of the ionized area is
estimated to be about ðc=2 2c=3Þ in the simulation,
where c is the light speed in vacuum. This is somewhat
larger than the experimental value. It can be partly attributed
to the much thinner target used in the simulation, where the
electric and the magnetic field at the backside of the target
can confine the hot electrons inside the target, making the
surface transport more efficient. Similar to our experimental
observation, the spatial extent of the magnetic field and the
electron density spread on the target surface are identical.
In conclusion, we have presented a comprehensive
investigation of the ultrafast surface transport of fast electrons created in a solid target by intense, femtosecond laser
pulses. By a combination of experimental methods (pumpprobe spatio-temporal reflectometry, polarimetry, and proton
acceleration measurements), we capture distinct images of
non-local surface ionization and magnetic field and strength
of the electric field at the surface. We establish that the nonlocal ionization at the target front surface is caused by the
E B drift. Our experimental findings are strongly backed
by 2D-PIC simulations. We believe that our results have significant implications for problems involving ultrafast surface
transport of hot electrons, particularly energetic particle
sources and fast ignition of laser fusion.
Z.M.S. thanks the support by NSFC (Grant Nos. 11121504
and 11075105). Numerical simulation has been performed on
the Magic Cube at Shanghai Supercomputer Center. G.R.K.
Phys. Plasmas 20, 110701 (2013)
acknowledges a J. C. Bose grant from the DST, Government
of India. We thank M. Dalui, T. M. Trivikram, and M.
Krishnamurthy for Thomson Parabola ion measurements.
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