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Under consideration for publication in J. Plasma Phys. 1
Measurement of the Angle, Temperature
and Flux of Fast Electrons Emitted from
Intense Laser-Solid Interactions
D. R. Rusby1,2, L. A. Wilson1, R. J. Gray2, R. J. Dance2, N. M. H.
Butler2, D. A. MacLellan2, G. G. Scott1, V. Bagnoud3, B. Zielbauer3,
P. McKenna2, D. Neely1,2
1STFC Rutherford Appleton Laboratory, Oxfordshire OX11 0QX, UK
2SUPA Department of Physics, University of Strathclyde, Glasgow G4 0NG, UK
3PHELIX Group, Gesellschaft fur Schwerionenforschung, D-64291 Darmstadt, Germany
(Received ?; revised ?; accepted ?. - To be entered by editorial office)
High-intensity laser-solid interactions generate relativistic electrons, as well as high-
energy (multi-MeV) ions and X-rays. The directionality, spectra and total number of
electrons that escape a target-foil is dependent on the absorption, transport and rear
side sheath conditions. Measuring the electrons escaping the target will aid in improv-
ing our understanding of these absorption processes and the rear-surface sheath fields
that retard the escaping electrons and accelerate ions via the Target Normal Sheath Ac-
celeration (TNSA) mechanism. A comprehensive Geant4 study was performed to help
analyse measurements made with a wrap-around diagnostic that surrounds the target
and uses differential filtering with a FUJI-film image plate detector. The contribution of
secondary sources such as x-rays and protons to the measured signal have been taken into
account to aid in the retrieval of the electron signal. Angular and spectral data from a
high-intensity laser-solid interaction are presented and accompanied by simulations. The
total number of emitted electrons has been measured as 2.6×1013 with an estimated
total energy of 12 ±1J from a 100µm Cu target with 140J of incident laser energy during
a 4 ×1020 W/cm2interaction.
1. Introduction
When a high-intensity laser ( I >1018W/cm2) pulse interacts with a solid target, elec-
trons are accelerated on the front surface and travel through the target where they will be
emitted from the rear surface of the target, accelerating protons and heavy ions with them
(McKenna et al. (2004)). The source of these electrons is the initial absorption processes
that occur at the front surface. At intensities ∼1016 W/cm2the dominant absorption
processes are resonance absorption and Brunel heating (Brunel (1987); Wilks & Kruer
(1997)). The latter is particularly dependent on minimal pre-plasma (scale length ( Ls)<
laser wavelength (λ)). Both of these processes accelerate the electrons perpendicular to
the target surface whereas for higher intensities (>1018 W/cm2) the ponderomotive
force (J×B) acts along the laser direction where there are intensity gradients away from
the peak. The dominant process has been shown to depend on the scale length of the
pre-plasma; Brunel heating for shorter scale lengths and the J×B mechanism for inter-
mediate scale lengths (Ls≈5λ) (Santala et al. (2000)). Angular measurements of these
absorption processes have been made (Norreys et al. (1999)) and different angular dis-
tributions have been proposed/observed due to longer pre-plasma influences on the front
surface (P´erez et al. (2014); Courtois et al. (2009)). The transport of electrons through
2D. R. RUSBY et al
the target is significantly influenced by the internal magnetic fields created by the elec-
tron beam and also the background resistivity(McKenna et al. (2011); MacLellan et al.
(2013)). The first electrons to reach the rear surface escape almost unimpeded, setting
up a rear-surface sheath. The electrons reflected by the electrostatic field reflux inside
the target, which increases the total emitted x-rays from the target (Quinn et al. (2011);
Fiorini et al. (2014); Myatt et al. (2007)). This time-evolving electrostatic force grows
stronger with time over the duration of the laser pulse, reducing the number and altering
the spectra of the escaping electrons (Link et al. (2011)). The ability to measure the entire
emitted beam of electrons from the rear surface with angular and spectral distributions
provides new insight into the front and rear surface field evolution processes.
Many significant measurements of the angular and spectral distributions of the elec-
trons emitted from the rear surface and bremsstrahlung from internal electrons stopping
within the target have been made and reported in the past (Hatchett et al. (2000); Ed-
wards et al. (2002); Schwoerer et al. (2001); Chen et al. (2013); Norreys et al. (1999)).
However, these measurements are often made at a single point as opposed to a contin-
uous angular distribution. These techniques can be very susceptible to beam pointing
or non-uniformities that may arise during the laser-plasma interaction. Measurements of
the entire beam escaping the target can yield improvements in the knowledge of such
interactions.
In this paper, we have used an angular wrap-around stack previously introduced by
Gray et al. (2011) to measure the total forward distribution of electrons escaping the
target. The diagnostic is a differentially filtered cylindrical stack with the target posi-
tioned in the centre. Significant improvements in the understanding of the diagnostic
sensitivity have been made using simulations of both electron and x-ray absorption and
scattering to infer spectral information about the escaping electrons. The diagnostic has
also been used on a laser-solid interaction experiment with the aim of measuring the
escaping electron distribution.
2. Design
The wrap-around stack is a 270ocylindrical diagnostic designed to provide angular
information about the escaping particles/radiation from the target which is positioned
at its centre, as shown in Figure 1. Multiple layers of Fuji BAS-TR image plate (IP)
which sits inbetween 0.85mm thick Fe filtering is used to infer information on the emit-
ted spectra. To initially ensure that the measured signal on the IP layer was primarily
electrons, simulations were conducted using the ion stopping code SRIM (Ziegler et al.
(2010)) to calculate the minimum filtering required to stop any protons accelerated from
the target contributing to the signal. During solid-target interaction, maximum proton
energies of 30MeV were measured with a separate diagnostic, which require the first layer
of Fe filtering to be 1.7mm thick as shown in Figure 1. The filtering design, highlighted
in Figure 1, separates the electron signals spectrally. The diagnostic is usually positioned
above or below the horizontal axis to enable other diagnostics to monitor the target si-
multaneously, and given the depth of 50mm of the plates; this also provides a vertical
angular distribution over ∼30o. The open side of the diagnostic enables the focusing
laser light to reach the target.
3. Simulations
To investigate how the differential filtered layers of IP inside the wrap-around stack
respond to electrons, the Monte Carlo code Geant4 (Agostinelli et al. (2003)) was em-
Measurement of the Angle, Temperature and Flux of Fast Electrons 3
Figure 1. Schematic of the diagnostic arrangement of Fuji BAS-TR Image Plate (IP) between
0.85mm Fe filters used in the wrap-around stack that covers 270 degrees around the target.
Figure 2. (a) The fractional absorption in the IP layers from mono-energetic electrons incident
onto the array of Fe filters as a function of energy. (b) The fractional absorption of Relativistic
Maxwellian electron distributions normalised to the maximum of each layer. The shaded region
represents where the signal has dropped to 10% on that layer. A temperature extraction is
unreliable below this region due to the contribution of X-rays.
ployed. The stack arrangement was built as shown in Figure 1 and the simulations were
performed using 106electrons, with each run using a single energy between 1MeV to
100MeV. Separating the energy deposited on each layer was achieved by Geant4 provid-
ing the position and amount of energy accumulated from the simulation results. Dividing
the energy in each layer of IP by the total input energy yields the fractional deposited
energy in each layer. The resulting response curve of the diagnostic for mono-energetic
electrons is shown in Figure 2 (a). Due to the heavy filtering required to stop proton
contamination, the threshold energy for electrons is approximately 2MeV.
An escaping relativistic Maxwellian electron distribution is assumed as the output to
represent the experimental escaping electron distribution. The output from these sim-
ulations can be compared to experimental data to find the temperature of the escaped
electron distribution. The normalised fractional absorbed energy from an incident rela-
tivistic Maxwellian electron distribution is show in Figure 2 (b).
Similar to the mono-energetic electrons shown in Figure 2 (a), each layer has a threshold
temperature for which electrons can be detected. The areas in which the absorption is
above this threshold can be considered a regions in which the data from the diagnostic
are reliable, or the working range of the diagnostic. This is shown by the shaded region in
2 b) where the absorption of each layer is 10% of the maximum for that layer. Below this
the signal may be dominated by x-rays. Monitoring the signal ratios between the layers
provides a diagnosis of the electron temperature. The dependence of the signal ratios on
the temperature is shown in Figure 3. The plots are truncated at the point at which the
fractional absorption of each layer has dropped to 10%.
4D. R. RUSBY et al
Figure 3. The ratios of layer 1 to each sequential layer for the total energy absorbed by the
image plate as a function of temperature.
As well as the target being a source of protons, it will also generate many bremsstrahlung
x-rays as the electrons pass through it. These x-rays will make a simultaneous contri-
bution to the IP signal regardless of the design/arrangement of layers. To estimate the
impact of the x-ray signal, electrons were sent into a thin target in Geant4 creating a
bremsstrahlung spectrum. An example target of 100 µm-thick Cu was used. The spectra
and numbers of electrons and x-rays that reached the back of the target were recorded.
These were both sent separately into the wrap-around stack and the absorption of en-
ergy into the IP layers was recorded, similar the previous simulations. The total energy
absorbed was found by summing the absorption for the x-rays and electrons, with the
escaping electron numbers reduced to 10% and 5% to act as upper and lower bound for
the expected escaping electron fractions (Link et al. (2011); Myatt et al. (2007); Fiorini
et al. (2014)). The electrons which reflux inside the target are not intrinsically included
in Geant4. Previous studies of the influence of refluxing on x-ray emission suggest an
increase of a factor of 2 (Fiorini et al. (2014)) for an escaping fraction of 10 %. Including
this consideration of refluxing, the signal due to x-rays makes up <5 % for the first two
layers of the diagnostic at a temperature of 1.5MeV; this increases to up to 20 % for the
later layers. As the temperature increases the x-ray contribution decreases as more elec-
trons are able to penetrate the deeper layers of the diagnostic. Below these temperatures,
which are beyond the working range of the diagnostic, the x-ray contribution increases
to values above 50 %.
4. Experimental Data
The wrap-around stack was installed on an experiment at the PHELIX laser system
at GSI in Darmstadt Bagnoud et al. (2010), which is capable of delivering up to 140J
of 1µm radiation pulse length of ∼700fs onto a 4µm focal spot, achieving intensities
of 3.9×1020 W/cm2. The contrast of the laser a nanosecond before the main pulse
is approximately 10−7. The S-polarized laser pulse was focused at 20 degrees onto a
100µm Cu target positioned in the centre of the 270owrap-around stack, with the stack
positioned just below the horizontal axis to enable a line of sight to other diagnostics.
Measurement of the Angle, Temperature and Flux of Fast Electrons 5
Figure 4. (a) PSL signal from the remapped layers of IP between the Fe filtering from a 140J
shot onto a 100um Cu target. (b) a polar plot of the data. The peak emmission apears to be
close to laser axis.
The first IP subtends a larger solid angle than the sequential layers and therefore the
data have been remapped to enable pixel to pixel ratio comparison. The measurements
taken on the angular wrap-around stack are shown in Figure 4 along with a polar plot
showing the incoming laser. It is quite clear to see that the majority of the electrons are
directed along the laser axis as is expected from interactions of this intensity (Malka &
Miquel (1996); Wilks & Kruer (1997)).
The digitalisation process of the IP converts the dose to PSL (Photo-Stimulated Lumi-
nescence) which is also a linear representation of the signal. Using the earlier simulations
showing that only electrons above 2MeV reach the IP layers and calibrations by Tanaka
et al. (2005), where the numbers of electrons per PSL were reported, the total number of
electrons can be calculated. Summing the total PSL signal on the first layer of IP leads
to the incident electron signal absorbed being ∼8×1010 on layer 1.
The signal ratio from this data can be calculated by dividing the signal in first layer by
the signal in any of the following layers pixel by pixel. An example of the ratio measured
from IP layer 1 to IP layers 2 and 3 is show in Figure 5, together with an angular plot
of the PSL data from layers 1,2 and 3. The upper and lower ratios obtained from each
comparison are plotted with the expected ratios as a function of temperature produced
from the simulations. This is shown on Figure 6 with the bounds shown as horizontal
lines intercepting the simulated ratios. Ratios corresponding to the escaping electron
fractions of 10% and 5% are also shown but do not differ significantly. The overlapping
shaded regions represent where data crosses the 10% ratios, which is between 1.4 and
1.7MeV. The working range of layers 1-4 set in section 3 puts the experimental data out
of range as can be seen in Figure 5.
For the temperatures of 1.4 and 1.7MeV, the number of electron escaping the target
can be estimated from the previously quoted total absorbed electrons by multiplying
by the known absorption fraction for these temperatures from the simulations shown in
Figure 2 (b). This yields an incident electron number of ∼2.6×1013 . This value assumes
that the escaping electrons are symmetric (above and below the horizontal axis) and as
the diagnostic is positioned just below the axis it will therefore capture 50 % of the beam.
Based on a single temperature distribution and the average energy of the electrons
leaving the target from the previous simulations, a total escaping electron energy of
∼12J±1J is obtained. This estimation is uses the assumption of a single temperature
6D. R. RUSBY et al
Figure 5. Angular profiles of the data shown in Figure 4(solid-lines,left-axis) with the ratios
of layers 1-2 and 1-3 (dotted-lines,right-axis) The ratios do not change quickly over the entire
angular range. The maximum and minimum of the ratios are taken and used as upper and lower
bounds in Figure 6.
Figure 6. Ratios of layer 1 to each sequential layers from a relativistic electron beam passing
through a 100um Cu target with an upper limit of the escaping electron fraction of 10% and a
lower limit of 5%. The data, represented by the horizontal lines, intersects the simulated ratios
which is shown by the shaded regions. The overlapping area for this shaded region lays between
the temperatures of 1.4 and 1.7MeV. For the ratio 1-4, the ratio is outside the working range of
the diagnostic.
Measurement of the Angle, Temperature and Flux of Fast Electrons 7
distribution, however it has been shown that the internal electrons can have a dual-
temperature distribution by monitoring the x-ray spectra (Chen et al. (2009); Zulick
et al. (2013)). Knowing this, future experiments using this diagnostic are planned in
conjunction with simultaneous x-ray and electron spectrometer measurement which will
provide a more accurate temperature diagnostic.
5. Conclusions
The response of a cylindrical electron diagnostic, designed to provide angular and
spectral information regarding the electrons escaping from a solid target has been as-
sessed. The first layers of filtering eliminates any proton contribution to the first layer
and any sequential layers. Using Monte-Carlo simulations, the response of each IP layer
of the diagnostic has been analysed for mono-energetic and relativistic Maxwellian elec-
tron distributions. Using the energy absorbed for these given electron distributions, an
electron temperature where the diagnostic can be reliable has been found for each layer
of IP. Experimentally the diagnostic has been used to measure half an escaping electron
beam with ∼2.6×1013 electrons with a temperature between 1.4 and 1.7MeV from a
3.9×1020 W/cm2interaction. Future experiments using this diagnostic are planned in
conjunction with x-ray and electron spectrometers to generate a more complete picture
of the interaction and help provide better estimates of the total energy of the escaping
electrons.
The authors gratefully acknowledge the expert assistance of the PHELIX laser opera-
tions team and funding from EPSRC (Grant Nos. EP/J003832/1 and EP/K022415/1).
This work has been carried out within the framework of the EUROfusion Consortium
and has received funding from the EURatom research and training programme 2014-
2018 (grant agreement No 633053) and from LASERLAB-EUROPE (grant agreement
no. 284464, EC’s Seventh Framework Programme). The views and opinions expressed
herein do not necessarily reflect those of the European Commission. Data associated with
research published in this paper is accessible at http://dx.doi.org/10.15129/f774dd94-
1861-47d5-b01e-04dda4a97292.
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