1992
IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 40, NO. 8, AUGUST 2012
High-Energy Bremsstrahlung Diagnostics to
Characterize Hot-Electron Production in
Short-Pulse Laser-Plasma Experiments
Anthony L. Meadowcroft and Ray D. Edwards
Abstract—Short-pulse (< 10 ps) high-intensity (1019 −
1021 W · cm−2 ) laser-target interactions produce high-density
plasmas, in which a hot (nonthermal) collisionless electron population is generated via a number of energy absorption mechanisms.
A key requirement in many applications of these interactions
is to achieve maximum conversion efficiency of laser energy
into hot electrons of a specific energy. Measurement of the
hot-electron temperature and the associated hot-electron fraction
supports the understanding of energy absorption mechanisms
present in the 1019 −1021 W · cm−2 intensity regime. One highly
useful signature of hot-electron generation is the bremsstrahlung
radiation emission due to the hot electrons interacting electromagnetically with cold target atoms. We present the design, characterization, and modeling of two target diagnostics to measure the
high-energy (100 keV–2 MeV) bremsstrahlung emission from
hot electrons in laser-plasma experiments; a thermoluminescent
dosimeter (TLD) array and a hard X-ray spectrometer (HXRS).
These diagnostics will exploit new techniques to determine the
hot-electron distribution generated with the short-pulse beamlines
of the upcoming high-power Orion laser system at AWE. Past
bremsstrahlung dose measurements obtained with a TLD array
(of similar design to the Orion one) are used to demonstrate
how the bremsstrahlung production efficiency, an indicator of
hot-electron generation, can change with laser parameters, target
type, and experimental geometry. In addition, we use results from
characterization of the HXRS, a diagnostic which collects channel
charges in defined bremsstrahlung spectral ranges, to establish a
new method enabling the diagnosis of hot-electron temperatures.
TABLE I
D IAGNOSTIC T ECHNIQUES TO M EASURE THE
H OT-E LECTRON E NERGY D ISTRIBUTION
Index
Terms—Bremsstrahlung
dose,
high-energy
bremsstrahlung emission, laser-plasma experiments, plasma diagnostics, short-pulse laser–target interactions, X-ray detectors.
I. I NTRODUCTION
S
HORT-PULSE (< 10 ps) laser-target interactions at intensities of 1019 −1021 W · cm−2 produce a hot (nonthermal) collisionless electron population via a number of energy
absorption mechanisms, primarily by Brunel absorption (or
vacuum heating) at low to moderate intensities and by direct
ponderomotive acceleration (or j × B heating) at the highest
intensities. These mechanisms, like resonance absorption, are
collisionless in nature. Unlike resonance absorption, however,
Manuscript received July 21, 2011; revised February 27, 2012; accepted
May 4, 2012. Date of publication June 21, 2012; date of current version
August 7, 2012.
The authors are with the Department of Plasma Physics, AWE Aldermaston, RG7 4PR Berkshire, U.K. (e-mail: [email protected];
[email protected]).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPS.2012.2201175
they are applicable to very short scale-length plasmas of the
kind common in short-pulse laser-matter interactions. Accurate
measurement of the hot-electron energy distribution supports
the understanding of various energy absorption mechanisms
present in the 1019 −1021 W · cm−2 intensity regime.
Past measurements of the hot-electron energy distribution have been obtained by a number of methods, including
electron spectrometers [1]–[3], Kα X-ray emission [4], [5],
bremsstrahlung radiation emission [6]–[9], and fast ion [10]
measurements. The advantages and disadvantages of using
these diagnostic techniques in the measurement of hot electrons
are summarized in Table I [11]–[14].
For short-pulse laser-target interactions at intensities of
1019 −1021 W · cm−2 , electron energies may be on the order
of several megaelectronvolts, with associated hot-electron temperatures of > 100 keV. These hot electrons interact with the
cold background material of the target to produce energetic
bremsstrahlung emission of > 100 keV. Unlike measurements
0093-3813/$31.00 © 2012 IEEE
MEADOWCROFT AND EDWARDS: DIAGNOSTICS TO CHARACTERIZE HOT-ELECTRON PRODUCTION
1993
made using electrons, fast ions, and Kα X-rays, the > 100-keV
bremsstrahlung emission clearly reveals the presence of two
or more hot-electron temperature components [15]. In order
to measure the hot-electron energy distribution, information on
both the hot-electron temperature and the hot-electron fraction
(which may be determined from the hot-electron temperature
[16]) is required.
The short-pulse beamlines of the upcoming high-power
Orion laser system at AWE will last ≈1 ps, and they will focus
onto targets at 1019 −1021 W · cm−2 intensities. Two target
diagnostics will be used to measure the resulting hot-electron
energy distribution by recording bremsstrahlung emission in the
range of 100 keV–2 MeV: a thermoluminescent (TL) dosimeter (TLD) array and a hard X-ray spectrometer (HXRS). In
order to diagnose the hot-electron production efficiency in a
laser–target interaction, the bremsstrahlung dose is modeled
and compared to the dose recorded by the TLD array. Hotelectron temperatures will be determined from measurements
of the bremsstrahlung emission in defined spectral ranges with
the HXRS diagnostic, using the difference in collected channel
charges in a technique similar to that utilized by a Ross pair
spectrometer. In this paper, we present the design, characterization, and modeling of the TLD array and the HXRS diagnostics
to acquire hot-electron distribution data from impending shortpulse laser-plasma experiments on the Orion laser.
II. TLD A RRAY D IAGNOSTIC
A. TLD Array Design
The Orion TLD array measures bremsstrahlung radiation
dose levels generated in the electromagnetic pulse environment
of a laser-plasma interaction. An overview of the diagnostic is
shown in Fig. 1. The Orion TLD array consists of nine TLD
collimators. The purpose of the collimator is to restrict the lineof-sight to the target chamber center (TCC). Each collimator is
fielded at the same radial distance from the TCC but at different
angles with respect to the laser axis to measure the anisotropy of
bremsstrahlung radiation emission (see Section II-B). Ten-inch
manipulators (TIMs) provide a practical means of deploying
sets of collimators over a total angular range of ±60◦ with
respect to the laser axis, within the Orion target chamber and
at equidistant location from the target. The collimators each
encloses a series of pots containing TL detector powder and
metal filters or “slugs.” A combination of TL lithium fluoride (LiF) phosphor and various thicknesses of tungsten slugs
enables bremsstrahlung radiation dose measurements over an
energy range of ∼0.1–20 MeV.
B. Modeling Bremsstrahlung Emission From Short-Pulse
Laser–Target Interactions
In order to be able to predict the dose expected at a given
location from a particular target configuration, one must first
be able to model the bremsstrahlung emission arising from
laser-target interactions. Data for experiments on the PETAL
laser at the Atomic Energy and Alternative Energies Commission (CEA), France, have been applied to simulations of
Fig. 1. Overview of the Orion TLD array: (a) Breakdown of structure,
(b) TIM, (c) deployment of TLD collimators on a TIM, (d) TLD collimator,
and (e) TLD collimator components.
bremsstrahlung emission on Monte Carlo N-Particle Code [17]
in conjunction with two different codes, CALDER at the CEA
[18] and PSC at the AWE [19], which are used to predict
electron generation for a laser beam incident on a gas jet target
(detailed as follows). The codes have been benchmarked against
published results, which have been obtained using accelerators
with monoenergetic electron beams [20].
The experiments considered use two different target configurations (see Fig. 2): a gas jet with a separate bremsstrahlung
1994
Fig. 2. Solid target and gas jet–solid target configurations for short-pulse
laser–target experiments.
converter and a solid metal plate. Electrons are accelerated
to produce bremsstrahlung radiation by different mechanisms
in each target configuration. In the solid target configuration,
ponderomotive acceleration occurs, whereas in the gas jet–solid
target configuration, self-modulated laser wakefield acceleration occurs.
A gas jet-solid target produces more efficient bremsstrahlung
emission for two reasons. First, self-modulated laser wakefield
acceleration generates a self-collimated and almost monodirectional (< 5◦ off-axis) beam of electrons incident on the target;
in ponderomotive acceleration, the electrons are incident on the
target over a broad range of angles. Second, a laser electromagnetic wave does not propagate very far into the solid target
material since the refractive index of the plasma becomes too
high; in laser wakefield acceleration, high-amplitude plasma
waves generated by the interaction of laser light with the plasma
medium accelerate the electron beam from the gas jet.
At energies beyond ∼1 MeV, the bremsstrahlung emission
becomes rather anisotropic due to Compton scattering, and the
angular distribution of scattered radiation is described by the
Klein–Nishina formula [21]. This leads naturally to anisotropy
in the recorded dose. As the gas jet-solid targets produce more
bremsstrahlung emission, they allow the dose anisotropy to be
more accurately measured, and so, simulations of the emitted
bremsstrahlung spectrum, including anisotropy contributions
from Compton scattering, were obtained for those experiments.
The simulation used for the dose model (see Section II-C)
included the maximum possible output of the PETAL as input
parameters: 3.6 kJ in 0.5 ps, a focal spot diameter of ≈ 20 μm,
a laser wavelength of 1.053 μm, and an intensity of ≈ 2 ×
1021 W · cm−2 , incident on a helium gas jet–tungsten target of
4-mm thickness. The simulated PETAL bremsstrahlung spectrum is shown in Fig. 3. Note that the maximum bremsstrahlung
yield is shown in Fig. 3 (detection along the target normal
direction only, which is aligned with the laser axis). Also,
energies are shown up to 400 MeV, rather than the 20-MeV
upper energy limit considered for the diagnostics in this paper.
However, most of the bremsstrahlung flux is emitted around
energies of 1–10 MeV (at 10 MeV, the bremsstrahlung yield
is already ∼10% of that at 1 MeV).
IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 40, NO. 8, AUGUST 2012
Fig. 3. Simulated bremsstrahlung spectrum produced by a gas jet-solid target
for the PETAL, generated with codes that have been validated against experimental data. The laser irradiance was ≈2 × 1021 W · cm−2 , incident on a gas
jet-tungsten plate target of 4-mm thickness.
Fig. 4. Schematic of the experimental configuration, with the relevant physical quantities identified.
that are important at each location. This information can be
used to help derive a simple model for the absorbed dose.
The calculations of how the bremsstrahlung dose D scales
with laser and target parameters assume that D ∝ Iλ2 [9], [22]
(for laser intensity I and laser wavelength λ), D ∝ Z [21], [23]
(for target atomic number Z), and D is dependent on the type
(gas or solid) of target. Dose has been reported to change with
solid target thickness for short-pulse experiments when using
target thicknesses in the range of 0.1–2.0 mm [23], but these
measurements were not filtered from high-energy electrons
emitted from the target. High-energy electrons contribute significantly to the dose measurement. Further experimental data
[24], [25], with filtering of high-energy electrons, have been
collected for target thicknesses within the range of 0.5–5.0 mm
considered in this paper. These results indicate some variation
of dose with target thickness but with no clear correlation. As
the laser-target interaction yields a spectrum of hot electrons
and the exact relationship between dose and target thickness
is unknown, the model initially assumes that D is independent
of target thickness. Comparison of the model calculation with
experimental data may then be used to determine how the target
thickness affects the bremsstrahlung production efficiency and,
thus, D.
Since bremsstrahlung dose is total bremsstrahlung energy
absorbed per unit mass of absorbing material, it follows that
C. Bremsstrahlung Dose Model
Fig. 4 shows the geometry of the general type of experiment
being considered, as well as identifying the physical quantities
1
D(φ, θ, E) =
m
∞
NX (φ, θ, E) dE
0
(1)
MEADOWCROFT AND EDWARDS: DIAGNOSTICS TO CHARACTERIZE HOT-ELECTRON PRODUCTION
where
D
m
NX
E
φ
θ
measured in grays;
mass of LiF phosphor in kilograms;
number of bremsstrahlung photons incident on the LiF
phosphor;
bremsstrahlung photon energy in joules;
angle between the laser axis and the target normal;
angle between the emitted bremsstrahlung photon and
the target normal.
In order to estimate NX , we use the simulated gas jet-solid
target bremsstrahlung spectrum for the PETAL (see Fig. 3).
Additionally, we implement the solid angle of πa2 /b2 for each
TLD pot (where a is the radius of the collimator channel and
b is distance of the pot from the target) and the filtering or absorption of bremsstrahlung by tungsten slugs and LiF phosphor
(E). Including normalization of
giving a spectral response SR
the bremsstrahlung spectrum, the number of bremsstrahlung
photons incident on the LiF phosphor for a solid target using the
laser and target scaling described earlier, with a point source, is
given by
NX (φ, θ, E) = 1.0 × 10−23 Zs(φ, Iλ2 )
× Iλ2 SR
(E)
a 2
b
ψ(φ, θ, E)
(2)
where
s(φ, Iλ2 )
I
λ
Z
ψ(φ, θ, E)
dose scaling for a gas jet–solid target to a solid
target;
laser intensity in watts per square centimeter;
laser wavelength in micrometers;
target atomic number;
bremsstrahlung yield per solid angle in photons
per steradian.
An important consideration when measuring the dose from
a short-pulse laser-target interaction is the laser prepulse. Prepulses may form preplasmas on the surface of a solid target prior to arrival of the main pulse. The preplasma has
a significant effect on laser-solid target interaction because
the refractive index of the plasma inhibits propagation of the
laser electromagnetic wave (see Section II-B). In comparison,
a gas jet-solid target interaction results in a larger proportion of the incident laser energy producing a self-collimated
monodirectional electron beam incident on the target. Therefore, a larger amount of preplasma may be produced for the
solid target configuration in comparison to the gas jet-solid
target configuration at increased laser intensity. Increasing the
laser intensity, however, may also produce either a larger hotelectron fraction or higher hot-electron temperatures in either
target configuration, which results in increased bremsstrahlung
emission. The resulting change in dose may be explained by
a change in bremsstrahlung production efficiency, and this is
implemented in the model using the dose scaling s(φ, Iλ2 ).
Therefore, the dose scaling s(φ, Iλ2 ) can be used to infer the
hot-electron fraction for a given laser-target interaction. Using
(1) and (2), the calculation giving the bremsstrahlung dose
1995
for collimator pot i [see Fig. 1(e)] at 1 m in milliradians is
given by
Di (φ, θ, E) =
1 × 10−18
Zs(φ, Iλ2 )
m
∞
× Iλ a
2 2
ψ(φ, θ, E)SR
(E)dE
(3)
0
where m is in milligrams and a is in millimeters.
As the angular dependence of the dose scaling depends on
the mechanism for bremsstrahlung production in the target,
it is assumed that the scaling takes the form s(φ, Iλ2 ) =
f (φ)f (Iλ2 ), where f is a function. In order to minimize
the preplasma contribution to the bremsstrahlung production efficiency, s(φ, Iλ2 ) was initially evaluated from Vulcan
100-TW laser experimental data [26] (with laser intensities
up to ≈ 7 × 1019 W · cm−2 · μm2 ) rather than from PETAL
experimental data (with laser intensities up to ≈ 2 × 1021 W ·
cm−2 · μm2 ). An expression for f (φ) was determined from filtered TLD measurements using the gas jet-solid target and solid
target experiments described in [26]. The value of s(φ, Iλ2 ) is
then normalized by setting f (Iλ2 ) = 1 for the Vulcan 100-TW
experiments. For other short-pulse laser-target experiments,
where prepulse characteristics are likely to differ (e.g., longer
pulse duration), the dose scaling is adjusted by setting f (Iλ2 )
such that the dose calculation has a best fit to experimental
results. It should be noted that, since prepulse effects and
bremsstrahlung production efficiency for a solid target are
inextricably linked, prepulse contributions are subsumed in the
evaluation of f (Iλ2 ).
D. Dose Model Validation
In order that (3) could be evaluated, a new code,
bremsstrahlung radiation dose calculator (BRADDOC), was
written in IGOR Pro [27]. BRADDOC consists of an algorithm
in which the integral in (3) is solved analytically and other parameters are changed until a solution is found. Besides handling
the complexity of the calculation, IGOR has a number of useful
features that can be implemented easily, such as a simple user
interface for data entry and altering code parameters, real-time
monitoring of the calculation, and clear graphical output.
BRADDOC results were initially generated using actual Vulcan 100-TW laser experimental parameters given in Table II.
A best fit was subsequently obtained by allowing for uncertainty in the focal spot size (laser spot for the solid target,
a focused electron beam for the gas jet–solid target), which
primarily affects the dose magnitude, as well as the angle of the
laser axis with respect to the target normal, which primarily affects the shape of the dose distribution (see Fig. 5). Subsequent
comparison of Vulcan PW experimental data with BRADDOC
results (see Fig. 6) confirmed that the dose scaling takes the
form s(φ, Iλ2 ) = f (φ)f (Iλ2 ). As mentioned in Section II-C,
this can be explained by the increase in preplasma formation,
the hot-electron fraction, or hot-electron temperature at increasing laser intensity. Also, using a target thickness of less than
1996
IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 40, NO. 8, AUGUST 2012
TABLE II
BRADDOC I NPUT PARAMETERS FOR F IG . 5
Fig. 6. Experimental data in markers and BRADDOC results in solid/dashed
lines. TLD pot 2: (Red) Best fit BRADDOC results to Vulcan 100-TW data
with initial gas jet-to-solid target scaling s(φ, Iλ2 ), BRADDOC results with
no scaling applied to f (Iλ2 ) for (solid green, pink, and gray lines) 1-mm ·
W targets with target normal along the laser axis and for (solid blue line) a
4-mm · W target with target normal at 15◦ to the laser axis, and (dashed lines)
best fit BRADDOC results to Vulcan PW data with scaling of f (Iλ2 ) as given
in Table III.
TABLE III
S UMMARY OF THE S CALINGS A PPLIED TO f (Iλ2 ) TO P RODUCE
B EST F IT BRADDOC R ESULTS TO V ULCAN PW DATA
Fig. 5. (Markers) Bremsstrahlung dose results for the Vulcan 100-TW laser
[5] and (solid line) BRADDOC results for (a) solid tantalum target 1.75 mm
thick and (b) helium gas jet-and-solid gold target. Note that actual experimental
errors are not shown; they have been assigned to show dose values with
10% uncertainty to check code reproducibility (given uncertainty in prepulse
contribution) and experimental alignment to within ≈ ±2.5◦ .
≈1.5 mm leads to an increase in the bremsstrahlung production
efficiency (see Table III). This indicates that, at a given laser
intensity, there is an optimum target thickness required to max-
imize the bremsstrahlung production efficiency. Increasing the
target thickness stops more hot electrons, and this yields more
bremsstrahlung. However, bremsstrahlung self-absorption also
rises with increased target thickness. If the target thickness is
reduced too much, not all hot electrons will be stopped, and the
bremsstrahlung yield is lower.
As a closing note, there will be some ambiguity in using
the scaling of f (Iλ2 ) as an indicator of the hot-electron fraction. In best fitting BRADDOC results to TLD experimental
data, uncertainties will primarily result from experimental data
(∼10%), prepulse contribution (∼20%), and focal spot size
(∼10%). If the root-mean-square value of these uncertainties is
taken, then there is a typical uncertainty of ∼25% in deducing
the hot-electron fraction. Although prepulse cannot be fully
mitigated, knowledge of the prepulse conditions could be used
to further reduce the uncertainty of experimental data serving
as BRADDOC input.
MEADOWCROFT AND EDWARDS: DIAGNOSTICS TO CHARACTERIZE HOT-ELECTRON PRODUCTION
Fig. 7.
1997
Functional breakdown of the HXRS.
III. HXRS D IAGNOSTIC
A. HXRS Design
The HXRS consists of an array of filtered detectors that
provides a time-integrated measurement of the hard X-ray
spectrum over ∼100 keV–2 MeV generated by laser-plasma
interactions. The HXRS has eight channels, each comprising
a filter, scintillator, and a photomultiplier tube (PMT) detector.
This configuration has been adopted to meet the required spectral coverage, satisfy the engineering constraints, and maximize
the dynamic range of the diagnostic. The choice and thickness of the filter and the scintillator, as well as the intensity
of the hard X-ray spectrum, determine the channel spectral
response. An outline of the operation of the HXRS is given in
Fig. 7.
In order to prevent any significant background signals arising from X-ray or particle interactions, each channel has a
line-of-sight to the target. These lines-of-sight are collimated
and shielded and also avoid the main directions of propagation of electrons and protons emitted by the laser–target
interaction.
Sufficient temporal resolution provides discrimination
against background signals from electrons, protons, and neutrons generated in the target chamber walls of Orion. Since
photon radiation generated in the Orion target chamber wall has
a cross-chamber transit time of ≈14 ns, it is desirable to have
an overall temporal resolution of < 14 ns. Background signals
resulting from X-ray scattering interactions are minimized by
using a high-Z material (lead) to collimate the HXRS channels.
Bremsstrahlung background is minimized by using a set of
sweeper magnets at the front of the HXRS, to deflect stray
electrons from the target into a plastic dump absorber. A crosssectional view of the HXRS design is shown in Fig. 8.
In addition to having collimated lead channels, the HXRS
channels use a column of air to separate the filter and scintillator pair and to minimize X-ray scattering and fluorescence
contributions detected by the scintillators. The length of the air
column (30 cm) is determined from calculations and simulations of the HXRS response.
Aluminum disks included in each channel isolate the HXRS
from the target chamber vacuum and filter out soft X-ray
radiation produced by secondary interactions. In order to
minimize the impact of electron scattering on the response
signal, these disks are located after the sweeper magnet section.
Electromagnetic interference originating from laser–target interactions is a problem, as it can overwhelm the detector signal.
To mitigate this effect, the HXRS is designed as a fully metallic enclosure, with collimators serving as waveguides beyond
cutoff.
Fig. 8. Cross-sectional view of the HXRS design.
B. Characterization of the HXRS
The HXRS was characterized using the miniature linear
accelerator (MINAC), a bespoke radio frequency linear accelerator, at AWE. The MINAC uses microwave energy to
create electric fields, which are then used to accelerate electrons
into a tungsten target, producing bremsstrahlung X-rays. The
MINAC is capable of producing variable energy X-rays, with
bremsstrahlung end-point energies in 2-MeV steps from 2 to
10 MeV. Variable dose rates can also be achieved by varying the
pulse repetition frequency (PRF) and the pulsewidth, where the
PRF can be set at 40–200 pulses per second and the pulsewidth
can be set at 100 ns–3 μs. In order for all eight channels to be
fully exposed to X-rays, the front of the HXRS was positioned
3 m away from the source. The source emission is not isotropic
but in the form of a beam with a maximum of 5◦ divergence.
Cables from the rear of the HXRS were routed into a control
room containing high-voltage power supply units (for the PMT
detectors) and oscilloscopes to record the data. The test setup
for the HXRS is shown in Fig. 9.
Throughout the tests, the PRF was set to either 40 or
200 pulses per second, with bremsstrahlung end-point energies
of 2, 4, or 6 MeV used (so the majority of X-rays were in
the HXRS energy range of ∼100 keV–2 MeV), and the dose
rate ranged from ∼6 to 250 rad/min. The low-dose rate was
necessary to minimize additional background from the MINAC,
specifically scattered X-rays and high-energy electrons.
Examples of oscilloscope traces recorded during these tests
are shown in Fig. 10. These traces demonstrate increase in
the signal level at an applied PMT bias of 0.9 kV, as the
end-point energy is increased from 2 to 6 MeV for channels
5–8 with LuAP scintillators (see Table IV). This is explained
by the increased efficiency of bremsstrahlung emission from
the MINAC as the end-point energy rises. Furthermore, the
individual channel signals are more clearly distinguished at
higher end-point energies.
The effect of increasing the MINAC bremsstrahlung endpoint energy was only investigated for the channels containing
LuAP scintillators as the channels containing Bicron BC-422
scintillators do not have sufficient stopping power for X-rays
at the upper end of the ∼100-keV–2-MeV energy range for
the HXRS. Therefore, channels 1–4 containing Bicron BC-422
scintillators were only tested at the 2-MeV end-point energy of
1998
IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 40, NO. 8, AUGUST 2012
TABLE IV
O PTIMIZED C HANNEL D ESIGN AND PMT G AIN S ETTINGS U SED IN
HXRS R ESPONSE S IGNAL C ALCULATIONS
Fig. 9. Photograph showing the HXRS in position, some 3 m from the
MINAC. The shielding and collimation requirements for the HXRS give the
HXRS a high mass (∼400 kg). Cranes and a compressor table were required to
move the diagnostic into position.
signals due to PMT light collection efficiency to be deduced
and implemented into an unfold of hot-electron temperatures.
C. Unfolding Hot-Electron Temperatures With the HXRS
Fig. 10. Oscilloscope traces recorded for the HXRS using the MINAC
bremsstrahlung X-ray source. Channels 5–8 (LuAP scintillators, Table IV) were
used, with an applied bias of 0.9 kV and bremsstrahlung end-point energies
of 2, 4, and 6 MeV. No attenuators were used with the oscilloscope, and the
oscilloscope input impedance was set to 1 MΩ.
the MINAC. As expected, the output signal level increased as
the applied PMT bias (and, thus, gain) was increased from 1.4
to 1.6 kV.
A separate calibration of each PMT and scintillator was
also conducted using the MINAC X-ray bremsstrahlung source,
including the installation cabling that allowed the attenuation
due to the cabling to be investigated. For these new tests, the
PMT and scintillator were housed in a lead tube configuration
similar to the channel geometry used in the HXRS. Testing
of the PMT and scintillator combinations was only effective
at 2 MeV, due to the absence of the HXRS channel filters.
All channel scintillators were coupled to the same PMT detector, and only the scintillators were changed. Data collected
from this calibration enabled relative changes in the channel
Characterization of the HXRS has shown that, in experiment,
the HXRS will require different values of PMT gain to be used
rather than the values shown in Table IV. Also, the channel
signal level is not a suitable measurement, as the difference
in signal level between a pair of the more sensitive channels
(containing Bicron BC-422) can be comparable to the noise
level. Therefore, we use collected channel charge rather than
the output current in order to unfold hot-electron temperatures
using the HXRS. A statistical analysis of errors and assumed
error values, which may vary significantly between laser shots,
has been used before in this approach [6]. Here, we present
a new method which entails establishing expressions for the
channel charge, comparing this to the integrated area for an
oscilloscope pulse and rearranging the result to obtain hotelectron temperature data.
First, we consider calculation of the HXRS channel charges
due to the bremsstrahlung emission at given hot-electron temperatures. Assuming that a temporal resolution of ≥ 17 ns is
attained during the laser shot (corresponding to the maximum
scintillator decay time) and the X-ray flux is isotropic over the
front face of the HXRS, the charge collected in a channel may
be expressed as
Qj (E, λv ) = Ij (E, λv )τj
= eφSj (E)Aj ηj (E)Lj Eχj s(λv )j εj Gj z (4)
where
e
φS
E
A
s(λv )
ε
= −1.6 × 10−19 C;
X-ray flux incident on the scintillators;
X-ray energy;
active area of the PMT;
relative sensitivity of the PMT photocathode at
the scintillator maximum wavelength of emission λv ;
quantum efficiency of the PMT photocathode
of ≈0.20;
MEADOWCROFT AND EDWARDS: DIAGNOSTICS TO CHARACTERIZE HOT-ELECTRON PRODUCTION
1999
the distribution of bremsstrahlung photons in the energy range
of E to E + dE is given by
E
dE
(5)
f (E)dE = κ exp −
kTH
where
κ
kTH
Fig. 11. X-ray spectral bands for HXRS using the difference in collected
channel charges over the ∼100-keV–2-MeV energy range.
G
τ
z
η, χ, and L
calculated gain of the PMT;
electron pulsewidth, equal to the sum of the
scintillator decay time (∼2–50 ns) τd and
the electron transit time spread (≈0.1 ns) in
the PMT tube ≈ τd ;
signal attenuation due to cabling between the
PMT output and the oscilloscope input;
scintillator absorption efficiency, absolute
light yield, and light collection efficiency,
respectively.
The variables L, A, and ε have to be taken as being specific
to each channel, rather than as constants for the instrument as,
for instance, the input face of the thickest LuAP scintillator has
a smaller area than the other scintillators. Also, each of these
variables is not absolutely known, and therefore, it is assumed
that L = 0.5, ε = 0.2, and z = 1 to enable evaluation of (4),
while the net relative differences between the channels due to
all the variables are implemented by the adjustment of each
previously calculated gain G (in Table IV) to an “effective”
value GC . The X-ray spectral bands for the HXRS (Fig. 11)
are determined by calculating (4) for each channel and taking
the difference between the results for two channels. The two
channels are selected to optimize the 100 keV–2 MeV spectral coverage, with the peak charges appearing at sufficiently
well-separated X-ray energies. Since the HXRS only detects
the cumulative X-ray yield and the channels are not energy
dispersive, Fig. 11 may be regarded as the typical instrumental
energy resolution. On this basis, the minimum resolution would
be ∼100 keV within the 100-keV–2-MeV range, with a typical
instrumental resolving power of ∼1.
It is noted that φS uses a bremsstrahlung spectrum from
a specific short-pulse laser-target interaction. For simplicity,
it will be assumed that the distribution of hot electrons producing bremsstrahlung X-rays from a short-pulse laser-target
interaction is a Maxwellian. Non-Maxwellian functions could
also be used in the unfold method, although it may not be
possible to extract an analytical expression to evaluate hotelectron temperatures. In the case of a Maxwellian distribution,
relative spectral intensity;
hot-electron temperature.
Total channel charges are then determined as a function of hotelectron temperature by including this distribution function in
(4) and integrating the result over all energies.
Using the channel differences shown in Fig. 11, combined
with the effective gain values, gives positive spectral bands
over the entire 0–2-MeV range. Therefore, the assumptions
that have got us to this point seem valid, suggesting that we
can use the charge differences between channels to obtain hotelectron temperatures. In order to use this approach to obtain
kTH , consider two channels j and k. In Section II, it was noted
that, at energies > 1 MeV, bremsstrahlung emission becomes
anisotropic. Such anisotropy is evident at 2-MeV energies for
the TLD array which has ≈ 15◦ intervals in the line-of-sight
to the target, but not for the HXRS channels where the lineof-sight ranges from ≈ 1◦ to 4◦ . Therefore, it is reasonable to
assume isotropic X-ray flux and the same input X-ray spectrum
from the laser-target interaction for two HXRS channels. As a
result, the hot-electron source is also assumed to be the same
for both channels.
From Fig. 11, the integrand range may be defined as
0–2 MeV, and from (5), the difference in charge collected by
the channels is given by
ΔQT (E, λv )
= Qj,T (E, λv ) − Qk,T (E, λv )
2 MeV
E
E exp −
kTH
= κez
0
× φSj (E)ηj (E)χj s(λv )j Lj GCj Aj εj
− φSk (E)ηk (E)χk s(λv )k Lk GCk Ak εk dE.
(6)
Now, we consider the measured channel charge. Using Ohm’s
law for a channel j, the charge collected from an oscilloscope
pulse is given by
Qj,exp =
1
R
Vj (t)dt
(7)
pulsej
where
Qj,exp
R
Vj (t)
charge collected from the oscilloscope pulse;
oscilloscope input impedance;
pulse amplitude (voltage) at time t.
In order to account for differences between the PMT gain used
in the experiment GE and the effective PMT gain used in the
2000
IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 40, NO. 8, AUGUST 2012
calculation GC to define the X-ray spectral bands, we introduce
a gain compensation factor δ = GC /GE in (7):
Qj,exp =
δj
R
Vj (t) dt.
(8)
pulsej
Setting the corresponding difference in measured charge,
ΔQT,exp = ΔQT , and assuming that the two channels use
the same oscilloscope input impedance yields the following
result:
⎛ 2 MeV
⎞
E
κez ⎝
Fjk (E) exp −
dE ⎠
kTH
0
⎛
1 ⎜
=
δj Vj (t) dt −
⎝
R
pulsej
where
Tj (E)
Φ(E)
⎞
⎟
δk Vk (t) dt⎠
(9)
pulsek
filter transmission for channel j;
X-ray flux incident on the front end of each HXRS
channel
Fjk (E) = EΦ(E) Tj (E)ηj (E)χj s(λv )j Lj GCj Aj εj
− Tk (E)ηk (E)χk s(λv )k Lk GCk Ak εk .
The solution to (9) requires numerical integration, with initial
estimates for the unknowns κ and kTH provided as input parameters in a computer program. However, the absolute values
of Φ(E), L, z, and ε are not known as they have not been
measured, nor is it possible to measure all of them. Relative
channel signals due to changes in L and ε may be determined
from tests using just the PMTs and scintillators, as described in
Section III-B. Consider two different channels for the HXRS,
l and m, where the charge difference is taken. An equation
similar to (9) may be written. Taking the ratio of (9) with this
result then enables evaluation of kTH from
2 MeV
0
2 MeV
0
Fjk (E) exp − kTEH dE
Flm (E) exp − kTEH dE
=
δj Vj (t) dt −
pulsej
pulsel
formation on the bremsstrahlung spectrum from the short-pulse
laser-target interaction.
δl Vl (t) dt −
δk Vk (t) dt
pulsek
δm Vm (t) dt
(10)
pulsem
in which Fjk (E) = EΦ(E)[Tj (E)ηj (E)Γj −Tk (E)ηk (E)Γk ],
where Γ corresponds to the peak signals measured from
the PMT and scintillator tests and it is assumed that Γ ∝
χs(λυ )LGC Aε. Since a ratio is given in (10), Γ does not have
to be in absolute units. As a result, (10) only has two unknowns
to solve for, which are the hot-electron temperature kTH and
the incident flux on the HXRS channels Φ(E), providing in-
IV. C ONCLUSION
The design, characterization, and use of two high-energy
bremsstrahlung target diagnostics, a TLD array and the HXRS,
to measure hot-electron production from Orion laser-plasma experiments, have been presented. Modeling the TLD array doses
as a function of laser, target, and geometric parameters provides
information on the bremsstrahlung production efficiency and
fraction of hot electrons generated in a laser-target interaction.
At Iλ2 exceeding ≈ 8 × 1019 W · cm−2 · μm2 , bremsstrahlung
production is optimized for high-Z targets less than ≈1.5 mm
thick. Using targets less than ≈1.5 mm thick gives an increase
of bremsstrahlung production efficiency with increasing Iλ2 ,
as reducing the target thickness reduces bremsstrahlung selfabsorption within the target when the hot electrons are stopped.
Increasing Iλ2 produces either a larger hot-electron fraction or
higher hot-electron temperatures. The HXRS has been characterized with the MINAC high-energy bremsstrahlung X-ray
source at AWE, prior to installation on the Orion target chamber. The testing produced results that invalidated previous assumptions as to how the data could be unfolded to determine
hot-electron temperatures in laser-plasma experiments, and a
new unfold method using the HXRS channel charges was
subsequently derived.
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Authors’ photographs and biographies not available at the time of publication.