Fig.1 Schematic arrangement of the Strip-Line X-ray Imager detection
system with the MCP input surface showing the four 500 nm thick Cu coated
regions. (Kentech Instr. Ltd., UK)
L.A.Gizzi, A.Giulietti, O.Willi*
Istituto di Fisica Atomica e Molecolare del CNR, Pisa, Italy
*Imperial College of Science, Technology and Medicine, London, England
A novel X-ray imaging system based on a microchannel-plate combined
with a multi-pin-hole camera has been employed to study X-ray emission
from laser-produced plasmas in the 0.5 - 3 keV photon energy range. In
particular, the interaction of intense laser radiation with such plasmas,
in conditions relevant to inertial confinement fusion, was monitored by
recording a sequence of consecutive X-ray images with a temporal resolution
of 140 ps and a spatial resolution of 10 um. These images provide valuable
information on the main physical mechanisms involved in the interaction
process, including collisional absorption of the incident laser energy
and electron thermal conduction.
Due to the strong X-ray emissivity of laser produced plasmas, a simple imaging device consisting of a pin-hole camera (PHC) can be employed to obtain X-ray images of the plasma. Both magnification and resolution of such a device can be easily calculated from simple geometrical consideration. The image thus obtained can be recorded directly by using X-ray sensitive detectors (windowless CCD cameras, X-ray films) or by employing phosphor screens coupled to optical image intensifiers. Presently available intensifiers based on the microchannel-plate[3] (MCP) technology can easily provide a thousand-fold overall gain in intensity. Ordinary CCD cameras or commercial photographic B&W film can then be used to record the intensified image.
Temporal resolution can be achieved by forming the X-ray image generated by the PHC on a position sensitive time resolving device. By using an X-ray streak camera, temporal resolution up to the picosecond range can be obtained. However the spatial information is restricted to the direction perpendicular to the streak direction (1-D time-resolved imaging). This technique has been successfully employed for several years[4] and is very useful when a continuous mapping of the temporal evolution is required. However, two-dimensional position sensitive devices with a temporal resolution as high as a few tens of picosecond based on microchannel-plates (MCP)[5] can now be employed. MCP's are characterised by a very low capacitance that enables fast switching of the externally applied electric fields. These devices can therefore be used as gated intensifiers as well as a DC intensifiers and usually do not require additional intensifiers due to their intrinsic high gain.
In all the applications considered above, in order to avoid motional blurring of the images, framing times as short as few tens of picoseconds[6] are often necessary. On the other hand, the scalelength of the features of interest can be as small as few microns, thus accounting for the need of high spatial resolutions. Furthermore, another important feature of such imaging systems is the number of frames that can be recorded on a single interaction event, so that the temporal evolution can be mapped with sufficient accuracy. The final configuration is therefore a trade-off between scientific requirements, spatial, temporal and spectral accuracy on one side, and flexibility, reliability, and ease of use on the other side.
In this paper we describe the implementation of multi-frame X-ray imaging with high temporal resolution for the study of laser interaction with preformed plasmas. A detailed description of the technique will be given here with emphasis on its application to the investigation of laser-plasma coupling processes. The interaction of a high intensity laser pulse with preformed plasmas, generated by laser heating of thin Al foils, was investigated by means of this diagnostic, in conditions of temperature, density and laser intensity typical of Inertial Confinement Fusion experiments.
Fig.1 Schematic arrangement of the Strip-Line X-ray Imager detection
system with the MCP input surface showing the four 500 nm thick Cu coated
regions. (Kentech Instr. Ltd., UK)
Fig.2. Schematic set-up of the imaging system showing the pin-hole set arrangement and the input window of the four-frame gated X-ray Imager SLIX. The geometry of the pin-hole array was defined by the image magnification in order to produce four images centred on the four sensitive areas of the detector.
and an
electron temperature of 450 eV.
Fig.3. X-ray transmittivity of the 3 um Al filter used in the
SLIX imaging system. The X-ray emissivity of a 450 eV, 1.5x1020
cm-3 Al plasma in collisional-radiative equilibrium is also
plotted for comparison.
)
of the Vulcan laser at the Central Laser Facility (Rutherford Appleton
Laboratory, Chilton, Didcot, UK) were superimposed on target, two on each
side, in order to generate and heat the plasma. The dashed ellipse around
the Al coating shows schematically the size of the focal spot of the four
heating beams. A fifth infrared laser beam (
)
was then focused on the target along its longitudinal axis using an f/10
optics, as shown in Fig.4 and was timed to reach the target typically between
2 and 3 ns after the peak of the plasma forming beams.
Fig.4 Target configuration and laser beams arrangement for the
production of laser plasmas. The Al coating was either 500nm or 700nm thick.
The Al target was 300um wide and 500um long (along the interaction beam
axis). The preformed plasma is created from the laser-heated exploding
foil and expands perpendicularly to the foil plane .
on each side, obtained with the SLIX working as a DC X-ray intensifier.
The 600 ps interaction pulse was delayed by 2.2 ns with respect to the
heating pulses and was focused on the (left) edge of the foil target at
an intensity was approximately 
,
in a 140 um (FWHM) focal spot using an 
optics. The shape of the bright X-ray emitting region, even though integrated
in time, clearly matches the shape of the Al heated target as shown in
Fig.4. This observation suggests that most of the X-ray emission occurs
during the plasma start-up phase, before hydrodynamic expansion takes place.
As a consequence, in time integrated images, the effects of the interaction
occurring in the field of view of the Al stripe are masked by the intense
X-ray emission occurring in the early stage of plasma formation. Therefore
temporal resolution is needed when studying interaction effects.
Fig.5 Time integrated X-ray image of a 700 nm thick, 500 um
long, 300 um wide Al target heated on each side by a 600 ps, 0.53 um laser
pulses at an intensity of ~2x1013 W/cm2. The 600ps
interaction pulse was delayed by 2.2 ns and was focused on target at an
intensity of approximately 1013 W/cm2. The image
was obtained with the SLIX working as a DC X-ray intensifier.
Images like the one shown in Fig.5 were produced on each of the four frames of the SLIX and then, by driving the frames at different times, a temporal sequence of four X-ray images of the laser-plasma interaction region was recorded. The timing of each frame was set according to the particular configuration of the interaction experiment as shown schematically in Fig.6. Typically the first frame was synchronised with the heating laser pulse while the remaining three frames were usually synchronised at different times during the interaction laser pulse.
Fig.6. Timing of the SLIX frames (1 to 4) relative to the timing
of the laser pulses. The frame#1 was synchronized with the heating (H)
pulse to monitor plasma formation. All the remaining three frames were
synchronized with the interaction (I) pulse.
on
each side, while the intensity of the 600 ps interaction pulse was 
.
As indicated in Fig.6, frame #1 was synchronised with the peak of the 600
ps heating pulse while the remaining three frames (#2, 3 & 4) were
timed consecutively to record the evolution of the interaction process
with the preformed plasma. X-ray emission relative to the heating phase
involves the whole Al target foil and, though very intense in the first
frame, drops below the detection level of the X-ray imaging system in the
following frames, that is, after ~2 ns. This is consistent with the X-ray
time resolved spectra taken in similar experimental conditions and presented
in a previous work[10]
in which a simple model of X-ray emissivity was presented and discussed
to explain the temporal behaviour of experimental X-ray emission.
Fig.7 Sequence of time resolved X-ray images of laser interaction with a preformed plasma produced by irradiation of a 700 nn thick, 300 um wide, 500 um long Al stripe at an intensity of ~ 4x1013 W/cm2 on each side. The interaction beam was focused on the left edge of the plasma, as shown schematically by the arrow, in a 140 um (FWHM) focal spot at an intensity of 5.8x1013 W/cm2. The framing time was 120 ps, while the first interframe, that is the peak-to-peak delay between gate #1 and gate #2, was 2.2 ns, as shown in Fig.6. The second and third interframes were zero and 100 ps respectively. The first frame, syncronized with the peak of the plasma heating pulse, shows X-ray emission from the plasma heating phase while the remaining three frames show the X-ray emission due to the interaction of the delayed laser pulse with the preformed plasma.
, that is, well
below the critical density for the wavelength of the infrared interaction
beam. In addition, the longitudinal density scalelength at the time of
interaction is of the order of 100 um, therefore, propagation of the interacting
beam occurs without strong refraction and/or deflection effects. In these
conditions the main absorption process is the classical collisional absorption,
i.e. inverse bremsstrahlung (IB), and electron heat transport accounts
for propagation of the absorbed energy across the whole plasma. These physical
mechanisms can be investigated by studying the features of X-ray emission
for different plasma and laser conditions as discussed below.
and 
.
Fig.8 Sequence of time resolved X-ray images of laser interaction
with a preformed plasma. The interaction beam was focused on the left edge
of the plasma, as shown schematically by the arrow, in a 140 um (FWHM)
focal spot at an intensity of 5.8x1013 W/cm2. The
framing time was 120 ps, while the first interframe, that is the peak-to-peak
delay between gate #1 and gate #2, was 2.2 ns, as shown in Fig.6. The second
and third interframes were zero and 100 ps respectively. A lower density
plasma at the time of interaction was obtained by using 500nm thick Al
instead of the 700nm used in the case of Fig.7. Due to the lower electron
density of the preformed plasma, energy from the interaction pulse is absorbed
over a much longer path than in the case of Fig.7 (see text).
) upon
the electron density. Therefore, according to our model, the length of
the X-ray emitting region is expected to increase strongly as the plasma
electron density decreases. This effect was indeed observed experimentally
performing interaction with a preformed plasmas characterised by a lower
electron density. In fact, the preformed plasma was generated in the same
experimental conditions of Fig.7, but using a thinner Al target (500 nm
thick instead of the 700 nm). In this case, the maximum electron density
is expected9 to be approximately 
and the electron temperature is expected to be 400 eV, that is only slightly
lower than in the previous case (450 eV). In this case, the absorption
length is expected to be approximately 1mm, that is, greater than the length
of our preformed plasma. In fact, according to the frames #2 and #3 of
Fig.8, the longitudinal extent of the X-ray emitting region is indeed comparable
to the length of the Al target. This result is in agreement with the conclusions
of our simple model based on IB absorption and bremsstrahlung emission
.
is given by 
, where 
is the Spitzer-Härm conductivity[11]
expressed in terms of the electron density, thermal velocity and collision
frequency. In the case of our experiment, assuming a fully ionised Al plasma
at an electron temperature and density of 450 eV and 
respectively,
and integrating over the 140 ps gate time of the X-ray imaging system,
one finds 
. Since
the longitudinal IB absorption length is typically greater than 175 um,
heat diffusion is not expected to play a dominant role in determining the
length of the X-ray emitting region.
In contrast, the nominal width of the focal spot is only 140 um, that is, smaller than the characteristic thermal diffusion length. Therefore, some contribution from heat diffusion can be expected in this case. It should be noted, however, that the value of the nominal intensity of the interaction beam represents only an average value calculated assuming that the beam energy is uniformly distributed in the 140 um focal spot during the 600 ps pulse duration.
The effect of the energy in the "wings" of the focal spot is therefore
not accounted for in details by this simple description. However, we note
that, as the laser pulse energy increases (decreases), the "effective"
width of the focal spot that contributes to X-ray emission will consequently
increase (decrease). Evidence of this effect is given by Fig.9 that shows
a sequence of time resolved X-ray images of the laser-plasma interaction
region obtained in similar conditions to that of Fig.7, but at a lower
interaction intensity of
.
The transverse size of the X-ray region as shown in frame #3 is now approximately
150 um compared to the 200 um of frame #3 in Fig.7.
Fig.9 Sequence of time resolved X-ray images of laser interaction
with a preformed plasma produced in analogous condition as that of Fig.7,
but at a lower interaction beam intensity 3.5x1013 W/cm2.
The arrow shows schematically the interaction beam configuration. The framing
time was 120 ps, while the first interframe, that is the peak-to-peak delay
between gate #1 and gate #2, was 2.2 ns, as shown in Fig.6. The second
and third interframes were zero and 100 ps respectively.
to 
obtained with
the same 140 um FWHM focal spot.
The first important feature of this graph is that, as the intensity increases, the transverse size also increases. This is consistent with the assumption made above that, in the high intensity limit, the width of the X-ray region can be mainly explained in terms of the contribution of the wings in the intensity distribution of the focal spot. Contribution to the spreading of the X-ray region may arise also from thermal diffusion processes. In fact, the energy of the interaction beam will heat the plasma locally and such heating will be increasingly important at higher laser intensities. This localised heating would give rise to enhanced thermal diffusion and the effect would increase with laser intensity. However we believe that such an effect can be neglected with respect to the spreading due to the wings of the laser focal. In fact, if this effect was quantitatively important in our conditions, it should play a role in time resolved images of Figures 7, 8 or 9. Frames #2, #3 and #4 of these images show the X-ray region at different times during the interaction pulse, i.e. at the beginning, at the peak and at the end of the pulse respectively, as described schematically in Fig.6. The energy deposited in the plasma at each frame is increasingly higher, therefore a spreading driven by thermal diffusion should increase from a frame to the following. In contrast, no sizeable increase in the transverse spread of the X-ray region is measured when going from frame #2 to frame #4.
Fig.10 Width of the X-ray emitting region as a function of the nominal intensity of the interaction beam focused on an Al plasma. The plasma heating intensity was approximately Å4´1013 W/cm2 on each side of the target. The horizontal dashed line indicates the limit set by the thermal diffusion length (175 µm) calculated in our experimental conditions.
On the other hand, as the laser intensity decreases, the width
of the X-ray emitting region stabilises between 150 um and 200 um. This
value is in good agreement with the value given above for the thermal diffusion
length (175 um). Therefore, in the low intensity regime, the width of the
X-ray region is mainly determined by classical thermal diffusion processes
and is therefore basically independent from the laser intensity, being
a function of hydrodynamic plasma parameters only.
The experimental results presented here with a preliminary analysis
and discussion, show how time-resolved X-ray imaging can provide valuable
information of the physics of laser-plasmas, which can be directly compared
with the results of simple analytical models or with the predictions of
numerical simulations. Fundamental aspects of the physics of laser-plasma
interactions relevant to ICF studies including absorption processes and
electron heat transport mechanisms can be investigated. In fact, the absorption
length inferred from the X-ray images presented in this work was found
to be in good agreement with the classical theory of linear collisional
absorption. Furthermore, the thermal diffusion length estimated from the
data was found to be consistent with the description provided by the classical
thermal transport theory.
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