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by selective optical filtering and a frequency shift of the probe beam before amplification. These techniques create a unique platform for performing spatially and temporally resolved measurements of the target evolution. We show results from an experiment at the Air Force Research Lab (AFRL) in which a flowing water jet target11, 12 is irradiated by nanosecond-scale and picosecond-scale pre-pulses that precede a 30-fs FWHM ultra-intense (1018 W/cm2 ) interaction. Section II describes the experimental setup, and Sec. III describes how the ultra-short timescale synchronization of the probe and pump pulse is achieved. Section IV describes the frequency shift of the probe pulse and selective filtering. Section V presents some preliminary data of the water jet expansion due to laser-target interactions, including Abel inversion of interferometric data. Section VI states our conclusions and describes how this instrument will be incorporated into future work. II. EXPERIMENTAL OVERVIEW
Interferometry and shadowgraphy are used to characterize plasma expansion in experiments at the AFRL at Wright Patterson Air Force Base in Dayton, OH. An 800 nm, 30-fs FWHM pump beam produces high intensities (1018 W/cm2 , 2.6 μm FWHM spot size) on flowing water jet column targets. To avoid disruption of the high intensity laser light as it propagates to focus and to prevent freezing of the water jet nozzle, the experiment is housed in a vacuum chamber that is held at 20 Torr partial vacuum using a thermocouple gauge solenoid valve feedback loop. Known pre-pulse artifacts of the amplification process pre-ablate the target, creating conditions of interest picoseconds and nanoseconds before the main laser pulse interaction. To interrogate these conditions, a 420 nm, 80-fs FWHM probe beam is passed through the interaction region and subsequently split to image the target for shadowgraphy and interferometry. The pump-probe experimental layout is shown in Fig. 1. The probe beam is frequency-shifted, as discussed in Sec. IV. Distortions to the probe pulse wavefront due to variations in the index of refraction along the line of sight are revealed by interfering the probe pulse with a reference pulse at the same frequency. In this laterally sheared Michelson interferometer setup,13 an image of the interaction region of the water jet is overlapped with a sheared image of the water jet downstream. Interference fringes shift in response to changes in line-ofsight index of refraction, allowing one to “see” ablated liquid and ionized plasma in a way complementary to shadowgraphy. With a high dynamic range timing setup (described next) and selective optical filtering, one can get a sense of the evolution of this ablated liquid and plasma. III. FEMTOSECOND RESOLUTION OVER MICROSECONDS
One commonly used approach to pump/probe experiment is to use two entirely separate femtosecond laser systems, synchronizing the laser oscillators via electronic signals. A typical setup gives picosecond stability between oscillators; achieving femtosecond stability requires advanced electron-
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FIG. 1. The experiment employs a high-intensity pump and low-intensity probe, relatively timed with better than 40-fs precision. The pump beam (sketched in red) and its pre-pulses irradiate the water jet target, creating a dynamic laser-plasma interaction region. The probe beam (sketched in blue) envelops the interaction region and is then split for target-imaged interferometry and shadowgraphy. Within the laterally sheared Michelson interferometer, a piezoelectric mirror allows for controlled adjustment of phase (mirror translation) and shear (mirror tilt). The shear angle is out of the page, though sketched in the plane of the page for easy visualization. Optical notch filters and an iris (spatial filter) exclude unwanted light such as that from plasma self-emission (see Fig. 2).
ics and a reduction in the output repetition rate.14 Utilizing two pulses from a single oscillator is simpler and results in a more stable relative timing. To achieve femtosecond relative precision in such a setup, the probe and pump beams must be seeded from a common oscillator. In a kHz system, a Pockels cell selects one oscillator pulse every millisecond to be further amplified as the pump pulse, rejecting all other pulses. The oscillator used in the experiment at AFRL produces pulses at 80 MHz, and the rejected pulses are routed into a second Pockels cell that selects a different pulse to be amplified as the probe pulse. By varying the pulse selected, coarse delays can be introduced between the pump and probe on the order of the oscillator rate, 80 MHz or 12.5 ns. After amplification, the probe pulse passes through a delay line. The double-passed delay line allows fine adjustments to the relative pump-probe delay, with < 40 fs resolution over 19 ns. Combining coarse and fine delay techniques results in 40 fs resolution over 10 μs, and potentially even longer times (e.g., 900 μs) if desired. The final resolution of the system is limited by the greater of the delay line resolution (< 40 fs in this setup) or probe pulse duration (80 fs in this setup). The combination of pulse seed selection and delay line adjustment allows roughly nine orders of magnitude temporal dynamic range. Fig. 3 exhibits this dynamic range, showing the pre-plasma expansion before the arrival of the main ultra-intense pulse (upper sequence) and the hydrodynamic response of the water jet over 10 μs of evolution (lower sequence). IV. ELIMINATION OF PLASMA SELF-EMISSION NOISE
Irradiated by the pump beam at 800 nm, the target will naturally emit light at the second harmonic (400 nm),15 which
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FIG. 2. The deleterious effect of plasma self-emission on the diagnostics is avoided by a frequency shift in the probe beam and aggressive optical filtering. (a) Near the critical surface of laser-plasma interaction, plasma selfemission at 400 nm saturates imagery. (b) To avoid this effect, the probe beam is frequency shifted to 840 nm, amplified, then frequency doubled to 420 nm. At the imaging cameras, notch filters are used to remove plasma self-emission at the pump’s second harmonic, 400 nm. The notch filter transmission band includes the entire probe beam spectrum and only the tail of the plasma selfemission spectrum. (c) The effect of the frequency shift and optical notch filters is to reveal previously obscured interaction areas.
is the source of the plasma self-emission that is the subject of this subsection. Plasma self-emission complicates and frustrates probe-beam interferometry and shadowgraphy because it obscures areas of interest near the critical surface (see Fig. 2(a)). The solution to this obfuscation problem, which we have implemented in this setup, is to apply optical filtering that excludes plasma self-emission while passing the probe beam. Even with specially selected optical notch filters, this is only possible if the probe spectrum sits outside of the plasma selfemission spectrum. However, because the pump and probe share a common oscillator, the probe pulse naturally shares the frequency of the pump harmonic. To circumvent this issue, the frequency of the probe pulse is shifted in two steps.
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Prior to amplification, the broadband 800 nm seed pulse of the probe beam is optically filtered using Schott RG850 glass, moving the central wavelength to 840 nm by preferentially attenuating lower wavelengths. Next, a hard spectral cutoff is applied in the pulse stretcher, by physically clipping lower wavelength regions of the beam during grating dispersion. This frequency-shifted (and much attenuated) pulse is next passed through a regenerative amplifier, which smooths the spectral profile, and after re-compression the pulse remains centered at 840 nm. Finally, the probe beam is frequency doubled to 420 nm via a β-barium borate crystal (AR/AR coated, 300 μm thick, Type I). During imaging, two optical notch filters (Semrock FF01-420/10-25; 10 nm bandwidth, and nominally 15 nm FWHM) select for the 420 nm probe and reject the plasma self-emission at 400 nm (Figs. 2(b) and 2(c)).
V. ACQUISITIONS AND ANALYSIS
By varying probe beam delay time, an image sequence can be created that shows the development of pre-plasma, the main ultra-intense pulse interaction, and the hydrodynamic recovery of the target (see Fig. 3). The image acquisitions are performed in the following way. A sequence of delay times is chosen so as to acquire many frames shortly before the main pulse interaction while keeping a wide temporal view of the interaction. Once programmed, the sequence is serially executed. To create a given delay, Pockels cell seed selection and delay line position are adjusted automatically. For each delay, one shadowgraphic frame and three interferometric frames are acquired (corresponding to three positions of the piezoelectric mirror which varies Michelson interferometer phase difference). Because stochastic events can cause occasional extreme outliers shot-to-shot, 10 images are acquired for each frame, corresponding to ten independent laser shots. The image most similar to the average is incorporated as the frame. Interferograms must be analyzed to recover phase data. Phase shifts are reconstructed from fringe shifts using the
FIG. 3. Precise probe pulse timing (< 40 fs resolution) over a wide dynamic range (> 10 μs) gives a detailed view of pre-plasma evolution, intense laser-plasma interaction, and target recovery. Upper sequence: Recovered phase shifts from interferometry show the in-vacuum development of pre-plasma nanoseconds before the main interaction, consistent with known pre-pulse on this timescale. Delay times relative to the main ultra-intense laser pulse are marked. Interferometric reconstruction after the main pulse arrives (≥ 0 fs, not shown) fails due to steep phase gradients. Lower sequence: Shadowgraphy shows timescales of in-air target evolution: hydrodynamic reaction in picoseconds, expansion in nanoseconds, and recovery in microseconds.
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FIG. 4. To aid in the reconstruction of phase dependent imagery from fringe shifts, three separate 120◦ phase-shifted (temporally sheared) interferograms are acquired for each probe delay. Left: an interferogram is shown for −15 ps delay for an in-vacuum target. Its corresponding phase image is reconstructed using the Speckle Phase of Difference algorithm in IDEA software – the vertical dashed line represents the rightmost boundary of reliable phase reconstruction. Abel inversion allows recovery of index of refraction and potentially electron density. Right: recovered index of refraction shifts for the interferogram at left are shown. The radial index change from negative to positive suggests pre-plasma on-axis and ablated neutral material off-axis.
IDEA software16 Speckle Phase of Difference algorithm (three-frame technique, 120◦ phase shift). Abel inversion can be performed to recover the changes in index of refraction (see Fig. 4 for an experimental example). Abel inversion analysis requires an added assumption of the experiment’s radial symmetry, about the laser axis. From the Abel inversion, electron densities can potentially be inferred. VI. SUMMARY AND CONCLUSIONS
We have described a frequency-shifted, femtosecondgated interferometric setup and demonstrated its capability for a flowing water jet experiment in which this target is irradiated by nanosecond-scale and picosecond-scale pre-pulses in advance of the arrival of an ultra-intense (1018 W/cm2 ) pulse. The combination of a timing system for observing evolution from femtoseconds to microseconds and elimination of plasma self-emission noise light delivers improved shadowgraphy and interferometry. Phase shift reconstruction from interferometry reveals changes in the index of refraction near the target. This information can be used to infer electron densities through Abel inversion. With precise optical filtering and by frequency shifting the probe pulse away from the selfemission frequencies, the problem of plasma self-emission is avoided. The diagnostic has been demonstrated to produce interferometric and shadowgraphic image sequences of lasermatter interactions which show nanosecond formation of preplasma, femtosecond interaction of the ultra-intense main pulse, picosecond hydrodynamic expansion, and microsecond recovery of the target. Fielding the diagnostic has already contributed in two ways to our experimental understanding. First, tens-of-microseconds target recovery time indicates that the experiment could be performed at significantly higher than
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kHz repetition rates. Second, expectations prior to the arrival of the main pulse of pre-plasma formation along the laser axis with neutral material off-axis are confirmed. By providing on-demand femtosecond resolution at arbitrary delay times, this diagnostic will soon be used to track the effects of known femtosecond-duration pre-pulses as they arrive on target picoseconds to nanoseconds prior to the main pulse, and to improve laser-driven electron acceleration and X-ray production techniques.17 Future improvements to the diagnostic may include additional views of the interaction region or on-the-fly interferogram analysis for fast feedback to the experimenter. ACKNOWLEDGMENTS
This research was sponsored by the Quantum and NonEquilibrium Processes Department of the (U.S.) Air Force Office of Scientific Research (USAFOSR), under the management of Dr. Enrique Parra, Program Manager. S.F. was supported in part by the DOD HPCMP high performance computing internship program. The authors thank Mario Manuel, University of Michigan, for insightful discussions. 1 T. Hosokai, K. Kinoshita, A. Zhidkov, K. Nakamura, T. Watanabe, T. Ueda,
H. Kotaki, M. Kando, K. Nakajima, and M. Uesaka, Phys. Rev. E 67, 036407 (2003). 2 M. Kaluza, J. Schreiber, M. I. K. Santala, G. D. Tsakiris, K. Eidmann, J. Meyer-ter Vehn, and K. J. Witte, Phys. Rev. Lett. 93, 045003 (2004). 3 K.-H. Hong, B. Hou, J. A. Nees, E. Power, and G. A. Mourou, Appl. Phys. B 81, 447 (2005). 4 C. Orban, M. Fatenejad, S. Chawla, S. C. Wilks, and D. Q. Lamb, e-print arXiv:1306.1584 [physics]. 5 F. Dollar, P. Cummings, V. Chvykov, L. Willingale, M. Vargas, V. Yanovsky, C. Zulick, A. Maksimchuk, A. G. R. Thomas, and K. Krushelnick, Phys. Rev. Lett. 110, 175002 (2013). 6 I. H. Hutchinson, Principles of Plasma Diagnostics (Cambridge University Press, 2005). 7 Z. Wu, X. Zhu, and N. Zhang, J. Appl. Phys. 109, 053113 (2011). 8 V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, and D. v. d. Linde, Appl. Phys. A 78, 483 (2004). 9 S. Le Pape, Y. Y. Tsui, A. Macphee, D. Hey, P. Patel, A. Mackinnon, M. Key, M. Wei, T. Ma, F. N. Beg, R. Stephens, K. Akli, T. Link, L. VanWoerkom, and R. R. Freeman, Opt. Lett. 34, 2997 (2009). 10 P. McKenna, D. Carroll, O. Lundh, F. Nürnberg, K. Markey, S. Bandyopadhyay, D. Batani, R. Evans, R. Jafer, S. Kar, D. Neely, D. Pepler, M. Quinn, R. Redaelli, M. Roth, C.-G. Wahlström, X. Yuan, and M. Zepf, Laser Part. Beams 26, 591 (2008). 11 J. Uhlig, C.-G. Wahlström, M. Walczak, V. Sundström, and W. Fullagar, Laser Part. Beams 29, 415 (2011). 12 W. Fullagar, M. Harbst, S. Canton, J. Uhlig, M. Walczak, C.-G. Wahlström, and V. Sundström, Rev. Sci. Instrum. 78, 115105 (2007). 13 Y. Y. Hung, Opt. Commun. 11, 132 (1974). 14 S. A. Crooker, F. D. Betz, J. Levy, and D. D. Awschalom, Rev. Sci. Instrum. 67, 2068 (1996). 15 D. von der Linde, H. Schulz, T. Engers, and H. Schuler, IEEE J. Quantum Electron. 28, 2388 (1992). 16 M. Hipp, J. Woisetschläger, P. Reiterer, and T. Neger, Measurement 36, 53 (2004). 17 C. Orban, J. T. Morrison, E. D. Chowdhury, J. A. Nees, K. Frische, and W. M. Roquemore, e-print arXiv:1405.6313 [physics].
REVIEW OF SCIENTIFIC INSTRUMENTS 85, 11D603 (2014)
Parallax diagnostics of radiation source geometric dilution for iron opacity experimentsa) T. Nagayama, J. E. Bailey, G. Loisel, G. A. Rochau, and R. E. Falcon Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
(Presented 2 June 2014; received 2 June 2014; accepted 27 June 2014; published online 17 July 2014) Experimental tests are in progress to evaluate the accuracy of the modeled iron opacity at solar interior conditions [J. E. Bailey et al., Phys. Plasmas 16, 058101 (2009)]. The iron sample is placed on top of the Sandia National Laboratories z-pinch dynamic hohlraum (ZPDH) radiation source. The samples are heated to 150–200 eV electron temperatures and 7× 1021 –4× 1022 cm−3 electron densities by the ZPDH radiation and backlit at its stagnation [T. Nagayama et al., Phys. Plasmas 21, 056502 (2014)]. The backlighter attenuated by the heated sample plasma is measured by four spectrometers along ±9◦ with respect to the z-pinch axis to infer the sample iron opacity. Here, we describe measurements of the source-to-sample distance that exploit the parallax of spectrometers that view the half-moonshaped sample from ±9◦ . The measured sample temperature decreases with increased source-tosample distance. This distance must be taken into account for understanding the sample heating. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4889776] I. INTRODUCTION
Opacity quantifies photon absorption in matter and plays a crucial role in many high energy density plasmas, including inertial fusion plasmas and stellar interiors.1 Modeling opacities of ions with multiple bound electrons is very challenging and employs approximations that need to be experimentally validated.2, 3 Performing reliable opacity experiments is also challenging and must satisfy many criteria.2, 3 Measuring opacity becomes more difficult at higher temperature because the opacity sample has to be heated to the high temperature without significant gradients and has to be backlit by a bright radiation to minimize the effect of the hot sample plasma emission on the absorption measurement. The Sandia National Laboratories (SNL) Z machine (Z) provides a unique platform to perform opacity experiments at temperatures above 150 eV.4 The Z-pinch dynamic hohlraum (ZPDH) is a terawatt xray radiation source at Z that makes high-temperature opacity measurements possible.5 The opacity sample is located above the ZPDH radiation source and is radiatively heated. Most of the photons have energies above 600 eV. This powerful radiation streams through the sample and heats it without significant gradients.6 The ZPDH also provides a bright backlighter to mitigate the sample self-emission. Recently, we found that the opacity sample can reach higher temperatures and densities using the same radiation source only by changing the target configuration.6, 7 However, it was not clear why the change in the target configuration affects the sample temperature if the sample is heated by the same radiation source. To further optimize this high temperature opacity experimental platform, it is crucial to understand what dictates a) Contributed paper, published as part of the Proceedings of the 20th
Topical Conference on High-Temperature Plasma Diagnostics, Atlanta, Georgia, USA, June 2014.
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the sample temperature. In this article, we provide experimental evidence that the source-to-sample distance depends on the sample configuration. This distance controls the source geometric dilution at the sample, thereby affecting the sample temperature. II. SNL OPACITY EXPERIMENTS AND PARALLAX
The typical SNL opacity experimental setup is shown in Fig. 1. The target consists of a semi-circular FeMg sample sandwiched by a circular tamping material (e.g., plastic, CH), which we call a “half-moon” target. Mg is mixed in the Fe sample to diagnose the Fe conditions (i.e., electron temperature, Te , and electron density, ne ) using Mg K-shell spectroscopy.6, 8 This target is placed above the ZPDH radiation source, and the ZPDH radiation heats and backlights the sample.3, 5 The backlighter attenuated through the target is recorded by potassium acid phthalate crystal (KAP) spectrometers fielded along ±9◦ from the z-axis.8 An aperture above the target limits the spectrometers’ views to a 4 mm × 1 mm area. Each spectrometer has 4-6 slits, each 50 μm in width, at the halfway distance to the sample to provide spatial resolution of ∼0.1 mm along the aperture direction with a magnification of ∼1. The transmitted backlighter images are recorded on Kodak 2492 x-ray films with spatial and spectral resolution. Due to the finite source-to-sample distance, h, the spectrometer at +9◦ observes the backlighter bright spot through +9◦ , while the one at −9◦ the FeMg embedded side at xBL −9◦ observes it on the CH-only side at xBL (black dots in Fig. 1). This spectrometer configuration measures the FeMgattenuated and unattenuated spectra simultaneously, providing FeMg transmission spectra in a single experiment (shot). However, taking advantage of this parallax, we can also infer the backlighter location with respect to the “half-moon” +9◦ −9◦ and xBL as boundary (i.e., h and δ in Fig. 1) based on xBL
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FIG. 3. Backlighter images attenuated through the target recorded from −9◦ and +9◦ . FeMg is embedded at x > 0. Horizontal red solid and dashed lines indicate the locations of the “half-moon” boundary at x = 0 and the apparent −9◦ +9◦ backlighter peaks at x = xBL and x = xBL , respectively.
FIG. 1. Two space-resolving spectrometers located at ±9◦ with respect to the z-axis record the sample-transmitted backlighter images. Due to the angle difference, the spectrometers at ±9◦ ◦ see the ◦backlighter centered at different +9 −9 locations on the sample (i.e., xBL and xBL ). This parallax not only measures FeMg-attenuated and unattenuated spectra simultaneously, but it also characterizes the backlighter relative location with respect to the “half-moon” boundary, h and δ.
follows: ◦
◦
−9 x +9 − xBL 1 +9◦ −9◦ h = BL , δ= x + xBL 2tan(9◦ ) 2 BL
(1)
assuming that the source-to-detector distance is much larger +9◦ −9◦ − xBL . than xBL +9◦ −9◦ and xBL from the data, one has to unTo extract xBL derstand the emergent intensity spatial profiles measured at ±9◦ (Fig. 2). The x-axis is defined such that the “half-moon” boundary is at x = 0 and the FeMg-embedded region is at x > 0. The hypothetical transmission spatial profile at a given wavelength (blue) is systematically lower at x > 0 due to the FeMg attenuation. The apparent backlighter spatial profiles (green) are centered at different locations with respect to the
FIG. 2. Idealized schematics illustrate how the backlighter (green) observed at different angles results in different emergent intensity spatial profiles (magenta).
◦
◦
+9 −9 sample for the ±9◦ spectrometers (i.e., xBL and xBL , respectively). While most of the backlighter spatial profile is attenuated through the FeMg region on the +9◦ spectrometer, only the backlighter wing is attenuated through FeMg on the −9◦ spectrometer. As a result, one expects to see a double peak in the emergent spatial profile at +9◦ , while one expects a skewed single peak at −9◦ . Figure 3 shows the data recorded by the spectrometers at ±9◦ . Each image is the average over four slit images to improve the signal-to-noise ratio and to average out random defects in the individual slit images.6 The horizontal (spectral) and vertical (spatial) axes are produced by the KAP crystals and the slits, respectively. The dark vertical lines correspond to Fe or Mg bound-bound absorption lines. The image recorded at +9◦ shows longer Fe and Mg lines than those recorded at −9◦ due to the apparent backlighter peak locations (Fig. 2). +9◦ −9◦ and xBL , one has to extract the In order to measure xBL locations of the “half-moon” boundary and the apparent backlighter peak. To objectively extract them, we take a spatial lineout on a strong bound-bound absorption line. The magenta curves in Fig. 4 show an example for the Mg Heα line (i.e., absorption due to 1s2 − 1s2p He-like Mg transition) at ∼9.17 Å (lineout λ = 0.02 Å). As discussed earlier, the magenta curve at +9◦ has a double peak, while the one at −9◦ has a skewed single peak. We approximate the spatial profile in the absence of the Mg Heα (green curves in Fig. 3) by averaging two spatial lineouts taken on each side of the Mg Heα line. The lineout locations for the +9◦ image are indicated by vertical green dashed lines in Fig. 3. The Heα line transmission is determined from the ratio of the magenta and green curves. The resultant transmission spatial profiles clearly show lowtransmission FeMg embedded regions, and the x-axis is defined from its inflection point. We note that the “half-moon” boundary is not as sharp as the one in Fig. 2. This is because of the instrument spatial resolution and the sample hydrody+9◦ namics integrated over the backlighter duration. Once xBL ◦ −9 and xBL are defined by the apparent backlighter peak locations on the defined x-axis, the backlighter location, h and δ, can be estimated from Eq. (1).
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FIG. 4. The spatial lineouts are extracted from Fig. 3 at Mg Heα (magenta) and its nearby continuum (green). Mg Heα bound-bound line transmission spatial lineouts (blue) are extracted by dividing the magenta by the green. The “half-moon” boundary and the x-axis are defined based on the transmission −9◦ +9◦ spatial lineouts, and xBL and xBL are defined based on the continuum peaks.
III. RESULTS
Parallax is systematically applied to ten Fe opacity shots performed under different sample configurations.6 There are three different CH configurations and multiple different Fe thicknesses for each configuration. There is one shot where the sample is raised by 1.5 mm from its nominal location. For each shot, parallax is applied to the available bound-bound lines that are strong enough to define the “half-moon” boundary from their line-transmission spatial profiles. The number of usable lines depends on their areal density, Stark line width, and the spectral range of the spectrometers used. For each shot, the mean h and its standard deviation are computed from parallax results of two to seven Fe and Mg lines. Parallax results from Fe and Mg lines agree with each other. The validity of this uncertainty estimate was also verified from the shots with four spectrometers, two each at +9◦ and −9◦ .
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Figure 5 summarizes the measured h as a function of Te inferred from Mg K-shell spectroscopy.6 We confirm a strong anti-correlation between h and Te (Pearson correlation coefficient = −0.91). To investigate this point synthetically, we use a 3D view factor code VISRAD9 and a calibrated ZPDH intensity image from one of our experiments to calculate the heating radiation at the sample as a function of the sample distance from the ZPDH radiation source. The details of the calculation will be discussed elsewhere. The blue curve in Fig. 5 shows the resultant radiation brightness temperature, TB , as a function of h. This result suggests that the radiation source heats the sample to different temperatures due to source radiation geometric dilution. The radiation brightness temperature is systematically higher than Te due to the complex heating mechanism involving radiation transport and hydrodynamics and beyond the scope of this article. Figure 5 also shows that, for similar Te , shot-to-shot variation in the inferred h is larger than the individual measurement uncertainties due to the 3D radiation transport effects of the backlighter. While Eq. (1) is derived assuming an instantaneous point backlighter, the actual backlighter emission is a result of the radiation transport through the 3D ZPDH plasma, which spatially varies over a few ns duration. Thus, the variation in the inferred h comes from the irreproducibility in the evolution of 3D ZPDH plasma and the resultant irreproducibility in the line-of-sight dependent effects on the measurements. We found that h was anti-correlated to Te and confirmed that the sample reached a different temperature due to the geometric dilution of the radiation source. The parallax results are important (i) to better understand our platform and further optimize SNL Z opacity experiments and (ii) to better understand the sample heating and accurately evaluate how close our sample is to local thermal equilibrium. ACKNOWLEDGMENTS
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the (U.S.) Department of Energy (DOE) under Contract No. DE-AC0494AL85000. 1 D.
FIG. 5. There is a strong correlation between the measured electron temperature, Te , and the measured source-to-sample distance, h. The blue curve is a modeled radiation brightness temperature as a function of h.
Mihalas, Stellar Atmospheres, A Series of Books in Astronomy and Astrophysics, 2nd edition (W. H. Freeman, 1978). 2 T. Perry et al., Phys. Rev. E 54, 5617 (1996). 3 J. E. Bailey et al., Phys. Plasmas 16, 058101 (2009). 4 J. Bailey et al., Phys. Rev. Lett. 99, 265002 (2007). 5 G. A. Rochau et al., Phys. Plasmas 21, 056308 (2014). 6 T. Nagayama et al., Phys. Plasmas 21, 056502 (2014). 7 T. J. Nash et al., Rev. Sci. Instrum. 81, 10E518 (2010). 8 J. E. Bailey et al., Rev. Sci. Instrum. 79, 113104 (2008). 9 J. J. MacFarlane, J. Quant. Spectrosc. Radiat. Transfer 81, 287 (2003).
REVIEW OF SCIENTIFIC INSTRUMENTS 85, 11D604 (2014)
X-ray tests of a two-dimensional stigmatic imaging scheme with variable magnificationsa) J. Lu,1,b) M. Bitter,2 K. W. Hill,2 L. F. Delgado-Aparicio,2 P. C. Efthimion,2 N. A. Pablant,2 P. Beiersdorfer,3 T. A. Caughey,4 and J. Brunner4 1 Key Laboratory of Optoelectronic Technology and System of Ministry of Education, Chongqing University, Chongqing 400030, China 2 Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA 3 Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA 4 Inrad Optics, 181 Legrand Avenue, Northvale, New Jersey 07647, USA
(Presented 4 June 2014; received 31 May 2014; accepted 2 July 2014; published online 22 July 2014) A two-dimensional stigmatic x-ray imaging scheme, consisting of two spherically bent crystals, one concave and one convex, was recently proposed [M. Bitter et al., Rev. Sci. Instrum. 83, 10E527 (2012)]. The Bragg angles and the radii of curvature of the two crystals of this imaging scheme are matched to eliminate the astigmatism and to satisfy the Bragg condition across both crystal surfaces for a given x-ray energy. In this paper, we consider more general configurations of this imaging scheme, which allow us to vary the magnification for a given pair of crystals and x-ray energy. The stigmatic imaging scheme has been validated for the first time by imaging x-rays generated by a micro-focus x-ray source with source size of 8.4 μm validated by knife-edge measurements. Results are presented from imaging the tungsten Lα1 emission at 8.3976 keV, using a convex Si-422 crystal and a concave Si-533 crystal with 2d-spacings of 2.21707 Å and 1.65635 Å and radii of curvature of 500 ± 1 mm and 823 ± 1 mm, respectively, showing a spatial resolution of 54.9 μm. This imaging scheme is expected to be of interest for the two-dimensional imaging of laser produced plasmas. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4890248] I. INTRODUCTION
X-ray 2D imaging systems with high spatial resolution and high spectral resolution that are suitable for recording and analyzing the compression of the imploded core of fuel capsules are very much needed in inertial confined fusion (ICF) research. X-ray monochromatic backlighting imaging of high-density plasmas, using spherically bent crystals, is one of the most effective target diagnostic methods in the ICF diagnostics.1–5 Spherically bent crystals offer many advantages for the imaging of plasmas: they provide a much higher luminosity than pin-hole cameras and high spatial resolution over a large field of view (FOV); and they can also be placed at large distances from the plasma where they are not at risk of being destroyed. However, there is also the disadvantage that they must be operated at Bragg angles near 90◦ in order to minimize the astigmatism, regardless of whether the image is formed by self-emitted radiation or backlighting of an object with an external x-ray source. Such restrictions on Bragg angles along with the fixed interplanar spacing (2d-spacing) of crystals limit the wavelength range that can be used for these diagnostics. A modification of the traditional x-ray monochromatic backlighting scheme is the x-ray crystal imaging microscope (XCIM),6–10 where the Bragg angles can deviate substantially a) Contributed paper, published as part of the Proceedings of the 20th
Topical Conference on High-Temperature Plasma Diagnostics, Atlanta, Georgia, USA, June 2014. b) Author to whom correspondence should be addressed. Electronic mail: [email protected] 0034-6748/2014/85(11)/11D604/4/$30.00
from 90◦ , e.g., 76.7◦ .11 It was, however, clearly pointed out by Labate et al.12 that a nearly monochromatic beam with a bandwidth of several mÅ, propagating in the meridional direction, can only be obtained if the source is placed on the Rowland circle. While in some applications,11 the X-ray source needs to be inside the Rowland circle to collect more photons, with the cost of smaller imaged area on the object. In such configurations, there is always a compromise between intensity and FOV. In a previous paper,13 we proposed a novel, twodimensional, stigmatic x-ray imaging system, which consists of two concentric, convex and concave, spherically bent crystals. This stigmatic x-ray imaging system, which is also designed for a monochromatic light source, has the unique properties that the Bragg condition is simultaneously fulfilled at each point on two crystal surfaces, and it allows choosing a wide range of Bragg angles. It also has an adjustable magnification, which is uniform in all directions. In principle, this imaging system could therefore be used for x-ray imaging of large, spatially extended objects as well as small objects, such as laser-produced plasmas, where spatial resolution of the order of microns would be required. We also presented tests with visible light, which verified this new imaging concept. In this paper, more general configurations of this imaging scheme, with theoretically arbitrary magnifications are considered. We present results from first tests of this imaging scheme with x-rays. The main goals of these x-ray tests were to verify that the Bragg condition is indeed satisfied at each point on the two crystal surfaces and to measure the achievable spatial resolution.
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by selective optical filtering and a frequency shift of the probe beam before amplification. These techniques create a unique platform for performing spatially and temporally resolved measurements of the target evolution. We show results from an experiment at the Air Force Research Lab (AFRL) in which a flowing water jet target11, 12 is irradiated by nanosecond-scale and picosecond-scale pre-pulses that precede a 30-fs FWHM ultra-intense (1018 W/cm2 ) interaction. Section II describes the experimental setup, and Sec. III describes how the ultra-short timescale synchronization of the probe and pump pulse is achieved. Section IV describes the frequency shift of the probe pulse and selective filtering. Section V presents some preliminary data of the water jet expansion due to laser-target interactions, including Abel inversion of interferometric data. Section VI states our conclusions and describes how this instrument will be incorporated into future work. II. EXPERIMENTAL OVERVIEW
Interferometry and shadowgraphy are used to characterize plasma expansion in experiments at the AFRL at Wright Patterson Air Force Base in Dayton, OH. An 800 nm, 30-fs FWHM pump beam produces high intensities (1018 W/cm2 , 2.6 μm FWHM spot size) on flowing water jet column targets. To avoid disruption of the high intensity laser light as it propagates to focus and to prevent freezing of the water jet nozzle, the experiment is housed in a vacuum chamber that is held at 20 Torr partial vacuum using a thermocouple gauge solenoid valve feedback loop. Known pre-pulse artifacts of the amplification process pre-ablate the target, creating conditions of interest picoseconds and nanoseconds before the main laser pulse interaction. To interrogate these conditions, a 420 nm, 80-fs FWHM probe beam is passed through the interaction region and subsequently split to image the target for shadowgraphy and interferometry. The pump-probe experimental layout is shown in Fig. 1. The probe beam is frequency-shifted, as discussed in Sec. IV. Distortions to the probe pulse wavefront due to variations in the index of refraction along the line of sight are revealed by interfering the probe pulse with a reference pulse at the same frequency. In this laterally sheared Michelson interferometer setup,13 an image of the interaction region of the water jet is overlapped with a sheared image of the water jet downstream. Interference fringes shift in response to changes in line-ofsight index of refraction, allowing one to “see” ablated liquid and ionized plasma in a way complementary to shadowgraphy. With a high dynamic range timing setup (described next) and selective optical filtering, one can get a sense of the evolution of this ablated liquid and plasma. III. FEMTOSECOND RESOLUTION OVER MICROSECONDS
One commonly used approach to pump/probe experiment is to use two entirely separate femtosecond laser systems, synchronizing the laser oscillators via electronic signals. A typical setup gives picosecond stability between oscillators; achieving femtosecond stability requires advanced electron-
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FIG. 1. The experiment employs a high-intensity pump and low-intensity probe, relatively timed with better than 40-fs precision. The pump beam (sketched in red) and its pre-pulses irradiate the water jet target, creating a dynamic laser-plasma interaction region. The probe beam (sketched in blue) envelops the interaction region and is then split for target-imaged interferometry and shadowgraphy. Within the laterally sheared Michelson interferometer, a piezoelectric mirror allows for controlled adjustment of phase (mirror translation) and shear (mirror tilt). The shear angle is out of the page, though sketched in the plane of the page for easy visualization. Optical notch filters and an iris (spatial filter) exclude unwanted light such as that from plasma self-emission (see Fig. 2).
ics and a reduction in the output repetition rate.14 Utilizing two pulses from a single oscillator is simpler and results in a more stable relative timing. To achieve femtosecond relative precision in such a setup, the probe and pump beams must be seeded from a common oscillator. In a kHz system, a Pockels cell selects one oscillator pulse every millisecond to be further amplified as the pump pulse, rejecting all other pulses. The oscillator used in the experiment at AFRL produces pulses at 80 MHz, and the rejected pulses are routed into a second Pockels cell that selects a different pulse to be amplified as the probe pulse. By varying the pulse selected, coarse delays can be introduced between the pump and probe on the order of the oscillator rate, 80 MHz or 12.5 ns. After amplification, the probe pulse passes through a delay line. The double-passed delay line allows fine adjustments to the relative pump-probe delay, with < 40 fs resolution over 19 ns. Combining coarse and fine delay techniques results in 40 fs resolution over 10 μs, and potentially even longer times (e.g., 900 μs) if desired. The final resolution of the system is limited by the greater of the delay line resolution (< 40 fs in this setup) or probe pulse duration (80 fs in this setup). The combination of pulse seed selection and delay line adjustment allows roughly nine orders of magnitude temporal dynamic range. Fig. 3 exhibits this dynamic range, showing the pre-plasma expansion before the arrival of the main ultra-intense pulse (upper sequence) and the hydrodynamic response of the water jet over 10 μs of evolution (lower sequence). IV. ELIMINATION OF PLASMA SELF-EMISSION NOISE
Irradiated by the pump beam at 800 nm, the target will naturally emit light at the second harmonic (400 nm),15 which
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FIG. 2. The deleterious effect of plasma self-emission on the diagnostics is avoided by a frequency shift in the probe beam and aggressive optical filtering. (a) Near the critical surface of laser-plasma interaction, plasma selfemission at 400 nm saturates imagery. (b) To avoid this effect, the probe beam is frequency shifted to 840 nm, amplified, then frequency doubled to 420 nm. At the imaging cameras, notch filters are used to remove plasma self-emission at the pump’s second harmonic, 400 nm. The notch filter transmission band includes the entire probe beam spectrum and only the tail of the plasma selfemission spectrum. (c) The effect of the frequency shift and optical notch filters is to reveal previously obscured interaction areas.
is the source of the plasma self-emission that is the subject of this subsection. Plasma self-emission complicates and frustrates probe-beam interferometry and shadowgraphy because it obscures areas of interest near the critical surface (see Fig. 2(a)). The solution to this obfuscation problem, which we have implemented in this setup, is to apply optical filtering that excludes plasma self-emission while passing the probe beam. Even with specially selected optical notch filters, this is only possible if the probe spectrum sits outside of the plasma selfemission spectrum. However, because the pump and probe share a common oscillator, the probe pulse naturally shares the frequency of the pump harmonic. To circumvent this issue, the frequency of the probe pulse is shifted in two steps.
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Prior to amplification, the broadband 800 nm seed pulse of the probe beam is optically filtered using Schott RG850 glass, moving the central wavelength to 840 nm by preferentially attenuating lower wavelengths. Next, a hard spectral cutoff is applied in the pulse stretcher, by physically clipping lower wavelength regions of the beam during grating dispersion. This frequency-shifted (and much attenuated) pulse is next passed through a regenerative amplifier, which smooths the spectral profile, and after re-compression the pulse remains centered at 840 nm. Finally, the probe beam is frequency doubled to 420 nm via a β-barium borate crystal (AR/AR coated, 300 μm thick, Type I). During imaging, two optical notch filters (Semrock FF01-420/10-25; 10 nm bandwidth, and nominally 15 nm FWHM) select for the 420 nm probe and reject the plasma self-emission at 400 nm (Figs. 2(b) and 2(c)).
V. ACQUISITIONS AND ANALYSIS
By varying probe beam delay time, an image sequence can be created that shows the development of pre-plasma, the main ultra-intense pulse interaction, and the hydrodynamic recovery of the target (see Fig. 3). The image acquisitions are performed in the following way. A sequence of delay times is chosen so as to acquire many frames shortly before the main pulse interaction while keeping a wide temporal view of the interaction. Once programmed, the sequence is serially executed. To create a given delay, Pockels cell seed selection and delay line position are adjusted automatically. For each delay, one shadowgraphic frame and three interferometric frames are acquired (corresponding to three positions of the piezoelectric mirror which varies Michelson interferometer phase difference). Because stochastic events can cause occasional extreme outliers shot-to-shot, 10 images are acquired for each frame, corresponding to ten independent laser shots. The image most similar to the average is incorporated as the frame. Interferograms must be analyzed to recover phase data. Phase shifts are reconstructed from fringe shifts using the
FIG. 3. Precise probe pulse timing (< 40 fs resolution) over a wide dynamic range (> 10 μs) gives a detailed view of pre-plasma evolution, intense laser-plasma interaction, and target recovery. Upper sequence: Recovered phase shifts from interferometry show the in-vacuum development of pre-plasma nanoseconds before the main interaction, consistent with known pre-pulse on this timescale. Delay times relative to the main ultra-intense laser pulse are marked. Interferometric reconstruction after the main pulse arrives (≥ 0 fs, not shown) fails due to steep phase gradients. Lower sequence: Shadowgraphy shows timescales of in-air target evolution: hydrodynamic reaction in picoseconds, expansion in nanoseconds, and recovery in microseconds.
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FIG. 4. To aid in the reconstruction of phase dependent imagery from fringe shifts, three separate 120◦ phase-shifted (temporally sheared) interferograms are acquired for each probe delay. Left: an interferogram is shown for −15 ps delay for an in-vacuum target. Its corresponding phase image is reconstructed using the Speckle Phase of Difference algorithm in IDEA software – the vertical dashed line represents the rightmost boundary of reliable phase reconstruction. Abel inversion allows recovery of index of refraction and potentially electron density. Right: recovered index of refraction shifts for the interferogram at left are shown. The radial index change from negative to positive suggests pre-plasma on-axis and ablated neutral material off-axis.
IDEA software16 Speckle Phase of Difference algorithm (three-frame technique, 120◦ phase shift). Abel inversion can be performed to recover the changes in index of refraction (see Fig. 4 for an experimental example). Abel inversion analysis requires an added assumption of the experiment’s radial symmetry, about the laser axis. From the Abel inversion, electron densities can potentially be inferred. VI. SUMMARY AND CONCLUSIONS
We have described a frequency-shifted, femtosecondgated interferometric setup and demonstrated its capability for a flowing water jet experiment in which this target is irradiated by nanosecond-scale and picosecond-scale pre-pulses in advance of the arrival of an ultra-intense (1018 W/cm2 ) pulse. The combination of a timing system for observing evolution from femtoseconds to microseconds and elimination of plasma self-emission noise light delivers improved shadowgraphy and interferometry. Phase shift reconstruction from interferometry reveals changes in the index of refraction near the target. This information can be used to infer electron densities through Abel inversion. With precise optical filtering and by frequency shifting the probe pulse away from the selfemission frequencies, the problem of plasma self-emission is avoided. The diagnostic has been demonstrated to produce interferometric and shadowgraphic image sequences of lasermatter interactions which show nanosecond formation of preplasma, femtosecond interaction of the ultra-intense main pulse, picosecond hydrodynamic expansion, and microsecond recovery of the target. Fielding the diagnostic has already contributed in two ways to our experimental understanding. First, tens-of-microseconds target recovery time indicates that the experiment could be performed at significantly higher than
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kHz repetition rates. Second, expectations prior to the arrival of the main pulse of pre-plasma formation along the laser axis with neutral material off-axis are confirmed. By providing on-demand femtosecond resolution at arbitrary delay times, this diagnostic will soon be used to track the effects of known femtosecond-duration pre-pulses as they arrive on target picoseconds to nanoseconds prior to the main pulse, and to improve laser-driven electron acceleration and X-ray production techniques.17 Future improvements to the diagnostic may include additional views of the interaction region or on-the-fly interferogram analysis for fast feedback to the experimenter. ACKNOWLEDGMENTS
This research was sponsored by the Quantum and NonEquilibrium Processes Department of the (U.S.) Air Force Office of Scientific Research (USAFOSR), under the management of Dr. Enrique Parra, Program Manager. S.F. was supported in part by the DOD HPCMP high performance computing internship program. The authors thank Mario Manuel, University of Michigan, for insightful discussions. 1 T. Hosokai, K. Kinoshita, A. Zhidkov, K. Nakamura, T. Watanabe, T. Ueda,
H. Kotaki, M. Kando, K. Nakajima, and M. Uesaka, Phys. Rev. E 67, 036407 (2003). 2 M. Kaluza, J. Schreiber, M. I. K. Santala, G. D. Tsakiris, K. Eidmann, J. Meyer-ter Vehn, and K. J. Witte, Phys. Rev. Lett. 93, 045003 (2004). 3 K.-H. Hong, B. Hou, J. A. Nees, E. Power, and G. A. Mourou, Appl. Phys. B 81, 447 (2005). 4 C. Orban, M. Fatenejad, S. Chawla, S. C. Wilks, and D. Q. Lamb, e-print arXiv:1306.1584 [physics]. 5 F. Dollar, P. Cummings, V. Chvykov, L. Willingale, M. Vargas, V. Yanovsky, C. Zulick, A. Maksimchuk, A. G. R. Thomas, and K. Krushelnick, Phys. Rev. Lett. 110, 175002 (2013). 6 I. H. Hutchinson, Principles of Plasma Diagnostics (Cambridge University Press, 2005). 7 Z. Wu, X. Zhu, and N. Zhang, J. Appl. Phys. 109, 053113 (2011). 8 V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, and D. v. d. Linde, Appl. Phys. A 78, 483 (2004). 9 S. Le Pape, Y. Y. Tsui, A. Macphee, D. Hey, P. Patel, A. Mackinnon, M. Key, M. Wei, T. Ma, F. N. Beg, R. Stephens, K. Akli, T. Link, L. VanWoerkom, and R. R. Freeman, Opt. Lett. 34, 2997 (2009). 10 P. McKenna, D. Carroll, O. Lundh, F. Nürnberg, K. Markey, S. Bandyopadhyay, D. Batani, R. Evans, R. Jafer, S. Kar, D. Neely, D. Pepler, M. Quinn, R. Redaelli, M. Roth, C.-G. Wahlström, X. Yuan, and M. Zepf, Laser Part. Beams 26, 591 (2008). 11 J. Uhlig, C.-G. Wahlström, M. Walczak, V. Sundström, and W. Fullagar, Laser Part. Beams 29, 415 (2011). 12 W. Fullagar, M. Harbst, S. Canton, J. Uhlig, M. Walczak, C.-G. Wahlström, and V. Sundström, Rev. Sci. Instrum. 78, 115105 (2007). 13 Y. Y. Hung, Opt. Commun. 11, 132 (1974). 14 S. A. Crooker, F. D. Betz, J. Levy, and D. D. Awschalom, Rev. Sci. Instrum. 67, 2068 (1996). 15 D. von der Linde, H. Schulz, T. Engers, and H. Schuler, IEEE J. Quantum Electron. 28, 2388 (1992). 16 M. Hipp, J. Woisetschläger, P. Reiterer, and T. Neger, Measurement 36, 53 (2004). 17 C. Orban, J. T. Morrison, E. D. Chowdhury, J. A. Nees, K. Frische, and W. M. Roquemore, e-print arXiv:1405.6313 [physics].
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Parallax diagnostics of radiation source geometric dilution for iron opacity experimentsa) T. Nagayama, J. E. Bailey, G. Loisel, G. A. Rochau, and R. E. Falcon Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
(Presented 2 June 2014; received 2 June 2014; accepted 27 June 2014; published online 17 July 2014) Experimental tests are in progress to evaluate the accuracy of the modeled iron opacity at solar interior conditions [J. E. Bailey et al., Phys. Plasmas 16, 058101 (2009)]. The iron sample is placed on top of the Sandia National Laboratories z-pinch dynamic hohlraum (ZPDH) radiation source. The samples are heated to 150–200 eV electron temperatures and 7× 1021 –4× 1022 cm−3 electron densities by the ZPDH radiation and backlit at its stagnation [T. Nagayama et al., Phys. Plasmas 21, 056502 (2014)]. The backlighter attenuated by the heated sample plasma is measured by four spectrometers along ±9◦ with respect to the z-pinch axis to infer the sample iron opacity. Here, we describe measurements of the source-to-sample distance that exploit the parallax of spectrometers that view the half-moonshaped sample from ±9◦ . The measured sample temperature decreases with increased source-tosample distance. This distance must be taken into account for understanding the sample heating. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4889776] I. INTRODUCTION
Opacity quantifies photon absorption in matter and plays a crucial role in many high energy density plasmas, including inertial fusion plasmas and stellar interiors.1 Modeling opacities of ions with multiple bound electrons is very challenging and employs approximations that need to be experimentally validated.2, 3 Performing reliable opacity experiments is also challenging and must satisfy many criteria.2, 3 Measuring opacity becomes more difficult at higher temperature because the opacity sample has to be heated to the high temperature without significant gradients and has to be backlit by a bright radiation to minimize the effect of the hot sample plasma emission on the absorption measurement. The Sandia National Laboratories (SNL) Z machine (Z) provides a unique platform to perform opacity experiments at temperatures above 150 eV.4 The Z-pinch dynamic hohlraum (ZPDH) is a terawatt xray radiation source at Z that makes high-temperature opacity measurements possible.5 The opacity sample is located above the ZPDH radiation source and is radiatively heated. Most of the photons have energies above 600 eV. This powerful radiation streams through the sample and heats it without significant gradients.6 The ZPDH also provides a bright backlighter to mitigate the sample self-emission. Recently, we found that the opacity sample can reach higher temperatures and densities using the same radiation source only by changing the target configuration.6, 7 However, it was not clear why the change in the target configuration affects the sample temperature if the sample is heated by the same radiation source. To further optimize this high temperature opacity experimental platform, it is crucial to understand what dictates a) Contributed paper, published as part of the Proceedings of the 20th
Topical Conference on High-Temperature Plasma Diagnostics, Atlanta, Georgia, USA, June 2014.
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the sample temperature. In this article, we provide experimental evidence that the source-to-sample distance depends on the sample configuration. This distance controls the source geometric dilution at the sample, thereby affecting the sample temperature. II. SNL OPACITY EXPERIMENTS AND PARALLAX
The typical SNL opacity experimental setup is shown in Fig. 1. The target consists of a semi-circular FeMg sample sandwiched by a circular tamping material (e.g., plastic, CH), which we call a “half-moon” target. Mg is mixed in the Fe sample to diagnose the Fe conditions (i.e., electron temperature, Te , and electron density, ne ) using Mg K-shell spectroscopy.6, 8 This target is placed above the ZPDH radiation source, and the ZPDH radiation heats and backlights the sample.3, 5 The backlighter attenuated through the target is recorded by potassium acid phthalate crystal (KAP) spectrometers fielded along ±9◦ from the z-axis.8 An aperture above the target limits the spectrometers’ views to a 4 mm × 1 mm area. Each spectrometer has 4-6 slits, each 50 μm in width, at the halfway distance to the sample to provide spatial resolution of ∼0.1 mm along the aperture direction with a magnification of ∼1. The transmitted backlighter images are recorded on Kodak 2492 x-ray films with spatial and spectral resolution. Due to the finite source-to-sample distance, h, the spectrometer at +9◦ observes the backlighter bright spot through +9◦ , while the one at −9◦ the FeMg embedded side at xBL −9◦ observes it on the CH-only side at xBL (black dots in Fig. 1). This spectrometer configuration measures the FeMgattenuated and unattenuated spectra simultaneously, providing FeMg transmission spectra in a single experiment (shot). However, taking advantage of this parallax, we can also infer the backlighter location with respect to the “half-moon” +9◦ −9◦ and xBL as boundary (i.e., h and δ in Fig. 1) based on xBL
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FIG. 3. Backlighter images attenuated through the target recorded from −9◦ and +9◦ . FeMg is embedded at x > 0. Horizontal red solid and dashed lines indicate the locations of the “half-moon” boundary at x = 0 and the apparent −9◦ +9◦ backlighter peaks at x = xBL and x = xBL , respectively.
FIG. 1. Two space-resolving spectrometers located at ±9◦ with respect to the z-axis record the sample-transmitted backlighter images. Due to the angle difference, the spectrometers at ±9◦ ◦ see the ◦backlighter centered at different +9 −9 locations on the sample (i.e., xBL and xBL ). This parallax not only measures FeMg-attenuated and unattenuated spectra simultaneously, but it also characterizes the backlighter relative location with respect to the “half-moon” boundary, h and δ.
follows: ◦
◦
−9 x +9 − xBL 1 +9◦ −9◦ h = BL , δ= x + xBL 2tan(9◦ ) 2 BL
(1)
assuming that the source-to-detector distance is much larger +9◦ −9◦ − xBL . than xBL +9◦ −9◦ and xBL from the data, one has to unTo extract xBL derstand the emergent intensity spatial profiles measured at ±9◦ (Fig. 2). The x-axis is defined such that the “half-moon” boundary is at x = 0 and the FeMg-embedded region is at x > 0. The hypothetical transmission spatial profile at a given wavelength (blue) is systematically lower at x > 0 due to the FeMg attenuation. The apparent backlighter spatial profiles (green) are centered at different locations with respect to the
FIG. 2. Idealized schematics illustrate how the backlighter (green) observed at different angles results in different emergent intensity spatial profiles (magenta).
◦
◦
+9 −9 sample for the ±9◦ spectrometers (i.e., xBL and xBL , respectively). While most of the backlighter spatial profile is attenuated through the FeMg region on the +9◦ spectrometer, only the backlighter wing is attenuated through FeMg on the −9◦ spectrometer. As a result, one expects to see a double peak in the emergent spatial profile at +9◦ , while one expects a skewed single peak at −9◦ . Figure 3 shows the data recorded by the spectrometers at ±9◦ . Each image is the average over four slit images to improve the signal-to-noise ratio and to average out random defects in the individual slit images.6 The horizontal (spectral) and vertical (spatial) axes are produced by the KAP crystals and the slits, respectively. The dark vertical lines correspond to Fe or Mg bound-bound absorption lines. The image recorded at +9◦ shows longer Fe and Mg lines than those recorded at −9◦ due to the apparent backlighter peak locations (Fig. 2). +9◦ −9◦ and xBL , one has to extract the In order to measure xBL locations of the “half-moon” boundary and the apparent backlighter peak. To objectively extract them, we take a spatial lineout on a strong bound-bound absorption line. The magenta curves in Fig. 4 show an example for the Mg Heα line (i.e., absorption due to 1s2 − 1s2p He-like Mg transition) at ∼9.17 Å (lineout λ = 0.02 Å). As discussed earlier, the magenta curve at +9◦ has a double peak, while the one at −9◦ has a skewed single peak. We approximate the spatial profile in the absence of the Mg Heα (green curves in Fig. 3) by averaging two spatial lineouts taken on each side of the Mg Heα line. The lineout locations for the +9◦ image are indicated by vertical green dashed lines in Fig. 3. The Heα line transmission is determined from the ratio of the magenta and green curves. The resultant transmission spatial profiles clearly show lowtransmission FeMg embedded regions, and the x-axis is defined from its inflection point. We note that the “half-moon” boundary is not as sharp as the one in Fig. 2. This is because of the instrument spatial resolution and the sample hydrody+9◦ namics integrated over the backlighter duration. Once xBL ◦ −9 and xBL are defined by the apparent backlighter peak locations on the defined x-axis, the backlighter location, h and δ, can be estimated from Eq. (1).
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FIG. 4. The spatial lineouts are extracted from Fig. 3 at Mg Heα (magenta) and its nearby continuum (green). Mg Heα bound-bound line transmission spatial lineouts (blue) are extracted by dividing the magenta by the green. The “half-moon” boundary and the x-axis are defined based on the transmission −9◦ +9◦ spatial lineouts, and xBL and xBL are defined based on the continuum peaks.
III. RESULTS
Parallax is systematically applied to ten Fe opacity shots performed under different sample configurations.6 There are three different CH configurations and multiple different Fe thicknesses for each configuration. There is one shot where the sample is raised by 1.5 mm from its nominal location. For each shot, parallax is applied to the available bound-bound lines that are strong enough to define the “half-moon” boundary from their line-transmission spatial profiles. The number of usable lines depends on their areal density, Stark line width, and the spectral range of the spectrometers used. For each shot, the mean h and its standard deviation are computed from parallax results of two to seven Fe and Mg lines. Parallax results from Fe and Mg lines agree with each other. The validity of this uncertainty estimate was also verified from the shots with four spectrometers, two each at +9◦ and −9◦ .
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Figure 5 summarizes the measured h as a function of Te inferred from Mg K-shell spectroscopy.6 We confirm a strong anti-correlation between h and Te (Pearson correlation coefficient = −0.91). To investigate this point synthetically, we use a 3D view factor code VISRAD9 and a calibrated ZPDH intensity image from one of our experiments to calculate the heating radiation at the sample as a function of the sample distance from the ZPDH radiation source. The details of the calculation will be discussed elsewhere. The blue curve in Fig. 5 shows the resultant radiation brightness temperature, TB , as a function of h. This result suggests that the radiation source heats the sample to different temperatures due to source radiation geometric dilution. The radiation brightness temperature is systematically higher than Te due to the complex heating mechanism involving radiation transport and hydrodynamics and beyond the scope of this article. Figure 5 also shows that, for similar Te , shot-to-shot variation in the inferred h is larger than the individual measurement uncertainties due to the 3D radiation transport effects of the backlighter. While Eq. (1) is derived assuming an instantaneous point backlighter, the actual backlighter emission is a result of the radiation transport through the 3D ZPDH plasma, which spatially varies over a few ns duration. Thus, the variation in the inferred h comes from the irreproducibility in the evolution of 3D ZPDH plasma and the resultant irreproducibility in the line-of-sight dependent effects on the measurements. We found that h was anti-correlated to Te and confirmed that the sample reached a different temperature due to the geometric dilution of the radiation source. The parallax results are important (i) to better understand our platform and further optimize SNL Z opacity experiments and (ii) to better understand the sample heating and accurately evaluate how close our sample is to local thermal equilibrium. ACKNOWLEDGMENTS
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the (U.S.) Department of Energy (DOE) under Contract No. DE-AC0494AL85000. 1 D.
FIG. 5. There is a strong correlation between the measured electron temperature, Te , and the measured source-to-sample distance, h. The blue curve is a modeled radiation brightness temperature as a function of h.
Mihalas, Stellar Atmospheres, A Series of Books in Astronomy and Astrophysics, 2nd edition (W. H. Freeman, 1978). 2 T. Perry et al., Phys. Rev. E 54, 5617 (1996). 3 J. E. Bailey et al., Phys. Plasmas 16, 058101 (2009). 4 J. Bailey et al., Phys. Rev. Lett. 99, 265002 (2007). 5 G. A. Rochau et al., Phys. Plasmas 21, 056308 (2014). 6 T. Nagayama et al., Phys. Plasmas 21, 056502 (2014). 7 T. J. Nash et al., Rev. Sci. Instrum. 81, 10E518 (2010). 8 J. E. Bailey et al., Rev. Sci. Instrum. 79, 113104 (2008). 9 J. J. MacFarlane, J. Quant. Spectrosc. Radiat. Transfer 81, 287 (2003).
REVIEW OF SCIENTIFIC INSTRUMENTS 85, 11D604 (2014)
X-ray tests of a two-dimensional stigmatic imaging scheme with variable magnificationsa) J. Lu,1,b) M. Bitter,2 K. W. Hill,2 L. F. Delgado-Aparicio,2 P. C. Efthimion,2 N. A. Pablant,2 P. Beiersdorfer,3 T. A. Caughey,4 and J. Brunner4 1 Key Laboratory of Optoelectronic Technology and System of Ministry of Education, Chongqing University, Chongqing 400030, China 2 Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA 3 Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA 4 Inrad Optics, 181 Legrand Avenue, Northvale, New Jersey 07647, USA
(Presented 4 June 2014; received 31 May 2014; accepted 2 July 2014; published online 22 July 2014) A two-dimensional stigmatic x-ray imaging scheme, consisting of two spherically bent crystals, one concave and one convex, was recently proposed [M. Bitter et al., Rev. Sci. Instrum. 83, 10E527 (2012)]. The Bragg angles and the radii of curvature of the two crystals of this imaging scheme are matched to eliminate the astigmatism and to satisfy the Bragg condition across both crystal surfaces for a given x-ray energy. In this paper, we consider more general configurations of this imaging scheme, which allow us to vary the magnification for a given pair of crystals and x-ray energy. The stigmatic imaging scheme has been validated for the first time by imaging x-rays generated by a micro-focus x-ray source with source size of 8.4 μm validated by knife-edge measurements. Results are presented from imaging the tungsten Lα1 emission at 8.3976 keV, using a convex Si-422 crystal and a concave Si-533 crystal with 2d-spacings of 2.21707 Å and 1.65635 Å and radii of curvature of 500 ± 1 mm and 823 ± 1 mm, respectively, showing a spatial resolution of 54.9 μm. This imaging scheme is expected to be of interest for the two-dimensional imaging of laser produced plasmas. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4890248] I. INTRODUCTION
X-ray 2D imaging systems with high spatial resolution and high spectral resolution that are suitable for recording and analyzing the compression of the imploded core of fuel capsules are very much needed in inertial confined fusion (ICF) research. X-ray monochromatic backlighting imaging of high-density plasmas, using spherically bent crystals, is one of the most effective target diagnostic methods in the ICF diagnostics.1–5 Spherically bent crystals offer many advantages for the imaging of plasmas: they provide a much higher luminosity than pin-hole cameras and high spatial resolution over a large field of view (FOV); and they can also be placed at large distances from the plasma where they are not at risk of being destroyed. However, there is also the disadvantage that they must be operated at Bragg angles near 90◦ in order to minimize the astigmatism, regardless of whether the image is formed by self-emitted radiation or backlighting of an object with an external x-ray source. Such restrictions on Bragg angles along with the fixed interplanar spacing (2d-spacing) of crystals limit the wavelength range that can be used for these diagnostics. A modification of the traditional x-ray monochromatic backlighting scheme is the x-ray crystal imaging microscope (XCIM),6–10 where the Bragg angles can deviate substantially a) Contributed paper, published as part of the Proceedings of the 20th
Topical Conference on High-Temperature Plasma Diagnostics, Atlanta, Georgia, USA, June 2014. b) Author to whom correspondence should be addressed. Electronic mail: [email protected] 0034-6748/2014/85(11)/11D604/4/$30.00
from 90◦ , e.g., 76.7◦ .11 It was, however, clearly pointed out by Labate et al.12 that a nearly monochromatic beam with a bandwidth of several mÅ, propagating in the meridional direction, can only be obtained if the source is placed on the Rowland circle. While in some applications,11 the X-ray source needs to be inside the Rowland circle to collect more photons, with the cost of smaller imaged area on the object. In such configurations, there is always a compromise between intensity and FOV. In a previous paper,13 we proposed a novel, twodimensional, stigmatic x-ray imaging system, which consists of two concentric, convex and concave, spherically bent crystals. This stigmatic x-ray imaging system, which is also designed for a monochromatic light source, has the unique properties that the Bragg condition is simultaneously fulfilled at each point on two crystal surfaces, and it allows choosing a wide range of Bragg angles. It also has an adjustable magnification, which is uniform in all directions. In principle, this imaging system could therefore be used for x-ray imaging of large, spatially extended objects as well as small objects, such as laser-produced plasmas, where spatial resolution of the order of microns would be required. We also presented tests with visible light, which verified this new imaging concept. In this paper, more general configurations of this imaging scheme, with theoretically arbitrary magnifications are considered. We present results from first tests of this imaging scheme with x-rays. The main goals of these x-ray tests were to verify that the Bragg condition is indeed satisfied at each point on the two crystal surfaces and to measure the achievable spatial resolution.
85, 11D604-1
© 2014 AIP Publishing LLC
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