Nike KrF laser for laser plasma instability research

A grid image refractometer (GIR) has been implemented at the Nike krypton fluoride laser facility of the Naval Research Laboratory. This instrument simultaneously measures propagation angles and transmissions of UV probe rays ( λ = 263 nm, ∆ t = 10 ps) refracted through plasma. We report results of the first Nike-GIR measurement on a CH plasma produced by the Nike laser pulse ( ∼ 1 ns FWHM) with the intensity of 1 . 1 × 10 15 W / cm 2 . The measured angles and transmissions were processed to construct spatial profiles of electron density ( n e ) and temperature ( T e ) in the underdense coronal region of the plasma. Using an inversion algorithm developed for the strongly refracted rays, the deployed GIR system probed electron densities up to 4 × 10 21 cm − 3 with the density scale length of 120 µ m along the plasma symmetry axis. The resulting n e and T e profiles are verified to be self-consistent with the measured quantities of the refracted probe light. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http: // dx.doi.org / 10.1063 / 1.4927452]


I. INTRODUCTION
Knowing plasma conditions in the underdense coronal region is crucial to understanding physical processes of laser plasma instabilities (LPIs) 1 in laser fusion research. The LPIs have been a major obstacle to achieving fusion ignition with high energy gain due to their destructive capabilities such as decrease of the laser energy deposition and preheat of the DT fuel before arrival of the imploding shock. In large scale plasmas relevant to laser fusion, two plasmon decay (TPD) and stimulated Raman scattering (SRS) draw particular attention among various LPIs for their low thresholds 1 and hot electron generation 2 that preheat the target. These instabilities exist in the underdense coronal region near or lower than the quarter critical density (n ec /4), where n ec is the critical density of the driver laser light. As predicted by linear theory, 1 the growth of the instabilities is dependent on the density scale length and temperature of the coronal plasma. Measurements of spatial profiles of electron density and temperature are, therefore, essential to the study of LPI initiation, which can lead to mitigating the harmful LPI effects and supporting better fusion target designs.
Optical techniques such as interferometry have provided a valuable way for measuring the plasma density profile by detecting phase changes in optical probe light traveling through the plasma. 3 But these techniques become deficient at higher plasma density which causes significant deflection of the probe light due to refraction. Ultraviolet laser interferometry, for instance, has been the primary density diagnostic for laserproduced plasmas and reported measurements of electron densities up to ∼1 × 10 21 cm −3 on plasmas with relatively small sizes. 4,5 Generally, ultraviolet interferometry is restricted to density-length products less than 2 × 10 19 cm −2 , limiting the a) Electronic mail: jaechul.oh@nrl.navy.mil maximum plasma density and size that can be diagnosed. 6,7 Thus, its observation is limited to electron densities below the order of 10 20 cm −3 for mm-size plasmas that are routinely created at large laser facilities in laser fusion research.
Over the last several decades of laser fusion research, the preference of the laser drive has been shifted towards short wavelength laser illumination (from infrared to ultraviolet). This transition has been directed by well known advantages of a short wavelength driver, i.e., efficient laser absorption, reduction of hydrodynamic instabilities, and higher LPI thresholds. Currently, all major laser fusion facilities operate in ultraviolet at 351 nm 8 or deep-ultraviolet at 248 nm. 9 Using the short wavelength laser drive, on the contrary, has made the density diagnostics more challenging in reaching the quarter critical density region since the critical density increases strongly as the laser wavelength decreases (n ec ∝ λ −2 laser ). For example, the quarter critical density is 2.3 × 10 21 cm −3 for λ laser = 351 nm and 4.5 × 10 21 cm −3 for λ laser = 248 nm. Experimental data are presently limited in this density region. Hence, numerical simulation has been the primary way to assess n e and T e profiles in plasmas produced by modern fusion laser drivers.
Grid image refractometry (GIR) 10 is an optical probing technique for determining electron density profiles especially in long scale-length plasmas. It was proposed to access higher plasma densities by measuring propagation angles of probe rays refracted by plasma (Fig. 1). When probe light passes through a grid, it is broken up into a well-defined two dimensional array of small beamlets. The beamlets are then sent from the side and refracted through the plasma plume. Apparent cross-sectional profiles of the emerging beamlets can be imaged at two or more object planes for measuring individual deflection angles. One contrasting difference of GIR from plasma interferometry is its ability to trace each probe beamlet. This provides unique advantages of using GIR for diagnosing plasma parameters. First, the impact parameters of all the probe beamlets are known with GIR, allowing more rigorous comparisons with theoretical predictions. Second, the angle measurement requires not absolute locations of the object planes but the relative distance between them. Hence, GIR is not sensitive to the focusing error (between the object plane and the plasma symmetry axis) originating from shot-to-shot variation of the irradiating laser pointing on the target. 11,28,29 And specifically in this article, the capability of measuring individual beamlet angles with known impact parameters was necessary to develop an iterative algorithm for constructing density profiles self-consistent with the measurement as described in Section III B. One other difference of GIR from interferometry is that GIR does not depend on probe-beam coherence. The deflection angle measurement is thus associated with geometrical (rather than wave) optics, making GIR more flexible to large light deflections than interferometry. 3 In addition, as pointed by Craxton et al., the probe pulse duration for GIR can be much greater than the fringe-blurring time, and hence GIR does not require inconveniently short probe times. 10 While the micron-size fringe resolution of interferometry is lost, the spatial resolution of GIR, determined by the grid spacing, is still adequate for long scale-length plasmas which are typical in laser fusion research. Therefore, one can expect to diagnose a higher density region with GIR for the plasmas in laser fusion research. Using 0.26 µm ultraviolet probe light and 50 µm grid spacing, the earliest GIR experiment measured a density profile up to n e ∼ 1 × 10 21 cm −3 . 10 The GIR method naturally provides a way to determine the electron temperature profile by simultaneously measuring beamlet transmissions (or absorptions) through the plasma. A shorter wavelength probe such as soft X-ray lasers, 6,12 if practical for the GIR implementation, 13 may be preferable to reach high electron density regions. However, the absorption of the X-ray probe is too small to measure in the coronal density region of interest suggesting that a longer wavelength probe should be used for the transmission measurement. We calculated absorption of 263 nm light through a plasma profile created by the FASTRAD3D code 14,15 with Nike laser parameters for the LPI studies. The resulting absorption values were around 50% along the ray trajectories near the quarter critical density region. Hence, the GIR technique with ultraviolet probing was expected to be feasible for the simultaneous measurements of both temperature and electron profiles.
The Nike krypton fluoride (KrF) laser of the Naval Research Laboratory (NRL) is the highest energy kryptonfluoride laser in operation and provides unique environments for laser fusion research with its short wavelength (248 nm), large bandwidth (1-3 THz), and echelon-free induced spatial incoherence (ISI) beam smoothing. [16][17][18][19] In the present paper, we report a new implementation of the GIR system on the Nike KrF laser facility and its application for measuring profiles of density and temperature in a plasma created for LPI research in the NRL KrF laser fusion program. In Sec. II, the arrangement and operation of the Nike-GIR system are described as well as the experimental parameters of the Nike laser for creating the plasma. In an attempt to probe a high density plasma region near the quarter critical density, the GIR optical system was designed using a steep (f/1.8) aspherical lens for the wideangle collection of the refracted probe rays. In Sec. III, we present measured data, data reduction, and the profiles of density and temperature in the coronal region. The density profile was first constructed under the assumption of weak refraction. This, however, revealed significant discrepancies in the beamlet angles in the high density region close to the target surface. A feedback algorithm was developed to remove this inconsistency and the resulting self-consistent density profile solution is reported. The derived density profile was then used to estimate the temperature profile from the measured transmission data. A summary with future expectations is given in Sec. IV.

A. Plasma Production
The plasma was created from a flat polystyrene (CH) target (190 µm thick and 1 mm wide) illuminated by the Nike main beams (λ = 248 µm and 0.8 ns FWHM). The individual laser beams were focused on the target surface by the final focusing lenses (f/40) within the 21 • × 21 • square array as shown in Fig. 2(a). The target was mounted to be normal to the center axis of the incident beam lines. We measured the focal intensity profile of the overlapped laser at low laser energy prior to the full energy shot. The measured focal profile was well-fitted with a circular Gaussian distribution with 210 µm FWHM and used to represent the full energy laser profile. The quality of the actual full energy beam overlap was monitored by imaging the plasma with an X-ray pinhole camera (hν > 1 keV). The standard Nike pulse shape diagnostics were operated to measure laser pulse shapes from 5 main beams. The probe laser illumination is slightly tilted toward the negative z-axis by 8.7 • from the x-axis. CCD#1 and CCD#2 record beamlet images at the object planes at x = 0.12 mm and x = 1.52 mm, respectively.
Calorimeter readings were also taken from 4 beams to estimate the total laser energy. The laser intensity was then defined as the average intensity within the FWHM spot size at the laser peak time.
In support of the LPI research for the laser fusion energy program, it was desired that the performance of the new Nike-GIR system should be tested with a LPI-compatible plasma, i.e., one capable of hosting LPIs in its corona. Previous Nike LPI experiments 20 reported observation of parametric instabilities from plasmas produced by Nike laser pulses with intensities above 1 × 10 15 W/cm 2 . In order to examine the plasma parameters in the LPI environments, the current experiment was conducted with a laser intensity of 1.1 × 10 15 W/cm 2 on target. We simultaneously operated time-resolved spectrometers for light detection at 300-550 nm and confirmed spectral signatures of TPD and the hybrid mode of TPD and SRS 20,21 radiating from the plasma presented in this paper.

Refractometer
We implemented the GIR technique on the Nike target facility during the recent LPI experiment as shown in Fig. 2(a). The main design goal was to reach deep into the corona near the quarter critical density (of λ = 248 nm) region by collecting the probe light in a wide angle from the plasma. The probe laser of GIR was a short (∼10 ps) 4th harmonic (λ = 263 nm) pulse of a Nd:YLF laser beam (energy ∼100 µJ). It was sliced into small beamlets passing through a copper-mesh grid of 51 × 51 µm periodicity with 28 × 28 µm square openings. The beamlet array was relayed by fairly slow (f/12) telescope optics onto the target center from the side with 1:1 magnification. The depth of focus of the telescope was measured to be 4 mm at the target. In order to let the beamlets pass through the more inner (higher density) region of the plasma, the beamlet illumination was slightly tilted toward the target surface by 8.7 • from the side-on direction. Cartesian coordinates were defined as described in Fig. 2(b) and used throughout this paper.
The probe rays were collected within a cone angle of 32 • using a steep (f/1.8) aspherical lens and sent to two imaging modules with CCD cameras. 22 The cross-sectional beamlet profiles were imaged from two different object planes near (x = 0.12 mm) and off (x = 1.52 mm) the target center onto CCD#1 and CCD#2, respectively. The image resolutions were 2.1 and 4.3 µm/pixel for CCD#1 and #2, respectively. Narrow bandpass filters (λ = 263 nm, 3 nm FWHM) were positioned in front of the CCD cameras to block self-emission light from the plasma. The obtained CCD images provided apparent positions of the individual beamlets at the two selected object planes. The shift in the apparent positions of each beamlet was divided by the relative distance ∆x obj = 1.40 mm between the object planes to calculate the deflection angle. As mentioned in Sec. I, GIR requires the relative distance between the object planes for the angle measurement, and thus avoids a potentially significant measurement error when the absolute location of the plasma is not known accurately. In this experiment, physical positions of the object planes were accurately measured but the absolute plasma location might slightly change due to the actual pointing of the Nike main beams (overlapped) varying from shot to shot. The GIR angle measurement does not suffer from this uncertainty in the absolute location of the laser illumination. The accuracy of the relative distance between the object planes was within ±30 µm, i.e., smaller than 2% of ∆x obj . Sample GIR images taken with no target (Fig. 3) demonstrate that the image qualities were high enough for locating individual beamlets at both the object planes. It is notable that the focal depth (4 mm) of the f/12 relay telescope optics conveniently encompassed the object planes.
The individual beamlet probes were identified with two dimensional indices (i, j) where i = 0-14 and j = 0-15 as shown in the plasma-free images (Fig. 3). The impact parameters ( y i , z j ) were defined by these unperturbed beamlet locations -the coordinates of the (i, j)-th beamlet at x = 0, i.e., in the y z-plane containing the center axis of the Nike beams. The target surface at x = 0 was located at the mid-plane between z 11 and z 12 within ±15 µm uncertainty. The impact parameters are, therefore, given by where i 0 (=8) and j 0 (=11.5) are the indices of locations of the center axis of the Nike beams and the target surface at x = 0, respectively. It should be noted that when the target was loaded at the shooting position, the probe rays in the columns of j = 11-15 were blocked by the solid volume of the target.

Transmission diagnostic
The Nike-GIR system was also equipped with the capability of measuring transmissions of the probe beamlets for the determination of plasma temperature profiles. Since probe laser performance varied from shot to shot due to the thermal sensitivity of the laser cavity, the incident probe laser intensity profile was monitored for every shot as illustrated in Fig. 2(a). The probe laser intensity profile was sampled on the grid right after the probe light slicing and recorded by CCD#3 with 1:2 optical magnification. The recorded profile was then used to calibrate intensities of the emerging probe beamlets out of the plasma. To account for contamination of vacuum optics from previous shots, we obtained a set of reference GIR images with no target shortly before the Nike target shot. The transmission of the (i, j)-th beamlet was then calculated by the following formula: where I preshot 0 and I preshot 1 are intensities in the preshot images recorded by CCD#3 and CCD#1, respectively, and I 0 and I 1 intensities in the target shot images taken by CCD#3 and CCD#1, respectively. It should be noted that the self emission contribution to I 1 was pre-excluded for the transmission calculation, see Section III A.

Timing fiducial
The relative timing of the GIR probe snapshot and the Nike laser pulse was measured by the optical fiducial diagnostic as shown in Fig. 2(a). Partial intensity of one Nike main beam was picked off the beam line in the Nike propagation bay after the main amplifiers and then optically combined with the probe light sampled before entering the target chamber. The obtained light signal was resolved in time by a fast phototube (60 ps rise time) providing a fiducial timing for the GIR measurement. The measured timing between the two laser pulses (the Nike main beam and the probe light) was used to determine the actual snapshot time with respect to the drive laser pulse arrival on target.
The fiducial timing was pre-calibrated by firing both the Nike main beam at low energy and the GIR probe laser onto a thin UV beam splitter placed at the target center. The two beams were collinearly overlapped by the beam splitter and relayed into the fiducial phototube to measure the relative timing of the two laser pulses on target. The fiducial calibration was then completed by comparing timings of all of the four laser pulse events at the phototube: two delivered from the beam splitter at the target center and the other two from the fiducial diagnostic as described in the previous paragraph.

A. Background emission subtraction
Our GIR optical system could pick up significant background intensities from thermal radiation of the hot plasma. The thermal light, due to its naturally broad angle radiation, can fill the collection angle more effectively than the highly directional GIR probe light. Moreover, the plasma emission was accumulated on the CCD sensors during the entire plasma evolution (>10 ns) while the probe laser was a snapshot flashing only in 10 ps. The narrow bandpass filters were placed in front of CCD#1 and #2 to block most of the background radiation, but the signal-to-background ratios of the GIR images were still measured to be as low as 1.5 with the available energy (∼100 µJ) of the GIR probe laser pulse. Hence, data reduction started with digital removal of the background. This step was necessary for making meaningful measurements of the beamlet transmissions. It is noted that the deflection angle measurement was insensitive to the detected background.
In contrast to the localized appearance of the beamlets, the background intensity varied smoothly over a fairly large area as shown in Fig. 4(a). Thus, the whole background profile was still well represented by intensities in the beamlet-free region where the localized beamlet areas were excluded. In other words, the missing background intensities in the excluded local areas could be recovered from the slowly changing trend of the background. We numerically separated the background profile via the following steps. First, the beamlet areas were manually excluded. Horizontal lineouts were then taken at selected vertical positions between the beamlet rows and fitted to polynomial functions. By performing spline interpolation along every vertical line across the obtained horizontal polynomials, the complete 2-dimensional background profile was recovered as displayed in Fig. 4(b). Last, the background distribution was subtracted from the original raw GIR image for the background-free image of the beamlets. The background-subtracted GIR images are displayed in Fig. 5.
As shown in Fig. 5(c), the timing fiducial diagnostic detected that the GIR probe laser flashed across the plasma 80 ps earlier than the peak time of the Nike laser pulse. The accompanying time-resolved LPI spectrometers observed signatures of TPD and the hybrid mode from the plasma near the laser peak time including the GIR snapshot time. This confirms that the GIR images presented in this paper were captured through a LPI-hosting plasma as intended to support the LPI research at Nike.

B. Electron density profile
The spatial distribution of the electron density was constructed in three steps: deflection angles of the probe light were extracted from the beamlet locations recorded in the GIR images, optical path differences (OPDs) of the individual beamlets were calculated from the angle data, and then the density profile was built by Abel-inverting 3 the OPDs for the cylindrically symmetric plasma structure. We first performed the inversion process under the weak refraction approximation 3 that has been commonly adopted in optical probing techniques. The obtained density profile, however, was inconsistent with the GIR measurements in the high density region, indicating that the effect of strong refraction had to be taken into account. A new inversion algorithm was then developed to find a self-consistent density profile, as will be described in this section.
The apparent beamlet displacements, ( y ′ , z ′ ), were defined as the difference between the refracted probe ray positions (see Fig. 5) and the corresponding unperturbed preshot positions (see Fig. 3). Comparing these apparent locations in the two object planes at x = 0.12 mm and 1.52 mm, the deflection angle components θ y and θ z in the y and z directions, respectively, were computed by the following formulas: where 1.52 and 0.12 represent the object planes at x=1.52 mm and 0.12 mm, respectively, i and j are indices of the incident beamlet indicating the i-th row and the j-th column (Fig. 3), and ∆x obj the distance between the two object planes (1.40 mm). It is noted that the impact parameters of the (i, j)-th beamlet are ( y i , z j ) as given by Eqs. (1) and (2). Within the collection angle of the f/1.8 lens, the 2% measurement uncertainty in ∆x obj estimates the instrumental error to be smaller than 0.3 • for the angle measurement, see Eq. (A1) in the Appendix. The obtained angles are plotted with respect to the impact parameters in Fig. 6 showing that the GIR system has collected probe rays in a wide range of deflection angles (0 • -25 • ). Assuming weak refraction (θ y, z ≪ 1 radian) through the plasma, the deflection angles can be directly related to the optical path difference (P) of the probe ray, 3 where P =  [1 − µ(x, y, z)]ds is accumulated along the ray trajectory with the refractive index µ = (1 − n e /n ec,263nm ) 1/2 . Note that when no plasma exists, the ray angles become θ y = θ z = 0 • . Based on the formulas in Eq. (6), we obtained optical path differences, P meas , by integrating θ y (θ z ) in the y (z) direction along selected pathways starting from a reference position. Beamlets in the outermost region (z 0 = 590 µm) experienced the weakest refraction (θ z ≃ 1 • and θ y ≃ 0 • ), and thus, we selected the (i 0 ,0)-th beamlet as the reference for the P meas evaluation setting P meas (i 0 , 0) to zero. Note that i 0 = 8 as defined in Eq. (1). The angle integration was then performed starting from ( y 8 , z 0 ) to every beamlet location ( y i , z j ) via two pathways: integrating θ z along z from ( y 8 , z 0 ) to ( y 8 , z j ) then θ y along y towards ( y i , z j ) to yield P 1 (i, j), and, if the angle data are available at every point along the pathway, integrating θ y along y from ( y 8 , z 0 ) to ( y i , z 0 ) then θ z along z towards ( y i , z j ) to yield P 2 (i, j). Since fewer beamlet points were available for the outer columns due to the circular shape of the viewing area as shown in Fig. 3, the actual pathway for the P 2 (i, j) calculation was established with additional steps: when the circular viewing boundary was encountered during the y-integration, the z-integration was performed toward the next inner column then the y-integration was resumed in the new column. The P meas components were evaluated as mean values of P 1 and P 2 and used for the density extraction. Ideally under the weak refraction approximation, the angle integration should be independent of the pathways, i.e., both P 1 and P 2 should be equal. We observed acceptable agreements in the optical path difference calculations: the average value of |P 1 − P meas |/P meas was 0.03 in the high density region where z j ≤ 180 µm.
In Fig. 7, the resulting P meas 's are plotted against the impact parameters y i and z j , showing good cylindrical symmetry with respect to y = 0. The P meas values, however, did not fall to a sufficiently low level at the lateral edges (| y | ∼ 400 µm) of the GIR viewing area, so the lack of measurements in the large y region could cause uncertainty in the inversion process. We circumvented this problem by extrapolating the P meas data into the large y region, i.e., fitting the data to a reasonable formula. Hinted by the Gaussian distribution of the Nike laser intensity at the target surface, we adopted a Gaussian form for the fitting. As shown in Fig. 7, the P meas data were excellently fitted to the least-squares Gaussian curves with standard deviations smaller than 2% of the peak values. Hence, we assumed that the OPD profiles were Gaussian over a sufficiently large area. The obtained Gaussian formulas of P meas 's were then used in the inversion process for the density profile extraction. In order to construct the cross-sectional density profile at a fixed distance z = z j , Abel inversion requires OPD values, P 0 (i, j), accumulated along straight line trajectories parallel to the x-axis passing the given impact parameter points (0, y i , z j ). Under the weak refraction approximation, the measured OPDs (P meas ) were considered to be accumulated on the unaltered straight lines (8.7 • -tilted) of the incident probe beamlets through the plasma. Assuming the plasma profile was cylindrically symmetric and locally linear in z near the z = z j plane, one can approximate P meas (i, j) to the OPD along the straight line parallel to the x-axis, P 0 (i, j) ≡  [1 − µ(x, y i , z j )]dx, as follows: The Abel inversion then reveals the plasma refractive index µ(x, y, z) from the OPD profile as follows: where r =  x 2 + y 2 and P 0 ( y, z j ) is the Gaussian curve from the P meas data fitting at the impact parameter z j . Another advantage of inverting the analytical fit curve was the avoided numerical error amplification associated with the differentiation of experimental data. Repeating the inversion process at every z j parameter, the 3-dimensional density profile n e (r, z j ) = n ec,263 nm {1 − [µ(r, z j )] 2 } was constructed for the z distances of 130-590 µm from the target surface ( Fig. 8(a)). The resulting densities ranged from 5 × 10 19 cm −3 up to 3.3 × 10 21 cm −3 at the symmetry axis, r = 0.
Due to the large deflection angles (up to 25 • as shown in Fig. 6) observed in this experiment, the validity of the weak refraction approximation was in question. We investigated the self consistency of the obtained density profile with the measured angles to address this question. The ray-tracing method 23 was used to calculate the beamlet angles refracted through the n e profile: a continuous 3-dimensional density profile was first established from the Abel-inverted n e distribution by bicubic spline interpolation 24 and then ray trajectories were numerically traced through the density profile for the individual incident probe beamlets. The agreement between the measured deflection angles and the ray-traced ones of the emerging rays from the plasma profile is displayed in Figs. 8(b) and 8(c). Good agreement was observed in the relatively low density region (n e 2 × 10 21 cm −3 ) as expected from its small deflection angles. Discrepancies were, however, clearly appreciable in the higher density region, suggesting that the weak refraction approximation results in underestimated electron densities. An iterative numerical algorithm was designed to find a self-consistent density profile that minimizes the deflection angle discrepancies (Fig. 9). Starting with the density profile constructed under the weak refraction approximation, we computed numerical quantities during each iteration stage for every probe beamlet: P 0 (i, j), the OPD integrated along the parallel line to the x-axis with the impact parameters y i and z j , and θ y,ray (i, j) and θ z,ray (i, j), the deflection angles in y and z, respectively, determined by ray-tracing through the given n e profile. P ray (i, j) was then calculated by integrating θ y,ray (i, j) and θ z,ray (i, j) along the pathways as described earlier for the P meas (i, j) calculation from the measured deflection angles, see Eq. (6). Differences between P ray and P meas were then negatively fed back into P 0 as follows: The computed OPD profile P ′ 0 (i, j) was then Abel-inverted to update the n e profile for the next iteration stage. The sequence of the algorithm converged to a stable solution fairly rapidly -no significant changes were observed after four iterations. FIG. 9. Flow chart of algorithm to find a density profile with self-consistency between the ray-traced beamlet angles (θ y,ray and θ z,ray ) and the measured ones (θ y,meas and θ z,meas ). The OPD discrepancy P ray (i, j) − P meas (i, j) is used as the tracking error to converge towards the desired output θ z,ray (i, j) ≈ θ z,meas (i, j) and θ y,ray (i, j) ≈ θ y,meas (i, j). The results from the 6th iteration are plotted in Fig. 10, indicating that the solution is reasonably consistent with the measured quantities of the experiment. The θ z -plot ( Fig. 10(b)) demonstrates that the self-consistency was remarkably improved for the inner beamlets at z 8 and z 9 and left relatively unchanged from the weak refraction solution for the outer ones. The θ y -plot (Fig. 10(c)) also shows enhanced agreement with the measured angles. As displayed in Fig. 10(a), the algorithm resulted in increased n e values from the ones given by the weak refraction approximation. At the innermost distance (z 9 = 130 µm), the accessible density was as high as 4.1 × 10 21 cm −3 . This density level exhibits the diagnostic capability of the GIR, using the ultraviolet probe light, to examine electron densities up to 0.23n ec for the Nike laser (λ = 248 nm) or 0.46n ec for the third harmonic laser (λ = 351 nm) of other laser facilities in the inertial confinement fusion research. By fitting the density values along the z-axis to an exponential form, n e (z) = n e0 exp(−z/L n ), the density scale-length (L n ) was estimated to be 120 µm over the broad region of densities near or less than the quarter critical density of the 248 nm wavelength light as shown in Fig. 11. The lateral profiles of n e in the x y planes at z = z j were virtually Gaussian in r with the full width of ∼600 µm at the half maximum.

C. Electron temperature measurement
In addition to the experimental determination of the electron density profile, the GIR method inherently provides a diagnostic way to evaluate plasma temperatures from its capability of the simultaneous measurement of the probe beamlet transmissions. Assuming that the probe light was collisionally absorbed with free electrons in the corona of the plasma, one can derive a formula to estimate the electron temperature out of the measured ray transmission (or absorption) data.
For non-magnetized plasma, the collisional absorption coefficient K is given by 25 K = ν e c n e n ec,263 nm where ν e is the electron collision frequency, c is the light speed, and µ is the local refractive index in the plasma as mentioned earlier. The collision frequency for the fully ionized plasma has the form 25 where Z i is the average ion charge, m e the electron mass, k B the Boltzmann constant, e the electron charge, T e the electron temperature, and lnΛ e the Coulomb logarithm of collisions between electrons. For k B T e ≥ 10 eV, we used 25 lnΛ e = 24.4 − ln(n 0.5 e,cm −3 /T e,eV ), with n e in cm −3 and T e in eV. The ray transmission Tr( y, z) can then be calculated by integrating Eq. (10) in x, Rewriting Eq. (13) as we get the Abel-inverted formula for K, Since the n e profile was given by the angle measurement and K is a function of n e and T e , one may use Eq. (15) to extract the T e profile out of the transmission data via Abel inversion. The beamlet transmissions were measured at x=0.12 mm by Eq. (3) as plotted in Fig. 12(a). In the outer region (z j ≥ 390 µm) where the peak densities were lower than  4 × 10 20 cm −3 , the plasma was observed to be quite transparent (attenuated less than 10%) to the UV probe light and the temperature extraction was thus not feasible for the poor signal-to-noise ratio of the absorption. In the inner region (z j ≤ 340 µm) where electron densities were higher, the transmission values (25%-80%) became more favorable for the temperature estimate, but available data were limited by the beamlet overlaps caused by the strong refraction. The number of the overlapped beamlets might be reduced if the object plane was taken at a slightly negative x position away from the collection lens. 26 Ray-tracing the incident beamlets through the density profile obtained in Sec. III B, we found that most beamlet overlaps were avoided if the object plane was chosen at x = −(0.1-0.3) mm instead of x = 0.12 mm. This will be tested in future experiments at Nike. In this paper, we analyzed the transmission data collected from non-overlapped beamlets at z 5 = 280 µm for the temperature investigation. The obtained transmission data appeared to be insufficient to meet the requirement for the Abel inversion process. The absorption -or ln(1/Tr) in Eq. (14) -did not decrease enough within the detection area and, different from the refraction angle case, it was difficult to find an acceptable data trend into the far region (| y | > 400 µm). Hence, instead of seeking a temperature profile via Abel inversion, we took a reverse approach: we assumed a T e profile, calculated transmissions of the probe rays through the measured density profile using Eq. (10)- (13), and then compared them with the measured transmission values. The first trial was made with a constant temperature profile. We repeated the above steps for various constant T e values ranging from 300 eV to 3500 eV in search of a reasonable match to the measured data. The resulting transmission profiles, however, were too narrow to represent the data as displayed in Fig. 12(b). This implies that the temperature should generally decrease as the | y |-value increases, since transmission decreases with temperature as seen in Eq. (10). One plausible candidate for the temperature shape was the Gaussian form given by T e (r, z j ) = T e0 e −r 2 /(0.5∆ T ) 2 * l n(2) , where T e0 and ∆ T are the peak temperature at the center and the full width at the half maximum, respectively. We again repeated the steps for various T e0 's (300-3000 eV with a 10 eV step) and ∆ T 's (200-1000 µm with a 10 µm step). The best fit occurred with the temperature profile of T e0 = 1380 eV and ∆ T = 400 µm showing reasonable agreement with the measured transmission data as plotted in Fig. 12(b).

IV. SUMMARY AND FUTURE PROSPECTS
We added a GIR diagnostic suite to the Nike target facility and measured deflection angles and transmissions of ultraviolet (λ = 263 nm) probe rays traveling through a plasma produced for laser fusion research. The GIR system demonstrated the capability of diagnosing the probe rays refracted over a wide range of angles (0 • -25 • ) as designed to measure plasma parameters in the underdense coronal region of interest.
The measured deflection angle profiles were processed to extract electron densities. The density profile obtained under the typical assumption of weak refraction, however, showed significant discrepancies between the computed ray trajectories and the measured ray angles in the inner region where strong refraction should take place. We thus developed a numerical algorithm to construct density profiles in which the probe ray trajectories were iteratively modified with the measured deflection angles. This approach was realizable with the GIR capability of measuring individual probe ray angles with known impact parameters. The resulting 3-dimensional density profile exhibited strong self-consistency with the GIR observations. We report that electron densities were accessible up to 4.1 × 10 21 cm −3 which is equivalent to 0.23n c and 0.46n c of λ laser = 248 nm and 351 nm, respectively, and the density scale length was 120 µm along the center axis of the Nike laser in the coronal plasma.
The simultaneously measured ray transmission data were also examined to estimate electron temperatures. We found that a Gaussian temperature profile with T peak = 1.4 keV and 400 µm FWHM was acceptable to represent the transmission data measured at the distance of 280 µm from the target surface where the peak electron density was 1.4 × 10 21 cm −3 . The Abel inversion, however, was not applicable to the temperature profile extraction due to the insufficient data limited by the size of the GIR detection area (diameter of 0.8 mm) on the target. The next experiment will be performed with a wider viewing area of the GIR (diameter of 1.6 mm) for more thorough experimental determination of the spatial profiles of the plasma parameters.
We are also planning an extension to a shorter wavelength ultraviolet probe for the GIR measurements adopting a fifth harmonic (λ = 213 nm) generator for the Nd:YAG laser. The ray-trace calculation was performed to investigate propagation of the 213 nm probe light through the plasma density profile obtained in this paper. The computed ray trajectories suggested that the fifth harmonic light might provide insight into a deeper coronal region with densities ∼20% higher than the ones reached by the 263 nm probe light. The new probing system will be implemented for the next GIR experiments at Nike.