Time resolved spectroscopy of large bore Xe ... - OSA Publishing

Time resolved spectroscopy of large bore Xe flashlamps for use in large aperture amplifiers John H. Kelly, David C. Brown, and Kenneth Teegarden

Time resolved spectroscopy was performed on 13-mm xenon filled flashlamps. The use of a well-characterized system allowed the acquisition of absolute radiometric data. The data were compared to the predictions of a phenomenological flashlamp model and differences noted. Specifically the arc for equal currents is not the same for dI/dt > 0 and dI/dt < 0, the continuum is a stronger function of current density than the model indicated, and different lines, linewidths, and line intensities were found.

1. Existing Models

The design of final amplifiers in high energy, high peak power laser systems is immensely aided by the development of relatively simple conceptual models, which may be embodied in computer codes. Indeed the high cost of hardware for prototypes, coupled with the large number of variables in such optimizations, mandate the use of reliable models. In the discussion below we describe one of the two presently available flashlamp models and a confirmation of its validity on an instantaneous basis. It should be noted that a great deal of interest has arisen recently in modeling flashlamps for short-pulse low energy applications. The discussion here is limited to very high energy (>100-J/in arc length) long pulse (>10-Msec) flashlamps. The first developed of the two available flashlamp models was that of Church et al.1- 3 This model calculates from first principles the transport properties of an ionized monatomic gas, transition probabilities, and continuum absorptivities. Using these values it then iteratively solves transport equations for the temperature profile in the flashtube and spectral radiance at the plasma surface at any given current density. No dependence on the derivative of the current is mentioned. The published reports describe some time resolved spectroscopy done in verification of the model.4 5 While this model is undoubtedly the more comprehensive of

All authors are with the University of Rochester, Rochester, New York 14623; Kenneth Teegarden is in the Institute of Optics, and the other authors in the Laboratory for Laser Energetics. Received 20 May 1980. 0003-6935/80/223817-00$00.50/0. © 1980 Optical Society of America.

the two, it suffers on two accounts. First, it is far too complex to be easily integrated into other codes modeling the buildup of inversion density in laser media with the change in current through the lamp, and, second, it was implemented in ALGOL, a less widely used language. The Trenholme-Emmett 6 7 (TE) model provides only a phenomenological description of the flashlamp. Lamp spectral radiance is calculated as a product of a blackbody function and an emissivity term. The fundamental assumption is that the xenon plasma is a volume absorber-emitter. Furthermore, a uniform temperature profile is assumed. For a flashlamp containing 300 Torr of xenon, a particle density of -1019 cm-3 , and an average particle energy of n10 eV, the assumption of local thermodynamic equilibrium is valid. Under these conditions Kirchhoffs law applies, and the xenon plasma may be characterized by its absorptionemission coefficient a(X) via the familiar equation 8 L = LB(T) 1 - exp[-a(X)1]},

where LB (T) is the radiance of a backbody at temperature T, and 1 is the path length in the plasma of the emitted ray. To implement this equation three operations were performed. First, the equation was integrated over a solid angle noting that 1 is a function of angle. The integral so derived is not analytical and hence was approximated by a polynomial for small values of optical depth and an asymptotic expansion for large values of optical depth. Second, a(X, T) is needed. This was obtained from experimental measurements made by Emmett 9 et al. Using a monochromatic probe beam, these experimenters measured the transmittance of a 1.2-cm 300Torr flashlamp at 500-A intervals. It is not clear from the reference whether the section of the flashlamp that 15 November 1980 / Vol. 19, No. 22 / APPLIED OPTICS

3817

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Since this model was used only in a time-integrated way, any difficulties with the instantaneous temperatures determined in this fashion were masked. In particular, differences between the beginning of the pulse where dIldt > 0 and the end of the pulse where dIldt < 0 may compensate for and therefore mask each other. The functional form that Trenholme finally arrives at is 6

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the probe beam traverses has the same cross section as the rest of the lamp. To check whether the derivative of the current had any effect on the flashtube opacity, measurements were made at 50-pusec intervals during a high current pulse. These were then compared with measurements made at the current maximum of a series of increasing peak current shots. The two series were compared at equal current densities, and no differences were noted. This check, however, suffers from the fact that during the portion of the pulse where dIldt >0, the rate of change of current is very large, and an accurate value of I for comparison is difficult to obtain. The absorption-emission coefficient a(X,t) was found to vary quadratically with the current density in both the line and continuum regions over a range of current densities from a few hundred to a few thousand A/cm 2 . The continuum absorption emission coefficient for a current density of 1000 A/cm 2 is given by ac = 0.15 exp[-8(

-

0.7)2] + 0.01,

cm-1

where cxc is in and X is in microns. The third parameter needed to complete the model is T(I), where I is the current through the flashtube. In the original model a very convoluted method was used to obtain T(I). First, the output of the lamp model is spectrally and temporally integrated over the pulse with a fixed temperature used. The results of this integration are then plotted as radiative efficiency vs peak current density with temperature as a parameter. On this same graph is plotted the experimentally determined radiative efficiencies as a function of peak current density. The intersection of the experimental curve with parameterized curves from the model yields the temperature as a function of peak current density. This is approximated analytically and used in the model as instantaneous temperatures. A power weighting function is then developed, which in effect gives the relative amount of time that the lamp spends at a given current density. This is used along with the now instantaneous model to determine a pulse-averaged efficiency. The coefficients in the T(I) formula are then further adjusted to reconcile the pulse-averaged efficiencies with the experimental data. 3818

.

APPLIED OPTICS / Vol. 19, No. 22 / 15 November 1980

01 6

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) + (93DO. JO. ) ],

where D is in meters and J is in A/m 2 . This model, because of its convenience, has been incorporated into our inversion modeling code (INVDEN). Since the inversion modeling code is time instantaneous (i.e., dynamic), it became imperative to check and modify the TE model on the basis of our measurements. 11. Experimental Apparatus A.

Optical System

Time resolved spectroscopy on 13-mm bore lamps was used to check the model. A typical current pulse driving these lamps has a rise time of between 200 and 250 t.sec so time increments of 20 usec were chosen. Since the average spectral width of an Nd+3 in the glass absorption line is 250 A a minimum resolution of 25 A was necessary. To check the model completely, it would be necessary to measure the entire spectral output from the UV cutoff of the lamp wall at 2200 A to the water absorption at 25000 A. To limit the experimental problem to a manageable size, only the spectral region between 3400 and 9000 A, which includes all the major Nd+3 absorption bands, was investigated. The experimental apparatus is shown in Fig. 1. The ISIT head is essentially a series pair of image intensifiers preceding an e-beam read silicon target vidicon manufactured by Princeton Applied Research. The first image intensifier may be gated electronically by pulsing its cathode negative with respect to its focusing grid. Both the time and duration of the gate pulse could be varied. The gate width was normally kept in the 110-psec range. Below 1 usec it becomes difficult to control the gate pulse amplitude, which has a large effect on tube gain. Gate values beyond 10,usec are undesirable because the separation between sampling intervals is only 20 sec. The monochromatic is a 0.25-m Ebert f4 instrument. When used in first order this grating has a dispersion of 240 A/mm. For this work it was used in second order with a dispersion of 120 A/mm. At any given time only 1524 A of the lamp spectrum could be captured. Edge effects in the tube made it prudent to sample only 1000-A segments at a time, thus necessitating six flashes to acquire an entire spectrum. With a 25 -Mentrance slit, the resolution is limited by cross talk between channels to -7 A. To eliminate shot to shot variations, it was necessary to average several shots for a single segment spectrum. The main contributions to such variations come from slight changes in the pulse forming network (PFN)

charging voltage and slight movements of the arc itself within the bore of the tube. The constraint on the amount of averaging to be done is the requirement that the spectroscopy be completed in a small fraction of the lamp's life to avoid lamp aging effects. If one takes the average life of a lamp conservatively to be 10,000 shots, one would like to complete the time resolved spectroscopy in -1000 shots. If a 500-,usec flash is to be observed at 20-,usec intervals with six segments per time interval, five shots may be averaged per segment to complete the spectroscopy in 750 total shots. Because the monochromator was operated in second order, it was necessary to discriminate against third and higher overlapping orders. Color glass filters were used even though these tended to introduce chromatic aberrations. An effort was made to equalize the optical path through the filter used for each segment so that refocusing would be unnecessary. The availability of filters with the correct bandpass dictated an unusual choice of center wavelengths. The color filters were placed away from image planes and behind the neutral density filters to avoid introducing filter fluorescence. The fi5 reflecting optics were used to image the arc onto the entrance slit of the monochromator. The curved mirror had a focal length of 258.8 mm with a diameter of 76.2 mm. The angle of incidence on both flat and curved mirrors was kept as low as possible, .6.5°, to minimize aberrations. Typically these large bore lamps are operated at 35-45% of their rated explosion energy. Lamps operated in air in this regime last for fewer than 100 shots before they fail explosively. The same lamp operated in a water jacket did not fail for more than 103 shots. Deionized water with a monitored resistivity of >1 M Q cm was used for cooling. The lamp jackets were 1.2-mm Pyrex, 20-mm o.d. Because the Pyrex showed an increase in absorption from 4000 A down, corrections were made for it. The lamp jacket, cooling water, and lamp wall all acted as an anamorphic lens. A ray trace indicated the shift of focal plane for meridional rays, and the lamp assembly, mounted on precision vernier slides, was moved 0.754 mm to compensate. In all cases the desired plane of focus was the plasma surface. During the experiments this was assumed to be the same as the inner side of the wall of the flashtube. Note that the depth of field 6 is given by'( 6 = D 2f3/A, where D is the distance to lens, A is the aperture, and 3 = 2X/A, the angle to the first Airy ring: = 2D2 X/A;

A = 76 mm; D = 751 mm; X = 0.0005 mm; and 6 = 0.1 mm. This is a very conservative estimate of the depth of field as it neglects aberrations other than diffraction. The actual depth of field is probably two to four times larger. The TE model assumes (for 13-mm 0 lamps) a cool sheath around the plasma of 0.377 mm. This assumed sheath is a time averaged value, while the actual sheath varies with time or current.

Fig. 2. Block diagram of the OMA. Signal flow indicated by boldface lines.

The anamorphic lensing introduces astigmatism into the system. Because the imaging optics operate at fi10 on the object side this is not a problem. The focal shift due to the lamp wall, water, and jacket in the vertical plane is 1.0310 mm in the same direction as the shift for the meridional plane. The difference between the two shifts is 0.277 mm, well within the depth of field. For convenience of focusing, the lamp was put at the plane of best meridional focus. A functional diagram of the Optical Multichannel Analyzer (OMA) 1 ' is shown in Fig. 2. The instrument consists of two connected units, an ISIT head, and control console. The control console contains two 500-word memories, analog-to-digital converters, and control and timing circuitry. In operation an array of photodiodes is e-beam scanned vertically column by column for 500 columns. The e-beam current required to charge each column of diodes is proportional to the number of photons incident on each column. For each column the current is digitized and stored in one word of one of the memories. The use of the two memories allows the acquisition of signal plus dark current option in one memory and dark current in the other. The analog subtraction of dark current was not used. A display option allows the difference of the two memories to be shown. Both memories are cumulative, that is, they allow the addition of a current signal to the signal(s) already stored. In this way the five shots could be summed in one memory. The console also contained a parallel-to-serial converter so that either of the memories or their difference could be transmitted to another device. The OMA console and a terminal were multiplexed to a modem, which in turn was connected to a Control Data 6600 computer (6600). All data processing was done on the 6600. This immensely facilitated calibration. Calibration was performed by substituting an Optronics Laboratories model 550 tungsten standard of spectral radiance. This standard is traceable to NBS. Like most tungsten radiators the Optronics source can be characterized by constant emissitivity at wavelengths shorter than -4000 A, and a wavelength-dependent emissivity for wavelengths >4000 A. These both multiply a Planck's function at 2610 K. 15 November 1980 / Vol. 19, No. 22 / APPLIED OPTICS

3819

The Ebert configuration monochromator as supplied by PAR is essentially a self-calibrating device. Initial setup is limited to centering the zero-order image of the slit on the middle channel of the ISIT. Wavelength calibration of each segment can be checked against the position of known xenon lines. The monochromator was resettable to within l10 A. All spectroscopy was performed with the lamp in a large aluminum box, which was anodized black. The box reduced EMI and ensured that no light was coupled back to the lamp itself. B.

PFN

Figure 3 shows an equivalent circuit for the PFN used in the 13-mm bore time resolved spectroscopy. This PFN was designed to drive a 21-sec of arc length with the same current pulse as proposed for use in driving a 28-sec of arc length for the OMEGA X laser booster amplifier.1 3 This is a 500-,usec 3'L- pulse width. The initial charge on the capacitor was 7000 ± 25 V for a stored energy of 6737 i 50 J; 1010 J of this energy was the calculated loss to the 123-MQ resistance. 1 4 The 5727 J delivered to the lamp are 31% of explosion energy. Deionized water with a resistivity >1 MQ cm was used as a coolant. The maximum current was 5300 A. The 0-8-kV low current supply and 50-kQ resistor were used as a constant current source to operate the lamps in simmer modes. Initial triggering was done with a 30-kV pulse to a nonreflecting back plane. Operation in the nonsimmered mode was precluded by the large amount of EMI generated by the trigger pulse. Figure 4 is a plot of the theoretical and experimental currents vs time. The theoretical curve was generated from the code LAMCUR using measured PFN component values. There are several points to be noted. First, the area underneath the two curves is approximately equal as the charge on the capacitor in both cases 3820

APPLIED OPTICS / Vol. 19, No. 22 / 15 November 1980

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ISIT Characterization

The ISIT head as supplied by PAR consists of an RCA 4804 SIT tube that has been coupled by PAR to a C20000 series inverting intensifier, also from RCA. The SIT tube is an extremely linear device. The ISIT head has several unique attributes that must be either carefully controlled or measured so that they may be corrected for. For the purposes of this experiment, the important measurements are: (1) Seidel distortion; (2) gain variations with gate voltage; (3) target lag; (4) shine through; (5) signal-induced noise; and (6) dynamic range. Seidel distortion was compensated for in the plotting program. Gate voltage and target lag were carefully controlled. Intensifier shine through was compensated for in the calibration process. Signal-induced noise was measured to be insignificant. Dynamic range was measured to be -40, which was adequate. Details are described elsewhere. 1 2 C.

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Predicted (left) and measured (right) pulse forming network current vs time.

is equal. The second effect is the slight delay between the leading edge of the theoretical curve and the experimental curve of -20 Asec. This is due to the time it takes for the arc to fill the bore of the lamps and correlates well with the minimum seen in voltage traces when the arc stops expanding. The third effect is an additional widening of the experimental pulse compared with the theoretical one by -25 sec. One would be reluctant to ascribe this to an error in measurement of the PFN parameters as this 4% change in pulse width translates into an 11% error in capacitance or inductance. The L and C were checked with an impedance bridge. LAMCUR calculates the current on the assumption that the lamp characteristic is strictly given by 1 5 V = Ko i 1/2, where Ko has the same sign as i and is given by Ko = 1.27-

liPHP0.2' -5

D 450

where and D are the arc length and bore of the flashtube in similar units, and P is the fill pressure in torr. We attribute the additional width to a weak hysteresis in the characteristic. This conclusion is borne out by the time-resolved spectroscopic results. No attempt was made to model this pending further voltage measurements.

For equal currents through the flashlamp, before and after the current peak, the radiances at a given wavelength are not equal. The radiance is determined by the emissivity and the blackbody temperature. The emissivity was determined by a direct measurement of flashtube opacity. 1 7 The blackbody temperature was

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ments. The T(J) function was therefore modified to match temperatures determined from these data by dividing the measured radiance by the measured emissivity from Ref. 17 and fitting a blackbody to the resultant. Four parameters were varied in the fit using a nonlinear least squares routine. This was done only for time intervals between 40 and 220 sec. This time trval was ch e ascosen for the fit because the current peak occurred at 245 ± 7 ,sec, and the arc is fully developed, as evidenced by voltage traces, at 40 Msec. Any changes due to pressure increase, a change in radial temperature profile, increase in arc diameter, or any other change in the arc for a constant current density are left to be modeled as an effective change in arc diameter, which stranslates into an effective change of opacity. Two spectra, taken at approximately the same current density, are shown in Figs. 5 and 6. The modified T(J) T(J) = [(9450D0 *0 3J0O01) 6 + (102.0D0.27 J0.35)6]1/6.

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Fig. 6.

Flashlamp spectral radiance at 420 ,usec into flash with a current density of 2643 A/cm 2 .

Because of these slight differences between the calculated and measured current values, the measured current value was always used as input to the TE model for comparison to measured spectra. Ill.

Experimental Results

Three disagreements were noted with the model predictions: (1) The arc is not the same with the same current density for dlidt > 0 and dIldt