Measurements of Spectral Emission and Absorption of a High
`Pressure Xenon Arc in the Stationary and the Flashed Modes
`
`Lothar Klein
`
`Concurrently with emission measurements of a high pressure xenon a1'c in the spectral range 3000 A to 2 1.4,
`its absorption in the ir was measured by a technique based on modulating the less intense radiation of a
`carbon are used as background source. The emission measurements were repeated with a rapid scanning
`spectrometer while flashing the xenon are for 0.1 sec at 10 kW, which is five times the normal power input.
`The are showed excellent stability and reproducibility both in the stationary and the flashed modes. The
`intensity increase of the continuum was proportional to the increase of power input during the flash. A
`simple expression was derived connecting the spectral radiance of the continuum directly with the tem-
`perature and pressure of the arc. The temperature profile of the xenon arc was obtained using this ex-
`pression and also by applying the Pla.nck—Kirchhoff method to the Abel inverted emission and absorption of
`an ir xenon line. Both approaches show fair agreement at the arc center. The wavelength dependence
`of the correction factor for departures from hydrogenic behavior of the xenon continuum was derived from
`the measured spectral radiances and compared with theoretical calculations.
`
`I.
`
`Introduction
`
`Emission spectra are extensively used in plasma
`diagnostics, but only rarely is the absorption of arc
`plasmas measured quantitatively. One reason seems
`to be the widely held opinion that are plasmas at
`atmospheric pressure viewed over short optical paths
`are always optically thin, except for the resonance lines.
`Another reason is the difficulty of finding a suitable
`background source
`for
`absorption measurements.
`Laboratory plasmas,
`typically at 10,000°K are so
`much brighter than the brightest light sources com-
`monly available (e.g., carbon arc or tungsten strip
`lamp),
`that the latter are unsuitable. Finally,
`the
`methods for deriving the radial distribution of emission
`and absorption coefficients of optically thick arc
`plasmas from line-of—sight measurements have been
`slow to develop, and this has limited the value of ab-
`sorption spectra for plasma diagnostics. Freeman and
`Katz were the first to obtain a practical solution for the
`Abel inversion of plasmas with self—absorption,1 but a
`more general approach was only recently found by
`Elder et al.2 Elder el al. also derived the radial tem-
`
`perature profile by the Planck-Kirchhoff method from
`the Abel inverted emission—absorption measurements.
`To demonstrate their method, Elder et al. used a plasma
`seeded with sodium and determined the temperature
`from a sodium resonance line. The peak temperature
`
`The author is with the Warner & Swasey Company, Control
`Instrument Division, Flushing, New York 1 1354.
`Received 10 October 1967.
`
`was below 3000°K, which is not typical for a laboratory
`plasma.
`Tourin3 found that the strong ir lines of argon can
`become optically thick (self-absorbing) at atmospheric
`pressure. He measured the absorption by a technique
`based on modulating the radiation from the back-
`ground source;
`thus, absorption measurements can be
`made even when the intensity of the plasma is higher
`than the intensity of the background source. For the
`measurements reported in Ref. 3 a tungsten strip lamp
`could be used, because the mismatch of intensities in
`their is less than at shorter wavelengths.
`If absorption
`measurements of plasmas are to be extended into the
`visible or uv regions of the spectrum, however, a much
`brighter light source has to be used.
`The high pressure xenon arc appears to have the
`desired characteristics. Since the early measurements
`of Baum and Dunkelmanf‘ its strong continuum in the
`uv and visible part of the spectrum is known to be
`considerably more intense than the radiation from the
`carbon arc. Goncz and l\'ewell’s"’ recent work with
`
`stationary and flashed xenon arcs covers a more ex-
`tended spectral
`range. However,
`their data were
`obtained by measuring the spectral
`irradiance from
`these arcs and are therefore of limited value for a back-
`
`ground source evaluation, where the spectral radiance
`of the brightest part of the arc is the parameter‘ of
`interest. The peak temperature of a high pressure
`xenon arc has been determined by Kopec“ from wave-
`length scans of two ir lines, using Bartels’ method’ to
`estimate the peak temperature of an inhomogeneous
`plasma from line—of—sight emission measurements of
`lines showing self-reversal.
`
`April 1958 / Vol. 7, N0. 4 / APPLIED OPTICS 677
`
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`ASML 1231ASML 1231
`(cid:34)(cid:52)(cid:46)(cid:45)(cid:1)(cid:18)(cid:18)(cid:20)(cid:19)
`ASML 1231
`
`ASML 1231
`
`

`
`ll. Experimental
`
`The optical system used for the measurements of the
`stationary arc is shown schematically in Fig. 1. The
`xenon lamp housing was mounted on a linear drive
`table for traversing the arc laterally to the optical axis
`with a precision of 0.01 mm. Through circular open-
`ings in the lamp housing on the two sides along the
`optical axis, light from the background source could be
`focused on the xenon arc, and the light emerging from
`the arc was collected by the foreoptics and focused on
`the entrance slit of the monochromator. For emission
`
`measurements of the arc in the stationary mode, a
`chopper placed in front of the entrance slit was used;
`for absorption measurements another chopper modu-
`lated only the radiation from the background source.
`By synchronous rectification of the ac signal from the
`detector, absorption was measured without interference
`from the dc signal due to the emission from the xenon
`are. This technique of concurrent measurement of
`emission and absorption has been described in greater
`detail by Tourin.”
`into units of
`The conversion of detector output
`spectral radiance was achieved by calibration against a
`tungsten strip lamp, done in two steps. A tungsten
`strip lamp, held at a constant voltage, was used as a
`reference lamp and incorporated into the foreoptics of
`the Perkin-Elmer monochromator (RL in Fig. 1). This
`type of lamp is also a standard component of the
`Warner & Swasey Model 501 rapid scanning spectrome-
`ter used in conjunction with the flashed xenon arc.
`The reference lamps can be imaged onto the entrance
`slit simply by rotating a mirror and their signal com-
`pared with the signal for the arc. This is done im-
`mediately after each measurement to eliminate errors
`due to changes in slit setting or electronic drift. From
`time to time the reference lamp is checked,
`in turn,
`against another strip lamp, which is positioned at the
`same location as the arc and whose spectral radiance is
`determined,
`following standard practice,
`from its
`
`Fig. 1. Optical system used for concurrent measurements of
`emission and absorption of the stationary xenon arc.
`
`EM. CHOP.
`
`The absorption of a xenon arc has been measured by
`Rovinskii and RazumtseVa,3 using another xenon arc
`as a background source. They determined the plasma
`to be optically thick, but, because of the use of inter-
`ference filters
`instead of a monochromator,
`their
`measurements were of poor spectral resolution and
`limited to three wavelength bands in the visible.
`It was the primary purpose of the work described
`here to measure by a refined technique the spectral
`absorption of the high pressure xenon arc and, simul-
`taneously, its emission. The temperature could then
`be derived by the Planck-Kirchhoff method. Local
`values for homogeneous zones of
`the plasma were
`obtained by Abel inversion, applying the technique of
`Elder el. (11.3 to the absorption measurements. A con-
`sistency check was made by comparing the temperature
`profile of the are obtained by the Planck-Kirchhoff
`method with the temperature profile derived inde-
`pendently from the emission measurements of the con-
`tinuum using the modified Kramers-Unsoeld theory.
`Since the xenon plasma is optically thick, recourse to
`seeding as in the work reported in Ref. 2 was unneces-
`sary. Because of its high electron density, the xenon
`plasma can be expected to be in strict local thermo-
`dynamic
`equilibrium.
`Thus,
`these measurements
`should provide a good case for comparing the emission—
`absorption method with established diagnostic tech-
`»niques for plasmas based only on emission.
`Concurrently with this program, the spectral radi-
`ance measurements were used to evaluate the xenon
`
`are as a background source for absorption measure-
`ments of plasmas. We selected a commercially avail-
`able high pressure xenon arc* since, as a distinct
`advantage, this lamp can be flashed at ten times the
`normal power input for pulse durations of the order of a
`tenth of a second. The increase of spectral radiance
`was measured with a rapid scanning spectrometer de-
`veloped in this laboratory.T
`
`* Hanovia 4101039.
`
`1‘ Warner & Swasey Model 501 rapid scanning spectrometer.
`
`Fig. 2. Zones of ditferent brightness in the high pressure xenon
`arc:
`(1) cathode spot, (2) are plasma, (3) red halo.
`
`678 APPLIED OPTICS / Vol. 7, No. 4 / April 1958
`
`6
`
`

`
`temperature accurately measured with an optical
`pyrometer.
`It has been our experience that this pro-
`cedure increases the ease of intensity measurements
`without loss of accuracy.
`The image of the xenon are projected on a screen
`appears to the eye as shown in Fig. 2. A small area of
`intense brightness—the cathode spot—~is discernible
`within the bell-shaped arc plasma. A dim reddish
`glow partially envelopes the cathode and extends from
`the cathode to the round tip of the anode. This phe-
`nomenon to which no reference in the literature could be
`found, is called here red halo.
`It has the characteristic
`of being asymmetric with respect to the arc axis and
`this asymmetry appeared always at the same location
`when the arc was started. When the arc is turned off,
`the red halo does not disappear instantly as does the
`bright central arc region, but persists over several
`seconds. We believe that it originates from convec-
`tively heated xenon gas streaming upwards from the
`white hot cathode.
`
`Our measurements were made in a horizontal plane
`through the arc containing the cathode spot, i.e., the
`hottest region of the xenon plasma. The entrance slit
`of both the spectrometers used was masked to a height
`of 0.25 mm, since spatial scanning of the arc in the
`Vertical direction had shown that near the center, i.e.,
`in the region of major interest, intensity gradients over
`this length were still small.
`In the stationary mode the arc was run at a current of
`100 A at 22.5 V. A welder rectifier with line voltage
`compensator and ripple filter* proved to be a con-
`venient and stable power supply. By displaying the
`output of the two detectors (1P21 and PbS) on an
`oscilloscope, the ac ripple of the light intensity was
`measured to be less than 2% in both cases.
`If started
`from cold, the arc reached a stable regime in about 5
`min, then the long term drift measured over 30 min was
`of the order of 1% for the peak of Xe I0 9923 A, and
`less than 5% for the continuum at 5000 A. When the
`arc was extinguished and restarted with the current
`control of the rectifier at a fixed position, spatial scan-
`ning of the arc proved that the cathode spot always
`formed at exactly the same location with very good
`repeatability of light intensity (typically to within 2%
`for the peak of Xe I 9923 A).
`It is standard practice to use a condenser discharge
`for flashing the xenon arc”;
`the total pulse duration
`is then at most of the order of a few milliseconds. To
`make the flashed xenon arc useful as an extremely
`bright source for absorption measurements in con-
`junction with modern fast scanning spectrometers, a
`different
`approach was
`followed. A water—cooled
`stainless steel tube was used as a resistor capable of
`dissipating a high load and was connected to the
`rectifier in parallel with the xenon arc.
`In the simmer-
`ing mode, 100 A flowed through the xenon arc and
`450 A through the parallel resistor. A power switch
`was used to flash the are by manually opening the
`
`EMISSION
`..__J
`
`7°
`“‘ABSORPT|0N
`ZERO LINE
`
`Fig. 3. Strip chart record for emission—absorption measurements
`of the cathode spot of the xenon arc. The gain was 20 for the
`emission and 350 for the I0 and absorption scans. Slit width:
`30 p.
`
`showed that
`resistor circuit. Oscilloscope displays
`after a fast rise time of the order of a few milliseconds,
`constant lamp current and voltage, i.e., a steady state,
`was achieved for the duration of the flash (typically
`100 msec). For our measurements we flashed the
`lamp at 10 kW, although double this power is still
`permissible.
`
`Ill. Measurements
`
`A. Stationary Mode
`A Perkin-Elmer Model 98 monochromator was used
`and the detector (IP21 tube or PbS) output displayed
`on a strip chart recorder. Measurements were made
`in the spectral range from 3000 A to 2.7 /.6, using a glass
`prism. Absorption measurements were made with a
`carbon aI'C'f‘ as background source. We resorted to
`hand regulation of the arc since the automatic regulator
`provided by the manufacturer was not sensitive enough
`for our purpose. The carbon are operated best under
`the conditions recommended by Null and Lozier,1° with
`a 6.5—mm thick pure graphite anode and the current
`held at about 11 A just below the hissing point. The
`use of a 6—mm diam cored cathode (Norris H), however,
`gave a definite improvement in arc stability over the
`thin (3.2-mm), pure graphite rod specified by Null and
`Lozier. This is in agreement with recent observations
`by Magdeburg and Schley.”
`Since long term stability of the carbon arc could’ not
`be achieved, it proved advisable when measuring the
`lateral absorption profile, to obtain an ID reading in
`conjunction with every measurement. This was also
`indicated because of other considerations (see Sec.
`V. A). Owing to its excellent
`reproducibility,
`ex-
`tinguishing and restarting the xenon arc did not alter
`its characteristics. A typical emission and absorption
`record is shown in Fig. 3. The absorptance of Xe 1
`
`* Miller SRH—444-Cl with LVC-3.
`
`T Made by Spindler & Hoyer, Goettingen, W. Germany.
`
`April 1968 / Vol. 7, No. 4 / APPLIED OPTICS 679
`
`

`
`opened. Successive scans are shifted vertically up-
`wards on the oscillogram. To test for reproducibility,
`the xenon arc was flashed two more times after an
`
`interval of a few seconds, and all spectra were recorded
`on the same photograph.
`In Fig. 4, each set of three
`superimposed traces appears as one trace, and all nine
`scans are identical. Thus, it is proved that the radi-
`ation from the xenon arc remains constant during a
`flash, and that there is excellent flash-to-flash reproduci-
`bility. The same results were obtained for two spectral
`ranges in the near ir from 7000 A to 1.9 [45 When the
`experiment was repeated in the uv (3000 A to 4200 A)
`we detected a variation in radiant output during a
`flash of less than 5%.
`Because of the excellent shot-to-shot reproducibility,
`it was possible to obtain a measure of the plasma ab-
`sorptance, imaging the cathode spot back on itself by
`means of a spherical mirror positioned on the optical
`axis on the opposite side of the xenon arc from the
`spectrometer. A measurement of emission alone, ob-
`tained by placing a shutter in front of the mirror
`while flashing the arc, was followed by a measurement
`of emission with added back reflection during a con-
`secutive flash. The reflection and transmission loss of
`the back-reflected light at the hot quartz envelope,
`which can be considerable,
`is difficult
`to determine.
`Therefore, measurements of absorption by this tech-
`nique are inherently inaccurate.
`It can, however, be
`determined unequivocally for which lines the absorptiop
`is very close to 100%. Thus, the core of Xe I 8232 A
`and the self—reversed peak of Xe 1 8819 A in Fig. 5 are
`black.
`
`IV. Theory
`
`the classical
`Following Unsoeld’s development of
`Kramers
`theory,
`the emission coefficient
`(spectral
`radiance per unit depth) for the combined recombina-
`tion (free—bound) and bremsstrahlung (free—free) con-
`tinuum of an optically thin plasma, expressed in
`
`Fig. 5. Wavelength scan of the emission and emission plus back
`reflection from a mirror of the cathode spot of a flashed xenon arc.
`The wavelength range 0.7-1.2 a was scanned in 10 msec using
`an RCA 7102 photomultiplier.
`
`Fig. 4. Oscillogram showing three wavelength scans for a flashed
`xenon arc. The wavelength range 4200—6500 A was scanned in 10
`msec, using an RCA 4473 photomultiplier. Three flashes are
`superimposed (total of nine scans shown).
`
`8819 A, for instance, could be accurately measured to
`be 91%, although the detector signal for the peak of
`this line is sixty times stronger than for the carbon arc
`(Io in Fig. 3).
`Because of the large number of Xe I lines in the near
`ii‘, the wavelength assignment of the lines in the spec-
`trum of the high pressure are proved to be diflicult.
`Therefore,
`the following procedure was used:
`the
`carbon arc was replaced by a mercury arc and the
`spectrometer focused at the edge of the xenon arc
`plasma, where the temperature is lower and conse-
`quently the lines are sharpe1' and match better the
`intensity of
`the mercury lines. With the emission
`chopper being used,
`the xenon and mercury spectra
`appeared simultaneously;
`an external wavelength
`standard had thus become, effectively, an internal
`standard. The increase in accuracy of wavelength
`correlation over the standard procedure based on a
`separately run reference spectrum permitted to assign
`unambiguously all spectral features of the xenon arc.
`
`B. Flashed Mode
`
`For the measurements of the flashed xenon arc the
`Warner & Swasey Model 501 rapid scanning spectrome-
`ter was used. This instrument has been described in
`detail elsewhere.” Four detectors (RCA 1P28, 4473,
`and 7102 photomultipliers, and an InAs photovoltaic
`detectpr) were used to scan the xenon spectrum from
`3000 A to 2 p,. Because of the availability of two exit
`slits, the contiguous spectral ranges for two detectors
`could be scanned simultaneously.
`The scans were displayed on oscilloscopes and re-
`corded photographically. An oscillogram of the flashed
`xenono arc spectrum in the wavelength range 4200-
`6500 A is shown in Fig. 4. For this measurement, the
`controls of the Model 501 were set for a scanning time
`of 10 msec, a repetition rate of one scan each 37.5 msec,
`and a delay of 30 msec. Thus, the start of the first scan
`occurred 30 msec, of the second 67.5 msec, and of the
`third scan 105 msec, after the flashing circuit had been
`
`680 APPLIED OPTICS / Vol. 7, No.4 / April 1968
`
`

`
`W cm“3p.‘1sr“‘, is given at wavelengths longer than a
`critical Wavelength Ac, by
`
`5;‘ = 1.63 X 10‘“[.§(>\)/)\2](n,,2/T3),
`
`(1)
`
`In deriving Eq. (1), it has
`with A in p. and T in °K.
`been assumed that the ionization stages beyond the
`first can be disregarded;
`then the concentration of first
`ions equals ne, the concentration of electrons (condition
`of plasma quasi—neutrality). The factor .§()\) accounts
`for departures from hydrogenic behavior and quantum
`mechanical (Gaunt) corrections. Schlueter” has calcu-
`lated g(>\) as a function of Wavelength at a temperature
`of 14,000°K, although he found this factor to be prac-
`tically temperature independent.
`In the limit of vanishing ionization, Dalton’s law and
`the Saha equation can be combined to a simple expres-
`sion for the electron density as a function of the state
`variables T and P of the plasma. With the pressure in
`atm,
`
`n, = 5.953 X 10“*(Q;/Qo)%P*T5 exp(—-E,-/2kT).
`
`(2)
`
`For a xenon plasma in the temperature range of
`9000—14000°K, an average value of 4.44 can be used for
`Q,/Q0, the ratio of the partition functions for first ions
`and neutrals, since this value is constant to within 2%
`in this range, and its pressure dependence is also very
`small.” Substituting ne from Eq. (2), with the ioniza-
`tion energy E, = 12.127 eV (Ref. 14), the emission
`coefficient for the continuum of a xenon plasma (in
`Wcm‘3/.c‘1sr“1) is given, approximately, by:
`
`“X9 = 2.57 x 107 5—;"2_) P cxp(—140,760/T).
`
`(3)
`
`In order to assess the Validity of this expression, we
`have calculated the electron density for a xenon plasma
`at 16 atm pressure, using Eq. (2) as compared with the
`electron density calculated more rigorously using
`Unsoeld’s and also Ecker and Weizel’s approach” to
`obtain the lowering of the ionization potential in a
`plasma.
`It appears
`that up to the temperature
`reached in a high pressure xenon arc (below 12,000°K),
`the departure of 17.,
`[Eq.
`(2)] from 77.,
`(Unsoeld) is
`smaller than the discrepancy between ne (Unsoeld) and
`12., (Ecker and Weizel). Since there exists no general
`agreement as to which theoretical approach gives the
`best quantitative estimate of
`the lowering of
`the
`ionization potential, the inaccuracy in ne of less than
`20% at the lower temperatures,
`introduced by the
`simplifications used in deriving Eq. (2), is of the same
`order of magnitude as the theoretical uncertainties.
`Recourse to an elaborate calculation seems therefore
`hardly to be justified, and, because of its simplicity,
`Eq. (3) is useful for obtaining the temperature directly
`from the measured emission coefficient if the pressure is
`known. The temperature derived by this method is
`quite insensitive to relatively large errors in the emis-
`sion coeflicient. Thus, it follows from Eq. (8) that an
`error of 40% results in an error of only 3% in tempera-
`ture at 11,000°K, the peak temperature of the station-
`ary xenon arc, and is still less at lower temperatures.
`
`It follows from Eq. (1) that N)9, the spectral radiance
`of the continuum measured through the center of an
`optically thin cylindrical symmetrical xenon plasma of
`radius R, is given by
`
`ATAO = fla E>‘(7,)d7, = C
`
`-3
`
`V
`
`R 7Lp2[PyT(T)l d7,‘
`
`Tl(7")
`
`-13
`
`Unlike the case of line radiation, the integral con-
`taining the temperature gradient is not a function of
`wavelength. Since the .§(>\)
`factors are practically
`temperature independent, relative experimental values
`for these factors can be obtained directly from line—of—
`sight measurements of an optically thin plasma.
`If
`the temperature profile and the pressure are known, the
`spectral radiance measurements of the continuum have
`to be inverted only for one wavelength in order to
`obtain the £(>\) at the other wavelengths Without an
`Abel
`inversion. The line-of-sight measurements are
`conveniently related to the emission coefficients at the
`center of the are by introducing the equivalent optical
`pathlength L:
`
`L E lN>.“/e>.(7‘ = 0)l-
`
`(5)
`
`From an Abel inversion at one wavelength A1, 6),,-
`(r = 0) is derived;
`thus, L can be calculated and used
`in turn to derive the emission coefficients at other Wave-
`lengths.
`inversion of cylindrically symmetrical
`The Abel
`plasmas is a straightforward procedure, provided the
`plasma is optically thin. Different numerical methods
`are available; we prefer the one proposed by Barr,”
`which combines effective smoothing of small random
`errors with ease of computation.
`If the plasma is
`optically thick, but
`its minimum measured trans-
`mittance higher than about 70—80%, a simple correc-
`tion procedure suffices. Thus, each intensity measure-
`ment has only to be divided by the square root of the
`transmittance measured along the same line of sight,
`otherwise the Abel inversion proceeds as in the optically
`thin case [see Eq. (4) in Ref. 2].
`If the transmittance is
`lower, accurate values of the radial intensity distribu-
`tion can only be obtained by iteration?
`The measurement of plasma absorption is important
`not only for correcting the emission measurements.
`If the absorption measurements are also Abel inverted,
`the radial distribution of emission and absorption can
`be used to derive the temperature profile of the plasma
`from first principles (the Planck-Kirchhoff law).
`In
`the case of strongly absorbing lines, however, Elder
`et al. in Ref. 2 point out difficulties in performing the
`Abel inversion of the measured absorption,
`if mono-
`chromators of only moderate Wavelength resolution are
`used.
`In effect, for large variations of transmittance
`over the spectral slit Width Au, the approximation used,
`
`log L r(.,)d.,) 2 i L log-r(v)du,
`
`(6)
`
`is valid only if the transmittance 'r(v) is larger than
`about 70% forall frequencies in the internal Au.
`
`April 1968 / Vol. 7, No.4 / APPLIED OPTICS 681
`
`

`
`TEMPERATUREIN1ooo°K
`
`ARC RADIUS
`
`(mm)
`
`Fig. 6. Radial temperature profile of the cathode spot of the 2.?
`kW xenon arc (stationary mode), as obtained from the emission
`coefficient of the continuum at 1.31 p. (solid line), and by the
`Planck-Kirchhoff method from the emission—absorption profile of
`Xe I 10528 K (broken line).
`
`V. Results and Discussion
`
`A. Radial Temperature Distribution of the
`Stationary Xenon Arc
`
`The large discrepancy in intensity between the xenon
`and carbon are at the shorter Wavelengths limited the
`absorption measurements to the ir region of the spec-
`trum. The accuracy of
`these measurements is im-
`paired, however, by two effects. VVhen the xenon arc
`is in operation, its quartz envelope becomes red hot
`with a marked increase of absorption in the ir. Sec-
`ondly, the red halo also shows noticeable absorption in
`the ir and its asymmetry causes an asymmetrical
`absorption profile. Taking advantage of the persis-
`tence of the red halo (see Sec. II), it proved to be advis-
`able to include the absorption of the hot quartz enve-
`lope and the red halo in the I0 reading by recording the
`signal for the carbon arc radiation at the instant when
`the xenon arc was extinguished. Even so, the accuracy
`of
`the absorption measurements, especially for low
`absorption near the boundary of the cathode spot, was
`considerably less than the accuracy of the emission
`measurements.
`In the emission measurements, a per-
`fectly symmetrical intensity distribution proved the
`plasma core to be cylindrical symmetrical. As ex-
`pected from theory, the curves giving the lateral in-
`tensity distribution of the continuum, normalized at
`peak intensity, were identical at all wavelengths
`measured.
`
`The Abel inversion requires the measurements to be
`cut off at a fixed distance from the arc center, where the
`intensity has gone to zero. Since the region of interest
`was the hot core of the arc (cathode spot), the boundary
`of the plasma was drawn somewhat arbitrarily at the
`point Where the intensity had dropped to 1% of its peak
`value. The intensity of the red halo was of this mag-
`nitude and its contribution to the total radiance was
`thus roughly subtracted. The resulting arc diameter
`was 4.6 mm. The radial
`temperature profile was
`derived by the Planck-Kirchhoff method from the
`
`682 APPLIED OPTICS / Vol. 7, No.4 / April 1968
`
`radial emission and absorption profiles of Xe I 10528 A,
`obtained by inverting the lateral emission and absorp-
`tion measurements of this line. This line was selected
`because its peak absorption Was 28.5% when measured
`with a spectral slit width which was small compared
`with the line width;
`the true peak absorption was
`therefore still not high enough to lead to difliculties in
`the inversion of the measured absorption or to make
`laborious iterations unavoidable.
`If the absorption is
`too low, the results become very sensitive to measure-
`ment errors. The continuum was therefore not used
`to derive the temperature profile, but its absorption was
`measured to correct the emission data for self-absorp-
`tion.
`In Fig. 6,
`the Planck-Kirchhoff temperature
`profile from the xenon line is compared with the tem-
`perature profile derived from the radial emission co-
`efficients of the continuum at 1.31 M by application of
`Eq. (3). The working pressure indicated by the lamp
`manufacturer (16 atm) and the £(>\) value taken from
`Ref. 13 were substituted in this equation.
`As expected,
`the two temperature profiles agree
`fairly well near the center of the arc, where the experi-
`mental accuracy is higher and diverge toward the
`periphery. Since the measurement of low intensity is
`inherently more accurate than the measurement of low
`absorption, more credence is given in this region to the
`temperature profile derived from the corrected con-
`tinuum intensity.
`It is noteworthy that the tempera-
`ture gradient appears
`to have a constant value
`(1600°K/mm)
`from close to the arc center to the
`periphery.
`From the inverted emission coefficient e(>\ = 1.31 ].l.,
`1- = O), the equivalent optical path length as defined by
`Eq. (5) is calculated to be L = 0.14 cm. To a good
`approximation, the spatially averaged spectral radiance
`N)5’ of the continuum at other wavelengths obtained by
`line-of-sight measurements through the arc center is
`therefore equivalent
`to the emission coefficient of a
`homogeneous xenon plasma of 0.14-cm diam at
`11,050°K and 16 atm. Using Eq. (3), the correction
`factors .§(>\) can then be related directly to the measured
`spectral radiance N(0:
`
`N).° = 178[.E()\)/X2].
`
`(7)
`
`The £(>\) values derived from our measurements of the
`stationary xenon arc are plotted on Fig. 7 and compared
`with correction factors calculated from theory by
`
`Fig. 7. Experimental .§(>\) factors for the xenon continuum com-
`pared with calculated values:
`(1) This paper, (2) Schlueter,“
`(3) Biberman et all“
`
`

`
`Table I. Emission and Absorption Measurements and Aver-
`age Temperature (Planck-Kirchhoff) of the Cathode Spot of the
`Xenon Arc in the Stationary Mode
`
`O
`MA)
`
`8232
`8500
`8819 (peak)
`(wing)
`
`9800
`9923
`10528
`11742
`12623
`13100
`14733
`15418
`
`Xe I
`
`Xe I
`
`Xe I
`Xe I
`Xe I
`Xe I
`Xe I
`cont
`Xe I
`Xe I
`
`NM
`(W cm’?
`Sr“ 1:“)
`
`Absorp-
`tion
`(%)
`
`5,900
`1,615
`4,390
`4,960
`3,400
`3,340
`892
`906
`640
`213
`575
`317
`
`89
`23
`97
`90
`89
`90
`28 ..
`42.;
`37
`17
`55
`37
`
`T (°K)
`
`10,020
`10,750
`9,160
`10,500
`9,820
`9,840
`9,950
`9,400
`9,920
`8,870
`10,060
`9,840
`
`Fig. 8. Wavelength scan in the range 0.7-1.2 pa for the stationary
`(lower trace) and flashed xenon are (both at same gain and with
`0.1-mm slit widths) and the reference tungsten strip lamp (1—mm
`slit widths).
`
`Biberman at al.” and by Schlueter, 13 as taken from Fig. 4
`of Ref. 13.
`It can be seen that the general shape of
`Schlueter’s curve is borne out by our experimental
`values, although the peak in the visible appears shifted
`toward the red. While the relative values of the
`experimental 50) appear well established, this is not
`true for the absolute values in view of the uncertainties
`in the plasma pressure, which could not be measured.
`Since we substituted Schlueter’s value for £(1.31 p.) in
`Eq. (3), the curve of the experimental correction factors
`has been obtained essentially by normalizing for the
`$(1.31 p.) value given by Schlueter.
`
`B. Line-of-Slight Measurements
`of the Xenon Arc
`
`In Table I, the emission—absorption data for repre-
`sentative ir lines and continua are presented, corre-
`sponding to line—of—sight measurements through the
`center of the stationary xenon arc.
`
`The tabulated temperatures have been derived by the
`Planck—Kirchhofl method from the measured peak
`emission and absorption and are not dependent on the
`slit
`function of
`the spectrometer.” Although the
`tabulated temperatures are only average temperatures,
`because of the temperature gradient along the line of
`sight, these average temperatures are weighted strongly
`toward the center of the arc and are only about 10%
`lower than the peak temperature. Since all measured
`lines originate from closely spaced high lying states, an
`influence of the upper energy level on the average
`temperature is not apparent.
`It is shown, evident,
`however, that strongly absorbing lines give a lower
`temperature. This effect
`is shown clearly for Xe I
`8819 A, whose self—reversed center is almost black and
`gives a lower temperature than the false peak in the
`Wing. The self—reversal of this line increases markedly
`at the higher temperatures of the flashed arc as shown
`on Fig. 8. While only Xe I 8819 A appears self-
`reversed in our spectra of the stationary and flashed
`are, four lines become black in the center when the arc
`is flashed. The peaks of these lines lie on the blackbody
`curve for 11,300°K as shown on Fig. 9 where the spec-
`tral radiance of the stationary and flashed xenon arc
`has been plotted against wavelength. From the
`measured radiance and this temperature (11,300°K),
`.a..value for the absorption was calculated for the other
`lines and these Values are consistent with the reflection
`data.
`It appears, therefore, that also for the flashed
`xenon are all ir lines give essentially the same average
`Planck-Kirchhoff temperature.
`The temperature increase during the flash is borne
`out by the strong enhancement ofothe only ion line in
`the scanned spectrum (Xe II 5292 A).
`In contrast, the
`strong, self-absorbed atomic lines in the ir have only
`double the intensity of the same lines in the stationary
`arc. The intensity increase of
`the continuum is
`around 44.5 times, matching closely the increase of
`electrical power input.
`It appears plausible for rough estimates to attribute
`the intensity increase of the continuum to an inc