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Spectral distribution of radiation from the cascade arc plasma
J. Quonr. S~CCWOSC. Rodiat. TwI.&.
SPECTRAL
Vol. 13, pp. 1539-1552. Pergamon Press 1973.
Printed inGreat Britain
DISTRIBUTION OF RADIATION THE CASCADE ARC PLASMA
FROM
J. B. LEE and F. P. INCROPERA School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, U.S.A. (Received 3 1 May 1973) Ah&act-A mathematical model has been developed for radiation emission and absorption in the cascade arc plasma, and calculations have been performed to determine the complete spectral distribution of radiation emerging from the argon arc. Although self-absorption effects are negligible for the continuum radiation, they are significant for much of the line radiation. The radiation flux emerging from the arc, as well as the efficiency for conversion from electrical to radiant energy, increase with increasing arc current and pressure and decreasing arc radius. The relative contribution of line radiation to the total arc radiation decreases with increasing current and pressure and decreasing radius. 1. INTRODUCTION IN RECENT years there has been considerable interest in using the high-pressure arc plasma as a radiation source for illumination, solar simulation, and photochemical processing. However, to varying degree, efforts to develop such applications have been hindered by uncertainties concerning the spectral distribution of radiation emerging from such arcs. Although the significance of radiation as a mode of arc energy transfer has long been recognized, little attention has been given to the detailed spectral distribution of this radiation or to the manner in which this distribution is affected by arc operating parameters. The purpose of this study is to predict the spectral emission and absorption characteristics of radiation from the cascade arc plasma. Emphasis is placed on determining the spectral radiant flux emerging from the arc, and detailed consideration is given to both line and continuum contributions. In addition calculations are performed for a range of arc operating parameters (pressure, current and arc radius) to determine optimum conditions for the conversion from electrical to radiant energy. Because of the considerable accuracy with which its thermochemical state is known, attention is focused on the Ar arc plasma. Although this study constitutes the first serious effort to compute the complete spectral distribution of line and continuum radiation from the cascade arc plasma, other plasma radiation calculations have been performed. Several investigators”-5) have computed line and continuum emission coefficients for an arc plasma, but the spectral ranges of the calculations have been restricted and, in all but one case, (‘I the calculations have assumed local thermochemical equilibrium. Arc plasma radiation depends strongly on the thermochemical state of the plasma, which in turn varies considerably with the degree of departure from equilibrium. Other plasma radiation calculations@-*) have considered the 1539
1540
J. B. LEE and F. P.
INCROPERA
complete spectral distribution of the line and continuum radiation, but simplifying assumptions have been made concerning the plasma geometry and thermochemical state. 2. THE
MATHEMATICAL
MODEL
The problem of computing the spectral distribution of the radiant heat flux from a cylindrical arc plasma is complicated by the fact that both line and continuum processes contribute to the radiation and by the fact that self-absorption effects may be significant over a portion of the spectral region. Hence, a solution must be obtained to the equation of radiative transfer for each process of interest. This solution is simplified somewhat by the existence of asymptotic arc conditions. That is, the portion of the arc which is of interest is characterized by thermochemical properties which are invariant in the axial direction. Hence, the infinite cylinder approximation (specific intensity varies only with radius) may be made. Although other investigators have attempted such solutions,‘5p9-‘2’ no consideration has been given to the complete spectral distribution of the radiation or to the effect of arc operating parameters on this distribution. Following the method of KEXJZN,(r3) the radiative transfer equation is solved(14’ to obtain the spectral heat flux at the arc periphery. The result is of the form
(1) where
n/2
D2(4 =
s
cos u e-*Icosa du,
(2)
0 F(q,
8)
=
[q2
-
R2 sin2 fl]“2/~k,.
(3)
The quantities a and fi are angles which define possible radiation pathways in the arc; SA is the source function, En/k, ; Ed and k, are volumetric emission and absorption coefficients, respectively ; and R is the arc radius. In view of the complexity of equation (l), it is desirable to have a simpler expression for the radiative heat flux. Such an expression does exist for optically thin conditions (k, = 0) and is of the form R 0
This expression is independent of the geometrical considerations (1). Alternatively, if k, = 0, equation (1) reduces to
which lead to equation
(5)
1541
Spectral distribution of radiation from the cascade arc plasma
Although equations (4) and (5) are independently obtained, they must provide equivalent results. To solve the foregoing equations, the emission and absorption coefficients must be known for both the line and continuum processes. In turn, these coefficients depend upon the structure of the atomic species (an intrinsic dependence) and on the radial distribution of the relevant plasma thermochemical properties (electron temperature and concentration). Although determination of these properties is complicated by the existence of nonequilibrium effects, accurate calculations have been performed by CLARK and INCROPECRA(’ ‘) for the Ar arc, and the results are used as a basis for the calculations of this study. Note that, despite the existence of thermochemical nonequilibrium effects, the excited electronic state populations remain close to equilibrium and may be evaluated by using the Boltzmann distribution at the electron temperature.“@ The intrinsic dependence of the emission and absorption coefficients is related to the oscillator strengths for the relevant lines and to the photoionization cross-sections for the continuum. The spectral line absorption coefficient is determined from the expression”” k, =
~n,&Pv(l -e-hy’kTe),
where v and P, are the line frequency and absorption profile, respectively; 1 and u refer to the lower and upper levels, respectively ; n, is the lower level number density ; fi. is the absorption oscillator strength; and T, is the electron temperature. Assuming identical absorption and emission line profiles, the line emission coefficient may be obtained from equation (6) by using Kirchoff’s law. (I’) The oscillator strengths for this study were taken from the compilation by WIESEet al., (is) who consider 417 lines of the ArI atom. These include more than 95 per cent of the most prominent lines in an argon plasma.og’ However, of these lines, many are of extremely small oscillator strength (fi. < 10e3) and contribute a negligible amount to the total radiation. Hence, a total of only 223 lines is included in the final calculations. For conditions of interest in this study ArII line radiation may be neglected. The resonance lines are known to be almost totally self-absorbed,‘16) and the remaining lines are known to be predominantly Stark broadened. (14) To simplify the calculations, the actual line profile is approximated by a “top-hat” model. This removes the need for integrating over frequency at each radial location and greatly reduces the computer time required to consider radiation from the various lines for a variety of arc conditions. The profile height is assumed equal to the inverse of its half-width, which is determined from the results of GRIEM.(*~**‘)Note that the half-width is a function of radial location in the arc due to its dependence on thermochemical properties. Accounting for free-free and electron freebound transitions, the continuum emission coefficient is computed from the expressions EY.C=
6.843 x 1O-38 en* expPv$kT,)C(v, T,) 4n JT, [exp(hvJkT,)-l] ’
6.843 x 10e3* en* exp@vg/k Te)S(v,T,) EY,C= 4A ,/T, [exp(hv/kT,)-l] ’
’ ’
vg’
(7) ’ 2 vg*
The expressions are of the classical form developed by UN~~LD,‘**)and the assumptions
1542
J. B. LEEand F. P. INCROPERA
of quasi-neutrality and single ionization are made. The factor c(v, T,) is included to account for quantum and nonhydrogenic effects. SCHL~~TER(~~) and BIB-N and NORMAN have evaluated <(v, T,), using the quantum defect method to obtain the required photoionization cross-sections. However, the results suffer from the fact that only the upper excited states are considered in the evaluation, and hence they pertain principally to the visible and infrared radiation. In a more recent study, MORRISand Yos(~) accounted for all excited states in their evaluation of the continuum emission coefficient and hence provide results which extend well into the ultraviolet. The <(v, 7”) factors obtained from various sources are plotted in Fig. 1. The low wavelength portion of the BIBWMANand NORMAN results was obtained from extrapolation under the assumption that <(v, T,) approaches zero exponentially as v approaches infinity. The ((v, T.) computed from the MORRIS and Yos(~) results agrees well with all but the BIBERMAN and NORMAN results over the entire spectrum and will be used as the primary basis for the calculations of this study. Calculation of the spectral radiative wall heat flux through equation (1) must be done numerically. However, such calculations for the numerous lines of interest and for the continuum at various wavelengths in the spectral range of interest (5 x lo2 < 1 < 5 x lo4 A) wo.uld require prohibitive computation times. These calculations are greatly simplified, however, if optically thin conditions may be assumed, in which case equation (4) may be used to evaluate the spectral flux. For selected wavelengths and arc operating conditions, equations (1) and (4) were used to compute the continuum flux. For each condition an absorption parameter, zI E j: k, dr, and the degree of self-absorption, defined as [l - q#)/q,,,#X)], where qA,ot
:
8 KREY IEXPltll
!I
ROY
FIG. 1. The continuum
radiation
8
TANKIN
t26l
( factor for an Ar plasma.
Spectral distribution of radiation from the cascade arc plasma
1543
800 d < x < 38,600 ;
/
A A o x A o v .
240~;latm;QOO5m 1~o0mp;hJhn;o.oo%l 50amp;latm; QOOSn I OOamp;l0atm;QOO5m lOOamp; lolm,Q005m I Om Q2a1m~Q005m 2ooaft~ lo*,d.O035m
.
2 00amp; I otm;a007m
2OOomp;letm;QOOSm
, , ,,,,,,,
A 2 0Oamp;latm;O.O09m ,,,cJ I
lb3
lG4
I
I
lG2
OPTICAL DEPTH FIG.
2. The degree of self-absorption
for continuum radiation in an Ar arc plasma.
is the flux which would exist under optically thin conditions, were computed and the results are summarized in Fig. 2. The most significant feature of the results is that, for the range of conditions of interest, continuum self-absorption effects are negligible. It should be noted that self-absorption increases with increasing wavelength, current and pressure, as well as decreasing radius; but even for the most severe conditi.ons considered (A = 3.86 x lo4 A, Z = 4OOA, p = 10atm and R = 3.5 x 10d3 m), the effect remains less than 1 per cent. In general, optically thin conditions cannot be assumed for the line radiation calculations. Many lines are strongly self-absorbed, with qA(R) being attenuated by as much as 80 per cent. However, it was found that self-absorption is small (5 1 per cent) for lines corresponding tofiu 6 lo-‘, which is the case for 121 of the 223 lines considered, and for these lines equation (4) may be used. Details of the numerical integration scheme are provided by LEE. The accuracy of the scheme was verified by comparing results obtained from equations (4) and (5). Agreement is to within 2 per cent if 60 or more radial nodal points are used. 3. RESULTS
For a range of arc operating conditions, continuum spectral heat flux calculations are performed for 950 I 1 I 6 x lo4 A. To obtain the heat flux for 1~ 6 x lo4 A, the spectral distribution is extrapolated using an exponentially decaying function determined from the values of qA(R)at 3 x lo4 and 6 x lo4 A. Although there is little practical interest in arc emission in the far infrared, the extrapolation is needed so that ql(R) may be integrated over all wavelengths for comparison with available total radiation data. Separate calculations are based upon the MORRIS and Yost4) and BI~WMAN and NORMAN 5
BIBERMAN 8 NORMAN 103r MORRIS 8 YOS
FIG. 3. Spectral distribution
---
of the continuum radiation flux from an Ar arc plasma as a function of current.
IO2
-MORRlSaYOS ---BIBERTvlAN 8 NORMAN I-100 R=0.005
WA”ELENGf%
amp
m
(8,
FIG. 4. Spectral distribution of the continuum radiation flux from an Ar arc plasma as a function of pressure.
Spectral distribution of radiation from the cascade arc plasma
1545
-MORRIS a YOS - --- BIBERMAN a NORMAN
IO35
\
FIG. 5. Spectral distribution of the continuum radiation flux from an Ar arc plasma as a function of radius.
functions, although those based on the MORRISand Yos results are thought to be the most accurate. The spectral distribution of the continuum flux is shown in Fig. 3 for selected values of the arc current. The magnitude of the spectral flux is a strong function of current, and the maximum in the distribution occurs at approximately 4600 A, irrespective of current. Note that the distributions based on the MORRISand Yos results exceed those obtained using the BIBERMAN and NORMANlj(v,7”) in the visible and infrared, but not in the ultraviolet. The dependence of the continuum spectral distribution on arc pressure and radius is shown in Figs. 4 and 5, respectively. Although the peak remains close to 4600 A, the flux increases significantly with increasing pressure and decreasing radius. With respect to the dependence on arc radius, it should be noted that the total output, as well as the flux, increases with decreasing radius. That is, the spectral radiation leaving the arc per unit length, which is given by 2nRq,(R), increases with decreasing radius. This behavior is due to an increase in the plasma thermochemical properties which is more than sufficient to compensate for the reduction in plasma volume. Ignoring only those lines which contribute a negligible amount to the arc radiation, extensive calculations have been performed for a total of 223 lines which comprise the following ten transition arrays : 4s--+, 4~5s, 4p-4d, 4p6s, 4s-5p, 3d-4f, 3d-Sp, 4p3d, 4p-7s and 4p-5d. The calculations have been performed for a range of arc operating conditions, and the flux associated with each line has been tabulated.‘i4) Representative results are presented in Table 1 and plotted in Fig. 6. Note that, for lines of large oscillator strength, for example the ArI 8115 A line, self-absorption may attenuate the radiation
1546
J. B. LEE and F. P. INCROPERA
TABLE 1.RADIATIVE FLUX (W/mz) FOR PROMINENTLINESOFTHEAr ARC PLASMA (I=240A,p=1atm,R=5x10-3m)
4s-4p
7635 8115 8424 8103 8408 7948 8014 7383 7514
3.71E4 3.26E4 2.8OE4 2.78E4 2.73E4 2.34E4 2.24E4 2.16E4 2.11E4
9122 7503 8264 7724 8521 8006 9224 6965 7067
2.05E4 1.98E4 1.93E4 1.80E4 1.73E4 1.32E4 1.25E4 1.24E4 1.23E4
7723 9657 8667 9784 1272 10470 9354 7147 11488
1.09E4 9.69E3 5.64E3 4.39E3 4.07E3 2.46E3 2.03E3 1.38E3 4.61E2
4p-5s
12487 12456 10673 13008 13825 13231 10478 12933 13367 13499
l.OlE4 5.51E3 5.49E3 4.4683 2.83E3 2.43E3 1.87E3 1.73E3 1.53E3 1.45E3
9149 12733 12746 11441 9291 15989 13573 15172 11393 16739
1.33E3 1.18E3 1.08E3 8.43E2 8.24E2 7.95E2 7.80E2 6.82E2 4.58E2 2.50E2
12621 11248 10683 16180 20317 15776 13543 15353 16264
1.85E2 1.57E2 1.24E2 1.06E2 6.31El 4.64El 4.16El 2.14El 1.46El
4p-4d
7372 6752 6871 7351 8605 7891 8761 6937 5912 8053 8620 6053 7510
3.16E3 1.95E3 1.71E3 1.27E3 8.23E2 8.1982 7.4182 6.34E2 5.39E2 4.58E2 4.52E2 3.77E2 3.40E2
7425 7412 7484 8384 7436 6604 8799 7618 7628 6888 8046 6960 6766
3.2OE2 3.02E2 289E2 2.5882 2.3982 228E2 2.19E2 2.15E2 2.14E2 2.05E2 2.OOE2 1.92E2 1.89E2
9075 6052 6951 6878 6887 7670 6664 7265 8490 8962 7789 7162
1.88E2 1.75E2 1.71E2 1.52E2 1.52E2 1.50E2 1.34E2 9.23El 8.16El 7.52El 6.70El 2.62El
4s-sp
4200 4158 4259 4198 4333
2.83E3 2.79E3 1.28E3 l.OlE3 9.58E2
4272 4300 4266 4044 4181
9.49E2 7.50E2 6.24E2 5.89E2 5.75E2
4191 4510 4335
5.57E2 4.18E2 3.70E2
3d-5p
23844
5.7382
20812
4.70E2
15816
2.57E2
3d4f
13406 14634 15302 14596
1.07E4 9.10E3 6.14E3 4.15E3
12356 11943 15899 10506
3.79E3 3.44E3 2.31E3 1.7383
15402 16549 11580 11733
9.17E2 8.97E2 4.58E2 1.95E2
4p6s
7030 6416 7206
2.37E3 1.13E3 1.09E3 1.06E3 8.53E2 7.60E2 4.14E2 3.91E2
7392 7158 7125 6384 5882 7353 7868 7350
3.64E2 3.06E2 2.69E2 2.45E2 2.22E2 1.6982 1.66E2 1.65E2
5860 8037 6660 8203 8066
1.48E2 1.42E2 1.24E2 1.18E2 1.15E2 6.84El 5.7lEl 3.8581
7311 7435 7316 7107
7916 9057
1541
Spectral distribution of radiation from the cascade arc plasma
TABLE
1. (continued)
4p-IS
5888 5928 6170 6025
9.95E2 4.74E2 3.69E2 3.50E2
6098 6155 5054 5971
2.30E2 2.24E2 2.07E2 1.39E2
6101 5940 6481
1.24E2 4.48El 4.05El
4p5d
6031 6034 5558 5606 5187 6105 6145 5512 5739
3.37E3 1.60E3 1.21E3 1.14E3 1.04E3 7.95E2 6.96E2 6.67E2 6.14E2
6296 5650 6170 6307 6212 6215 5834 6756 5772
5.85E2 5.54E2 5.07E2 4.60E2 4.06E2 3.71E2 3.53E2 2.56E2 2.OOE2
6369 6827 6992 6719 6754 6364 6466 5964
1.91E2 1.07E2 1.05E2 1.04E2 9.03El 8.77El 6.20El 3.05El
4p3d
13273 13504 13313 13622 12402 12439 12802 12956 13678 12112 11668 12702
1.47E4 1.34E4 1.03E4 6.74E3 6.06E3 5.90E3 5.88E3 5.4OE3 5.06E3 4.64E3 3.7OE3 3.53E3
12343 12139 14093 16940 15046 13214 13599 11078 11719 11467 20616 16520
2.93E3 2.38E3 2.25E3 2.21E3 2.19E3 2.03E3 1.94E3 9.02E2 6.20E2 3.80E2 3.OOE2 2.53E2
10950 12026 12554 15329 14739 21534 22017 23967 16122 22039 21332 23133
2.41E2 2.35E2 1.4OE2 1.30E2 1.21E2 7.44El 6.25El 5.26El 2.37El 1.87El 1.54El 0.0
flux by as much as 80 per cent. The effect is particularly strong for certain visible and near infrared lines of the 4s4p transition array. However, for many other lines, for example the 4259 A line of the 4s-5p array, the effect is negligible. Note that the flux associated with many of the lines is significant (N lo4 W/m’). The aggregate contribution of the lines to the total radiation is comparable to that of the continuum. Since radiation in the visible and ultraviolet regions of the spectrum is germane to many applications of the arc as a radiation source, the fraction of the electrical power input which is converted to radiation has been computed. The results are presented in Figs. 7-9 in terms of the conversion efficiency
where E is the electric field intensity and E. I is the electric power input per unit length of arc. The designations UV, VIS-UV, and TOTAL refer to the ultraviolet continuum (A I 4000 A), the visible and ultraviolet line plus continuum (2 I 7800 A), and the total line plus continuum radiation (0 I I I cc). Although use of the BIBFXMANand NORMANtz4) <-functions suggests higher UV conversion efficiencies, r-functions obtained from the MORRISand Yos(~) results predict higher VIS-UV and total radiation efficiencies. The conversion efficiencies increase with increasing current and pressure and decreasing
1548
J. B. LEE and F. P.
INCROPERA
:
a .
=
0
0
IO3 0 .
0-6115
OPTICALLY
l-6ll5 b-7635
WITH ABSORPTION
A-7635
WITH ABscmPnoN
OPTICALLY
THIN (t ‘CIS, THIN ( f = 02391
FIG. 6. Radiation flux from an Ar arc plasma for selected spectral lines.
I
-
I
-8
I
I.,
/
/’
R=O.O05m ,,/ /
/
-__ I (amp)
-_
FIG. 7. Variation of radiation conversion efficiency with current in an Ar arc plasma.
Spectral distribution of radiation from the cascade arc plasma
-Biberman
8 Normon
.’
--Monk B Yes
.’
1549
-435
I
p--+
,n4 .--
___
,
_-_---____
I
I
n
FIG. 8. Variation of radiation conversion efficiency with pressure in an Ar arc plasma.
The effect of current on the relative contributions of the continuum and line radiation to the total radiation is shown in Fig. 10. Although line radiation provides the dominant contribution at low arc currents, the contribution of the continuum increases with increasing 25 -6ibemKn~Norman
Cl
0.002
0004
OCQ6 O.OQ6 001 ( m1
ARC RADIUS
FIG. 9. Variation of radiation conversion efficiency with radius in an Ar arc plasma.
1550
J. B. LEE and F. P.
INCROPERA
36.0.4p-5% 4~-7s,4~-4d,4p-61, ( 4r-SP
--
.
80-
P-l atm
R=0.005 m
0100
400 1 (amp)
FIG. 10. Relative contributions of continuum and line radiation in an Ar arc plasma as a function of current.
current and dominates at 400 A. The relative contribution of the continuum also increases with increasing pressure and decreasing radius. (14) The strongest contribution to the line radiation is made by the 4s-4~ array. This is also the array for which the effects of self-absorption are most pronounced.
lotol rodiotla mearurement[29l total mdiation fran Warkltll total radiation fran this study cantinwm radiation from this study c~tintum rcdioticm frcm EauderOl total watt heat flux measurementiL9, totol wall heal flux from UorkCl51
‘“oL 200
300
400
I (amp)
FIG.
11. Comparison between total radiation predictions and measurements for an Ar arc plasma.
Spectral distribution of radiation from the cascade arc plasma
1551
As a means of partially verifying the radiation calculations of this study, comparisons are made in Fig. 11 with the total radiation calculations of CLARKand INCROPERA,('5) the continuum calculations of BAUDER,'@ and the total radiation measurements of LUKENS and INCROPEBA.(~‘)For comparative purposes, total (radiation plus convection) heat transfer calculationso 5, and measurements(2g) are also included. The calculations of this study are based on the <-functions determined from the MORRISand Yost4) results. Note the excellent agreement between the total radiation predictions of this study and the data of LUKJWSand INCROPERA.(~‘)Although this agreement does not confirm the detailed spectral accuracy of the predictive method, it does provide some confidence in the model and the associated numerics. SUMMARY This study constitutes the first attempt to determine the complete spectral distribution of radiation emerging from the cascade arc plasma. Calculations have been performed for the Ar arc, and the principal conclusions are as follows. (i) For the wavelength range in which continuum emission is significant, absorption effects due to photoionization processes provide for less than a 1 per cent reduction in the radiation emerging from the arc. Continuum absorption increases with increasing arc current and pressure and decreasing radius, but it is only in the far infrared (where arc emission is small) that absorption effects become important. (ii) Self-absorption effects are not, in general, negligible for the line radiation. The effect increases with increasing oscillator strength and is particularly significant for the strong lines of the 4s4p Ar I transition array. For example, the strongest line of this array (7635 A) experiences approximately an 80 per cent reduction of the energy which it would emit were it optically thin. (iii) Radiation emerging from the arc, as well as the efficiency for conversion from electrical to radiant energy, increases with increasing arc current and pressure and decreasing arc radius. (iv) A significant portion of the arc continuum radiation appears in the visible and ultraviolet regions of the spectrum. (v) Since a large number of weak lines may still contribute significantly to the radiation flux, it is important to give careful consideration to these lines when attempting to accurately quantify arc radiation. A total of 223 lines have been considered. The contribution which the lines make to the total arc radiation is predominantly in the near infrared. The contribution of the visible lines to the total radiation is large (approximately 21 per cent), and the contribution of the small number of ultraviolet lines is negligible. (vi) The relative contribution of line radiation to the total radiation emerging from the arc decreases with increasing arc current and pressure and decreasing arc radius. The inverse is true for the continuum radiation. (vii) The radiation calculations of this study are in excellent agreement with available total radiation measurements. REFERENCES 1. J. C. MORRIS,R. U. K~EYand R. W. LIBBRMAN, ARL Rep. 65-164 (1965). 2. D. L. EVANSand R. S. TANKIN,Phys. Huti 10, 1137 (1967).
1552 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.
J. B. LEE and F. P. INCROPERA
P. W. SCHRE~BER and A. M HUNTER,ARL Rep. 70-0135 (1970). J. C. Memos and J. M. Yes. ARL Reo. 71-0317 (1971). R. J. GIANNARISand F. P. 1i~c~o~ma~JQSR2’1j, 183(1973). U. BAUDER,J. Appl. Phys. 139,148 (1968). I. T. YAKUBOV,0p1. Spectrosc. 19,277 (1965). K. P. HORN, SU-IPR No. 79, Stanford University (1966). C. H. CHURCH,R. G. SCHLECHT,I. LIBERMANand B. W. SWANSON,AIAA J. 4, 1947 (1966). M. A. HEASLETand R. F. WARMING,JQSRT6,751 (1966). J. J. LQWKEand E. R. CAPRIOI?I, JQSRT9,207 (1969). R. PYAREand M. M. ABU-ROML+,ASME Paper 71-HT-18 (1971). A. KlXsTEN,JQSRT8,419 (1968). J. B. LEE, Ph.D. Thesis, Purdue Univ. (1973). K. J. CLARK and F. P. INCROPERA, AIAA Paper 71-593 (1971). R. J. GIANNARISand F. P. INCROPERA. JOSRT 13. 167 (1973). J. RICHTER,Plasma Diagnostics, (Edited-by W. I.&&-HOLTGREVEN). Wiley, New York (1968). W. L. WIESE,M. W. SMITHand B. M. MILES, NBS 22, Vol. II (1969). A. R. STRIGANOV and N. S. SVENTITSKII, IFI/Plenum (1968). R. H. GRIGM,Plusma Spectroscopy. McGraw-Hill, New York (1964). R. H. Gnmru, Private Communication (1972). V. A. UNTOLD,Ann. Phys. 33,607 (1923). D. SCHL~~ER,Z. Astrophys. 56.43 (1962). L. M. BIBERMANand G. E. NORMAN,Sov. Phys. Uspekhi lo,52 (1967). J. C. MORRISand R. U. MORRIS,ARL Rep. 70-0038 (1970). 0. E. BERGE, A. B6m1 and L. REHDER,Z. Naturj: 2Oa, 120 (1965). B. WENDE, Z. Phys. 19B, 1 (1967). D. N. G. ROY and R. S. TANKIN,JQSRT 12,1685 (1972). L. A. LUKENSand F. P. INCROPERA,AIAA J. 10,359 (1972).
SPECTRAL
Vol. 13, pp. 1539-1552. Pergamon Press 1973.
Printed inGreat Britain
DISTRIBUTION OF RADIATION THE CASCADE ARC PLASMA
FROM
J. B. LEE and F. P. INCROPERA School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, U.S.A. (Received 3 1 May 1973) Ah&act-A mathematical model has been developed for radiation emission and absorption in the cascade arc plasma, and calculations have been performed to determine the complete spectral distribution of radiation emerging from the argon arc. Although self-absorption effects are negligible for the continuum radiation, they are significant for much of the line radiation. The radiation flux emerging from the arc, as well as the efficiency for conversion from electrical to radiant energy, increase with increasing arc current and pressure and decreasing arc radius. The relative contribution of line radiation to the total arc radiation decreases with increasing current and pressure and decreasing radius. 1. INTRODUCTION IN RECENT years there has been considerable interest in using the high-pressure arc plasma as a radiation source for illumination, solar simulation, and photochemical processing. However, to varying degree, efforts to develop such applications have been hindered by uncertainties concerning the spectral distribution of radiation emerging from such arcs. Although the significance of radiation as a mode of arc energy transfer has long been recognized, little attention has been given to the detailed spectral distribution of this radiation or to the manner in which this distribution is affected by arc operating parameters. The purpose of this study is to predict the spectral emission and absorption characteristics of radiation from the cascade arc plasma. Emphasis is placed on determining the spectral radiant flux emerging from the arc, and detailed consideration is given to both line and continuum contributions. In addition calculations are performed for a range of arc operating parameters (pressure, current and arc radius) to determine optimum conditions for the conversion from electrical to radiant energy. Because of the considerable accuracy with which its thermochemical state is known, attention is focused on the Ar arc plasma. Although this study constitutes the first serious effort to compute the complete spectral distribution of line and continuum radiation from the cascade arc plasma, other plasma radiation calculations have been performed. Several investigators”-5) have computed line and continuum emission coefficients for an arc plasma, but the spectral ranges of the calculations have been restricted and, in all but one case, (‘I the calculations have assumed local thermochemical equilibrium. Arc plasma radiation depends strongly on the thermochemical state of the plasma, which in turn varies considerably with the degree of departure from equilibrium. Other plasma radiation calculations@-*) have considered the 1539
1540
J. B. LEE and F. P.
INCROPERA
complete spectral distribution of the line and continuum radiation, but simplifying assumptions have been made concerning the plasma geometry and thermochemical state. 2. THE
MATHEMATICAL
MODEL
The problem of computing the spectral distribution of the radiant heat flux from a cylindrical arc plasma is complicated by the fact that both line and continuum processes contribute to the radiation and by the fact that self-absorption effects may be significant over a portion of the spectral region. Hence, a solution must be obtained to the equation of radiative transfer for each process of interest. This solution is simplified somewhat by the existence of asymptotic arc conditions. That is, the portion of the arc which is of interest is characterized by thermochemical properties which are invariant in the axial direction. Hence, the infinite cylinder approximation (specific intensity varies only with radius) may be made. Although other investigators have attempted such solutions,‘5p9-‘2’ no consideration has been given to the complete spectral distribution of the radiation or to the effect of arc operating parameters on this distribution. Following the method of KEXJZN,(r3) the radiative transfer equation is solved(14’ to obtain the spectral heat flux at the arc periphery. The result is of the form
(1) where
n/2
D2(4 =
s
cos u e-*Icosa du,
(2)
0 F(q,
8)
=
[q2
-
R2 sin2 fl]“2/~k,.
(3)
The quantities a and fi are angles which define possible radiation pathways in the arc; SA is the source function, En/k, ; Ed and k, are volumetric emission and absorption coefficients, respectively ; and R is the arc radius. In view of the complexity of equation (l), it is desirable to have a simpler expression for the radiative heat flux. Such an expression does exist for optically thin conditions (k, = 0) and is of the form R 0
This expression is independent of the geometrical considerations (1). Alternatively, if k, = 0, equation (1) reduces to
which lead to equation
(5)
1541
Spectral distribution of radiation from the cascade arc plasma
Although equations (4) and (5) are independently obtained, they must provide equivalent results. To solve the foregoing equations, the emission and absorption coefficients must be known for both the line and continuum processes. In turn, these coefficients depend upon the structure of the atomic species (an intrinsic dependence) and on the radial distribution of the relevant plasma thermochemical properties (electron temperature and concentration). Although determination of these properties is complicated by the existence of nonequilibrium effects, accurate calculations have been performed by CLARK and INCROPECRA(’ ‘) for the Ar arc, and the results are used as a basis for the calculations of this study. Note that, despite the existence of thermochemical nonequilibrium effects, the excited electronic state populations remain close to equilibrium and may be evaluated by using the Boltzmann distribution at the electron temperature.“@ The intrinsic dependence of the emission and absorption coefficients is related to the oscillator strengths for the relevant lines and to the photoionization cross-sections for the continuum. The spectral line absorption coefficient is determined from the expression”” k, =
~n,&Pv(l -e-hy’kTe),
where v and P, are the line frequency and absorption profile, respectively; 1 and u refer to the lower and upper levels, respectively ; n, is the lower level number density ; fi. is the absorption oscillator strength; and T, is the electron temperature. Assuming identical absorption and emission line profiles, the line emission coefficient may be obtained from equation (6) by using Kirchoff’s law. (I’) The oscillator strengths for this study were taken from the compilation by WIESEet al., (is) who consider 417 lines of the ArI atom. These include more than 95 per cent of the most prominent lines in an argon plasma.og’ However, of these lines, many are of extremely small oscillator strength (fi. < 10e3) and contribute a negligible amount to the total radiation. Hence, a total of only 223 lines is included in the final calculations. For conditions of interest in this study ArII line radiation may be neglected. The resonance lines are known to be almost totally self-absorbed,‘16) and the remaining lines are known to be predominantly Stark broadened. (14) To simplify the calculations, the actual line profile is approximated by a “top-hat” model. This removes the need for integrating over frequency at each radial location and greatly reduces the computer time required to consider radiation from the various lines for a variety of arc conditions. The profile height is assumed equal to the inverse of its half-width, which is determined from the results of GRIEM.(*~**‘)Note that the half-width is a function of radial location in the arc due to its dependence on thermochemical properties. Accounting for free-free and electron freebound transitions, the continuum emission coefficient is computed from the expressions EY.C=
6.843 x 1O-38 en* expPv$kT,)C(v, T,) 4n JT, [exp(hvJkT,)-l] ’
6.843 x 10e3* en* exp@vg/k Te)S(v,T,) EY,C= 4A ,/T, [exp(hv/kT,)-l] ’
’ ’
vg’
(7) ’ 2 vg*
The expressions are of the classical form developed by UN~~LD,‘**)and the assumptions
1542
J. B. LEEand F. P. INCROPERA
of quasi-neutrality and single ionization are made. The factor c(v, T,) is included to account for quantum and nonhydrogenic effects. SCHL~~TER(~~) and BIB-N and NORMAN have evaluated <(v, T,), using the quantum defect method to obtain the required photoionization cross-sections. However, the results suffer from the fact that only the upper excited states are considered in the evaluation, and hence they pertain principally to the visible and infrared radiation. In a more recent study, MORRISand Yos(~) accounted for all excited states in their evaluation of the continuum emission coefficient and hence provide results which extend well into the ultraviolet. The <(v, 7”) factors obtained from various sources are plotted in Fig. 1. The low wavelength portion of the BIBWMANand NORMAN results was obtained from extrapolation under the assumption that <(v, T,) approaches zero exponentially as v approaches infinity. The ((v, T.) computed from the MORRIS and Yos(~) results agrees well with all but the BIBERMAN and NORMAN results over the entire spectrum and will be used as the primary basis for the calculations of this study. Calculation of the spectral radiative wall heat flux through equation (1) must be done numerically. However, such calculations for the numerous lines of interest and for the continuum at various wavelengths in the spectral range of interest (5 x lo2 < 1 < 5 x lo4 A) wo.uld require prohibitive computation times. These calculations are greatly simplified, however, if optically thin conditions may be assumed, in which case equation (4) may be used to evaluate the spectral flux. For selected wavelengths and arc operating conditions, equations (1) and (4) were used to compute the continuum flux. For each condition an absorption parameter, zI E j: k, dr, and the degree of self-absorption, defined as [l - q#)/q,,,#X)], where qA,ot
:
8 KREY IEXPltll
!I
ROY
FIG. 1. The continuum
radiation
8
TANKIN
t26l
( factor for an Ar plasma.
Spectral distribution of radiation from the cascade arc plasma
1543
800 d < x < 38,600 ;
/
A A o x A o v .
240~;latm;QOO5m 1~o0mp;hJhn;o.oo%l 50amp;latm; QOOSn I OOamp;l0atm;QOO5m lOOamp; lolm,Q005m I Om Q2a1m~Q005m 2ooaft~ lo*,d.O035m
.
2 00amp; I otm;a007m
2OOomp;letm;QOOSm
, , ,,,,,,,
A 2 0Oamp;latm;O.O09m ,,,cJ I
lb3
lG4
I
I
lG2
OPTICAL DEPTH FIG.
2. The degree of self-absorption
for continuum radiation in an Ar arc plasma.
is the flux which would exist under optically thin conditions, were computed and the results are summarized in Fig. 2. The most significant feature of the results is that, for the range of conditions of interest, continuum self-absorption effects are negligible. It should be noted that self-absorption increases with increasing wavelength, current and pressure, as well as decreasing radius; but even for the most severe conditi.ons considered (A = 3.86 x lo4 A, Z = 4OOA, p = 10atm and R = 3.5 x 10d3 m), the effect remains less than 1 per cent. In general, optically thin conditions cannot be assumed for the line radiation calculations. Many lines are strongly self-absorbed, with qA(R) being attenuated by as much as 80 per cent. However, it was found that self-absorption is small (5 1 per cent) for lines corresponding tofiu 6 lo-‘, which is the case for 121 of the 223 lines considered, and for these lines equation (4) may be used. Details of the numerical integration scheme are provided by LEE. The accuracy of the scheme was verified by comparing results obtained from equations (4) and (5). Agreement is to within 2 per cent if 60 or more radial nodal points are used. 3. RESULTS
For a range of arc operating conditions, continuum spectral heat flux calculations are performed for 950 I 1 I 6 x lo4 A. To obtain the heat flux for 1~ 6 x lo4 A, the spectral distribution is extrapolated using an exponentially decaying function determined from the values of qA(R)at 3 x lo4 and 6 x lo4 A. Although there is little practical interest in arc emission in the far infrared, the extrapolation is needed so that ql(R) may be integrated over all wavelengths for comparison with available total radiation data. Separate calculations are based upon the MORRIS and Yost4) and BI~WMAN and NORMAN 5
BIBERMAN 8 NORMAN 103r MORRIS 8 YOS
FIG. 3. Spectral distribution
---
of the continuum radiation flux from an Ar arc plasma as a function of current.
IO2
-MORRlSaYOS ---BIBERTvlAN 8 NORMAN I-100 R=0.005
WA”ELENGf%
amp
m
(8,
FIG. 4. Spectral distribution of the continuum radiation flux from an Ar arc plasma as a function of pressure.
Spectral distribution of radiation from the cascade arc plasma
1545
-MORRIS a YOS - --- BIBERMAN a NORMAN
IO35
\
FIG. 5. Spectral distribution of the continuum radiation flux from an Ar arc plasma as a function of radius.
functions, although those based on the MORRISand Yos results are thought to be the most accurate. The spectral distribution of the continuum flux is shown in Fig. 3 for selected values of the arc current. The magnitude of the spectral flux is a strong function of current, and the maximum in the distribution occurs at approximately 4600 A, irrespective of current. Note that the distributions based on the MORRISand Yos results exceed those obtained using the BIBERMAN and NORMANlj(v,7”) in the visible and infrared, but not in the ultraviolet. The dependence of the continuum spectral distribution on arc pressure and radius is shown in Figs. 4 and 5, respectively. Although the peak remains close to 4600 A, the flux increases significantly with increasing pressure and decreasing radius. With respect to the dependence on arc radius, it should be noted that the total output, as well as the flux, increases with decreasing radius. That is, the spectral radiation leaving the arc per unit length, which is given by 2nRq,(R), increases with decreasing radius. This behavior is due to an increase in the plasma thermochemical properties which is more than sufficient to compensate for the reduction in plasma volume. Ignoring only those lines which contribute a negligible amount to the arc radiation, extensive calculations have been performed for a total of 223 lines which comprise the following ten transition arrays : 4s--+, 4~5s, 4p-4d, 4p6s, 4s-5p, 3d-4f, 3d-Sp, 4p3d, 4p-7s and 4p-5d. The calculations have been performed for a range of arc operating conditions, and the flux associated with each line has been tabulated.‘i4) Representative results are presented in Table 1 and plotted in Fig. 6. Note that, for lines of large oscillator strength, for example the ArI 8115 A line, self-absorption may attenuate the radiation
1546
J. B. LEE and F. P. INCROPERA
TABLE 1.RADIATIVE FLUX (W/mz) FOR PROMINENTLINESOFTHEAr ARC PLASMA (I=240A,p=1atm,R=5x10-3m)
4s-4p
7635 8115 8424 8103 8408 7948 8014 7383 7514
3.71E4 3.26E4 2.8OE4 2.78E4 2.73E4 2.34E4 2.24E4 2.16E4 2.11E4
9122 7503 8264 7724 8521 8006 9224 6965 7067
2.05E4 1.98E4 1.93E4 1.80E4 1.73E4 1.32E4 1.25E4 1.24E4 1.23E4
7723 9657 8667 9784 1272 10470 9354 7147 11488
1.09E4 9.69E3 5.64E3 4.39E3 4.07E3 2.46E3 2.03E3 1.38E3 4.61E2
4p-5s
12487 12456 10673 13008 13825 13231 10478 12933 13367 13499
l.OlE4 5.51E3 5.49E3 4.4683 2.83E3 2.43E3 1.87E3 1.73E3 1.53E3 1.45E3
9149 12733 12746 11441 9291 15989 13573 15172 11393 16739
1.33E3 1.18E3 1.08E3 8.43E2 8.24E2 7.95E2 7.80E2 6.82E2 4.58E2 2.50E2
12621 11248 10683 16180 20317 15776 13543 15353 16264
1.85E2 1.57E2 1.24E2 1.06E2 6.31El 4.64El 4.16El 2.14El 1.46El
4p-4d
7372 6752 6871 7351 8605 7891 8761 6937 5912 8053 8620 6053 7510
3.16E3 1.95E3 1.71E3 1.27E3 8.23E2 8.1982 7.4182 6.34E2 5.39E2 4.58E2 4.52E2 3.77E2 3.40E2
7425 7412 7484 8384 7436 6604 8799 7618 7628 6888 8046 6960 6766
3.2OE2 3.02E2 289E2 2.5882 2.3982 228E2 2.19E2 2.15E2 2.14E2 2.05E2 2.OOE2 1.92E2 1.89E2
9075 6052 6951 6878 6887 7670 6664 7265 8490 8962 7789 7162
1.88E2 1.75E2 1.71E2 1.52E2 1.52E2 1.50E2 1.34E2 9.23El 8.16El 7.52El 6.70El 2.62El
4s-sp
4200 4158 4259 4198 4333
2.83E3 2.79E3 1.28E3 l.OlE3 9.58E2
4272 4300 4266 4044 4181
9.49E2 7.50E2 6.24E2 5.89E2 5.75E2
4191 4510 4335
5.57E2 4.18E2 3.70E2
3d-5p
23844
5.7382
20812
4.70E2
15816
2.57E2
3d4f
13406 14634 15302 14596
1.07E4 9.10E3 6.14E3 4.15E3
12356 11943 15899 10506
3.79E3 3.44E3 2.31E3 1.7383
15402 16549 11580 11733
9.17E2 8.97E2 4.58E2 1.95E2
4p6s
7030 6416 7206
2.37E3 1.13E3 1.09E3 1.06E3 8.53E2 7.60E2 4.14E2 3.91E2
7392 7158 7125 6384 5882 7353 7868 7350
3.64E2 3.06E2 2.69E2 2.45E2 2.22E2 1.6982 1.66E2 1.65E2
5860 8037 6660 8203 8066
1.48E2 1.42E2 1.24E2 1.18E2 1.15E2 6.84El 5.7lEl 3.8581
7311 7435 7316 7107
7916 9057
1541
Spectral distribution of radiation from the cascade arc plasma
TABLE
1. (continued)
4p-IS
5888 5928 6170 6025
9.95E2 4.74E2 3.69E2 3.50E2
6098 6155 5054 5971
2.30E2 2.24E2 2.07E2 1.39E2
6101 5940 6481
1.24E2 4.48El 4.05El
4p5d
6031 6034 5558 5606 5187 6105 6145 5512 5739
3.37E3 1.60E3 1.21E3 1.14E3 1.04E3 7.95E2 6.96E2 6.67E2 6.14E2
6296 5650 6170 6307 6212 6215 5834 6756 5772
5.85E2 5.54E2 5.07E2 4.60E2 4.06E2 3.71E2 3.53E2 2.56E2 2.OOE2
6369 6827 6992 6719 6754 6364 6466 5964
1.91E2 1.07E2 1.05E2 1.04E2 9.03El 8.77El 6.20El 3.05El
4p3d
13273 13504 13313 13622 12402 12439 12802 12956 13678 12112 11668 12702
1.47E4 1.34E4 1.03E4 6.74E3 6.06E3 5.90E3 5.88E3 5.4OE3 5.06E3 4.64E3 3.7OE3 3.53E3
12343 12139 14093 16940 15046 13214 13599 11078 11719 11467 20616 16520
2.93E3 2.38E3 2.25E3 2.21E3 2.19E3 2.03E3 1.94E3 9.02E2 6.20E2 3.80E2 3.OOE2 2.53E2
10950 12026 12554 15329 14739 21534 22017 23967 16122 22039 21332 23133
2.41E2 2.35E2 1.4OE2 1.30E2 1.21E2 7.44El 6.25El 5.26El 2.37El 1.87El 1.54El 0.0
flux by as much as 80 per cent. The effect is particularly strong for certain visible and near infrared lines of the 4s4p transition array. However, for many other lines, for example the 4259 A line of the 4s-5p array, the effect is negligible. Note that the flux associated with many of the lines is significant (N lo4 W/m’). The aggregate contribution of the lines to the total radiation is comparable to that of the continuum. Since radiation in the visible and ultraviolet regions of the spectrum is germane to many applications of the arc as a radiation source, the fraction of the electrical power input which is converted to radiation has been computed. The results are presented in Figs. 7-9 in terms of the conversion efficiency
where E is the electric field intensity and E. I is the electric power input per unit length of arc. The designations UV, VIS-UV, and TOTAL refer to the ultraviolet continuum (A I 4000 A), the visible and ultraviolet line plus continuum (2 I 7800 A), and the total line plus continuum radiation (0 I I I cc). Although use of the BIBFXMANand NORMANtz4) <-functions suggests higher UV conversion efficiencies, r-functions obtained from the MORRISand Yos(~) results predict higher VIS-UV and total radiation efficiencies. The conversion efficiencies increase with increasing current and pressure and decreasing
1548
J. B. LEE and F. P.
INCROPERA
:
a .
=
0
0
IO3 0 .
0-6115
OPTICALLY
l-6ll5 b-7635
WITH ABSORPTION
A-7635
WITH ABscmPnoN
OPTICALLY
THIN (t ‘CIS, THIN ( f = 02391
FIG. 6. Radiation flux from an Ar arc plasma for selected spectral lines.
I
-
I
-8
I
I.,
/
/’
R=O.O05m ,,/ /
/
-__ I (amp)
-_
FIG. 7. Variation of radiation conversion efficiency with current in an Ar arc plasma.
Spectral distribution of radiation from the cascade arc plasma
-Biberman
8 Normon
.’
--Monk B Yes
.’
1549
-435
I
p--+
,n4 .--
___
,
_-_---____
I
I
n
FIG. 8. Variation of radiation conversion efficiency with pressure in an Ar arc plasma.
The effect of current on the relative contributions of the continuum and line radiation to the total radiation is shown in Fig. 10. Although line radiation provides the dominant contribution at low arc currents, the contribution of the continuum increases with increasing 25 -6ibemKn~Norman
Cl
0.002
0004
OCQ6 O.OQ6 001 ( m1
ARC RADIUS
FIG. 9. Variation of radiation conversion efficiency with radius in an Ar arc plasma.
1550
J. B. LEE and F. P.
INCROPERA
36.0.4p-5% 4~-7s,4~-4d,4p-61, ( 4r-SP
--
.
80-
P-l atm
R=0.005 m
0100
400 1 (amp)
FIG. 10. Relative contributions of continuum and line radiation in an Ar arc plasma as a function of current.
current and dominates at 400 A. The relative contribution of the continuum also increases with increasing pressure and decreasing radius. (14) The strongest contribution to the line radiation is made by the 4s-4~ array. This is also the array for which the effects of self-absorption are most pronounced.
lotol rodiotla mearurement[29l total mdiation fran Warkltll total radiation fran this study cantinwm radiation from this study c~tintum rcdioticm frcm EauderOl total watt heat flux measurementiL9, totol wall heal flux from UorkCl51
‘“oL 200
300
400
I (amp)
FIG.
11. Comparison between total radiation predictions and measurements for an Ar arc plasma.
Spectral distribution of radiation from the cascade arc plasma
1551
As a means of partially verifying the radiation calculations of this study, comparisons are made in Fig. 11 with the total radiation calculations of CLARKand INCROPERA,('5) the continuum calculations of BAUDER,'@ and the total radiation measurements of LUKENS and INCROPEBA.(~‘)For comparative purposes, total (radiation plus convection) heat transfer calculationso 5, and measurements(2g) are also included. The calculations of this study are based on the <-functions determined from the MORRISand Yost4) results. Note the excellent agreement between the total radiation predictions of this study and the data of LUKJWSand INCROPERA.(~‘)Although this agreement does not confirm the detailed spectral accuracy of the predictive method, it does provide some confidence in the model and the associated numerics. SUMMARY This study constitutes the first attempt to determine the complete spectral distribution of radiation emerging from the cascade arc plasma. Calculations have been performed for the Ar arc, and the principal conclusions are as follows. (i) For the wavelength range in which continuum emission is significant, absorption effects due to photoionization processes provide for less than a 1 per cent reduction in the radiation emerging from the arc. Continuum absorption increases with increasing arc current and pressure and decreasing radius, but it is only in the far infrared (where arc emission is small) that absorption effects become important. (ii) Self-absorption effects are not, in general, negligible for the line radiation. The effect increases with increasing oscillator strength and is particularly significant for the strong lines of the 4s4p Ar I transition array. For example, the strongest line of this array (7635 A) experiences approximately an 80 per cent reduction of the energy which it would emit were it optically thin. (iii) Radiation emerging from the arc, as well as the efficiency for conversion from electrical to radiant energy, increases with increasing arc current and pressure and decreasing arc radius. (iv) A significant portion of the arc continuum radiation appears in the visible and ultraviolet regions of the spectrum. (v) Since a large number of weak lines may still contribute significantly to the radiation flux, it is important to give careful consideration to these lines when attempting to accurately quantify arc radiation. A total of 223 lines have been considered. The contribution which the lines make to the total arc radiation is predominantly in the near infrared. The contribution of the visible lines to the total radiation is large (approximately 21 per cent), and the contribution of the small number of ultraviolet lines is negligible. (vi) The relative contribution of line radiation to the total radiation emerging from the arc decreases with increasing arc current and pressure and decreasing arc radius. The inverse is true for the continuum radiation. (vii) The radiation calculations of this study are in excellent agreement with available total radiation measurements. REFERENCES 1. J. C. MORRIS,R. U. K~EYand R. W. LIBBRMAN, ARL Rep. 65-164 (1965). 2. D. L. EVANSand R. S. TANKIN,Phys. Huti 10, 1137 (1967).
1552 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.
J. B. LEE and F. P. INCROPERA
P. W. SCHRE~BER and A. M HUNTER,ARL Rep. 70-0135 (1970). J. C. Memos and J. M. Yes. ARL Reo. 71-0317 (1971). R. J. GIANNARISand F. P. 1i~c~o~ma~JQSR2’1j, 183(1973). U. BAUDER,J. Appl. Phys. 139,148 (1968). I. T. YAKUBOV,0p1. Spectrosc. 19,277 (1965). K. P. HORN, SU-IPR No. 79, Stanford University (1966). C. H. CHURCH,R. G. SCHLECHT,I. LIBERMANand B. W. SWANSON,AIAA J. 4, 1947 (1966). M. A. HEASLETand R. F. WARMING,JQSRT6,751 (1966). J. J. LQWKEand E. R. CAPRIOI?I, JQSRT9,207 (1969). R. PYAREand M. M. ABU-ROML+,ASME Paper 71-HT-18 (1971). A. KlXsTEN,JQSRT8,419 (1968). J. B. LEE, Ph.D. Thesis, Purdue Univ. (1973). K. J. CLARK and F. P. INCROPERA, AIAA Paper 71-593 (1971). R. J. GIANNARISand F. P. INCROPERA. JOSRT 13. 167 (1973). J. RICHTER,Plasma Diagnostics, (Edited-by W. I.&&-HOLTGREVEN). Wiley, New York (1968). W. L. WIESE,M. W. SMITHand B. M. MILES, NBS 22, Vol. II (1969). A. R. STRIGANOV and N. S. SVENTITSKII, IFI/Plenum (1968). R. H. GRIGM,Plusma Spectroscopy. McGraw-Hill, New York (1964). R. H. Gnmru, Private Communication (1972). V. A. UNTOLD,Ann. Phys. 33,607 (1923). D. SCHL~~ER,Z. Astrophys. 56.43 (1962). L. M. BIBERMANand G. E. NORMAN,Sov. Phys. Uspekhi lo,52 (1967). J. C. MORRISand R. U. MORRIS,ARL Rep. 70-0038 (1970). 0. E. BERGE, A. B6m1 and L. REHDER,Z. Naturj: 2Oa, 120 (1965). B. WENDE, Z. Phys. 19B, 1 (1967). D. N. G. ROY and R. S. TANKIN,JQSRT 12,1685 (1972). L. A. LUKENSand F. P. INCROPERA,AIAA J. 10,359 (1972).