J. Quanl. Spectrasc. Radiat. Transfer Vol. 44, No. 1, pp. 47-56, 1990
`Printed in Great Britain. All rights reserved
`
`0022-4073/90 $3.00+0.00
`Copyright © 1990 Pergamon Press plc
`
`Ht,-LINE PROFILE MEASUREMENTS IN
`OPTICAL DISCHARGES
`
`J. U1-ILENBUSCH and W. Vi(")L
`
`Institute of Laser and Plasma Physics, University of Diisseldorf, Universitéitsstrasse 1,
`4000 Diisseldorf, F.R.G.
`
`Abstract-—In the electrical field of a focused beam of a cw or repetitively pulsed high power
`CO2 laser, a so called optical discharge can be continuously sustained. Under cw conditions,
`using laser power up to several kW, the plasma has typically a charge carrier density of about
`102‘ m’3 and a temperature of about 2 x 10‘ K. The maintenance of the discharge requires gas
`pressures 20.5 MPa in the discharge vessel. By applying a pulsed C0, laser system in our
`experiment with a maximum of 10‘ pulses/sec, 50 rr1J/pulse, pulse length 0.2 psec and average
`power 500 W, the plasma density during the laser pulse can be enhanced up to about the cut-off
`density at A = 10.6 pm (z 10” m‘3); the electron temperature can also be increased. This paper
`presents a short survey of the equilibrium state and energy balance of the cw and pulsed
`discharge. Experimental data concerning the minimum maintenance power and the tempera-
`ture field of the cw discharge, as well as the temporal development of electron temperature
`and density in the pulsed discharge, are given. In particular, results are shown for optical
`discharges in hydrogen, where the Balmer H5-line is studied in the cw discharge up to electron
`densities of 1.2 x l02‘m‘3 and in the pulsed discharge up to 5 x 102" m’3. Line profiles,
`asymmetry and broadening of the H,,-line are compared with theoretical data available in the
`literature.
`
`1. INTRODUCTION
`
`The development of powerful pulsed and cw lasers since the mid-1960s has encouraged scientists
`to study new phenomena occurring in a gas or on a solid or liquid surface during irradiation by
`strong laser light. In the electrical field of a focused laser beam oscillating with optical frequencies
`a discharge can be sustained. We call this an optical discharge (OD). The first experiments used
`pulsed laser systems, Maker et al;‘
`later cw lasers were used, Raizer,2 Generalov et al.3 The
`experiments described below are characterized by the following data: as a light source an
`osci1lator—amplifier CO2-laser system of the axial type is used, which delivers cw power up to 5 kW
`running in the TEMOO mode. Pulsed operation with a maximum repetition rate of about 10‘ Hz,
`pulse width 0.2 usec, maximum power of 250 kW and average power of 1 kW is also possible.
`Typical parameters of the continuous optical discharge (COD) in Hz, Ar, N2 and He are: pressure
`0.5—20 MPa, equal temperature of charge carriers and neutrals (1-2) x 104 K, and electron density
`l0”—l.2 x 102‘ m"3. The pulsed optical discharge (POD) was exclusively studied in a hydrogen
`atmosphere under pressure of 1-5.5 MPa. The electron temperature unequal to the heavy particle
`temperature, reaches 105 K and the electron density is raised to nearly 10” m" (cut-ofi" density).
`The non-ideality factor in COD and POD experiments is about 0.1.
`
`2. IGNITION AND MAINTENANCE OF OD
`
`Ignition of OD is possible if the applied alternating electrical field in the laser focus accelerates,
`at random, a few electrons and if their final kinetic energy is sufficient to ionize neutrals. The
`developing avalanche can survive if the electron number during the build-up phase is not reduced
`too much by dilfusion, recombination and attachment processes. Thus, a threshold field strength
`(intensity I,,,) is needed to start the breakdown. Typical threshold intensities are of the order of
`l0'3—l0"‘ Wm” for the CO,-laser wavelength. This beam intensity in a focus is easily realized by
`chopping the laser between oscillator and amplifier by means of a toothed wheel (100 turns/sec,
`1000 teeth on the periphery) or by an electro-optical shutter (see Sec. 3).
`
`47
`
`ASML 1030
`ASML 1030
`
`

`
`48
`
`J. U1-[LENBUSCH and W. VI(")L
`
`is much lower and can be estimated from a simple energy
`The cw maintenance intensity Im,
`balance of the electrons. As can be seen from Fig. 1, the average laser intensity near the laser focus,
`assuming a focused laser beam of power PL, can be written
`
`I=PL/vtwfi.
`
`(l)
`
`The electron gas is powered by the process of inverse bremsstrahlung in the course of collisions
`between electrons and ions (atoms), where the absorptive regime in the beam direction has a
`length
`
`where the absorption coefficient (m") is given by Offenberger et al‘ as
`
`K, = 2.25 x l0‘”n§ T;3/2,
`
`Labs W 1/Kw
`
`(2)
`
`(3)
`
`with ne the electron density (m’3) and T, electron temperature (K). ‘L’ is the time of dwell of electrons
`in the absorption regime of volume Lab, - nwfi. The laser beam has to supply at least the energy
`nun
`PL .
`' 1.’ to provide the ionization energy E, for all electrons in the volume (where we neglect their
`kinetic energy), thus we have
`
`2
`.
`.
`~E,
`ne nwo
`ll.
`Kv,.L.
`min
`
`(4)
`
`The dwell time 1' is governed by ambipolar diffusion losses, attachment, radiative and three-body
`collisional recombination losses. Introducing the diffusion length A and neglecting attachment we
`can write
`
`~ 15 Am)
`A2
`
`Lmin
`
`+W3'B(Te)+W3'ne'C(Te),
`
`(5)
`
`where A, B and C are related to the coefficient of diffusion, radiative and three-body collisional
`recombination. In low pressure OD the diffusion term governs the minimum maintenance power
`PLM, where the beam waist nearly cancels because A z wo. At higher pressures the three-body
`recombination dominates, PLm ~ w}, and, therefore, the advantage of optical focusing systems with
`large aperture is obvious (see Fig. 1). Figure 2 compares values of PLM calculated according to
`Eq. (5) with experimental data determined from a hydrogen COD.
`If the laser power PL exceeds PLm a COD burns in the vicinity of the focal point. With slowly
`increasing laser power the COD widens up and the position of maximum temperature is shifted
`more and more towards the focusing optical system, see Uh1enbusch.5 A similar behavior can be
`found in POD.
`
`.1-_1rI:A"D
`
`
`
`'orK\\\\':w/////3 2W,=
`-2. ‘J
`
`-L.
`
`0.
`g D
`
`2.
`
`_2.Lr_vr3-1A.[;]’
`229'
`A.
`* 1:
`D
`Fig. 1. Lines of constant intensity in a focal point.
`
`
`
`

`
`H,,-line profile measurements
`
`49
`
`" kw
`
`Hydrogen
`
`experiment
`
`hree body recombination
`
`radiative recombin i
`
`Fig. 2. Minimum maintenance laser power plotted vs pressure.
`
`3. THE EXPERIMENTAL SET-UP
`
`COD and POD are produced by the beam of a powerful CO2 laser in the cw or pulsed mode
`and focused into a high pressure chamber (see Fig. 3).
`To achieve good mode structure (O0-mode), stability of the laser beam, and high pulse repetition
`rate, the laser is built-up as an oscillator—amplifier system (see Fig. 4 and Mucha et a1‘).
`The output of a maximum 80W cw CO2 laser oscillator running in the OO-mode is amplified
`by means of 14 discharge tubes of 0.61 m length each with superimposed axial gas flow. To produce
`POD, an intracavity CdTe Pockels cell is operated with a maximum repetition rate of 10‘ Hz, a
`rise time of 75 nsec and a pulse width of 500 nsec. The intracavity switching of the oscillator
`generates laser pulses with maximum 10‘ Hz repetition rate, 200 nsec pulse width, 2~4 mJ pulse
`energy and 10-20 kW peak power. After passing the amplifier, pulses of 50 m] energy and 500 W
`average power are available. The maximum pulse power of around 250 kW is sufficient to ignite
`POD in hydrogen without any external agent. Ignition of COD is performed by a toothed wheel
`(see Fig. 4) brought in between oscillator and amplifier. Lateral ports of the discharge chamber
`(see Fig. 3) allow a thorough diagnosis of the COD plasma,
`see also Uhlenbusch.5 We
`
`
`
`
`
`
` //,
`\7/41/111111”
`f///’///’./’(//
`
`
`\
`
`
`:.:v.-:=_74/’!1%‘
`
`
`
`I ‘
`
`V
`
`'iL\.\\‘
`
`
`
`Fig. 3. Discharge vessel for the optical discharge.
`
`
`
`

`
`50
`
`J. UHLENBUSCH and W. Vi6L
`
`
`
`IV : 5.51. m
`dv: 35
`mm
`ti
`: 127 mm
`f'2:
`191
`mm
`
`lo : 32 m
`do:
`12 mm
`L0: 4.9 m
`R -.11.1 m
`T : 50%
`P2: Pockels cell
`
`C : chopper
`
`Fig. 4. The C0, laser system.
`
`note that (i) spatially and time resolved absolute line and continuum spectroscopy, in connection
`with Abel’s inversion, is a very useful tool to find local temperatures and densities in COD and
`POD and to derive gas temperatures from switched-ofi” discharges; (ii) interferometry is applied to
`study the stability of COD and to measure temperature profiles in the vicinity of the optical
`discharge, see Carlhofl‘ et al;7 (iii) laser-Doppler-anemometry is used to measure the local flow field
`inside the discharge vessel during COD operation, see Krametzf’
`The most significant information can be derived from spectroscopy. The complete set-up for
`spectroscopic measurements is shown in Fig. 5.
`For COD side-on measurements the plasma is imaged by the two lenses, L, and L2, on the
`entrance slit of a spectrograph (f = 0.125 m). The spectrally resolved side-on signals are recorded
`by an optical multichannel analyser (OMA system) with 500 channels. After averaging over 30
`cycles the signals are stored on a disk. Spatial resolution is achieved by moving the lens L2
`horizontally across the plasma, thereby recording the spectral intensity and performing Abel’s
`inversion at 50 positions. The procedure is repeated after having tilted the line of sight into another
`vertical position. Calibration is made with a tungsten ribbon lamp.
`
`high pressure
`
`chamber
`
`beam splitter
`carbon an
`
`pockels
`C02 laser ostillator can
`
`
`
`
`
`__
`lspecfr .. - ‘
`
`HV—pulse
`amplifier
`
`pulse
`generator
`fiber optic
`transmitter
`
` I‘ ?B'eF'£aEii: cable
`‘inn-ad_ay_ scrgg
`I
`Fig. 5. Optical set-up and trigger system.
`
`
`
`

`
`H,-line profile measurements
`
`51
`
`In the case of POD, the OMA system is additionally gated by a pulse with 1.2 kV height, 100 nsec
`pulse width and the same repetition rate as the CO,-laser pulse. By shifting the “time window”
`a temporal resolution of spectroscopic signals is possible. For calibration purposes a carbon arc
`is now used.
`
`4. EXPERIMENTAL RESULTS
`
`Applying the diagnostic techniques mentioned in Sec. 3, the density, temperature and flow
`field within and outside COD burning in argon, helium and hydrogen were measured. Thus,
`the local properties of the COD plasma as a function of laser power, pressure, working gas
`etc. were well known. COD plasmas are near to LTE conditions with T,z T3 and are
`quite convenient for producing electron densities up to 1.2 x l02‘m‘3 at moderate (2 X 10‘ K)
`temperature.
`POD discharges in hydrogen of the type studied here reach nearly cut-ofl‘ densities (1025 m‘3 for
`the CO2 laser wavelength), electron temperatures in the 105 K regime with T, 95 T3, and PLTE
`conditions. In the following, the properties of COD and POD in hydrogen are studied with
`emphasis on the absolute spectral intensity of the H,-line and its underlying continuum emitted
`by neutral hydrogen atoms.
`In Fig. 6, a section of the H,,-line with the underlying continuum emitted by a COD plasma
`is shown. The ambient pressure was lMPa,
`the cw laser power supplied to the COD was
`2.8 kW,
`the emitting volume had a temperature of l6,400K and the appropriate electron
`density was 1.1 x l0"m". The resulting line width is 25.6 nm. Evaluation of this extremely
`broadened line profile is troublesome because the far wings were not measured, the blue wing is
`distorted by H, and the quadratic Stark effect induces asymmetrices of the line. For evaluation of
`this line, we proceed with the following trial and error method (see also Carlhofl et a1”).
`Assuming an estimated n, which follows roughly from the (full) line width Aim using Griem’s'°
`formula
`
`we can derive an appropriate ‘Te 2 T, = T value from Saha’s equation. Using this T-value, the
`absolute line intensity of the H, line and the underlying continuum (dash—dotted line in Fig. 6)
`
`n, = C - A13”,
`
`(6)
`
`E16
`L.
`
`2 /w m‘ 2.4
`
`
`
`.45
`
`.46
`
`.47
`
`.43
`.49
`I 10'6m
`
`.5
`
`.51
`
`52
`
`Fig. 6. Measured I-1,,-line profile from COD with fitted theoretical profile and continuum. p = IO‘ Pa,
`PL = 2800 W, 2 AA”, —_- 25.6 x 10"m, T = 16,356 K and n, = 1.10 x lo" m‘3.
`
`
`
`

`
`52
`
`J. UHLENBUSCH and W. V161.
`
`can be easily evaluated. After subtraction of the known continuum data from the measured line
`profile (see Fig. 6), the remaining purified profile is approximated by
`
`at = T—‘-‘’-———
`2.(,1_,1o) 5/2
`1+[
`“U2
`i
`
`(7)
`
`(see the dashed line in Fig. 6). This hypothetical profile fits the line center at 10 = 486 nm, is reduced
`to (co/2) at |/l — A0] = §A}.,,2 and approaches the Holtsmark profile in the far wing. From Eq. (7)
`for the complete line intensity it follows that
`2
`3 1t
`Sine n) 60 All/2
`
`L
`Jline EA
`
`=
`
`= hcA,,,,,
`—— E,,
`4Tt’loU0 gn"0 cxp(kBTe);
`
`where A,,,,, = 8.41 x 10° see" is the transition probability, g,, = 32 the statistical weight of the upper
`level, U,, the partition function, E,, = 12.75 eV and the neutral hydrogen density from Saha’s
`relation. Using Eq. (8), the evaluation of co and consequently of the 5} profile is possible. If the
`calculated 6} profile does not fit the purified experimental data, the evaluation procedure is repeated
`starting with a slightly enlarged or diminished value of the electron density, until the theoretical
`and experimental data agree within a few percent. Figure 6 refiects the optimum agreement which
`can be achieved.
`
`Our evaluation does not take into account the line asymmetry, which has already been observed
`in arc experiments by Helbig and Nick" up to electron densities of 1.4 x l0”m‘3.
`The relative difference between the maximum of the blue peak, [3 and the red peak, IR is a
`function of electron density. A comparison between theoretical data by Kudrin and Sholin,”
`experimental values from COD, and are measurements is shown in Fig. 7. There is an obvious
`disagreement between measurement and calculated data.
`The wavelength distance AR — /1,, between the red and blue peak of the H,-line is another sensitive
`function of electron density. Theoretical considerations suggest
`
`in "‘ AB = a ‘ A3142:
`
`(9)
`
`0 (1)0
`
`o Helblg.Nick
`——+ Theory: Kudrin.Sholin
`
`
`
`20
`
`15
`
`10
`
`5
`
`0
`
`
`
`1
`
`S
`
`10
`-- 1-0%
`Fig. 7. Asymmetry of H, as a function of the electron density.
`
`

`
`H,,-line profile measurements
`
`53
`
`PULSE) EXP.
`O
`
`,/
`
`/
`
`I
`
`, ’
`
`° C”
`o Helbig, Nick
`--+-Theory 2 Kudrin.ShoIin
`—----Theory : Seidel
`
`7/.
`/'
`1°
`I
`
`,'
`
`75
`
`50
`
`25
`
`I
`
`_I'
`_” ,1
`
`
`
`17
`10 cm
`_
`Fig. 8. Wavelength distance between the red- and blue-line maxima of H, as a function of the electron
`density.
`
`-3
`
`'
`
`where a =0.35 according to Seidel" and a =0.18 according to Kudrin and Sholin." Our
`measurements and those of Helbig and Nick" confirm Seidel’s result (see Fig. 8).
`For completeness, the isotherm field of a COD discharge burning in hydrogen at 1 MPa pressure
`is plotted in Fig, 9, as derived from side-on intensity measurements of H5. To perform Abel’s
`inversion technique, symmetry around the z-axis (laser beam axis) is assumed. The temperature
`maximum is slightly shifted towards the laser source.
`
`H yd rogen
`
`0.25
`
`05
`
`0.75
`--—>
`
`1
`
`I‘
`
`10'3 m
`
`Fig. 9. Temperature field of COD for hydrogen.
`
`
`
`

`
`54
`
`J. UHLENBUSCH and W. Vioi.
`
`The evaluation of POD data is more elaborate. The rapid change of all plasma parameters after
`the power is supplied within 200 nsec necessitates a fast data acquisition system with a large storage
`capability to monitor signals from about 50,000 subsequent laser pulses. Secondly, the relaxation
`times for development of equilibrium states are comparable to the laser pulse rise time and decay
`time. Therefore, neither kinetic equilibrium (T, aé Tg) nor chemical equilibrium (validity of Saha’s
`equation) are realized. The situation of partial local thermal equilibrium, however, is established
`throughout the laser pulse. Thus one can write, instead of Eq. (8).
`
`LmeEdA= ‘WOA... 2g+n3h3(21rm.ksT.) ”’exp( '
`
`hc
`
`g,,
`
`_
`
`E ——E,,
`
`k, T,
`
`(10)
`
`where g + = 1 is the statistical weight of the protons, E. — E,, is the ionization energy of the hydrogen
`state with the quantum number n (n = 4 for the H5-line). A trial and error method, as described
`above, starting with an estimated electron density and temperature, gives T, and n, from the
`complete line intensity and the underlying continuum. It was carefully determined that the
`H,,-transition radiates from optically thin layers.
`Some results of this evaluation are given in Fig. 10. Here the maximum electron temperature
`and density are plotted vs time for plasma produced by a 200 nsec laser pulse of E = 20 m] energy
`each, and a repetition rate of 5 kHz in a 1 MPa pressure surrounding. Much higher temperature
`and density values can be reached than in COD, at least during the laser pulse. The subsequent
`discharge phase is characterized by nearly constant T, and n, values. During this plateau period,
`the initial strong spatial expansion comes to rest, a fact which can be substantiated by measuring
`spatial electron density profiles at succeeding time intervals. The spatial halfwidth of the POD
`characterized by its electron density profile is plotted in Fig. 11.
`With respect to line profile evaluation at high electron densities, POD experiments cover the
`density regime up to 1025 electrons In” for the case of pulsed CO2-lasers as the heating agent. The
`HI,-profile presented in Fig. 12 is emitted by a plasma with n, = 1.35 x 10“ m"3 and T, = 27,000 K
`under an ambient pressure of 1 MPa. The contribution of H, is taken into account in a similar way
`as prescribed by Eq. (7). The measured distance between the red and blue peak fits the data
`evaluated from COD measurements very well (see Fig. 8).
`Larger densities are available at higher chamber pressures. Figure 13 gives an example at
`p = 5.5 MPa yielding n, = 5.3 x 102" m‘3. A reliable evaluation of these profiles is not possible; the
`line structures more and more merge into the background.
`
`nel(1021°- m'3 )
`
`Te/no‘ Kl
`
`
`
`0
`0.0
`
`0.5
`
`1.0
`
`1.5
`
`0
`tlp.s
`
`Fig. 10. Electron density and temperature of a pulsed optical discharge (POD) plotted vs time.
`
`
`
`

`
`H,-line profile measurements
`
`55
`
`0,3,2/mm
`
`p : 1.0 MP0
`f
`: 5.0 kHz
`
`E : 0.02 J
`
`
`
`' 0.0
`
`0.5
`
`1.0
`
`1.5
`
`tips
`
`Fig. 11. The spatial half-width of the POD characterized by its electron density profile.
`
`8/(1015-w-m"°-sr-1)
`
`ne: 1.35-102‘-m'3
`Te: 27000 K
`p .- 1.0 MP0
`
`
`
`1.1.0
`
`1.60
`
`1.80
`
`500
`
`S20 A/nm
`
`Fig. 12. Measured I-1,,-line profile from the center of POD with fitted theoretical profile and continuum.
`p = 1 MPa, E =0.02 J, f= 5 kHz, T: = 27,000 K and n, = 1.35 x 10" m".
`
`s/(1017-m"~-sr")
`
`ne: 5.3-102"m"3
`Te: 25000 K
`
`
`
`1.60
`
`1.70
`
`1.80
`
`1.90
`
`500
`
`510
`
`A/nm
`
`Fig. 13. Measured H,,-line profile from the center of POD with fitted theretocial profile and continuum.
`p = 5.5 MPa, E = 0.05 J, f = 5 kHz, T, = 25,000 K and n, = 5.3 x l0“m”’.
`
`

`
`J. U}-[LENBUSCH and W. V16L
`
`5. CONCLUSIONS
`
`fo
`
`Continuous and pulsed optical discharges sustained by C02 laser are a very reliable light source
`r producing plasma under high pressure in the eV regime. In hydrogen, electron densities up to
`l02"m‘3 can be achieved by COD, while densities up to 1025 m‘3 are possible in POD.
`Investigation of H5-line transitions at such high electron densities confirm Griem’s broadening
`rmula for the line half-widths and makes obvious the growing influence of the quadratic Stark
`effect on the line profile with increasing electron density. Evaluation of line and continuum
`intensities verifies the nonequilibrium state of the POD plasma during the heating period (200 nsec).
`The plasma produced in COD and POD is characterized by a non-ideality factor of 0.1.
`
`fo
`
`REFERENCES
`
`l 2
`
`4 5
`
`. P. D. Maker, R. W. Terhune, and C. M. Savage, III Int. Conf. on Quant. Electronics, Paris (1963).
`.
`Yu. P. Raizer, JETP Lett. 11, 120 (1970).
`3.
`N. A. Generalov, V. P. Zimakov, G. I. Kozlov, V. A. Masyukov, and Yu. P. Raizer, JETP Lett. 11, 302
`(1970); ibid. 11, 407 (1970).
`. A. A. Offenberger, R. D. Kerr, and P. M. Smy, J. Appl. Phys. 43, 547 (1972).
`.
`J. Uhlenbusch, Proc. 16th Int. Conf. on Physics of Ionized Gases, Diisseldorf, p. 119 (1983).
`6
`. Z. Mucha, S. Miiller, J. H. Schafer, J. Uhlenbusch, and W. Viél, Proc. 6th Int. Symp. on Gas Flow and
`Chemical Lasers, Springer Proc. in Physics 15, 442 (1986).
`C. Carlhofi, E. Krametz, J . H. Schéifer, K. Schildbach, J. Uhlenbusch, and D. Wroblewski, Physica 103C,
`439 (1981).
`E. Krametz, Ph.D. Thesis, University of Diisseldorf (1985).
`C. Carlhoff, E. Krametz, J . H. Schéifer, and J. Uhlenbusch, J. Phys. B 19, 2629 (1986).
`H. Griem, Plasma Spectroscopy, Chap. 5, McGraw—Hill, New York, NY (1964); Spectral Line Broadening
`by Plasmas, Appendix III, Academic Press, New York, NY (1974).
`. V. Helbig and K. P. Nick, J. Phys. B 14, 3573 (1981).
`. L. P. Kudrin and G. V. Sholin, Soviet Phys. Dokl. 7, 1015 (1963).
`. J. Seidel, Z. Naturf. A32, 1207 (1977).
`
`ll
`12
`13