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Measurement of gas temperature in a CO2-N2-He TEA amplifier using laser interferometry
Volume
12. number
3
MEASUREMENT
OPTICS COMMUNICATIONS
OF GAS TEMPERATURE USING LASER
IN A C02-N2-He
November
1974
TEA AMPLIFIER
INTERFEROMETRY
R4.C.GOWER* Physics Department and CRESS, York University, Toronto. Ontario, Canada
Received
8 August
1974
Using a laser interferometric technique changes in the refractive index at 633 nm of the pulsed discharge of a TEA C02-N2-He laser amplifier have been observed. Heating of the medium by the discharge reduces the density and hence the refractive index of the gas. The peak temperature was found to be reached between 0.15 and 0.25 msec after the current pulse. For values of voltage and pressure typical for 10.6 pm laser operation a temperature of -430 K was measured. The system returned to thermal equilibrium after 23 and 27 msec. Thermal diffusion time calculations indicate that the heating is confined to within 3 to 4 mm of the central axis.
Changes in refractive index at 633 nm of the pulsed discharge of a CO,--N2--He TEA amplifier have been observed. From these observations it is possible to derive information on the gas temperature fluctuations. The experimental technique used is somewhat similar to that employed for measuring electron densities in high density plasmas [ 11. The 10.6 pm TEA amplifier, similar to that of Beauiieu [2], was placed in the external optical cavity formed by a Spectra-Physics 133 FIeeNe laser and a partially transmitting plane mirror which reflected the light output back into the laser. Any change in the refractive index of the plasma will result in a change in the optical path length giving resonances on the laser output. The light emerging from behind the plane mirror was monitored as a function f time with a photomultiplier (RCA 1P28) givi $ a detection system response time of 60 nsec. Across the single row of 55 resistively loaded pins of the amplifier a 0.012 I.~F capacitor at 30 kV was discharged through a spark gap. The pressure of the sealed 9.5512.5578 CO, ~ N2-He mixture in the amplifier was kept at 300 torr. Because of the relatively small electron densities in * Present address:
Physical Gasdynamics NASA Ames Research Center, Moffett 94035, U.S.A.
246
and Laser Branch, Field, California
these TEA type devices [3] the observed refractive index changes will be solely due to thermal fluctuations of the gas. Using the ideal gas equation and assuming that the pressure P relaxes with the speed of sound across the discharge (after - 10 psec), so that P, = PO for times f > 10 psec, then the rise in gas temperature from its equilibrium value To is given by: AT = Tt - To = T,( 1 -~ pt/po),
where p = gas density and subscripts refer to values of parameters at times 0 and t after the onset of the discharge. Using the empirical Gladstone-Dale equation: n-l=Kp, where K is a constant
and n = refractive index, then:
The change in refractive index An is obtained from the resonance condition for TEM,,, mode oscillation in the cavity and is given by: An = kX/2d,
Volume 12, number 3
OPTICS COMMUNICATIONS
Fig.
1. Output from the laser interferometer as a function of time (0.1 msec/div).
where d = TEA plasma length and k = number of resonances to or from the peak gas temperature (for the slow repetition rates used here - 1p.p.s. - it is assumed the gas returns to thermal equilibrium after each pulse). The temperature at time t after disonset is then given by:
Several of the fringes are shown in fig. 1. The shift in the base line is due to low-frequency vibration of the system. However the fringes can easily be seen superimposed on this structure. No fringes were observed until -5 psec after the current pulse. This is probably because the rate of decrease of the refractive index due to the fast rising current pulse is much greater than the frequency response of the laser interferometer itself (-100 kHz, see ref. [l].)! For this reason only 2 to 4 closely spaced resonances were observed as the temperature approached its maximum value. However as the temperature slowly decreased in a time determined by that for thermal diffusion, the fringe separation was between 0.15 and 0.3 msec and ceased after 23 to 27 msec when the gas had reached thermal equilibrium again. The number of fringes so observed, k, gave a peak temperature of -430 K using eq. (l), reached between 0.15 and 0.25 msec after the beginning of the discharge. Of course this temperature represents a spatial
November 1974
average along the laser axis so that in some regions, i.e. within the ‘brush’ discharge, it will undoubtedly be higher than this value. Taking values of thermal conductivities, specific heats and viscosities from ref. [4], and using an empirical formula to calculate the thermal conductivity of the ternary gas mixture [5], a value of 25 msec was obtained for the thermal diffusion time if it was assumed that no gas heating took place transverse to the central axis for distances > 3 mn If this distance was increased to 4 and 5 mm then the diffusion time became 45 and 70 msec respectively. It thus seems that heating of the gas IS primarily confined to within 3 to 4 mm of the axis. In addition to reducing the gain by thermal pumping of the lower laser level, this heating can give rise to a diverging lens effect [6] and acoustic wave propagation [7]. The peak temperature of 430 K obtained here contrasts with -600 K measured in a conventional low pressure, long current, longitudinally pulsed device [8]. However the characteristics of the two types of plasmas are vastly different. For a similar type of discharge this value agrees well with calculations [9]. The funding of this research by the Defence Research Board of Canada is greatly appreciated.
References [l] D.E.T.F. Ashby, D.F. Jephcott, A. Malein and F.A. Raynor, J. Appl. Phys. 36 (1965) 29. [2] A.J. Beaulieu, Appl. Phys. Letts. 16 (1970) 504. [3] H.J.J. Seguin, J. Tulip and D. McKen, Appl. Phys. Lett. 23 (1973) 521. [4] Handbook of Chemistry and Physics, Chemical Rubber Co.; P. Mukhopahyay and A. Barua, Trans. Far. Sot. 63 (1967) 2379. [S] E.A. Mason and S.C. Saxena, Phys. Fluids 1 (1958) 361. [6] G. Otis and R. Tremblay, Can. J. Phys. 52 (1974) 257. [7] J-N. Seguin and A.I. Carswell, 7th Int. Quant. Electr. Conf., Montreal, (1972) Paper Q4. [8] D.J. Booth and W.E.K. Gibbs, IEEE J. Quant. Electr. QE-7 (1971) 17. [9] A.M. Robinson, Can. J. Phys. 50 (1972) 2138.
247
12. number
3
MEASUREMENT
OPTICS COMMUNICATIONS
OF GAS TEMPERATURE USING LASER
IN A C02-N2-He
November
1974
TEA AMPLIFIER
INTERFEROMETRY
R4.C.GOWER* Physics Department and CRESS, York University, Toronto. Ontario, Canada
Received
8 August
1974
Using a laser interferometric technique changes in the refractive index at 633 nm of the pulsed discharge of a TEA C02-N2-He laser amplifier have been observed. Heating of the medium by the discharge reduces the density and hence the refractive index of the gas. The peak temperature was found to be reached between 0.15 and 0.25 msec after the current pulse. For values of voltage and pressure typical for 10.6 pm laser operation a temperature of -430 K was measured. The system returned to thermal equilibrium after 23 and 27 msec. Thermal diffusion time calculations indicate that the heating is confined to within 3 to 4 mm of the central axis.
Changes in refractive index at 633 nm of the pulsed discharge of a CO,--N2--He TEA amplifier have been observed. From these observations it is possible to derive information on the gas temperature fluctuations. The experimental technique used is somewhat similar to that employed for measuring electron densities in high density plasmas [ 11. The 10.6 pm TEA amplifier, similar to that of Beauiieu [2], was placed in the external optical cavity formed by a Spectra-Physics 133 FIeeNe laser and a partially transmitting plane mirror which reflected the light output back into the laser. Any change in the refractive index of the plasma will result in a change in the optical path length giving resonances on the laser output. The light emerging from behind the plane mirror was monitored as a function f time with a photomultiplier (RCA 1P28) givi $ a detection system response time of 60 nsec. Across the single row of 55 resistively loaded pins of the amplifier a 0.012 I.~F capacitor at 30 kV was discharged through a spark gap. The pressure of the sealed 9.5512.5578 CO, ~ N2-He mixture in the amplifier was kept at 300 torr. Because of the relatively small electron densities in * Present address:
Physical Gasdynamics NASA Ames Research Center, Moffett 94035, U.S.A.
246
and Laser Branch, Field, California
these TEA type devices [3] the observed refractive index changes will be solely due to thermal fluctuations of the gas. Using the ideal gas equation and assuming that the pressure P relaxes with the speed of sound across the discharge (after - 10 psec), so that P, = PO for times f > 10 psec, then the rise in gas temperature from its equilibrium value To is given by: AT = Tt - To = T,( 1 -~ pt/po),
where p = gas density and subscripts refer to values of parameters at times 0 and t after the onset of the discharge. Using the empirical Gladstone-Dale equation: n-l=Kp, where K is a constant
and n = refractive index, then:
The change in refractive index An is obtained from the resonance condition for TEM,,, mode oscillation in the cavity and is given by: An = kX/2d,
Volume 12, number 3
OPTICS COMMUNICATIONS
Fig.
1. Output from the laser interferometer as a function of time (0.1 msec/div).
where d = TEA plasma length and k = number of resonances to or from the peak gas temperature (for the slow repetition rates used here - 1p.p.s. - it is assumed the gas returns to thermal equilibrium after each pulse). The temperature at time t after disonset is then given by:
Several of the fringes are shown in fig. 1. The shift in the base line is due to low-frequency vibration of the system. However the fringes can easily be seen superimposed on this structure. No fringes were observed until -5 psec after the current pulse. This is probably because the rate of decrease of the refractive index due to the fast rising current pulse is much greater than the frequency response of the laser interferometer itself (-100 kHz, see ref. [l].)! For this reason only 2 to 4 closely spaced resonances were observed as the temperature approached its maximum value. However as the temperature slowly decreased in a time determined by that for thermal diffusion, the fringe separation was between 0.15 and 0.3 msec and ceased after 23 to 27 msec when the gas had reached thermal equilibrium again. The number of fringes so observed, k, gave a peak temperature of -430 K using eq. (l), reached between 0.15 and 0.25 msec after the beginning of the discharge. Of course this temperature represents a spatial
November 1974
average along the laser axis so that in some regions, i.e. within the ‘brush’ discharge, it will undoubtedly be higher than this value. Taking values of thermal conductivities, specific heats and viscosities from ref. [4], and using an empirical formula to calculate the thermal conductivity of the ternary gas mixture [5], a value of 25 msec was obtained for the thermal diffusion time if it was assumed that no gas heating took place transverse to the central axis for distances > 3 mn If this distance was increased to 4 and 5 mm then the diffusion time became 45 and 70 msec respectively. It thus seems that heating of the gas IS primarily confined to within 3 to 4 mm of the axis. In addition to reducing the gain by thermal pumping of the lower laser level, this heating can give rise to a diverging lens effect [6] and acoustic wave propagation [7]. The peak temperature of 430 K obtained here contrasts with -600 K measured in a conventional low pressure, long current, longitudinally pulsed device [8]. However the characteristics of the two types of plasmas are vastly different. For a similar type of discharge this value agrees well with calculations [9]. The funding of this research by the Defence Research Board of Canada is greatly appreciated.
References [l] D.E.T.F. Ashby, D.F. Jephcott, A. Malein and F.A. Raynor, J. Appl. Phys. 36 (1965) 29. [2] A.J. Beaulieu, Appl. Phys. Letts. 16 (1970) 504. [3] H.J.J. Seguin, J. Tulip and D. McKen, Appl. Phys. Lett. 23 (1973) 521. [4] Handbook of Chemistry and Physics, Chemical Rubber Co.; P. Mukhopahyay and A. Barua, Trans. Far. Sot. 63 (1967) 2379. [S] E.A. Mason and S.C. Saxena, Phys. Fluids 1 (1958) 361. [6] G. Otis and R. Tremblay, Can. J. Phys. 52 (1974) 257. [7] J-N. Seguin and A.I. Carswell, 7th Int. Quant. Electr. Conf., Montreal, (1972) Paper Q4. [8] D.J. Booth and W.E.K. Gibbs, IEEE J. Quant. Electr. QE-7 (1971) 17. [9] A.M. Robinson, Can. J. Phys. 50 (1972) 2138.
247