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Cooling or heating of gases through energy transfer using lasers
15 August 1982
OPTICS COMMUNICATIONS
Volume 42, number 6
COOLING OR HEATING OF GASES THROUGH ENERGY TRANSFER J.S. GOELA * and R.K. THAREJA
USING LASERS
**
Indian Institute of Technology, Kanpur-208016, India Received 23 April 1982
A scheme for cooling or heating of gases using laser radiation is proposed. The scheme consists of pumping an excited state of an atom/molecule followed by near resonant energy transfer to another atom/molecule which then radiates at higher or lower frequencies.
Recently a number of schemes have been proposed to cool a gas in a transient or steady state manner by employing laser radiation [l-7]. While the transient cooling schemes are based upon one of the effects: radiative recoil, laser excitation to a lower half of a Doppler broadened transition, collisionally aided fluorescence and the storage of energy in a vibrationally stable mode [I-S], the steady state cooling or heating schemes are based on the absorption of tunable laser radiation by the system and reradiating at higher or lower frequencies [6,7]. In the present note we propose a scheme for steady state cooling or heating of a gas, which may particularly be useful for gaseous mixtures. Essentially, the proposed scheme consists of pump ing an excited state of an atom/molecule followed by near resonant energy transfer to another atom/molecule which then radiates at higher or lower frequencies. To illustrate the scheme, consider fig. 1. A laser of appropriate frequency excites particles of G from level 1 to level 2. The level 2 could either be an electronic level, a vibrational level or a rotational level, the excited particles of G collide with the particles of H and the resonance energy transfer takes place between particles in level 2 of G and particles in level 3 of H, viz. G(2) + H(4) ==G(1) t H(3) - AE .
(1)
* Department of Mechanical Engineering. ** Department of Physics.
0 030-4018/82/0000-0000/$02.75
0 1982 North-Holland
“,”
I”Si~S
j
G
H
Fig. 1. Scheme of producing steady state cooling through energy transfer.
For cooling it is necessary that (E3 - E4) > (E2 - El) so that AE in eq. (1) is positive. For heating, AE is
negative. Once the particles of H are excited to level 3, they will decay to the ground state via spontaneous emission resulting in the cooling or heating of the system. To determine the conditions for steady state cooling or heating, consider the rate of change of translational energy of the gas, dE,ldr =n&,(E2
-E,)+n&(E3
- E4)
- “2k23(E3 - E2) +n&(E3
- E2) 9
(2)
where nj is the population density of the ith level and can be determined by writing the rate equations, Ej is the corresponding energy; kq (i = 2,3, j = 1,4) is the rate constant in s-l when the particle makes a transition from the state i to the state j viz V-T, E-T 417
Volume
42, number
or R-T collisions; and k,,, k,, are the rates for resonant energy transfer between levels 2 and 3. In the steady state, dnz/dt = dn,ldt = 0 i.e., there is no net change in the population of level 2 and level 3, and assuming n1 +n2 =NG )
(3)
n3tn4=NH,
(4)
where NG, NH are the total number of particles of gas G and gas H respectively, we can write the population density of level 2, n2 and level 3, n3 as follows: n2 = Wl2NG k23k32 x
(~12+~21+~21+k21+k23)
A34+k32+k34
1 -’
(5)
and k23n2
n3=A34+k32
(6)
+k34’
where IU12, W21 are the rates of absorption and stimulated emission and Aij is the Einstein A coefficient for spontaneous emission from level i to level j. Using eqs. (5) and (6), we can re-write eq. (2) as = n3(E2 - El)
ti,/dt
k21 i;;;’
’
E3 - E2 k34 - A34m
It follows from eq. (7), for producing cooling we have ~
1[ >
(A34+k32+k34)G
steady state
k21
+ k34
*
1. (8) (9)
This condition can easily be satisfied at low temperatures and low pressures. Effectiveness of the proposed scheme can be demonstrated by considering a mixture of carbonmonooxide and carbon dioxide gases; CO being gas G and CO2 gas H. The level u = 1 at 2143 cm-l of CO corresponds to level 2 and the level 000 1 at 2349 418
1982
cm-l of CO, corresponds to level 3 in fig. 1. The level u = 1 of CO can easily be excited by frequency doubling the CO, laser radiation [8]. The values of various ratess_1arerloy; A 103 P torr 4oo s-l i9], k23 = 1*38 k34=193Ptorrs_i
3&3*68X
1;3ptorrs-l
[lo],
= loPC0 [lo] and A,, = 33.8 s-l [9] wherkik the total pressure of the mixture and PC0 is that of CO. Thus for CO-CO2 mixture, k2, < k2, and the inequality, eq. (9) holds. It follows from the eq. (9) that cooling will be produced for CO-CO, gaseous mixture if the pressure is less than 0.199 torr. However, for pressure in excess of 0.199 torr, heating will be produced. This critical value of pressure, 0.199 torr, can be increased or decreased by decreasing or increasing the temperature of the gas. An estimate of the maximum cooling for CO-CO2 gaseous mixture can be made by assuming saturation of the transition 1 * 2, if the pumping rate of the frequency doubled CO2 laser radiation is less than k23, k32. Saturation condition implies, n2 = nl (assuming degeneracy ratio to be unity) and n3 = n2/ 2.67 = NG/5.34, yielding maximum cooling in the gas mixture at pressure 0.1 torr of 0.286 mW which is substantial at such low pressure of the gaseous mixture, To calculate laser power requirements, let us assume that only 10% of the frequency doubled CO, laser photons actually get absorbed by CO, pumping power required is -0.5 mW which is readily available. In conclusion, the proposed scheme is simple in operation and can easily be extended to various gas mixtures.
1* c7)
For many mixtures of gases, usually k,, Q k23. Thus the condition for steady state cooling, eq. (8), reduces to ‘k34
15 August
OPTICS COMMUNICATIONS
6
[ l] T.W. Hansch and A.L. Schawlow, [2] [3] [4] [5] [6] [7] 181 [9] [lo]
Optics Comm. 13 (1975) 68. W.H. Christiansen and A. Hertzberg, Proc. IEEE 61 (1973) 1060. V.S. Letokhov, V.G. Minogin and B.D. Pavlik, Optics Comm. 19 (1976) 72. A. Ashkin, Phys Rev. Lett 40 (1978) 729. P.R. Berman and S. Stenholm, Optics Comm. 24 (1979) 155. N. Djeu, Optics Comm. 26 (1978) 354. J.S. Goela and R.K. Thareja, Optics Comm. 40 (1982) 254. W.H. Green and J.K. Hancock, J. Chem. Phys. 59 (1973) 4326. P.K. Cheo, in: Lasers, VoL 3, eds. A.K. Levine and AJ. Demaria (Marcel Dekker Inc., N.Y. 1971). T.A. Cool, in: Handbook of chemical lasers, eds. R.W.F. Gross and J.F. Bott (John Wiley & Sons, N.Y. 1976).
OPTICS COMMUNICATIONS
Volume 42, number 6
COOLING OR HEATING OF GASES THROUGH ENERGY TRANSFER J.S. GOELA * and R.K. THAREJA
USING LASERS
**
Indian Institute of Technology, Kanpur-208016, India Received 23 April 1982
A scheme for cooling or heating of gases using laser radiation is proposed. The scheme consists of pumping an excited state of an atom/molecule followed by near resonant energy transfer to another atom/molecule which then radiates at higher or lower frequencies.
Recently a number of schemes have been proposed to cool a gas in a transient or steady state manner by employing laser radiation [l-7]. While the transient cooling schemes are based upon one of the effects: radiative recoil, laser excitation to a lower half of a Doppler broadened transition, collisionally aided fluorescence and the storage of energy in a vibrationally stable mode [I-S], the steady state cooling or heating schemes are based on the absorption of tunable laser radiation by the system and reradiating at higher or lower frequencies [6,7]. In the present note we propose a scheme for steady state cooling or heating of a gas, which may particularly be useful for gaseous mixtures. Essentially, the proposed scheme consists of pump ing an excited state of an atom/molecule followed by near resonant energy transfer to another atom/molecule which then radiates at higher or lower frequencies. To illustrate the scheme, consider fig. 1. A laser of appropriate frequency excites particles of G from level 1 to level 2. The level 2 could either be an electronic level, a vibrational level or a rotational level, the excited particles of G collide with the particles of H and the resonance energy transfer takes place between particles in level 2 of G and particles in level 3 of H, viz. G(2) + H(4) ==G(1) t H(3) - AE .
(1)
* Department of Mechanical Engineering. ** Department of Physics.
0 030-4018/82/0000-0000/$02.75
0 1982 North-Holland
“,”
I”Si~S
j
G
H
Fig. 1. Scheme of producing steady state cooling through energy transfer.
For cooling it is necessary that (E3 - E4) > (E2 - El) so that AE in eq. (1) is positive. For heating, AE is
negative. Once the particles of H are excited to level 3, they will decay to the ground state via spontaneous emission resulting in the cooling or heating of the system. To determine the conditions for steady state cooling or heating, consider the rate of change of translational energy of the gas, dE,ldr =n&,(E2
-E,)+n&(E3
- E4)
- “2k23(E3 - E2) +n&(E3
- E2) 9
(2)
where nj is the population density of the ith level and can be determined by writing the rate equations, Ej is the corresponding energy; kq (i = 2,3, j = 1,4) is the rate constant in s-l when the particle makes a transition from the state i to the state j viz V-T, E-T 417
Volume
42, number
or R-T collisions; and k,,, k,, are the rates for resonant energy transfer between levels 2 and 3. In the steady state, dnz/dt = dn,ldt = 0 i.e., there is no net change in the population of level 2 and level 3, and assuming n1 +n2 =NG )
(3)
n3tn4=NH,
(4)
where NG, NH are the total number of particles of gas G and gas H respectively, we can write the population density of level 2, n2 and level 3, n3 as follows: n2 = Wl2NG k23k32 x
(~12+~21+~21+k21+k23)
A34+k32+k34
1 -’
(5)
and k23n2
n3=A34+k32
(6)
+k34’
where IU12, W21 are the rates of absorption and stimulated emission and Aij is the Einstein A coefficient for spontaneous emission from level i to level j. Using eqs. (5) and (6), we can re-write eq. (2) as = n3(E2 - El)
ti,/dt
k21 i;;;’
’
E3 - E2 k34 - A34m
It follows from eq. (7), for producing cooling we have ~
1[ >
(A34+k32+k34)G
steady state
k21
+ k34
*
1. (8) (9)
This condition can easily be satisfied at low temperatures and low pressures. Effectiveness of the proposed scheme can be demonstrated by considering a mixture of carbonmonooxide and carbon dioxide gases; CO being gas G and CO2 gas H. The level u = 1 at 2143 cm-l of CO corresponds to level 2 and the level 000 1 at 2349 418
1982
cm-l of CO, corresponds to level 3 in fig. 1. The level u = 1 of CO can easily be excited by frequency doubling the CO, laser radiation [8]. The values of various ratess_1arerloy; A 103 P torr 4oo s-l i9], k23 = 1*38 k34=193Ptorrs_i
3&3*68X
1;3ptorrs-l
[lo],
= loPC0 [lo] and A,, = 33.8 s-l [9] wherkik the total pressure of the mixture and PC0 is that of CO. Thus for CO-CO2 mixture, k2, < k2, and the inequality, eq. (9) holds. It follows from the eq. (9) that cooling will be produced for CO-CO, gaseous mixture if the pressure is less than 0.199 torr. However, for pressure in excess of 0.199 torr, heating will be produced. This critical value of pressure, 0.199 torr, can be increased or decreased by decreasing or increasing the temperature of the gas. An estimate of the maximum cooling for CO-CO2 gaseous mixture can be made by assuming saturation of the transition 1 * 2, if the pumping rate of the frequency doubled CO2 laser radiation is less than k23, k32. Saturation condition implies, n2 = nl (assuming degeneracy ratio to be unity) and n3 = n2/ 2.67 = NG/5.34, yielding maximum cooling in the gas mixture at pressure 0.1 torr of 0.286 mW which is substantial at such low pressure of the gaseous mixture, To calculate laser power requirements, let us assume that only 10% of the frequency doubled CO, laser photons actually get absorbed by CO, pumping power required is -0.5 mW which is readily available. In conclusion, the proposed scheme is simple in operation and can easily be extended to various gas mixtures.
1* c7)
For many mixtures of gases, usually k,, Q k23. Thus the condition for steady state cooling, eq. (8), reduces to ‘k34
15 August
OPTICS COMMUNICATIONS
6
[ l] T.W. Hansch and A.L. Schawlow, [2] [3] [4] [5] [6] [7] 181 [9] [lo]
Optics Comm. 13 (1975) 68. W.H. Christiansen and A. Hertzberg, Proc. IEEE 61 (1973) 1060. V.S. Letokhov, V.G. Minogin and B.D. Pavlik, Optics Comm. 19 (1976) 72. A. Ashkin, Phys Rev. Lett 40 (1978) 729. P.R. Berman and S. Stenholm, Optics Comm. 24 (1979) 155. N. Djeu, Optics Comm. 26 (1978) 354. J.S. Goela and R.K. Thareja, Optics Comm. 40 (1982) 254. W.H. Green and J.K. Hancock, J. Chem. Phys. 59 (1973) 4326. P.K. Cheo, in: Lasers, VoL 3, eds. A.K. Levine and AJ. Demaria (Marcel Dekker Inc., N.Y. 1971). T.A. Cool, in: Handbook of chemical lasers, eds. R.W.F. Gross and J.F. Bott (John Wiley & Sons, N.Y. 1976).