alignment and light induced gas dynamic tension

2
Volume 111 A, number 6 PHYSICS LETTERS 23 September 1985 ALIGNMENT AND LIGHT INDUCED GAS DYNAMIC TENSION L.V. IL’ICHOV Instiiute of Automation and Electrometty, Siberian Branch, USSR Academy of Sciences, 630090 Novosibirsk, USSR Received 27 June 1985; accepted for publication 11 July 1985 Grad’s method of moments for the solution of kinetic equations is applied to the analysis of alignment and gas dynamic tension in an irradiated medium. A qualitatively new effect in the case of chiral molecules is predicted. The discovery of light-induced drift phenomena in gases (LID) [ 1,2] has started a new field in the physics of irradiated media - gas dynamics in a laser radiation field. A consistent description of LID as a gas dynamic phenomenon has been proposed in ref. [3], where the system of transport equations in an irradiated gas has been obtained and solved on the basis of Grad’s method of moments. In ref. [3] consideration is limited to the model of absorptive particles with two nondegen- erate levels. Meanwhile the counting of particle level degeneracy over angular momentum directions leads us to predict the excistence of new interesting phe- nomena, related to LID [4-71. In the present paper the results of the application of Grad’s method to the consideration of some light-induced effects in a media of particles with degenerate levels are stated. Developing the formalism of ref. [3], we intro- duce Grad’s expansion for the velocity distribution of polar moments pa(~q u) of excited ((u= m), nonexcited (o = n) and buffer (cw = b) particles (1) Here the polar moments are introduced as the elements of a density matrix in the representation of irreducible tensor operators &q-representation; see, for example, ref. 181); P,(K~)&(K~), h,(W), na,(Kd are the ad- agues of density, particle flow, heat flow and tension ten- sor respectively, in ordinary gas dynamics; W,(u) is the maxwellian distribution for particles of component (Y with temperature T, and mass rnJ T,/m, = iTi). The applicability of the expansion (1) requires a small ratio of a Doppler llnewidth kv and homogeneous llnewidth P(kB/l? Q 1). In a linear radiation intensity approximation only the three first polar moments are induced: population (K = 0), orientation (K = I), align- ment (K = 2). The velocity moments can be called polar-gas-dy- namic (PGD) moments, since they simultaneously re- flect the non-equilibrium state of the particles with respect to translational degrees of freedom and the population of magnetic sublevels. Collisions relate the relaxation of various PGD moments. The results ob- tained are most obvious in the ordinary Cartesian rep- resentation of tensors. Here we consider the relation between irreducible tensors of the second rank. As can be simply shown there are only seven such quan- tities. That is, the alignment density pii, the ordinary tension tensor n(O)ii, the tensor n(2)ii and four pseudo- tenSOrsj(l)ij, h(l)ij,j(2)ijp h(2)ij. The last five tensors are constructed from the alignment tension tensor aik,jl, the flOWS of orientation~~,i, hi,j and alignment jjk,l hjk,l in the following way: n(2)jj = f (n&JR ’ njk,ik)- 3 &jnkl,kl, i(l>ij = 4 oi,j +ij,j) - 4 aijjk,k 2 h(l)jj = 3 (hi,j +hj,i) - B Sij hkp 3 289

Upload: lv-ilichov

Post on 21-Jun-2016

216 views

Category:

Documents


2 download

TRANSCRIPT

Volume 111 A, number 6 PHYSICS LETTERS 23 September 1985

ALIGNMENT AND LIGHT INDUCED GAS DYNAMIC TENSION

L.V. IL’ICHOV

Instiiute of Automation and Electrometty, Siberian Branch, USSR Academy of Sciences, 630090 Novosibirsk, USSR

Received 27 June 1985; accepted for publication 11 July 1985

Grad’s method of moments for the solution of kinetic equations is applied to the analysis of alignment and gas dynamic

tension in an irradiated medium. A qualitatively new effect in the case of chiral molecules is predicted.

The discovery of light-induced drift phenomena in gases (LID) [ 1,2] has started a new field in the physics of irradiated media - gas dynamics in a laser radiation field. A consistent description of LID as a gas dynamic phenomenon has been proposed in ref. [3], where the system of transport equations in an irradiated gas has been obtained and solved on the basis of Grad’s method of moments. In ref. [3] consideration is limited to the model of absorptive particles with two nondegen- erate levels. Meanwhile the counting of particle level degeneracy over angular momentum directions leads us to predict the excistence of new interesting phe-

nomena, related to LID [4-71. In the present paper the results of the application of Grad’s method to the consideration of some light-induced effects in a media of particles with degenerate levels are stated.

Developing the formalism of ref. [3], we intro- duce Grad’s expansion for the velocity distribution of polar moments pa(~q u) of excited ((u = m), nonexcited (o = n) and buffer (cw = b) particles

(1)

Here the polar moments are introduced as the elements of a density matrix in the representation of irreducible tensor operators &q-representation; see, for example,

ref. 181); P,(K~)&(K~), h,(W), na,(Kd are the ad- agues of density, particle flow, heat flow and tension ten- sor respectively, in ordinary gas dynamics; W,(u) is the maxwellian distribution for particles of component (Y with temperature T, and mass rnJ T,/m, = iTi). The applicability of the expansion (1) requires a small ratio of a Doppler llnewidth kv and homogeneous llnewidth P(kB/l? Q 1). In a linear radiation intensity approximation only the three first polar moments are induced: population (K = 0), orientation (K = I), align- ment (K = 2).

The velocity moments can be called polar-gas-dy- namic (PGD) moments, since they simultaneously re- flect the non-equilibrium state of the particles with respect to translational degrees of freedom and the population of magnetic sublevels. Collisions relate the relaxation of various PGD moments. The results ob- tained are most obvious in the ordinary Cartesian rep- resentation of tensors. Here we consider the relation between irreducible tensors of the second rank. As can be simply shown there are only seven such quan- tities. That is, the alignment density pii, the ordinary tension tensor n(O)ii, the tensor n(2)ii and four pseudo- tenSOrsj(l)ij, h(l)ij,j(2)ijp h(2)ij. The last five tensors are constructed from the alignment tension tensor aik,jl, the flOWS of orientation~~,i, hi,j and alignment jjk,l hjk,l in the following way:

n(2)jj = f (n&JR ’ njk,ik)- 3 &jnkl,kl,

i(l>ij = 4 oi,j +ij,j) - 4 aijjk,k 2

h(l)jj = 3 (hi,j +hj,i) - B Sij hkp 3

289

Volume 111 A, number 6 PHYSICS LETTERS 23 September 1985

i(2)ji = if (‘i/cl jjk,l + eijkl jik,[) ,

h(2>ij = !Z (‘i/cl hjk,l ’ ejkl jik,[) . A collisional relation between the true tensors piZ>

n(O)ij and n(2)ii and pseudotensors j(l)iZ, h(l)iZ, j(2)ii and h(2)ji is possible in a medium of chiral mol- ecules only, whose structure has pseudoscalar quan- tities.

The solution of the kinetic equations with field terms, exact quantum mechanical collision integrals and with the use of the expansion (1) gives the general form of a PGD moment Tjj which is a second rank tensor (z-axis directed along the wave vector k):

Tii = ~ii{ (36, - 1) (aZ + eZ,) t bZii

t c[(3$, - 1) Zii - I,,1 I + deijz (Iii - ‘ii> ,

where Z is the radiation intensity; Zii are the compo- nents of the polarization tensor [8] (its main axes coincide with the x- and y-axes); I, is the only com- ponent of the polarization vector (in the case of non- polarized or linearly polarized radiation Zr = 0). The contribution of the tension tensor n(O), to (2) is proportional toa; the term ab reflects the contribution of the alignment density pii; and the term ac that of the tensor ~(2)~~; the terms ad and me are conditioned by the flows of alignment and orientation respectively and are present only in a medium of chiral molecules.

As it is evident from (2) both the alignment tensor and the tension tensor as the particular realizations of Tij acquire a complicated structure due to collisions, especially in a chiral molecule gas. The contribution

of orientation flows does not change qualitatively the geometric structure of Tij in contrast to the flows of alignment (ad), which deflect the main axes of Tii from those of the polarization tensor (x - and y-axes). The deflection angle cp in the xy plane has opposite sign for opposite stereomodifications of a chiral mole- cule and is proportional to the frequency detuning 52, when cp Q l(C? = w - a,,,, w is the radiation fre- quency, o,, is that of the transition m-n). The closer the radiation polarization to the linear one, the greater is the described effect, as is evident from (2).

The deflection of the main axes from those of the polarization ellipse can be detected experimentally by the test field method. As is known, the expression for the test field work P, has a term which is propor- tional to Z~jpii, where Z .. is the polarization tensor of the test field and Pij ic?he alignment induced by the strong field. Due to the term ad in the tensor pij, the work has a term antisymmetric and linear to a first approximation over the strong field frequency detuning a. The angle $ between the polarization planes of the strong and test fields must be different

from 0 and n/2 for the existence of this term. The maximum effect will be observed, when J/ = n/4 (see also ref. [9]). Proceeding from that, the predicted phenomenon is proposed to be identified by detect- ing the signal of Pp, as a function of the detuning Q at the double frequency of $-modulation near n/4.

Investigation of the alignment, induced by radiation and collision can give much information about colli- sions, especially anisotropic.

The author is thankful to F.Kh. Gel’mukhanov and A.M. Shalagin for discussions.

References

[II

I21

]31

]41

t51

]61

171

is1

PI

F.Kh. Gel’mukhanov and A.M. Shalagin, Pis’ma Zh. Eksp. Teor. Fiz. 29 (1979) 773 [JETP Lett. 29 (1979) 7111. F.Kh. Gel’mukhanov and A.M. Shalagin, Zh. Eksp. Teor. Fiz. 78 (1980) 1672 [Sov. Phys. JETP 51 (1980) 8391. F.Kh. Gel’mukhanov and L.V. Il’ichov, Khim. Fir. 3 (1984) 1544. F.Kh. Gel’mukhanov and L.V. Il’ichov, Khim. Fiz. 2 (1983) 590. F.Kh. Gel’mukhanov and L.V. Il’ichov, Chem. Phys. Lett. 98 (1983) 349. F.Kh. Gel’mukhanov and L.V. Il’ichov, Zh. Eksp. Teor. Fir. 88 (1985) 40. F.Kh. Gel’mukhanov and L.V. Il’ichov, Opt. Commun. 53 (1985) 381. S.G. Rautian, G.N. Smirnov, A.M. Shalagin, Nonlinear resonances in atomic and molecular spectra (Nauka, Novosibirsk, 1979). S.G. Rautian and G.N. Nikolaev, Preprint No. 25 1 (Institute of Automation and Electrometry, Siberian Branch USSR AC. Sci., 1985).

290