Inversion of hydrogen level populations in stationary plasmas

Volume 46A, number 7

PHYSICS LETTERS

11 February 1974

INVERSION OF HYDROGEN LEVEL POPULATIONS IN STATIONARY PLASMAS A.A.. SKORUPSKI and S. SUCKEWER Institute of Nuclear Research, 00-681 Warsaw, Ho~a69, Poland Received 10 December 1973 Large inversions in the dense two-temperature hydrogen plasma are obtained by solving balance equations with inelastic collisions between heavy particles taken into account.

We discuss a new possibility for obtaining large inversions of atomic level populations in stationary hy-

(aNn!at)coii,

drogen plasmas. This seems interesting from the point of view of high power stationary lasers. An interesting idea for obtaining inversion in extremally non-equilibrium plasma was given by Gudzenko et al. [1—3].It consisted in very fast cooling than the relaxation time for recombination (108_ lO~sec). The feasibility of this idea has been demonstrated [41,but it was impossible, due to experimental difficulties, to achieve the cooling times as short as required. Recently an attempt was made, both theoretical and experimental, to realize this idea also in stationary conditions [5]. A common feature of these proposals was an expansion of plasma to a low density region. In contrast to this our calculations show that large stationary inversions can also be ob-

state

tinned for relatively high atom densities. In such calculations, however, one cannot neglect inelastic processes caused by heavy particle impacts (atom-atom type collisions). Principle idea of our proposal is the following: A container with a low temperature neutral gas is supplied with a hot plasma which cools and recombines in the process of mixing with the neutral gas; the weekly ionized mixture is taken from the container to ensure stationary operation (a closed cycle operation is conceivable). In some region of the container a strongly recombining non-equilibrium plasma with low ion and atom temperatures will be obtained. To describe our system we adopt a quasi steadystate model [6] but with atom-atom collisions taken into account. Hence

~ = 0, for n = 2, 3 ng~ (1) whereas for the population density N1 of the ground

(aN1 /at)~011,rad > 0. The latter derivative defines the rate at which atoms are created and should be taken away from unit volume (Na ~N1 in all our cases). We assume maxwellian velocity distributions for all species atom and ion ternperatures equal to each other (7~= T1) but different from the electron temperature 1~.Earlier and set of eqs. (1), under these assumptions, was solved numerically by Drawin [7] for diagnostical applications (measurements of 7k). Here the solution of(l) is discussed from the point of view of inversion. We define to’~ ~

HYDROGEN

sQ

~ PLA5IIA OPTICALLY THIN T,~T~~fUOOK (n.3; m.2)

~ 50

~

40

~

30

~

20

sQ

sQ R~1 ‘°~ ‘°~-~‘ A,,

—

—

I

10e

—

—

I

~

Fig. 1. Inversion ~

—

—

—

—

I

10a

and

~ fO,o Ne[cm~J its stability R.

473

Volume 46A, number 7

PHYSICS LETIERS

11 February 1974

Table 1 Inversions in optically thick plasma; Ta

=

1000°K.

Te= 1000°K 3]

Na [cm

1.0, +16

1.0, +15

Here 1.0, +16

=

Te=3000°K

Ne [cm3)

Ninv[cm3)

R

Ninv[cm~3]

R

1.0, +10 1.0, +12 1.0, +13

8.6, +2 2.0, +7 6.0, +8

1.61 1.75 1.04

2.6, +2 —7.6, +7

1.58 1.35 0.67

1.0, +10 1.0, +12 1.0, +13

2.3, +1 1.0, +7 1.0, +9

1.08 1.69 1.07

1.2, +1 1.1, +5 —3.6, +7

1.15 1.23 0.67

9.5, +5

1.0 xlO’6, and so on. Table 2 Dependence onN

Na [cm3]

Ne [cm3l

1~~ on Te. Optically thin plasma. Ta 3] N~nv[cm Te 10000K 2000°K

1.0, +15

1.0, +13 1.0, +14

1.4, +9 2.5, +12

Here 1.0, +15

=

=N~

—

3000°K

10000°K

1.3, +7 8.7, +9

3.0, +7

—

1.0 X1015, and so on.

Nm (n/rn)2.

(2)

The solution is defined by four plasma parameters (T~,Ta, Ne, Na), which are fixed in calculations. Thus we leave aside here detailed calculations concerning particle and radiation transport phenomena, or the attainable size of the inversion region, relevant to concrete experimental devices. We solved eqs. (1) numerically (ng = 25) for: (1) optically thin plasma, (ii) plasma optically thick towards Lyman lines and Lyman continuum and thin towards other transitions. In (ii) effective emission coefficients for discrete and continuous transitions to the ground state were assumed zero. Those for other transitions were taken from [8], whereas collisional rate coefficients from [9]. We found that inversions in (i) were always much larger and involved more transitions (2 ~ m, n ~ 5) than those in (ii) (3 ~ m, n ~ 5). In (i) relatively large intervals of the electron density Ne are obtained in which ~ is large and the ratio R = Nn/fNm(n/m)2 related to the stability of inversion, not to close to unity (fig. 1). These intervals in (ii) are much smaller (table 1).

474

1000°K

6.3, +7 6.0, +10

the inversion between levels m and n (rn
=

As it may be difficult in experiment to work with low electron temperatures, 7. dependence of inversion was examined. As can be expected the inversion decreases for 7 increasing, but the drop is not dramatic (table 2). It can be seen that all parameters leading to large inversions are reasonable from experimental point of view. References [1] LI.

Gudzenko

and L.A. Shelepin, Zh. Exp. Theor. Fiz.

45 (1963) 1445.

[2] LI. Gudzenko, S.S. Fiippov and L.A. Shelepin, Zh. Exp. Theor. Fiz. 51(1966)1115. [3) S.S. Filippov, L.I. Gudzenko, Y.I. Sytsko, S.I. Yakovlenko and V.V. Yevstigneyev, Proc. XI mt. Conf. Phenomena in ionized gases, Prague (1973) p. 38. [4] E.F. Gippius, V.N. Kolesnikov and LI. Shumskaya, Proc. IX Int. Conf. Phenomena in ionized gases, Bucharest (1969) p. 14. [5] P. Hoffmann and W.L. Bohn, Z. Naturfor. 27a (1972)

878. [6) D.R. Bates, A.E. Kingston and R.W.P. McWhirter, Proc. Roy. Soc. A267 (1962) 297. [7] H.W. Drawin, Z. Naturfor. 25a (1970) 145. [8] C.W. Allen, Astrophysical quantities (Athlone Press, London 1963).

[91 H.W.

Drawin, Z. Physik 225 (1969) 483.