Nonstationary argon plasma, containing Nelike and Nalike ions. ‘‘fast compression’’ and population inversion

I N T R O D U C T I O N and M E T H O D . We study the argon plasma under conditions where Nelike and Nalike ions are the most abundant. This includes a sufficiently large region of plasma electron density Nez and plasma electron temperature Tet to be realized and investigated experimentally. Under these conditions in the steady state plasma with electron density Nel > 1017; the population inversion for all pairs of lasing candidates is small, not more than 0.001 of the total number of argon atoms. Recently ].J.Rocca et.al. [1,2], in there experiments with capillary discharge showed, that the preionized plasma column with a diameter 0.2 cm can be rapidly heated by magnetic field arising during the fast increasing of the discharge voltage. The radiating region, under the influence of the compressing magnetic field, shrinks and its temperature increases. During the whole cycle of compression expansion, the hot dense plasma never contacts with the capillary walls. In [3] the idea of the simultaneous confinement and heating of the thermonuclear plasma inside tubelike powerful laser beam, has been suggested. We believe, that the same idea would be useful in the capillary discharge problem. The tubelike laser beam, enveloping capillary additionally compress its plasma due to ponderomotive forces and serves as an additional source of heating energy, that moderates the requirements to the characteristics of the discharge. As it is noticed in [3], such laser beam protects plasma against sausagetype instability. The nonstationarity features in the compressing plasma, drastically influence the inversion of "lasing" levels population. The maximum of inversion does not obligatory coincides with the maximum of compression or temperature. Thus an appreciable inversion can appear at the decompression phase with moderate plasma temperature and relatively high electron density. Here we investigate this question theoretically. A definite time dependence of the diameter D(t) of the compressing column, is accepted. The model of the Maxwellian homogeneous plasma, characterized by the correlated functions of electron temperature Tel(t) and electron density Net(t) is considered. The Tet ~ D -t/3 and Net ~ D -2 time dependencies follow from the simplest model of the homogeneous compression of the plasma obeying the local neutrality condition. Certainly it is a very simplified model of the process. Experiment shows that energy transfer between electromagnetic field and plasma proceeds much faster than it follows from this model, possibly due to other physical processes in the plasma column. Nevertheless, we believe,that, the accurate calculation of the evolution 388 9 1994 American Institute of Physics This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.187.97.22 On: Tue, 01 Apr 2014 20:20:14 L. N. I v a n o v a n d L. V. K n i g h t 389 of tile states populations in the plasma with tile phenomenological t ime dependence of parameters of the active media, is a realistic way to evaluate perspectives of lazing, even if we do not specialize real physical processes that manifest itself in such a manner. Thus, we use here the terminus "compression" and "expansion", by convention, to designate some phenomenological model of the correlated variation of the p lasma parameters. In our calculations, we account, for all the elementary atomic processes of the states populat ion, in the framework of the coltisional radiational model. The rate coefficients of the processes changing the s ta te of the Ne like ion or Ne like residue in the Na like ion, are calculated due to the relativistic many body per turbat ion theory with the model bare potential [4]. All the other rate coefficients are calculated in the semi classical approximation. [5,6]. 37 basic states of the Ne like ion and 37 mult i tudes of adjacent Rydberg states of the Na like ion are accounted for. The infinite number of states of each Rydberg series is included. We investigated the role of the diffusion like migration of the state of the system "Ne like ion plus electron" over the overlapping Rydberg mult i tudes on the states population kinetics. It proved that the contribution of this migration into the relative populations of the states of the Ne like ion is important , even in the case when Na like ion states are poorly populated themselves. It is due to intensive population fluxes through these states and immensely large number of reaction channels. The summary effect of populat ing of Rydberg levels through dielectron recombination followed by different ionization processes, is very selective in relation to final state of system; it is impor tant for creation of inversion. Time dependent populat ion calculations are based on our code [5], that solves the system of kinetic equations for populations of 37 lowest Nelike levels and 37 populat ion distr ibution functions for the mult i tudes of Rydberg states. Reabsorption of the spontaneous radiat ion for all transit ions is accounted for due to the s tandard routine [7]. We considered the case of p lasma cylinder with diameter 0.10 0.02 cm., the ion temperature is supposed to be equal to Tez. We experimented with the ion temperature function other than Tet: i ts reasonable variation did not change qualitatively the results presented below. R E S U L T S . As usuM, we numerate the states of the Ne like ion in accordance with increasing energies. Special at tention is paid to the states 3,5 and 6,8-15. The first two are assumed to be lower, the other nine upper levels in the collisional radiat ional lasing scheme. Transitions 15-5 (3p,J=0 3 s , J= l ) and 13-5 (3p,J=2 3 s , J= l ) are usually under especial at tention in experimental and theoretical investigations. For the "compressed" column, with high temperature T,t > 100 e V , three other transitions show high inversion. Those are: transit ion 37-33 (,k = 520.5,~i and radiat ion transit ion probabil i ty A = 3.2 + 09sec-~) , 35-33 (,k = 572.1A, A = 2.5 + 09sec -~) , 34-33 (,k = 572 .4~A = 1.1 + 09 see -1) . All wavelengths and transit ion probabili t ies are due to our calculations, see [5], and references therein. Figure 1 shows evolution of the populations inversion for the transit ion 13-5 during the ~ w expansion s tar t ing from the s teady state hot dense plasma. Two slightly different s tar t ing densities are considered. Line A: Net ~ 35 + 1 6 c m -3, while t o% D --4 0,1, cm.; line B: Net ---* 30 + 16cm -3. The unambiguous transient effect manifests itself as increase of relative inversion I ( i j ) = ( P ( i ) g ( j ) P ( j ) g ( i ) ) / P g( j ) , This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.187.97.22 On: Tue, 01 Apr 2014 20:20:14 390 Nonstationary Argon Plasma where P(i), P( j ) are levels populations, g(i), g(j) statistical weights, Ptotal number of Nelike and Nalike ions that is close to the total number of Ar ions, for the processes here considered.