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TWO ELECTRON CAPTURE PROCESSES IN PLASMAS CONTAINING MULTIPLY CHARGED
IONS
T. Grozdanov, R.K. Janev
To cite this version:
T. Grozdanov, R.K. Janev. TWO ELECTRON CAPTURE PROCESSES IN PLASMAS CONTAIN- ING MULTIPLY CHARGED IONS. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-71-C7-72.
�10.1051/jphyscol:1979735�. �jpa-00219344�
JOURNAL DE PHYSIQUE CoZZoque C7, suppl6ment au n07, Tome 40, JuiZZet 2979, page C7- 71
TWO ELECTRON CAPTURE PROCESSES M PLASMAS CONTAINING MULTIPLY CHARGED IONS
T.P. Grozdanov and R.K. Janev.
I n s t i t u t e o f Physics, Belgrade, Yugos Zavia.
It has recently been recognized that
the electron transfer processes between
A+Bz++A+
+ (Z-1) ++A2+ + (Z-2) +,
z>>1the multicharged ions and neutral species (1)
in a crucial way influence the ionization equillibrium, energy balance, radiation and transport properties of many labora- tory and astrophysical high--temperature
Such a role of these 2rocesses is a result of their extremely large cross sections ( a c l ~ - ~ ~ cm 2 ; o*zq, q=1-2) and the fact that highly excited states of the product ions are preferencially created by them. In Tokamak-type thermonuclear plasmas, additionally heated by neutral beams, the multicharged impurity ions play a detrimental role, which even may prevent reaching the fusion burning conditions 1
.
The important neutral species, which under-
The capture mechanism is supposed to be an electron funneling4l5 from the atomic (A) and ionic (A+) potential well into the
"quasi-continuous" spectrum of the exci- ted states of the ions B ('-1)+ and B(Z-2)+
At internuclear separation 2 the electron transition probability per unit time (in atomic units) is given by5 :
x exp C- ---7 R~ f(a)-$(a) 1 (2) Z n
go charge-changing collisions with multi-
@ (a) =2 (2pn-1) an (ma+&') charged ions in the outer layers ~f the
Tokamak plasma, are D, T and He. Almost equally important role plays the electron transfer collisions between multicharged ions and neutrals in the expanding laser produced plasmas2. In such plasmas, the above mentioned processes serve as an effi- cient mechanism for creation of inverted population of the electronic levels of the product ions. The radiative decay of these levels is responsible for the EUV emission from laser produced plasmas.
flost of the experimental and theore-- tical work on the charge-changing colli- sions of multicharged ions with atoms has so far been done for one-electron transfer processes3-5. However, the experimental data6 indicate that the two-electron cap- ture processes in these collisions have also large cross sections, being only a
In the above formulae n=(2I) -1'2, I is the electron binding energy in the initial sta- te (atom A or ion A
+
) , p is the charge of the atomic (p=l) or ionic (p=2) core, a is the electron initial orbital angular mo- mentum and N is the normalization constant of the asymptotic atomic (ionic) electron wavef unction.The method of calculation of the cross section for process (1) is in some sense iterative one. We shall neglect, in the first approximation, the capture of the second electron, and using the expres- sion (2) with the parameters of the atom A, we can calculate the electron capture cross section from5 :
factor of 5
-
G smaller than the cross where, v is the relative velocity of the sections for one-electron capture. colliding particles, p is the impact para-In the present communication we pro- meter and the strainght line trajectories pose a model for a successive capture of are assumed.
two electrons in slow collision (relative Now, an effective radius Xo of
=locity v<2x10a crn/s) of multiply charged the one-electron capture process can be ions with atoms: defined from the relation p=*;io. Further, 2
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979735
we shall assume that all atoms that enter the sphere of the radius Ro will underge one-electron loss. The two-electron capture cross section u2 can be calculated from Eq.(3) in which the upper limits of the integrals are replaced by Ro, and W(R) taken from Eq. (2) with the parameters of the ion A+ and with the substitution Z+Z-1. It is clear from this procedure that o represents the total electron cap- ture cross section and that real one- -electron cross section is given by
We have performed the cross section calculations for the collision of He-atom with an ion of charge Z=6 (the only cha- racteristics of the multiply charged ion that enters into the present theory). The parameters taken for He atom (ion) were:
N = 2.250 (5.657), n = 0.744 (0.5), p=1(2) and i=O (0). The results of calculations are shown in Fig. 1 together with the cxperinental data6 for one and two-electron capture cross sections in H~-A$+ collisions as a function of the ion impact energy E
(relative velocity v). As it can be seen from the figure, the agreement of the theoretical results and the experimental data is quite satisfactory. This figure also shows that the cross section for
Fig. 1
References
1. C.F.Barnett, in: "The Physics of Elec- tron. Atom. Collisions", Inv. Lectures and Progr. Repts. of IX ICPEAC, Ed.J.S.
Risley and R.Geballe (University of Washington, Seattle, 1975), p.846.
2. A.V.Vinogradov and I.I.Sobelrman, Sov.
Phys.- JETP,
36,
1115 (1973).double electron transfer for He on Z=6 3. L.P.Presnyakov and A.D.Ulantsev, Sov.
ions is smaller only for a factor of 3-4 J.Quantum Electron.
4,
1320 (1975) with respect to the one-electron cagture 4. M.I.Chibisov, JETP Lett.24,
56 (1976).cross section in the whole energy range 5. T.P.Grozdanov and R.K.Janev, Phys.
investiqated. Since within the proposed Rev. A
17,
880 (1978).- -
-theory both ol and o2 scales according 6. A. filler and E.Salzborn, Phys. Lett.
to o.%Z&nZ (i=1,2), one can infer that the
-
59A, 19 (1976).same ratio of u1/u2 approximately holds for charge-changing collisions of He with an arbitrary Z(>6)
