Revision of the Temperature Dependence of the Ionization Rates of Neon Ions

EINΛR HINNOV Plasma Physics Laboratory, Princeton University,

Princeton, New Jersey 08540 (Received 1 July 1067)

INDEX HEADINGS: Neon; Scattering.

IN a recent paper1 on the ionization rates of neon ions, we noted that the rate coefficients expected from extrapolation

of known data on ionization cross sections were somewhat in­consistent with the measurements. It appears that a substantial part of these discrepancies is due to an error in the evaluation of the electron temperature from the electrical conductivity of the stellarator plasma, consisting of hydrogen with about 3 % neon admixture, and 2 % - 3 % oxygen and carbon impurities. In the original discussion, we had used for the effective ion charge the average, ΣjZjNj/ΣjNj, while properly we should use the rms value

because the cross sections increase as Z2 and the number of scat­tering centers decreases with Z. In a single-component plasma the distinction is rather trivial, but in a mixture of high-Z and low-Z ions, the difference can be sizable. In our present case, referring to Fig. 1 of Ref. 1, the appropriately corrected electron temperature is very nearly given by a straight line drawn from the top of the "kink" at 1.7 msec through the point at 62 eV at 4 msec, i.e., toward the end of the discharge the electron tempera­ture is 30%-40% higher than our original estimate.

This does not appreciably change the results of Ref. 1, except for the last section, and there the change is mostly in the inter­pretation, although the evaluation of the ionization-rate coeffi­cients is also slightly affected because the last term in Eq. (13) increases linearly with temperature.

The results of the new interpretation are shown in Fig. 1, which is the revised Fig. 8 of Ref. 1. The new values are con­siderably more self-consistent, and allow deduction of probable values of the assumed constants bj that give the magnitude of the

FIG. 1. Measured ionization-rate coefficients. The shaded areas indicate estimated uncertainties of measurement. The solid curves are calculated from Eq. (9) of Ref. 1, with the b's stated in the text.

cross section for ionization Nj+ → N ( j + 1 ) + [from Eqs. (7) and (9) of Ref. 1]. These probable values are b2 = 1.0;b3 =1.6; b4 = 2.0; b5 = 2.8, and b7 = 2.3. For the lower j , the uncertainties are still sizable, and are probably caused by partial spatial separation of the ions during different times in the discharge (i.e., the center of the discharge column being depleted of ions of given j earlier than the periphery). For the last observable ionization, b7 appears to be roughly unity, but here the uncertainties are again large because of the inadequately known triplet population of Ne VII. The solid curves in Fig. 1 are the expression Eq. (9) of Ref. 1 with the bj quoted above.

This re-interpretation of the ionization rates enhances the reputation of electrical conductivity as a measure of electron temperature in stellarator plasmas.

The author is indebted to Dr. John M. Dawson for pointing out the error in the Z correction for conductivity.

This work was performed under the auspices of the U. S. Atomic Energy Commission, Contract AT(30-1)-1238.

1 Einar Hinnov, J. Opt. Soc. Am. 56, 1179 (1966).

1392 L E T T E R S T O T H E E D I T O R Vol.57