Sensitivity of results to the electron density Unless stated otherwise, the results presented here

r /

' / ' 'N

J i /

>' /

J / _/

\.J

1 1 ITIIM| 1 1 1 H i l l

03

• - 1 0

"O

^ 1 0

10° 10

1

10

2

10

3

10

4

10

5

T (eV)

FIG. 11. Radiative loss junctions as a Junction of temperature, for oxygen steady ionization balance. The various contributions shown are as in Fig. 3.

A ' •

10° 10

1

10

2

10

3

10

4

10

5

T (eV)

FIG. 13. Effective ion charges of carbon and oxygen ions as a function of electron temperature, computed at steady ionization

balance.

. - 1 3

Oxygen

I f r iiini i rrrriwr i i i | i i i m i q i i i m i

1 0 ' * * " "*"* • • r n f f'*

10° 10

1

iO

2

10

3

10

4

10

5

T (eV)

FIG. 12. Electron cooling functions as a function of temperature, for oxygen at steady ionization balance. The various contributions

shown are as in Fig. 4.

4.4. Sensitivity of results to the electron density Unless stated otherwise, the results presented here are for an electron density of 10²⁰ m~³. Because of the weak density dependence of dielectronic recombination rates and because of the small but finite transition probability of metastable states, we expect our results to show some sensitivity to the electron density. This point has been examined by varying the electron density

TABLE IV. VALUES OF THE RADIATIVE COOLING FUNCTION (in units of aW-m3) COMPUTED AT VARIOUS ELECTRON

TEMPERATURES FOR CARBON AND OXYGEN IMPURITIES AT STEADY IONIZATION BALANCE*

T(eV) 1.00 1.70 2.89 4.90 8.33 14.1 24.0 40.8 69.3 117.7 200.0 339.7 577.1 980.3 1665 2828 4804 8161 13863 23548 40000

Carbon 2.720 xlO"^{1 6}

1.063 X10'1 5

6.720 x 10"'3

2.539 x 10"14

5.073 x lO"14

4.551 X 10"15

4.448 x 10"16

1.502 XlO"'6

3.812 X10"16

5.615 X10~16

2.848 X10"16

1.454 X 10"16

8.879 X 10-17

6.433 X10~"

5.458 x 10"17

5.347 X 10~17

5.842 X 10:17

6.865 x 10"17

8.435 x"l0"17

1.063 xlO"1 6

1.360 xlO"1 6

Oxygen 1.291 x 10"17

2.847 x 10"17

1.173 xlO"1 5

' 6.778 x 10"5

2.173 X10"14

4.465 X 10"14

3.133 xlO"'4

2.740 x 10"'5

4.268 x 10"'6

4.906 x l O " '6

1.261 x 10",s

7.504 x 10"'6

3.518 xlO"^{1 6} 2.063 x 10"'6

1.483 xlO"1 6

1.265 XlO"16

1.242 XlO"'⁶ 1.358 X10"¹⁶ 1.596 xlO"1 6

1.959 X10"16

2.467 x 10"16

* The electron density assumed in the calculations is 1020 m

127

in the range 1016 to 1020 m"3. The computed rates were found to be nearly independent of the density in that range. This weak sensitivity has been confirmed independently by Clark and Abdallah [51]. At higher densities, however, the rate coefficients become more sensitive to the electron density. It then becomes necessary to account for multistep processes, not only for transitions involving metastable states but also for transitions between all excited states.

5. CONCLUSION

Radiative loss and electron cooling rates have been calculated for carbon and oxygen impurity ions, for plasma conditions of relevance to fusion. These rates, have been calculated with the most recent recommended atomic data available. The radiative loss function enters the total energy balance. The electron cooling rate enters the electron thermal energy balance. The two rates are equal under steady ionization balance conditions. They may differ significantly under non-steady conditions.

A simple method has been used to calculate loss rates while approximately accounting for the effects of metastable states. The importance of metastable states has been assessed by making comparisons with results obtained in the standard coronal approximation. For both radiative losses and electron cooling rates, signifi-cant differences have been found. We stress that such calculations are contingent upon the availability and accuracy of data for a wealth of atomic processes. We would like to conclude with a short list of processes for which more accurate or detailed data would be desirable. These are:

(a) Excitation. When metastable states are taken into account, excitations to higher states become significant.

In practice, these would correspond to transitions with An up to two, from the ground state.

(b) Ionization. Recommended data for the ionization cross-sections typically account for a number of processes. For example,

e + O V (ls²2s²) - e + e + O VI (ls²2s) e + O V (ls22s2) - e + e + 0 VI (ls2s2)

p e + e + e + O VII (Is2)

X L^e + e + he + O VI (Is²2s²) e + O V (ls22s2) - e + O V (ls2s22p)

p e + e + O VI (ls²2s) x i~e + hv + O V (ls22s2)

Because these processes have different energy thresholds, they will contribute differently to the radiative losses and electron cooling rates. Accurate cross-sections and, when appropriate, Auger rates and branching ratios are therefore required for each process.

(c) Dielectronic recombination. Cross-sections for dielectronic recombination corresponding to specific transitions are required. The results presented here have relied largely on scaled hydrogenic rates that were normalized to reproduce recommended total recombination rates. Accurate calculations with finite density effects are also needed.

(d) Radiative recombination. Detailed cross-sections for radiative recombination to specific states are needed.

This includes recombination into metastable states, from ions initially in the ground state or the metastable states.

(e) Transition probabilities. Some transition probabi-lities needed to calculate the relative populations of the ground state and the metastable states are missing and had to be evaluated from scaled hydrogenic values.

Transition probabilities are also required for forbidden transitions from metastable states.

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129

Appendix

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