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The theoretical intensity ratios from individual ion species can provide a measurement of electron density which is independent of any assumptions about the volume of the emitting region.
Spectral lines may be grouped into different categories according to the behaviour of the upper level population: allowed lines collisionally excited from the ground level; forbidden or intersystem lines originating from a metastable level - m; allowed lines excited from a metastable level.
For simplicity we again consider a two level model. For forbidden and intersystem transitions the radiative decay rate is generally very small (Am,g @ 100 - 102 sec-1) collisional de-excitation then becomes an important depopulating mechanism (Am,g @ Ne Cem,g) and may even be the dominant mechanism; moreover the population of the metastable level becomes comparable with the population of the ground level and we have:
| (20) |
For small electron densities, Ne ® 0, Am,g >> Ne Cem,g, then the intensity has the same dependence on the density as an allowed line (IA):
| (21) |
For very large values of electron density, Ne® ¥ , the collisional de-population dominates, Ne Cem,g >> Am,g ; the metastable level is in Boltzman equilibrium with the ground level:
| (22) |
The line intensity has the form:
| (23) |
For intermediate values of electron density Am,g @ Ne Cem,g the population of the metastable level is significant and the intensity varies as:
| (24) |
The intensity ratio of a forbidden to an allowed transition (IF/IA) for different spectral lines from the same ion can be used to determine an average electron density for the emitting volume. This value is independent of the elemental abundance, ionisation ratio and any assumptions about the size of that volume.
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Spectral diagnostics in the EUV |
UNIVERSITY OF CAMBRIDGE Department of Applied Mathematics and Theoretical Physics |
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