8.1.6. Non-thermal electron distributions

In the current version of SPEX it is possible to include the effects of non-thermal (NT) electron distributions. Such NT distributions affect the spectrum in two ways: by changing the ionization balance and the emitted spectrum. Currently we take both effects into account for all our plasma models. The only exception is the NEI model, for non-equilibrium ionisation. The way we calculate the ionisation balance does not allow us to include the NT effects in the ionisation balance, but we do take it into account in the spectrum.

The way we implemented it is as follows. Our atomic data (like collision strengths) are all parameterized in a way that allow for analytical integration over simple electron distributions like delta-functions, Maxwellians or power laws. But there are other processes like radiative recombination where such an analytical approach fails. However, one way or the other, we use expressions for Maxwellian-averaged rates in all our calculations. In principle, it is possible to decompose any electron distribution as a linear combination of Maxwellians. The total rate, for example a recombination rate, is then the sum of the rates caused by the individual Maxwellian components.

Therefore, in all our rate calcualtions we build the total rate based upon such a linear combination of Maxwellians. This is done for all relevant processes (ionization, recombination, excitation, etc.)

In all our thermal models, there is an ascii-parameter called “file”; if this value is defined (i.e. when a file name of an existing file is entered), it will read the parameters of the Maxwellians from an ascii-file with that filename. If there is not such a file, or if the filename is reset by entering the par file aval none command, no file will be taken into account (i.e., we have a simple, single Maxwellian again).

The (ascii) file should have the following format. On the first line, the number of Maxwellians is given. Then for each Maxwellian there is a separate line containing two numbers: the first number is the temperature of the Maxwellian, in units of the main temperature of the plasma; the second number is the total number of electrons in this Maxwellian, relative to the main component. It is wise to have the parameters of the main component as the first line of this list.

Let us give an example. Suppose we have a plasma with three components: 2, 20 and 200 keV Maxwellians, with electron densities of 3000, 300 and 30 \mathrm{m}^{-3}, respectively. In this case the parameters of the cie model should be: temperature 2 keV, electron density 3000 \mathrm{m}^{-3}, and the corresponding file should be as follows:

1 1
10 0.1
100 0.01

The first line tells us that there are three Maxwellians. The second line contains the parameters of the first Maxwellian, that we scale here to 1 1 (it is the one with temperature 2 keV and electron density 3000 \mathrm{m}^{-3}). The third lines contain the second Maxwellian, which has a 10 times higher temperature but also a 10 times lower electron density as the first component. Finally, the fourth line contains the parameters of the third Maxwellian, which has a 100 times higher temperature and a 100 times lower electron density as the first component.