2 Plasma diagnostics

In the X-ray range, the three most intense lines of helium-like ions ("triplet'') are: the resonance line (w, also called r: 1s²¹S₀-1s2p¹P₁), the intercombination lines (x+y, also called i: 1s²¹S₀-1s2p³P_2,1) and the forbidden line (z, also called f: 1s² $^{1}{\rm S}_{0}$-1s2s $^{3}{\rm S}_{1}$). They correspond to transitions between the n=2 shell and the n=1 ground-state shell (see Fig. 1). The wavelengths in Å of each line from C V (Z=6) to Si XIII (Z=14) are reported in Table 1.

Figure 1: Simplified level scheme for helium-like ions. w (or r), x, y (or i), and z (or f): resonance, intercombination, and forbidden lines, respectively. Full upward arrows: collisional excitation transitions, broken arrows: radiative transitions (including photo-excitation from 23S1 to 23P0,1,2 levels, and 2-photon continuum from 21S0 to the ground level), and thick skew arrows: recombination (radiative and dielectronic) plus cascade processes.

 

 

Table 1: Wavelengths in Å of the three main X-ray lines of C V, N VI, O VII, Ne IX, Mg XI and Si XIII (from Vainshtein & Safronova 1978).

line	label	C V	N VI	O VII	Ne IX	Mg XI	Si XIII
resonance	w (r)	40.279	28.792	21.603	13.447	9.1681	6.6471
inter-	x	40.711	29.074	21.796	13.548	9.2267	6.6838
combination	y	40.714	29.076	21.799	13.551	9.2298	6.6869
forbidden	z (f)	41.464	29.531	22.095	13.697	9.3134	6.7394

As shown by Gabriel & Jordan (1969), the ratios defined below are sensitive to the electron density and to the electron temperature:

  

$$% R~(n_{\rm e}) \frac{z}{x+y}~~~~~ \left({\rm {also~~}} \frac{f}{i} \right)$$ (1)

$$G~(T_{\rm e}) \frac{z+(x+y)}{w} ~~~~~ \left({\rm {also}}~~ \frac{f+i}{r}\right)\cdot$$ (2)

  
2.1 Density diagnostic

In the low-density limit, all n=2 states are populated directly or via upper-level radiative cascades by electron impact from the He-like ground state and/or by (radiative and dielectronic) recombination of H-like ions (see Fig. 2). These states decay radiatively directly or by cascades to the ground level. The relative intensities of the three intense lines are then independent of density. As $n_{\rm e}$ increases from the low-density limit, some of these states (1s2s³S₁ and ¹S₀) are depleted by collisions to the nearby states where $n_{\rm crit}$C$\sim$A, with C being the collisional coefficient rate, A being the radiative transition probability from n=2 to n=1 (ground state), and $n_{\rm crit}$ being the critical density. Collisional excitation depopulates first the 1s2s ³S₁ level (upper level of the forbidden line) to the 1s2p ³P_0,1,2 levels (upper levels of the intercombination lines). The intensity of the forbidden line decreases while those of the intercombination lines increase, hence implying a reduction of the ratio R (according to Eq. (1)), over approximately two or three decades of density (see Fig. 8 in Paper I). For much higher densities, 1s2s¹S₀ is also depopulated to 1s2p¹P₁, and the resonance line becomes sensitive to the density (this has been nicely illustrated by Gabriel & Jordan 1972 in their Fig. 4.6.9).

Figure 2: Simplified diagram showing the different contributions to the population of a given n=2 shell level. (1): direct contribution due to collisional excitation from the ground level (1s2) of He-like ions; (2)+(2'): collisional excitation plus upper-level radiative cascade contribution; (3): direct radiative recombination or direct dielectronic recombination from H-like ions; and (4)+(4'): radiative recombination or dielectronic recombination plus upper-level radiative cascade contribution.

However, caution should be applied for low-Z ions (i.e. C V, N VI, O VII) since in the case of an intense UV radiation field, the photo-excitation between the ³S term and the ³P term is not negligible. This process has the same effect on the forbidden line and on the intercombination line as the collisional coupling, i.e. lowering of the ratio R, and thus could mimic a high-density plasma. It should be taken into account to avoid any confusion between a high-density plasma and a high radiation field (see Sect. 4.4 for more details).

  
2.2 Temperature and ionization process diagnostics

The ratio G (see Eq. (2)) is sensitive to the electron temperature since the collisional excitation rates do not have the same dependence on temperature for the resonance line as for the forbidden and intercombination lines. In addition, as detailed in Paper I (see also Mewe 1999; Liedahl 1999), the relative intensity of the resonance w (or r) line, compared to the forbidden z (or f) and the intercombination x+y (or i) lines, contains information about the ionization processes that occur: a strong resonance line compared to the forbidden or the intercombination lines corresponds to collision-dominated plasmas. It leads to a ratio of $G=(z+(x+y))/w\sim 1$ (or $(f+i)/r\sim 1$). On the contrary, a weak resonance line corresponds to plasmas dominated by photo-ionization ( G=(z+(x+y))/w>4, or (f+i)/r>4).