## 1 Introduction  
Nowadays magnetic fusion devices operate with either pure hydrogen, pure deuterium or with hydrogen-deuterium mixtures. However, magnetic fusion-based power plants will operate with D-T mixtures as fusion reaction rates are optimal when D\({}^{+}\) and T\({}^{+}\) ions fuse together as compared to fusion between D\({}^{+}\) ions. Up to now, only a few operations have been conducted or are being prepared with deuterium-tritium (D-T) mixtures like in JET during the 1997 DTE1 campaign and the DTE2 planned experimental campaign [1; 2; 3]. However, due to the radioactivity of tritium, its content in any device is limited for obvious safety reasons. Therefore, the content of tritium is strictly controlled. For this reason, an accurate inventory of the content of tritium is mandatory. Such an inventory cannot be made by simply subtracting the quantity exhausted by the pumping systems from the injected quantity because of the wall retention of all hydrogen isotopes [4]. In plasmas with D-T mixtures, one can quantify the content of tritium by the isotopic ratio, defined as:  
\[IR_{\text{D-T}}=\frac{n_{\text{D}}}{(n_{\text{D}}+n_{\text{T}})}. \tag{1}\]  
This is the ratio between the density of deuterium atoms \(n_{\text{D}}\) and the total density of deuterium plus tritium atoms \((n_{\text{D}}+n_{\text{T}})\). Another way to define the isotopic ratio is to use:  
\[IR_{\text{T-D}}=\frac{n_{\text{T}}}{(n_{\text{D}}+n_{\text{T}})}. \tag{2}\]  
In practice, as:  
\[IR_{\text{D-T}}+IR_{\text{T-D}}=1, \tag{3}\]one can use either the first or the second definitions of the isotopic ratio, i.e., \(IR_{\text{D-T}}\) or \(IR_{\text{T-D}}\). In a similar manner to D-T mixtures, one defines the following isotopic ratios for hydrogen-deuterium (H-D) mixtures:  
\[IR_{\text{H-D}}=n_{\text{H}}/(n_{\text{H}}+n_{\text{D}}) \tag{4}\]  
\[IR_{\text{D-H}}=n_{\text{D}}/(n_{\text{H}}+n_{\text{D}}) \tag{5}\]  
In Equations (4) and (5), \(n_{\text{H}}\) stands for the neutral hydrogen density. Note also that \(IR_{\text{H-D}}\) and \(IR_{\text{D-H}}\) satisfy the following condition:  
\[IR_{\text{H-D}}+IR_{\text{D-H}}=1 \tag{6}\]  
It should also be noted that in some references, instead of Equations (4) and (5) concise notations are used for the isotopic ratios for H-D mixtures:  
\[IR_{\text{H-D}}=\frac{H}{(H+D)} \tag{7}\]  
\[IR_{\text{D-H}}=\frac{D}{(H+D)} \tag{8}\]  
The same remark applies to D-T mixtures. To our knowledge, two methods are used for the evaluation of such isotopic ratios in magnetic fusion devices. The first one is based on the residual gas analysis and have been applied by [PERSON] et al. [5] to JET and ASDEX-Upgrade (AUG) devices. This technique has also been used for other devices like Tore-Supra by [PERSON] et al. [6]. However, it is the second method which is widely and commonly used for the evaluation of the hydrogen isotope contents. It is based on the spectroscopic analysis of the emitted Balmer-alpha line. In tokamaks, this line is one of the most intense emission lines of hydrogen isotopes (H, D and T). The intensities of the corresponding H\(\alpha\), D\(\alpha\) and T\(\alpha\) lines depend on the concentration of each isotope. In tokamaks, the major emission of these lines comes from the divertor and scrape-off-layer (SOL) regions. In these regions, especially in the divertor where plasma-surface interactions take place, several neutral populations co-exist due to the different recycling mechanisms taking place as can be found in [PERSON] et al. [7], [PERSON] et al. [8] and [PERSON] et al. [9]. Under typical divertor conditions, i.e., electron densities \(n_{e}\) of the order of \(10^{14}\) cm\({}^{-3}\) and electron temperatures \(T_{e}\) of a few eV, the spectral profiles of the hydrogen isotope Balmer-\(\alpha\) lines H\(\alpha\), D\(\alpha\) and T\(\alpha\) are governed by Zeeman and Doppler effects, as Stark effects can be neglected for such low electron densities; see [PERSON] and [PERSON] [10].