## 2 Classical Physical Model for the Hydrogen Isotopic Ratio Determination  
For simplicity, we consider here tokamak plasmas where the dominant gas is deuterium with the presence of hydrogen as a trace up to a significant concentration of 25%. The results can easily be extended to the opposite situation, where the dominant gas is hydrogen with the presence of deuterium with concentrations varying between 1 to 25%. Therefore, we will consider here plasmas with H-D mixtures for which we aim to infer one of the previously defined isotopic ratios: \(IR_{\text{H-D}}\) or \(IR_{\text{D-H}}\) (see Section 1). In such tokamak plasmas, the Balmer-\(\alpha\) line is emitted by hydrogen and deuterium neutrals that are present in the tokamak divertor region. We will explain later why there exist neutrals and even molecules in the peripheral regions of tokamak. More precisely, Balmer-\(\alpha\) photons are emitted as a result of electrons decaying from the upper excited level \(n=3\) of the atom to its lower excited level \(n=2\), \(n\) and \(n^{\prime}\) being the principal quantum numbers. Because of the different reduced masses for hydrogen, deuterium and tritium, the wavelengths of the \(\text{H}\alpha/\text{D}\alpha/\text{T}\alpha\) emission lines are separated by a small isotope shift. In Angstrom units, the wavelengths of the \(\text{H}\alpha/\text{D}\alpha/\text{T}\alpha\) lines are respectively \(\lambda_{H_{a}}=6562.8\), \(\lambda_{D_{a}}=6561.04\) and \(\lambda_{T_{a}}=6560.45\)[22; 23]. This means that the non-perturbed wavelengths of \(\text{H}\alpha\) and \(\text{D}\alpha\) lines \(\lambda_{H_{a}}\) and \(\lambda_{D_{a}}\) are separated by about 1.8 A while the T\(\alpha\) line is distant from the D\(\alpha\) line by only about 0.6 A, i.e., \((\lambda_{D_{a}}-\lambda_{T_{a}})\) is about one-third of the separation \((\lambda_{H_{a}}-\lambda_{D_{a}})\) between H\(\alpha\) and D\(\alpha\) lines. Now, let us explain the origin of presence of hydrogen isotope neutrals in the peripheral regions of tokamaks. The interesting plasma of a tokamak is the high-temperature magnetically confined plasma called the core plasma. The confined plasma core does not contain any neutrals but only ions and electrons. The core plasma is confined inside closed magnetic flux surfaces. Besides these closed flux surfaces, there are open magnetic field lines which hit the plasma facing components. The charged particles rotating around these open field lines interact with the plasma wall materials, especially in the divertor region. The plasma-wall or plasma-surface interactions are at the origin of the presence of neutrals. More precisely, hydrogen and deuterium neutrals are produced through several chemical and physical sputtering mechanisms [7; 8; 9] leading to the coexistence of at least two neutral populations. The first is a cold neutral population resulting from molecular dissociation of desorbed molecules from the divertor target (release of trapped neutrals as molecules) whose velocity distribution can be considered as Maxwellian with a temperature of a fraction of eV to few eVs. The second neutral population originates from reflected atoms, i.e., H\({}^{+}\) or D\({}^{+}\) ions capture electrons when hitting the target, and are released (return back to the plasma) as H or D neutrals. Such a population can thermalize before emitting radiation (\(\text{H}\alpha/\text{D}\alpha\) photons) in which case their velocity distribution can be assumed to be Maxwellian (or close to a Maxwellian) with a temperature of some tens of eVs. A third neutral population due to charge exchanges between plasma ions and released neutrals may exist; its velocity distribution is also Maxwellian with a temperature of about 100 eV. This third population gives rise to a broad and weak line profile and therefore was not considered in our calculations of synthetic \(\text{H}\alpha/\text{D}\alpha\) line profiles.