Effects of the Chodura sheath on tungsten ionization and emission in tokamak divertors

The decay of the electric potential in the sheath region in tokamak divertors occurs on a scale length on the order of the main ion gyroradius (Chodura sheath) due to magnetic fields lines intersecting the divertor plates at grazing incidence. As a consequence, high-Z impurities like tungsten ionize within the sheath region in attached plasma conditions. The modification of the electron distribution in the sheath region must thus be taken into account to accurately model ionization and emission of impurities within the sheath region. To that end, an analytical expression of the distribution of the vertical ionization path for impurities sputtered from divertor plasma-facing components is derived. This expression is then used to estimate the fraction of neutral impurities ionizing within the sheath and the average vertical ionization path, and to derive an effective SXB (the number of ionizations per emitted photon) coefficient which includes the effects of the variation of the electron distribution in the sheath region. These results are applied to tungsten impurities sputtered from divertor plates. It is shown that the SXB coefficient for neutral tungsten is significantly reduced in high-density attached divertor plasma conditions (n_e ≳ 5 × 10¹³ cm⁻³) because of the ionization of neutral tungsten well within the sheath region.