Description
At the divertor targets in a fusion device, the incoming ions can knock a neutral atom from the target surface. This process, called (physical) sputtering, erodes the target on the long run and is a source of impurities in the Scrape-Off Layer (SOL), where the emitted neutrals re-ionise. Sputtering thus plays a key role in plasma-wall interaction. Its calculation requires the velocity distribution of ions at the target, which is strongly non-Maxwellian.
To obtain the ion velocity distribution, one must solve a 1D3V Vlasov-Poisson system in the region next to the target. The ions approaching the target are gyrating about a magnetic field and simultaneously being pulled towards the target by a strong electric field, which is present to reflect most electrons away from the target and ensure an ambipolar plasma flow. Closest to the wall, in the Debye sheath, the electrostatic potential varies on the scale of the Debye length, the electric force dominates and only accelerates the ion velocity component normal to the wall (1D1V). However, the distribution function of ions reaching the Debye sheath depends on the shape of the potential in a wider region, called the magnetic presheath, whose length scale is comparable to the size of ion gyro-orbits (1D3V).
We present an analytical model for the electrostatic potential in the magnetic presheath and the distribution function of ions reaching the Debye sheath. Both are determined by two parameters, which are iteratively calculated from physical constraints that take advantage of the grazing incidence of the magnetic field at the target (typical of fusion devices). The gyrokinetic grazing-incidence code GYRAZE [1] is used to verify that the model potential satisfies quasineutrality with an average error of around 1%. While the GYRAZE solution reaches an average error of under 0.1%, it runs in tens of seconds on a laptop. The model calculation only takes milliseconds, and is thus 10000 times faster. This makes the analytical model an accurate and powerful tool for sputtering calculations.
[1] Geraldini, Ewart, Brunner, Parra, submitted to PPCF, arXiv:2508.09067