Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field. (15th February 2021) - Geraldini, Alessandro
Abstract : A model is presented for the ion distribution function in a plasma at a solid target with a magnetic field B inclined at a small angle, α 1 (in radians), to the target. Adiabatic electrons are assumed, requiring α Zm_e/m_i, where m_e and m_i are the electron and ion mass, respectively, and Z is the charge state of the ion. An electric field E is present to repel electrons, and so the characteristic size of the electrostatic potential φ is set by the electron temperature T_e, eφ T_e, where e is the proton charge. An asymptotic scale separation between the Debye length λ _D = ε _0 T_e / e^2 n_e , the ion sound gyro-radius ρ _s = m_i ( ZT_e + T_i ) / (ZeB) and the size of the collisional region d_c = α λ _mfp is assumed, λ _D ρ _s d_c . Here ε _0 is the permittivity of free space, n_e is the electron density, T_i is the ion temperature, B= |B| and λ _mfp is the collisional mean free path of an ion. The form of the ion distribution function is assumed at distances x from the wall such that ρ _s x d_c, that is, collisions are not treated. A self-consistent solution of the electrostatic potential for x ρ _s is required to solve for the quasi-periodic ion trajectories and for the ion distribution function at the target. The large gyro-orbit model presented here allows to bypass the numerical solution of φ (x) and results in an analytical expression for the ion distribution function at the target. It assumes that τ =T_i/(ZT_e)1, and ignores the electric force on the quasi-periodic ion trajectory until close to the target. For τ 1, the model provides an extremely fast approximation to energy–angle distributions of ions at the target. These can be used to make sputtering predictions.