Gyrokinetic modeling of magnetized technical plasmas

Summary form only given. Many technical plasma processes, like magnetically enhanced reactive ion etching (MERIE), plasma ion assisted deposition (PIAD), and conventional and high-power impulse magnetron sputtering (dcMS/HiPIMS) employ (partially) magnetized high density plasmas at relatively low pressures. (Typical values are p~0.01-1 Pa, B~10-100 mT, n_e ~10¹⁵-10²⁰ m^-3.) These plasmas are, at least in their active regions, characterized by a peculiar ordering of the dynamic length and corresponding time scales: λ_D ≪ s ≪ L~λ ≪ λ*, with λ_D Debye length, s sheath thickness, r_L Larmor radius, L system length, and λ and λ* elastic and inelastic electron mean free path, respectively. Such plasmas are very difficult to analyze. Fluid models do not apply and numerical kinetic approaches like particle-in-cell are rather expensive. An alternative may be “gyrokinetics”. This theory - actually more a class of theories - was designed and successfully employed in the field of fusion plasmas¹. It relies on the insight that the fast gyro motion of magnetized particles can be mathematically separated from the slower drift motion and be “integrated out”, leaving only the dynamics on slower time scales and longer length scales. Unfortunately, however, magnetized technical plasmas are considerably different from fusion plasmas. (Differences concern the magnetic field topology, the presence of material walls and of collisions with neutrals, the fact that only electrons are magnetized, etc.). Direct application of theories developed for fusion is thus not possible. This paper will present a gyrokinetic theory for magnetized technical plasmas that is based on first principles. The outset is a general kinetic description of the electron component which incorporates the scaling mentioned above. A mul- i-time scale formalism is employed which results in four separate levels. Explicitly solving the first three levels and substituting into the last gives the desired self-consistent transport theory on the slowest time scale. The approach shares features both with “bounced averaged gyrokinetics”² (of fusion theory) and with “nonlocal theory”³ (of low temperature plasma physics).