Quasineutrality in the ionization region of a magnetron in the presence of electron number perturbations

In low pressure magnetron discharges, the so called spoke phenomenom describes the emergence of large scale drifting plasma structures in the ionization region. These perturbative structures break the discharge symmetry and are characterized by enhanced plasma potential, density and ionization rate. The plasma potential and density are related via Poisson’s equation, and when the electrons are in Boltzmann equilibrium, the Poisson-Boltzmann (PB) equation governs the plasma potential. In the bulk region, this equation is often dropped by assuming quasineutrality, therefore simplifying the plasma model. But is the assumption of quasineutrality still justified in the presence of large scale electron number and potential perturbations? In this contribution, we show finite element solutions of the perturbed PB equation in the so called flux coordinate system (ψ,θ,s) and how electron number perturbations influence quasineutrality in the bulk. The perturbations are assumed to be periodic perpendicular to the magnetic field vector, either in θ- or ψ-direction. In this regard, it is shown that violation of quasineutrality depends on the length scales of the perturbation compared to that of the magnetic field lines and the cathode sheath width.