Kinetic model for stochastic heating in the INCA discharge

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A novel electron heating mechanism based on periodically structured vortex fields induced in a plane was first proposed in 2014 (Czarnetzki and Tarnev 2014 Phys. Plasmas 21 123508). This theoretical concept has now been realized in an experiment which confirms efficient collisionless heating in such array structures (Ahr et al 2018 Plasma Sources Sci. Technol. 27 105010). The new concept is called ‘INductively Coupled Array’: INCA. Here, the physical mechanism behind the collisionless (stochastic) heating is investigated by two analytical models. Firstly, the electron heating rate in an array field structure with an exponential spatial decay of the field in the direction perpendicular to the plane is investigated by stochastically averaging single electron trajectories. The approach is similar to the Lieberman model for the classical stochastic heating in standard inductively coupled plasmas. This analysis shows that classical stochastic heating by thermal motion along the vertical direction makes a negligible contribution. However, there is a strong collisionless nonlocal heating effect in the plane. In conclusion, heating is nonlocal in the plane but local in the vertical direction. This insight allows a straightforward solution of the collisionless Boltzmann equation which not only confirms the results of the Lieberman model but provides also explicit expressions for the complex conductivity. Based on the conductivity an effective stochastic collision frequency, the complex damping coefficient and the related penetration of the field into the plasma is calculated. Finally, elastic collisions with neutral background atoms are included in the model and a condition for dominance of stochastic heating over Ohmic heating is derived.