  A novel electron heating mechanism based on periodically structured vortex
fields induced in a plane was first proposed in 2014 [U. Czarnetzki and Kh.
Tarnev, Physics of Plasmas 21, 123508 (2014)]. This theoretical concept has now
been realized in an experiment which confirms efficient collisionless heating
in such array structures [Ph. Ahr, T.V. Tsankov, J. Kuhfeld, U. Czarnetzki,
submitted to Plasma Sources Science and Technology, arXiv:1806.02043v1 (2018)].
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
collisonless non-local heating effect in the plane. In conclusion, heating is
non-local 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 field 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.
