Nonlinear electron resonance heating vs. the Herlofson paradox

In the regime of low gas pressure, capacitive rf discharges exhibit resonant behavior which can have a profound impact on the energy budget. This contribution compares two scenarios of resonance-related electron heating known as, respectively, ``nonlinear electron resonance heating'' (NERH) and ``the Herlofson paradox''. NERH arises from the self-excitation of the plasma series resonance by harmonics generated via the nonlinearity of the plasma sheath. $^{1}$ The Herlofson paradox, on the other hand, is a linear phenomenon that occurs at points where the electron plasma frequency is locally equal to the rf frequency. $^{2,3,4}$ This contribution intended to point out similarities and differences of the two scenarios. $^1$ T. Mussenbrock and R.P. Brinkmann, Appl. Phys. Lett. {\bf 88}, 151503 (2006), $^2$ F.W. Crawford and K.J. Harker, J. Plasma Phys. {\bf 8}, 261 (1972), $^2$ V.P.T. Ku, B.M. Annaratone, and J.E. Allen, J. Appl. Phys {\bf 84}, 6536 (1998), $^3$ V.P.T. Ku, B.M. Annaratone, and J.E. Allen, J. Appl. Phys {\bf 84}, 6546 (1998), $^4$ F.W. Crawford and K.J. Harker, J. Plasma Phys. {\bf 8}, 261 (1972).