## 7 Plasmon-Polariton Propagation in Linear Periodic Ionic System
The periodic structure of the myelinated axon does not form a chain of electrolyte spheres, but rather is a thin electrolyte cord wrapped in myelin sheath on periodically distributed sectors separated  
Figure 11: In the effective chain-model of the continuous axon corrugated by periodic myelin sectors corresponds rather to a series of rods or prolate spheroids; because of linearity with respect to the dipole field of the dynamic equation it is possible to renormalize equations for both polarizations without changing their structure. by very short unmyelinated intervals--Ranvier nodes. The periodic corrugated structure of the dielectric isolation allows, however, for consideration of collective plasmon wave-type oscillations, \(\sim\)\(e^{i}qz\) with \(q\) governed by the periodicity, propagating along the cord which resolve themselves to wave-type synchronic dipole polarization of consecutive Ranvier intervals. Taking into account that Ranvier nodes are short, these polarization dipoles are equivalent with similarly synchronically oscillating dipoles of myelinated sectors. The latter can be thus treated as dipole surface plasmon oscillations propagating along the chain of prolate spheroids with small separations and with the longitudinal dipole polarization, despite actually continuous character of the cord--this is sketched in Figure 6 (right panel). To estimate characteristics of such collective dipole wave-type excitation along the cord sectors one can use the model of the chain of spherical electrolyte systems with suitably diluted ion concentration (resulted in the same total ion number as in the cord fragments) and with the decreased resonance frequency as for the longitudinal polarization in the case of highly prolate spheroid (or elongated cylinder). The model allows the quantitative estimation of the relevant propagation characteristics and the verification whether plasmon-polariton dynamics might fit to the observed features of the saltatory conduction in myelinated axons, being mysterious and obscure as of yet. Plasmon-polariton wave-packet triggers at consecutive Ranvier nodes the release of ions through the non-myelinated membrane and the formation of the action potential (its renewal at each Ranvier node). The relatively low polarization induced by plasmon-polariton initiates at a Ranvier node opening of the \(Na^{+}\) and \(K^{+}\) across-membrane ion channels, which results in a characteristically large action signal due to the transfer of ions through the opened gates caused by the difference in their concentrations on either sides of the membrane. The entire cycle requires a few milliseconds, but the initial increase in polarization caused by the rapid opening of the \(Na^{+}\) channel occurs on the scale of a single millisecond. Because the myelin layer wrapped by the Schwann cell prohibits cross-membrane ion transfer, the local polarization/depolarization of the internal cytoplasm of the axon takes place only at the Ranvier nodes, thus strengthening the dipole formation in the axon fragment wrapped by the Schwann cell and strengthening the amplitude ot the wave-type collective dipole oscillations in the whole chain. Each Ranvier node activity triggered by the plasmon-polariton one-by-one lifts the plasmon-polariton amplitude to the constant value despite the Ohmic losses. The plasmon-polariton mode that traverses the axon structure consisting of periodically polarized electrolyte segments wrapped with myelin sheath cause the consecutive individual ignitions of the Ranvier nodes in sequence along the axon. This triggering role of the plasmon-polariton elucidates thus how the action signal jumps between neighboring active Ranvier nodes. The plasmon-polariton scenario in an ionic chain, even in the simplified version, might share certain features in common with the ability of nerve systems to achieve very efficient and energetically economical electric signaling despite the rather poor ordinary electric conductivity of axons.