## 10 Conclusions  
For spherical electrolyte micro-system one deals with the surface and volume plasmons in analogy to metallic nanosphere as demonstrated in the previous paragraph. The ionic surface plasmon frequencies are given for \(l\)-th multipole mode by the formula \(\omega_{l}=\omega_{p}\sqrt{\frac{l}{\varepsilon(2l+1)}}\), where the bulk plasmon frequency \(\omega_{p}=\sqrt{\frac{4\pi q^{2}n}{m}}\) (\(n\) is ion concentration, \(q\) and \(m\) are ion charge and mass, respectively, \(\varepsilon\) is the dielectric relative permittivity of the surroundings). For dipole-type surface plasmons (\(l=1\)) the frequency is given by so-called Mie-type formula, [1; 6]\(\omega_{1}=\frac{\omega_{p}}{\sqrt{3}\varepsilon}\). In the linear chain of ionic systems the irradiation losses are completely reduced to zero, exactly in the same manner as in metallic nano-chains [25; 26; 27]. The large irradiation energy losses expressed by the Lorentz friction at each chain element [8; 22] are ideally compensated by the income of energy due to radiation of the chain rest. In the result the radiative losses are ideally balanced by mutual radiation exchange and there remains only relatively small Ohmic irreversible energy dissipation. The collective plasmon-polaritons can thus propagate in the ionic chain with strongly reduced damping as in almost perfect wave-guide. If additionally the energy is supplemented in a minor scale to compensate small Ohmic losses, the propagation can reach arbitrarily long distances without any damping. This is what is observed in saltatory conduction in myelinated axons, moreover, plasmon-polaritons in this axons cannot be neither detected not perturbed by external EM field. Advantages of plasmon-polariton kinetics in agreement with observed myelinated neuron signaling properties can be listed as follows:  
* Plasmon-polaritons cannot be neither perturbed nor detected by EM waves (EEG signals are related to grey matter activity with ordinary conduction [according to the cable theory] and producing weak EM field, whereas myelinated white matter does not produce EEG signal). * Immunity with respect to EM perturbation is convenient in long links in myelinated neurons of peripheral nervous system (motorics and sensing cannot be disturbed by EM field). * All the EM field of plasmon-polaritons is compressed along the tight tunnel around the axon cord. * The myelin sheath must be sufficiently thick not for the insulation reason but for creation of the dielectric tunnel in surrounding inter-cellular electrolyte to allow plasmon-polariton formation (reducing in myelin sheath thickness perturbs formation of plasmon-polaritons or lowers plasmon-polariton group velocity, resulting in Multiple Sclerosis). * Increase of the temperature causes enhancement of Ohmic losses but does not reduce the plasmon-polariton group velocity (however, more energy ADP/ATP, residual to action potential spike formation, is needed to compensate the temperature increase of Ohmic losses). * Any radiative losses do not occur for plasmon-polaritons; if plasmon-polariton is residually aided by spike formation (renovation) at consecutive Ranvier nodes, the arbitrary long range plasmon-polariton kinetics is possible with constant amplitude of the dipole signal. * The plasmon-polariton group velocity increases with the cross-section of the axon cord. * The plasmon-polariton group velocity for real neuron electrolyte and size parameters fits to the observed velocity of the saltatory conduction. * Wave type of plasmon-polariton kinetics explains the maintenance of the signal transduction despite of small breaks and gaps in neuron cord or damage of some Ranvier nodes (these observations were impossible to be explained either within the cable theory or by compression-soliton model). * One-direction kinetics if started from one end of the axon but two-direction kinetics if plasmon-polariton is ignited from some central point of an axon.