The Propagation of Nerve Impulses

The paper presents a theory of ion acoustic waves in the axoplasm of nerve fibres. A set of non-linear wave equations can be established from first principles starting from the Vlasov equation- a collisionless Boltzmann equation- and its moment equations. There exists a density regime where collisions are negligeable and the entropy is conserved. In this regime nerve pulses experience little or no attenuation. The linear theory shows a rich spectrum of ion acoustic modes depending on the composition of the axoplasma. These waves travel in the interior of the nerve fibre and not along the membrane as in the theories of Hodgkin-Huxley and Heimburg-Jackson. The non-linear theory of ion acoustic modes exhibits nonlinear waves and solitons. The relation to the Korteveg-de-Vries equation is discussed. The theory identifies the importance of organic molecules in nerve pulse propagation, however, a unique identification is not possible. The paper investigates the excitation of nerve pulses via plasma-beam interaction, which may be one explanation how mechanical signals can be converted into electric signals.