Innovative investigation on ion flows by an ad hoc Lagrangian formulation

• This Lagrangian is recommended for an intelligible physical overview of ion drift performances.
• It is the result of an advanced degree of specialisation with respect to previous formulations.
• In both moving and at-rest fluids the electric field in a given gap identifies with a common and steady Laplacian substrate.
• The ionisation region both masks the detailed geometry of the active electrode and affects the electrodynamic field performances in the drift region.

A specialised Lagrangian formulation is here recommended to describe the main performances of unipolar ion flows driven by partial discharges. The subject fits into a number of electrostatic applications also governed by fluid-dynamic laws, which is why it needs careful examination by a solid and comprehensive approach. A reasoned selection of referential case studies are proposed in order to better appreciate the value of this predictive framework. The interdisciplinary character of the general problem under examination makes the role of the Lagrangian approach pivotal for the physical interpretation of theoretical results. These are given by resolving the Euler-Lagrange differential equation associated to individual examples.