A new model of electronic vortices in plasma is studied. The model assumes that the profile of the Lagrangian invariant I, equal to the ratio I=O/n of the electronic vorticity to the electron density, is given. The proposed approach takes into account the magnetic Debye scale rB≃B/4πen, which leads to breakdown of plasma quasineutrality. It is shown that the Abrikosov singular model cannot be used to describe electron vortices in plasmas because of the fundamental limitation on the electron vorticity on the axis of a vortex in a plasma. Analysis of the equations shows that in the model considered for the electronic vorticity, the total magnetic flux decreases when the size r0 of the region in which I≠0 becomes less than c/ωpe (ωpe is the electron plasma frequency). For ωper0/c≪1, an electronic vortex is formed in which the magnetic flux decreases as r02 and the inertial component predominates in the electronic vorticity. The structure arising as ωper0/c⇒0 is a narrow "hole" in the electron density, which can be identified from the spectrum of electromagnetic waves in this region.