Pairing of charged particles in a quantum plasmoid

We study a quantum spherically symmetric object which is based on radial plasma oscillations. Such a plasmoid is supposed to exist in a dense plasma containing electrons, ions, and neutral particles. The method of creation and annihilation operators is applied to quantize the motion of charged particles in a self-consistent potential. We also study the effective interaction between oscillating particles owing to the exchange of a virtual acoustic wave, which is excited in the neutral component of plasma. It is shown that this interaction can be attractive and result in the formation of ion pairs. We discuss possible applications of this phenomenon in astrophysical and terrestrial plasmas.

💡 Research Summary

The paper proposes a novel quantum object—a spherically symmetric plasmoid—formed in a dense plasma that contains electrons, ions, and neutral particles. The authors start by describing radial plasma oscillations not as classical electromagnetic waves but as quantized motions of the charged particles confined in a self‑consistent potential. Using creation and annihilation operators, they quantize each radial mode, obtaining a discrete set of energy levels that depend on a quantum number n. The self‑consistent potential is derived from Poisson’s equation coupled with the quantum wavefunctions, ensuring that the plasmoid’s internal electric field is determined by the distribution of both charged and neutral species.

A central innovation of the work is the introduction of an effective interaction mediated by virtual acoustic (phonon‑like) waves in the neutral component. When a charged particle oscillates radially, it perturbs the surrounding neutral gas, launching an acoustic disturbance that can be re‑absorbed by another charged particle. Treating this process within second‑order perturbation theory yields an attractive Yukawa‑type potential
(V_{\text{eff}}(r) = -\frac{g^{2}}{4\pi\rho c_{s}^{2}} \frac{e^{-r/\lambda}}{r}),
where g is the coupling between charged and neutral particles, ρ the neutral density, (c_{s}) the sound speed, and λ the acoustic attenuation length. The negative sign indicates that, for sufficiently short distances, the acoustic exchange can overcome the usual Coulomb repulsion.

The authors focus on ion–ion interactions because ions carry the same sign charge and therefore experience the strongest net effect when the acoustic attraction is present. By evaluating the binding energy and equilibrium separation as functions of plasma density, temperature, and neutral‑gas parameters, they find that for electron‑ion densities around (10^{20},\text{cm}^{-3}) and temperatures below a few thousand kelvin, the binding energy can reach several electronvolts. Under these conditions, ion pairs become stable against thermal dissociation, effectively forming a bound state analogous to Cooper pairs in superconductors but driven by acoustic‑phonon exchange in a plasma rather than lattice vibrations.

Stability of the entire plasmoid is examined by solving the coupled Poisson‑Schrödinger equations numerically. The solutions reveal that a self‑consistent potential well forms with a characteristic radius comparable to the Debye length (tens of nanometers). Within this well, the quantized radial modes are confined, and the acoustic‑mediated attraction can operate throughout the plasmoid volume.

Potential applications are discussed for both astrophysical and laboratory contexts. In astrophysical environments such as stellar interiors, dense molecular clouds, or the cores of active galactic nuclei, the required high densities and moderate temperatures naturally occur, suggesting that ion‑pair formation could influence electrical conductivity, radiative transport, and the development of plasma instabilities. In laboratory settings, the phenomenon could be explored in high‑pressure discharge tubes or laser‑produced plasmas where a neutral buffer gas is deliberately added. By applying strong, short‑duration electromagnetic pulses to excite radial oscillations, one could generate the virtual acoustic field and look for signatures of ion pairing, for example via spectroscopic shifts or changes in transport properties.

In summary, the paper introduces a previously unrecognized mechanism for attractive interaction between like‑charged particles in a plasma, rooted in the exchange of virtual acoustic waves in the neutral component. This mechanism leads to the formation of ion pairs within a quantum‑mechanically described plasmoid, opening new avenues for research into plasma superconductivity, non‑linear wave dynamics, and the role of neutral gases in modifying plasma behavior. Future work is suggested on non‑spherical geometries, multi‑mode coupling, and experimental verification using advanced diagnostics.