  I study stable spatial Langmuir solitons in plasma based on nonlinear radial
oscillations of charged particles. I discuss two situations when a Langmuir
soliton can be stable. In the former case the stability of solitons against the
collapse is due to electron-electron interactions which result in the nonlocal
terms in the nonlinear Schr\"{o}dinger equation. In the latter situation I
derive the new cubic-quintic nonlinear Schr\"{o}dinger equation with accounts
for the interaction of induced dipole moments of diatomic ions with a rapidly
oscillating electric field and show that the collapse of Langmuir waves can be
also arrested. In both cases I find the numerical solutions of the nonlinear
Schr\"{o}dinger equation and analyze their stability using the
Vakhitov-Kolokolov criterion. I discuss the application of my results for the
description of long-lived atmospheric plasma structures. I show that, using my
model, one can explain the existence of atmospheric plasmoids in the upper
ionosphere. It is also demonstrated that Langmuir solitons described by the
cubic-quintic nonlinear Schr\"{o}dinger equation can describe atmospheric
plasmoids at the initial stages of their evolution. Note that, besides the
modeling of atmospheric plasma structures, my results can be applied for the
explanation of the results of experiments where long-lived glowing plasmoids
weere obtained in electric discharges in liquid nitrogen.
