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Motivated by the precedent study of Ordenes-Huanca and Velazquez [JSTAT\textbf{093303} (2016)], we address the study of a simple model of a purenon-neutral plasma: a system of identical non-relativistic charged particlesconfined under an external harmonic field with frequency $\omega$. We performthe equilibrium thermo-statistical analysis in the framework of continuumapproximation. This study reveals the existence of two asymptotic limits: theknown Brillouin steady state at zero temperature, and the gas of harmonicoscillators in the limit of high temperatures. The non-extensive character ofthis model is evidenced by the associated thermodynamic limit,$N\rightarrow+\infty: U/N^{7/3}=const$, which coincides with the thermodynamiclimit of a self-gravitating system of non-relativistic point particles inpresence of Newtonian gravitation. Afterwards, the dynamics of this model isanalyzed through numerical simulations. It is verified the agreement ofthermo-statistical estimations and the temporal expectation values of the samemacroscopic observables. The system chaoticity is addressed via numericalcomputation of Lyapunov exponents in the framework of the known \emph{tangentdynamics}. The temperature dependence of Lyapunov exponent $\lambda$ approachesto zero in the two asymptotic limits of this model, reaching its maximum duringthe transit between them. The chaos of the present model is very strong, sinceits rate is faster than the characteristic timescale of the microscopicdynamics $\tau_{dyn}=1/\omega$. A qualitative analysis suggests that such astrong chaoticity cannot be explained in terms of collision events because oftheir respective characteristic timescales are quite different,$\tau_{ch}\propto \tau_{dyn}/N^{1/4}$ and $\tau_{coll}\propto \tau_{dyn}$.

A pure non-neutral plasma under an external harmonic field: equilibrium thermodynamics and chaos