A collisional trapped non-neutral plasma is described by an hydrodynamical model in onedimensional geometry. For suitable initial conditions and velocity field, the Lagrangian variables method reduces the pressure dominated problem to a damped autonomous Pinney equation, representing a dissipative nonlinear oscillator with an inverse cubic force. An accurate approximate analytic solution derived from the Kuzmak-Luke perturbation theory is applied, allowing the assessment of the fully nonlinear dynamics. On the other hand, in the cold plasma case the Lagrangian variables approach allows the derivation of exact damped nonlinear oscillations. The conditions for the applicability of the hot, pressure dominated, or the cold gas assumptions are derived.

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Confined atomic clouds in a magneto-optical trap can be formally interpreted as a single component trapped plasma. A hydrodynamical model in a three-dimensional geometry with radial symmetry is applied. A general polytropic equation of state is assumed. For suitable initial conditions and velocity fields, the Lagrangian variables method reduces the problem to ordinary differential equations in the limiting cases according to the prevalence of thermal or multiple-scattering (MS) effects. The thermal, pressure dominated case with adiabatic equation of state leads to a dissipative nonlinear oscillator with an inverse cubic force, in the form of a damped Pinney equation. An accurate approximate analytic solution derived from Kuzmak–Luke perturbation theory allows the assessment of the fully nonlinear dynamics. The applicability conditions of the two regimes are discussed. The intermediate case where both thermal and MS effects are equally relevant is also analytically studied.

A non-neutral plasma is confined in a quasi-1D device and described by a fluid model. The use of the Lagrangian variables method together with a certain Ansatz for the velocity field reduces the problem essentially to ordinary differential equations satisfied by a scale function. In the case of thermal dominated plasma, the governing equation is the Pinney equation, having a close connection with the time-dependent harmonic oscillator. For a slowly varying frequency of the trap potential, an approximate solution is derived and shown to be accurate in the adiabatic limit. In the case of negligible thermal effects, the resulting non-homogeneous time-dependent oscillator equation for the scale function is also approximately solved, in the adiabatic limit. The validity conditions of the thermal dominated and Coulomb dominated cases are determined. The results are applied to a confined antiproton plasma, with implication on antimatter atom experiments.

We briefly review some recent advances in the field of nonlinear dynamics of atomic clouds in magneto-optical traps. A hydrodynamical model in a three-dimensional geometry is applied and analyzed using a variational approach. A Lagrangian density is proposed in the case where thermal and multiple scattering effects are both relevant, where the confinement damping and harmonic potential are both included. For generality, a general polytropic equation of state is assumed. After adopting a Gaussian profile for the fluid density and appropriate spatial dependencies of the scalar potential and potential fluid velocity field, a set of ordinary differential equations is derived. These equations are applied to compare cylindrical and spherical geometry approximations. The results are restricted to potential flows.

An antiproton plasma confined in a quasi-1D device is described in terms of a self-consistent fluid formulation using a variational approach. Unlike previous treatments, the use of the timedependent variational method allows to retain the thermal and Coulomb effects. A certain Ansatz is proposed for the number density and fluid velocity fields, which reduces the problem essentially to ordinary nonlinear differential equations. In adiabatic cooling, the frequency of the trap potential is slowly decreased. An adiabatic equation of state is assumed for closure. The numerical simulation of the nonlinear dynamics is performed, for realistic parameters.

An antiproton plasma confined in a quasi-1D device is described in terms of a self-consistent fluid formulation using a variational approach. Unlike previous treatments, the use of the time-dependent variational method allows to retain the thermal and Coulomb effects. A certain Ansatz is proposed for the number density and fluid velocity fields, which reduces the problem essentially to ordinary nonlinear differential equations. In adiabatic cooling, the frequency of the trap potential is slowly decreased. An adiabatic equation of state is assumed for closure. The numerical simulation of the nonlinear dynamics is performed for realistic parameters.