  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.
