Pure electron plasmas are routinely confined within cylindrically symmetric Penning traps. In this paper the static and dynamic properties of plasmas confined in traps with applied electric field asymmetries are investigated. Simple analytical theories are derived and used to predict the shapes of the stable noncircular plasma equilibria observed in experiments. Both analytical and experimental results agree with those of a vortex-in-cell simulation. For an /= 1 diocotron mode in a cylindrically symmetric trap, the plasma rotates as a rigid column in a circular orbit. In contrast, plasmas in systems with electric field asymmetries are shown to have an analog to the /= 1 mode in which the shape of the plasma changes as it rotates in a noncircular orbit. These bulk plasma features are studied with a Hamiltonian model. It is seen that, for a small plasma, the area enclosed by the orbit of the center of charge is an invariant when electric field perturbations are applied adiabatically. This invariant has been observed experimentally. The breaking of the invariant is also studied. The dynamic Hamiltonian model is also used to predict the shape and frequency of the large amplitude /= 1 and /=2 diocotron modes in symmetric traps.

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