Plasma states dominated by single helical modes are often observed in the Reverse Field Pinch (RFP) plasma confinement devices. In this paper the properties of these states are studied on the basis of a relaxation model that assumes the existence of several topological invariants related to the dominant mode. It is hypothesized that the value of the first invariant in this chain, is determined by the existence of a plasma dynamo mechanism that transport helicity. This hypothesis enables us to determine the steady state properties of the plasma equilibrium and some other interesting physical consequences. Further, by considering the properties of the transfer of helicity from the mesoscale (fluctuations) to the macroscale (equilibrium), through the dynamo field, a nonlinear dynamical model can be constructed, that evolves in time to a steady state with a non-vanishing dynamo field, when helicity is injected in the system, as in the case of the ohmic sustained RFP, while the dynamo oscillates initially, but is damped later in time, for vanishing helicity input.Magnetic helicity conservation is an important plasma property in ideal magneto-hydro-dynamics, describing the invariance of the degree of twist and linkage of the magnetic field lines [1]. In presence of even a small amount of dissipation, it becomes an approximate invariant. In fact in a resistive plasma, reconnection can produce magnetic field topological rearrangements. Even in this case magnetic helicity can play a crucial role in determining the properties of large scale fields in astrophysics and/or in laboratory plasmas, since it is generally better conserved than energy during reconnection and therefore can determine the plasma relaxation pattern toward minimum magnetic energy states, as was first observed by Woltjer [2] for astrophysical plasmas and by Taylor [3] in interpreting the results obtained in a pinch machine. Moreover, the role played by the topological invariants is considered to be very important for the origin and sustainment of large scale magnetic fields in several natural systems, as galaxies, stars and planets. In fact, it is believed that in most, maybe in all of these cases, a MHD dynamo mechanism is needed to produce and/or amplify the magnetic field. Therefore the study of the relationship between the helicity related invariants and the dynamo amplification and sustainment of the magnetic field, is of fundamental importance for a deeper understanding of different natural phenomena, covering a large variety of space and time scales. While helical symmetric turbulence is generally associated with the dynamo process, in principle, also a single large helical mode could amplify an existing magnetic field. Examples of the presence of large scale helical fields are found in planets [4], in solar eruptions [5] and in active galactic nuclei [6] and also in RFP experiments, where, under certain conditions, a single dominant helical mode emerges [7] over a generally much wider fluctuations spectrum. In a series of recent papers [8-10] thi...