This paper is a study of plasma equilibrium in Vintotrons toroidal traps with a spatial magnetic axis established by various combinations of magnetic fields from helical conductors. The authors determine the displacement of the vacuum magnetic axis in the presence of a plasma as a function of the relationship between the curvature of the helical magnetic axis, the curvature of the torus and a parameter characterizing the ellipticity of the vacuum magnetic surfaces. The limiting equilibrium values of are determined from the displacement of the magnetic axis. Characteristic equilibrium values of β are compared for Vintotrons and stellarators. The authors also discuss the possible effects of resonance phenomenon which can occur in a toroidal Vintotron in the presence of a plasma.