The authors study the structure of the magnetic field in an ℓ = 1 toroidal torsatron. Experiments on the Vint-20 device and numerical calculations on a computer have shown that closed magnetic surfaces with high parameters exist in an ℓ = 1 torsatron. The forms of the magnetic surfaces are given together with graphs showing how their parameters vary within the working volume under different operating conditions. It has been established that the magnetic surface parameters can be adjusted within wide limits by changing the vertical field. It is shown that this type of system is characterized by high inhomogeneity of the magnetic field in the working volume and that this inhomogeneity can be substantially reduced by applying a vertical field or by changing some parameters of the helical winding.