One of the most effective ways of synthesizing carbon nanotubes is the arc discharge method. This paper describes a system supported by a magnetic field which can be generated by an external coil. An electric arc between two electrodes is stabilized by the magnetic field following mass flux stabilization from the anode to the cathode. In this work four constructions are compared. Different configurations of cathode and coils are calculated and presented. Exemplary results are discussed. The paper describes attempts of magnetic field optimization for different configurations of electrodes.