Experimental results are presented on copper-cathode erosion for magnetically driven arcs in air, for currents in the range 0.025-1 kA, magnetic induction values 0.03-0.24 T, are velocities 19.3-344 m s(-1) and electrode surface temperatures 300-1073 K. From experimental data we obtained the important characteristic parameters for the copper-cathode's erosion process; namely the effective enthalpy of electrode material ablation in the are spot, h(ef), and the specific microerosion value, g(O). The experiments demonstrated that, just like the near-cathode thermal volt equivalent U, the are spot current density j is also a monotonic ascending function of the magnetic field strength. We have shown a good agreement between the theory and the experimental data for a wide range of are-heater operating regimes. A mathematical analysis and diagrams are provided for predicting the best conditions for an are heater to work with the minimum erosion level. The minimum erosion is shown to depend on the temperature attained by the electrode and on the degree of influence of the gas velocity on the electrode temperature. It is predicted that the erosion decreases with increasing are velocity, then stabilizes at a given minimum level and then increases as one increases the value of the are velocity.301724212430