A mathematical model for the ablation-dominated arcs has been developed. The ablation is caused by arc radiation. It has been assumed that the ablated wall material mixes completely with the arc quenching gas to form a mixing layer surrounding the arc. It has been shown that for a given gas and nozzle material the arc behaviour in affinely related nozzles is fully determined by two non-dimensional parameters, one of which is the nozzle coefficient N. The other is the ablation coefficient determined by the arc radiation characteristics and the nozzle material. When the nozzle coefficient reaches a certain value, the flow of the arc quenching gas is entirely blocked. Further decreasing the value of N (i.e. increasing the current), a reverse flow is established and the arc burns in the ablated material. For a given tank pressure, the pressure within the nozzle, the reverse mass flow rate and enthalpy flux are proportional to the square of the current. This is consistent with the trend observed experimentally.

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