An electrode assembly comprising concentric tubular electrodes is provided for high temperature processing of materials. The electrode assembly is connected with a power supply that includes switching means for alternatively operating the electrode assembly in a transferred mode of operation, in a non-transferred mode of operation, or according to a controlled sequence of non-transferred and transferred modes of operation. The power supply system includes variable inductors, such as leakage-coupled reactors, for controlling the electrical power supplied to the electrodes for producing a DC arc. The electrode assembly can be incorporated into an arc furnace for processing waste material in the furnace. The electrode assembly is also suitable for use in the practice of in-situ vitrification and remediation of contaminated soil. During in-situ vitrification, the electrode assembly may also be operated in the non-transferred mode, while being withdrawn from holes in the earth, to produce vitrified columns of soil. The vitrified columns of soil can be coalesced with similar adjacent columns of soil in order to form a composite or unitary subterranean mass or barrier for contaminated material in a selected area. Multiple electrode assemblies can be employed to treat contamination located within a large area. An AC potential can be applied to adjacent electrode assemblies in order to promote coalescence of the adjacent columns of treated soil to form a composite or unitary mass.