Apparatus and methods of operation are provided for a cold-crucible-induction melter for vitrifying waste wherein a single induction power supply may be used to effect a selected thermal distribution by independently energizing at least two inductors. Also, a bottom drain assembly may be heated by an inductor and may include an electrically resistive heater. The bottom drain assembly may be cooled to solidify molten material passing therethrough to prevent discharge of molten material therefrom. Configurations are provided wherein the induction flux skin depth substantially corresponds with the central longitudinal axis of the crucible. Further, the drain tube may be positioned within the induction flux skin depth in relation to material within the crucible or may be substantially aligned with a direction of flow of molten material within the crucible. An improved head design including four shells forming thermal radiation shields and at least two gas-cooled plenums is also disclosed.