Generation of an intense magnetic field to erase high coercivity magnetic media uses delivery of energy to a degaussing cavity. To conserve energy storage and delivery requirements and to obtain a desired magnetic strength generally uniformly within the cavity, strategic placement of supplemental turns at ends of the magnetic field generating coil wound around the cavity can promote uniformity. Construction of at least cavity ends from an adequate quantity of magnetically soft ferrous material can also promote uniformity. A combination of both approaches is possible.