The absorption of the power in cylindrical DC glow discharge is proportional to the J(dot)E .
If J is constant throughout the discharge the power absorbed depends on the local electric field only. Since the electric field is highest in the cathode sheath, it becomes the region which absorbs maximum power. Or the weak field of positive column combined with large axial extent absorbs larger power?
References would be greatly appreciated, e.g. book, article etc.