A radio frequency source includes a coaxial non-linear transmission line. The coaxial non-linear transmission line may include a closed, non-magnetic, cylindrical outer conductor defining a cavity therein; and a plurality of stages enclosed by the outer conductor. Each stage may then includes an axial field solenoid wound about the outer conductor; a non-magnetic, cylindrical inner conductor disposed within the cavity and coaxially aligned with the outer conductor; a plurality of cylindrical ferrite switch elements, each defining a respective bore through which the inner conductor runs; and a plurality of inner and outer cups coaxially aligned with the inner and outer conductors, each defining a respective bore through which the inner conductor runs.