Reducing the AC-Losses in Superconducting ELF/VLF Antennas
Edwin C. Jones

	Following the discovery of high temperature superconductors (HTS), the application of these novel materials towards improving commercial products quickly became the focus of many applied scientists.  Many of the proposed applications are aimed towards improving energy efficiency such as low loss transmission lines, very efficient generators, smaller transformers, superconducting magnetic energy storage systems (SMES), fault current limiters, and smaller submarine motors.  The applications that would potentially have the most impact on society such as the ones listed above require that these materials maintain low ac‑losses while carrying an alternating current (ac).  Unlike the direct current (dc) properties such as a zero resistance below a characteristic critical current Ic, the changing magnetic field in an ac‑environment induces non-negligible ac‑losses which are discussed in this paper with an emphasis on how to reduce these losses.
	Ever since the development of low-temperature superconducting Nb3Sn wires, there has been an ongoing interest at reducing the ac–power losses in superconducting materials. Although the Joule losses are vanishingly small in superconductors below their characteristic critical current density Jc, the fluctuating magnetic fields that occur in ac-applications induces three types of important ac‑losses and these must be minimized to prevent the superconductor from quenching and going normal.  Although the ac‑losses in Nb3Sn have already been reduced to extremely low levels, it is possible that these materials may never conduct significant 60 Hz ac‑currents at 4.2K due to the extremely low specific heat capacities in these materials at this operating temperature range.  However, the higher transition temperatures of the newer high–Tc superconductors allow these materials to operate at a higher temperature range where greater heat capacities significantly reduce the threat of quenching.
	Pioneering work in the 1970's on Nb3Sn and NbTi revealed that the reduction of ac‑losses in superconducting wires could be accomplished by subdividing the wires into many fine, twisted superconducting filaments embedded in a non-superconducting metallic matrix.  Due to flux pinning in Type-II superconductors, hysteretic losses occur under an ac‑field with an associated energy loss density described by6
                                                                (1)

where Q is the energy loss density in J/m3, Bmax is the maximum field amplitude, Jc is the critical current density, d is the filament diameter, and  is the field at which complete flux penetration occurs.  Given typical Nb3Sn filament dimensions, the values of the penetration field typically range from ~ 5 G to 130 G causing most ac applications to operate in the fully penetrated regime Bmax > Bpt.  From Eqn. 1, it follows that the hysteretic losses are proportional to the filament diameter d in the fully penetrated regime necessitating the subdivision of the wires into the fine multifilamentary structure.
 	Unfortunately, this subdivision creates a new source of ac‑losses known as coupling losses.  Coupling losses arise from current loops connecting the filaments through the normal metal matrix.  Moreover, these losses can effectively cause the multifilamentary wire to behave as a “large” hysteretic monofilament conductor having ac‑losses proportional to the diameter of the overall wire instead of the individual filaments unless the filaments are twisted tighter than a critical twist pitch.  In a round conductor, this critical twist pitch, , is defined by6
 		                                                                                       (2)	
where r is the effective normal metal matrix resistivity.  For a high aspect ratio rectangular conductor, the critical twist pitch is more accurately defined by
 		                                                                                       (3)	
where d|| is the diameter of the filaments parallel to the applied field and d is the diameter of the filaments perpendicular to the applied field.  Finally, a third type of ac‑loss is the eddy losses that occur in the normal metal matrix (i.e. silver in most of the high temperature superconductors).
	Finally, in order for superconducting wires to have low enough ac-losses necessary for successful use in ELF/VLF antenna loading coils, the wires must be of a twisted multifilamentary design. Furthermore, the individual filaments must not be “shorted” together and the wire’s twist pitch must be less than the critical twist pitch  (Eqns. 2‑3). 8 This guarantees that each filament in the conductor will behave independently thereby allowing the hysteretic losses to be proportional to the filament dimensions rather than the overall conductor dimensions. To estimate these critical twist pitches, the effective matrix resistivity r must include factors from both the resistivity of the normal metal matrix (e.g., silver) and the contact sheet resistivity between the superconductor and matrix metal.  Interestingly, Ekin recently measured the contact sheet resistivity between several high‑Tc ceramics and noble metals as a function of various annealing conditions.  For good contact diffusion such as those expected in BSCCO/Ag tapes, the contact sheet resistivity typically lies between    10‑12 W m2 and    10‑14 W m2 depending on the exact degree of interface diffusion.10  Dividing these sheet resistivities by a filament separation of 10-50 mm, allows us to estimate the contact contribution to the total effective matrix resistivity.  Using the above values, we would expect the contribution to fall between reff  1 x 10‑7 W m and reff  2 x 10‑10 W m, respectively, which are at a minimum comparable to the value of the silver matrix (rAg  3 x 10‑9 W m) at 77 K.  Therefore, the effective matrix resistivity used in Eqns. 2‑3 should include the effects of the superconductor to silver contact resistivity. If these critical twist pitches are met, the superconducting wires can easily be used in the loading coils of ELF/VLF antennas reducing the size of the coils, while increasing the antenna efficiencies and reducing the transmitter power requirements.

Copyright 2003 Edwin C. Jones

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