The Spiral Solenoids and the Leaf Antenna in Phyllotaxis Differential Geometry
In this paper new classes of spiral thin filamentary wire magnetic coils and antennas are introduced theoretically. This study shows that the thin wire circular loop coil as well as the cylindrical solenoid are particular cases of these classes. If the small spiral filamentary wire leaf loop coil is driven by an alternating electrical current, it will radiate as an antenna, whose theoretical analysis is provided throughout the paper. The fundamental spiral coil named leaf coil is obtained by joining together the so called forward and backward spiral coils which define the new concept of the Phyllotaxis differential geometry. The other spiral coils are composed of symmetrically rotated leaf coils, combined together in such a way to eliminate the transverse magnetic components along the longitudinal z axis. The magnetic moments and the multi-pole expansions of the various types of spiral loop coils are obtained by using the Taylor series of the spiral vector magnetic potentials.
According to the formulas and simulations, the magnetic flux density created by the long spiral solenoids is uniform and dovetails with the one created by the long cylindrical solenoid.
The bifolium coil may be flattened along one axis to meet the requirements of specific geometrical needs in space technology. Furthermore the crown solenoids may be cooled down to low temperatures by exploiting
the holes in between their coils.
Applications of the spiral induction coils are countless and can be found in space technology measurements, spacecraft magnetic shielding, telemetry, telecommunication, electron optics, physics and engineer.
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