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Experimental Tesla Coil Using a Multiple Wavelength
Saskia's Toroidal Secondary
Suppose we make a Tesla coil secondary that is exactly one wavelength long, then suppose we wind it around a toroid instead of a cylinder, and when we are finished winding our coil we connect the ends of the wires and solder them (making one really large closed loop). Theory says that a full wavelength should fit nicely in a coil that is one full wavelength long (seems reasonable). Interestingly we could argue that the very same secondary coil is really two wavelengths long (or three or more) and if we drive the secondary at the right frequency this becomes true. With a two wave length coil we would have 4 voltage nodes and with a three wavelength coil we would get 6 voltage nodes (and these nodes will alternate in polarity as they must).
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The Levi Configuration
We will present an incomplete description of the operation of our recently-developed, two-part, groundless, resonant transformers using results borrowed from mechanics.

Let's start with a simple LC circuit. We will show that this system corresponds with a spring and mass system by using Lagrange equations. (Textbooks usually use Newton's approach for showing correspondence, as Newton's approach is more intuitive, but the Lagrange is unbeatable for solving difficult problems.)
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The Behavior of Ideal Resonant Inductors
We developed the following equations to describe the ideal behavior of our resonant transformer designs. However, these results apply to all resonant inductors.
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Capacitance to Free Space and the Rope Resonance Model
The following picture depicts four different inductors, each inductor was wound with the same wire length of 2027 ft (1/2 lb. 31 gauge equals 2027 ft by Mfg.). The total sum of wire from the four inductors give this system the frequency of 121,000 Hz, this is also the frequency of the tank circuit.
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A High-Performance Half-Wave
We will start with the ballast coil. This is made with two 500 foot lengths of insulated #6AWG stranded wire laid side by side. The ballast is wired in an unconventional manner.
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Self-Resonance in Inductors
In this paper we will be describing standing wave self resonance in an inductor using ideal inductor arguments. We will develop a generalized equation to describe the formation of any number of nodes within an inductor. We will show that under self resonance the frequency of each quarter wave region will be in agreement with the frequency of the inductor as a whole. We will also show how the velocity factor (which others have measured) is describing a relativistic observation.
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