TSSP: Time Domain Modeling

We are working towards efficient time domain modeling, the software for which is currently under test. This page shows some of the outputs obtained so far. The system modeled for these plots is Marco Denicolai's Thor. All plots are for the linear regime below breakout. The simulator will also model the non-linear behaviour, but this has not yet been tested.

Updated: 19 Jul 2008

Theory Notes The first part of a DRAFT document pn1401. Still a work in progress.
Waveforms Example time domain plots.
Waveform Comparisons Comparison with measured response.
More Waveform Comparisons Looking more closely at the higher modes.
Secondary in motion Waveforms and animations for various tunings and couplings.
Mode Spectrum The spectrum of mode amplitudes in a Tesla coil.
Mode Functions Voltage distributions of the resonant modes.


Time domain response predicted for Thor. The initial bang was 20kV across 56nF. The breakout voltage estimated by E-Tesla for this toroid, on the basis of a 26kV/cm surface gradient as the threshold for avalanche, is around 440kV, so this coil should just break out at the peak of the first beat. Note the small amount of higher mode ringing, most visible in the secondary base current.

For an experimental comparison of a similar set of waveforms made by Terry Fritz, see

  Mode Spectrum

The relative amplitudes of the lowest 25 normal modes of the coupled resonator. Note that the bulk of the energy is to be found in the lowest two modes, with the higher modes at less than 10% of these. As long as the system remains linear, ie below breakout, the mode spectrum remains constant. Discharges from the topload result in a redistribution of energy amongst the available modes, ie a mixing or scattering of the modes, and the nice neat picture above alters significantly.

  Mode Functions

The spatial distribution of the first eight normal modes. Modeled at modest resolution for speed of software testing, hence the slight distortions - caused by aliasing between the differing resolutions of the capacitance matrix and mutual inductance matrix. Note the similarity of the two lowest 'operational' modes. These two modes differ in the polarity of the associated primary current.

Maintainer Paul Nicholson,