While quite a bit of knowhow regarding TCs can be found in the net, quantitative information about TC arcs remains a white region in the maps of knowledge. This is mostly due to the scarcity of measurements available. These are difficult, since arc currents need to be measured between the top load and the breakout point. The first measurement of this kind can be found here: http://web.archive.org/web/20160329212336/http://lod.org/Projects/electrum/techdata/waveforms.htm . Since the Electrum was a huge coil, it was possible that someone could sit in the top load and operate a scope there. Since battery operated scopes are now readily available, other measurements became feasible, like mine: https://4hv.org/e107_plugins/forum/forum_viewtopic.php?153922 and Hydrons: https://highvoltageforum.net/index.php?topic=117.0 .

Starting from the available data at that time I've tried to develop an electrical arc model. That was posted here: https://4hv.org/e107_plugins/forum/forum_viewtopic.php?156391 . An arc simulation can be extremely useful. It can serve as a tool to choose primary and secondary tank parameters, will give a hint at achievable arc lengths, allows a guess at primary currents in a DRSSTC, can answer questions like "Are bigger top loads better than smaller ones", are higher or lower operating frequencies better, is there a choice between long and thin versus short and fat sparks, what is the effect of shorter or longer bursts, how does upper pole perform in comparison to lower pole operation etc.

The model posted 2013 on 4hv was based on my measurements alone. It could reasonably well reproduce the current waveform of an arc at different power levels. So I was very excited by Hydrons data, which he posted about 2 years ago, since it allowed a check of the model at much larger power, i.e. 2m arcs instead of 1m and at a different frequency, i.e. 70Khz instead of 140kHz. Sadly the model failed drastically. It predicted more than twice the currents that Hydron measured. I've now revised the model, so that it can reproduce both my old measurements and Hydrons.

The model is basically a chain of RC circuits as shown below.



The resistors aren't really resistors in this case but are a conductivity models, where the current is calculated from the voltage and and arc temperature based on the energy deposited at that point by the arc. The capacitors are charge buckets, which represent the space charges floating in and around the arc. The top diagram of the arc model is below.



On the left is a simple DRSSTC circuit taken from what I know about Hydrons coil. On the right is a chain of blocks. Along the upper 2 wires the arc current is conducted. The lower 2 wires carry position information. The voltages there are centimeters from the end of the breakout point. This information is necessary for the calculation, since I've noticed, that the field of the toroid has an significant impact on the arc currents. With a meter stick like this, I'm able to calcualte the toroids field at each point of the arc and include this effect. The length of the chain depends on the arc length you expect. Each block is worth about 7cm of arc. The voltage at the end of the chain shouldn't exceed more than 30-40kV, because that is about where the arc ends. You can make the chain longer than necessary, but that will cause LTSpice to run slower.

Below is a schematic of the block.



The block is a short chain of subcircuits. The only reason to have this is to avoid a too long chain in the main diagram. Again, the upper 2 connections conduct the arc current and the lower 2 comprise the meter stick.

The meat of the arc model is in the circuit below. I won't go into the details here, they justify another post. A short description anyway: B2 calulates the power dissipated, B3 the conductivity, G1 the arc current and B4 takes the effect of the top load field into account. The only user supplied values are the parameters RTOR, which is the radius of the toroid measured from the center to the outer rim and LBRP, which is the length of the breakout rod measured from the toroid rim to the rods end.



I've checked the model by applying the measured voltages to the model and comparing predicted and measured currents. I've done this for the 3 power levels of Hydrons measurement and mine. Below are shown simulations and real data. The blue traces are top load voltages and the red the arc currents.

Hydron max power:




Hydron high power:




Hydron medium power:




Generally the simulated current rises faster initially than the measured ones. So the model is far from perfect.

Uspring max power:




Each unit on the left in the lower diagram is to be interpreted as about 90kV.
I've left out my lower power measurements, since I've already shown too many diagrams. The model performs quite well there. Below is a simulation for Hydrons coil at max power. In this case not by using the measured voltages as an input to the model, but a complete simulation with the voltage supplied by the DRSSTC circuitry.



The blue trace is the voltage, current is red. Primary current rises up to about 900A, which is quite a bit larger than Hydrons OCD setting of 750A. I'm not sure, why. It might be because I don't have his primary specs right or because of the too large load my model predicts initially, which brings the coil out of tune.

A zip file for the circuitry is appended. Comments and questions are welcome. A later post will detail the thoughts behind the model.
arcv2.zip