200kV Voltage Multiplier

PowerLabs 200kV Voltage Multiplier!

Project Introduction:

The Cockroft-Walton voltage multiplier was invented in the 30's by two men who gave it their names to serve as a way of producing very high voltages which would be unpractical to obtain from transformers due to the bulk of the insulation required. By using only capacitors and diodes, these voltage multipliers can step up relatively low voltages to extremely high values, while at the same time being far lighter and cheaper than transformers. They were, and still are used in x-ray tubes, particle accelerators, electrostatic devices, and many other devices making use of very high voltages at DC values.
Needing a high voltage DC source for its electrostatic research, PowerLabs searched all over the Internet trying to find a supplier... Sadly, the few companies out there who make such devices want way too much money for them. So, here's my take on it:

Project Description and Goals:

The objective of this experiment was to produce the highest possible voltage using just parts that were laying around. The capacitors used are the same TDK UHV-12A 173K Strontium Titanate units used on my Twin Tesla Coils; ratings are 1.7nF and 50kV DC RMS. Eight units are arranged in 4 stages, effectively producing a 4 stage halfwave voltage multiplier. Each unit stores 2.125J at peak charge, so the total potential energy for the system is about 17Joules. This number has more to do with the stability of the voltage under load than with any sort of pulse discharge characteristic, as attempting to rapidly discharge a cascade will usually over current the rectifiers and cause them al to fail.
Rectifiers are 20kV, 10mA units from Ebay. These are very cheap chinese diodes, and a quick look at their length will reveal that there is little chance they will actually hold off 20kV each in air; such devices are always meant to be run under oil immersion.
Keeping up with the "using parts that are laying around" theme, charging is provided by an automotive ignition coil (albeit a very powerful one) that is being driven by an IGBT driver. To prevent all diodes from failing when an arc is drawn, the output current is limited by a water resistor, which consists of a silicon tube filled with regular tap water and capped at both ends with electrodes.

Theory (a simplified overview):

The output voltage (Eout) is nominally the twice the peak input voltage (Eac) multiplied by the number of stages,

The voltage drop under load can be calculated as:

Edrop = I1/ (f*C) * (2 /3*n^3 + n^2/2- n/6)where:
I is the load current
C is the stage capacitance
f is the AC frequency
n is the number of stages.

The ripple voltage, in the case where all stage capacitances (C1 through C(2*n)) may be calculated from:
Eripple = Iload/(f * C)*n*(n+1)/2

As you can see from this equation, the ripple grows quite rapidly as the number of stages increases (as n squared, in fact). A common modification to the design is to make the stage capacitances larger at the bottom, with C1 & C2 = nC, C3 & C4= (n-1)C, and so forth. In this case, the ripple is:
Eripple = Iload/(f*C)

For large values of n (>= 5), the n²/2 and n/6 terms in the voltage drop equation become small compared to the 2/3n³. Differentiating the drop equation with respect to the number of stages gives an equation for the optimum number of stages (for the equal valued capacitor design:

Noptimum = SQRT( Vmax * f * C/Iload)

Increasing the frequency can dramatically reduce the ripple, and the voltage drop under load, which accounts for the popularity driving a multipler stack with a switching power supply.

Construction

Here are a few construction pictures showing the tools and parts used to assemble the multiplier. The first prototype used three diodes out in the air; it flashed over almost instantly at around 120kV, destroying 2 legs.
For the second prototype the shape of the diode strings was worked on a bit in order to increase the distance between diodes. That flashed over at around 140kV.
The final prototype uses a tight fitting silicone tube around the diodes, and the diodes are coated in oil, both to help prevent flashover and to help them slide on around the tube. This flashed over twice, but it can hold off over 180kV before flashing over.
The future plan is to use 4 diode strings for an 80kV holdoff. This should help eliminate the flashovers. Meanwhile I am looking for more capacitors to add more stages to the system.
Ideally I would like to run 10 stages for 500,000V DC. I need 12 more capacitors for that, at a cost of around $80 a capacitor. This won't happen any time soon.

Results:

Here are some spark pictures showing the best sparks to date, a bit over 7" (before the first stage flashed over). The corona and Ozone smell are extrmely noticeable, and everything around the output becomes strongly charged.

More pictures to come!

Videos:

Here are a few videos of the device in action:

This video shows a later test with the cascade being driven to full power and a 7+ inch spark occuring at the output, which is being limited by a water resistor. One of the diodes on the first stage rectifier stack fails, shorting out the entire device.

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