I had the chance to fire up my ANSYS simulation and thought you would enjoy some examples of what it can do. Attached is an animation and plot of a nominal induction launcher design with the following parameters. Note that this is a time harmonic solution (not transient) with 10 identical coils and an armature that is longer than the "barrel". A case which would be great for efficiency, since all of the coils are running at the same frequency and all doing work on the armature. So a bit of a simplified launcher.

Armature diameter: 25mm
Armature wall thickness: 3mm
Armature material: Aluminum
Armature weight: 200g

Coil number: 10
Coil cross section: 20mm x 15mm
Coil wire gauge: 10 AWG
Coil turns: 45
Coil drive current: 1kA

With this model I can sweep all sorts of variables like armature-coil gap spacing (one I knew you were keen on), drive phase number, drive frequency, etc. etc.

The animation shows the product of the azimuthal current density J and the radial magnetic field density B which has units N/m^3 (if you do a volume integral you get total force on the armature). The plot shows the total armature force vs drive frequency for gap spacing of 1, 2, and 3mm. As you can see, a smaller gap is better, but the gains aren't astronomical, more on the order of 10 or 15%, at least for this design.

I would be happy to plug in your numbers and run a similar simulation sweeping whatever variables you are interested in. Just let me know!

Depending on the type of snubber (C, RC, RCD) an oversized snubber capacitor could lead to large inrush currents which could damage components with high dI/dt

However it is more likely to not be an issue unless you are over sizing by orders of magnitude

what factors would prevent one from using coils with less and less resistance so less capacitance is needed to generate the same current and timing? Especially for a reluctance coilgun. Would it not make sense to design the coil to be the least resistance possible so as to need less capacitor mass?

In theory less resistance is always better, all else equal. However it is rarely possible to keep all else equal. In this case depending on your method of lowering resistance, it will have inherent effects on the number of turns and inductance.

First off, the peak current will almost certainly be limited by the coil inductance rather than resistance, scaling with sqrt(C/L). Assuming we are talking about changing winding configurations rather than materials, (and maintaining the barrel diameter) you could lower resistance in one of two ways: maintaining the coil cross section and increasing wire size, or maintain the wire size and use less turns (shrinking the coil cross section).

In the first case, it turns out that for a fixed coil cross section to the first order changing the wire size gives you the same amp turns, which is what matters. Double the wire cross section to cut the resistance by a factor of 4 and you also halve the number of turns which is a 4x reduction in inductance leading to double the peak current. Your losses (again to the first order) will stay the same since RI^2=(R/4)(2I)^2

In the second case, if you were to say cut the number of turns in half, your resistance would only halve and your inductance would be ~4x lower (assuming your coil cross section is approximately square, for single layer coils your inductance would only drop by a factor of 2) . This means a doubled peak current again and therefore the same amp turns, but now your losses are doubled! Not great, which is fundamentally why small launchers are hard to make efficient (think how increasing coil/barrel diameter has the same relationship). Note that efficiency does not quite scale with launcher diameter, since for multilayer coils there are second order effects (skin and proximity) that change the resistance and inductance scaling. However, it does still stand that you gain some efficiency going larger.

So, generally you will want to pick a coil cross section that gives you the field distribution you want (another topic, but nominally close to square is desirable), then pick your wire gauge to give you the inductance you want. This will be driven by component availability on one end, namely what is the maximum voltage your components can handle, and launcher parameters on the other, namely what resonant frequency do you want.

If you fix the resonant frequency then you basically have a fixed LC product. To maximize force you want to maximize current. Given our progression of constraints up to this point, you can double the current by either doubling voltage, or doubling capacitance and halving inductance. You can basically pick your poison within reason. Though if you choose to decrease inductance (lower voltage higher capacitance) and therefore increase wire size, you will stray from the linearity assumed above as the skin depth becomes less than your wire radius and you are no longer efficiently using your wire cross section. Litz wire would be an (expensive) way to overcome this. At the other end, with high voltage comes expensive semiconductors and thick insulation (reducing coupling and coil packing density). There is usually a reasonable middle ground that fits the semiconductors, capacitors, etc. that you have available.

Hope this is helpful, also since this was a bit hand wavy and not tied to exact math, please double check my reasoning!

It was when intermittently powering the OBIT (say 3 times per second) that the problem occurred.

Terry, in addition to what Dave and Twospoons commented, it sounds like you could be getting voltage spikes on the output of the transformer due to turn off transients. Im not sure how you are driving it (directly from mains AC?) or switching it on and off, but presumably when you switch it off it results in a large negative dI/dt across the primary as the switch opens. This quickly changing flux induces a large voltage in the secondary.

Welcome Download!

I seem to be in a very similar boat as you, finding the HV hobby in my teens and wanting to return to it with more experience/resources.

Your nuclear hobby sounds interesting and I would love to read your blog and/or paper once released. I am currently riding the nuclear fusion startup wave that has high demand for pulsed power engineers. No background in anything nuclear before this though, so I am curious to learn tidbits of history along the way.

-Ben

As pointed out by Twospoons and klugesmith, the total circuit inductance will be the main current limiter in most pulsed power situations. It would be helpful to know what capcitor(s) you are using to get 40uF at 5kV. Also what does your discharge circuit look like? Is it two meter-long wires attached to chicken sticks (not recommended). Or are you wiring up a relatively low inductance discharge path by minimizing loop area etc. ?

• Unless you are being very conscious of inductance in your design, it is unlikely that you are below 500nH. A big contribution to your ESR will be from your capacitor (all depending on its type), so lets say you aren't getting away with anything less than 10-20mOhm total. This puts your peak current about 40kA and quite underdamped, ringing at ~35kHz for several cycles. Note, f = 1/(2pi*sqrt(LC))

As MRMILSTAR eludes to, the entire cross section of your conductor is not all used. Commonly this is referred to as the skin effect, which for AC signals can be reduced to:

• d = sqrt(1/(pi*f*sigma*u_r*u₀))
  
  Where d is the depth in meters at which the current density has reduced by 63% (ie. most of the current is within this depth). sigma is the material conductivity, which for copper is about 5.8*10⁷ and u_r is 1 for copper. So this can condense to:
  
  d = 0.066/sqrt(f)
  
  Which is 0.35mm at 35kHz. In your case you will likely be utilizing less than a 0.5mm layer on the outside of your conductor, almost certainly less than a 1mm layer. This effect is not limited to true "AC" signals. Any time changing pulse has the same effect present. This is due to the magnetic field taking time do diffuse into conductors (details are out of the scope of this discussion).

Getting back to your question, klugesmith's approach of assuming an adiabatic temperature rise is excellent for getting an upper bound on the current capacity of a conductor. In fact there is a famous paper from 1944 by Onderdonk addressing the problem this way (including temperature varying resistivity etc.) a more modern review of this is attached here and produces the following equation for the fusing of copper conductors:

• (i/A)²t = 9.6*10⁴
  
  Or, rearranged:
  
  i_fuse = A*sqrt( 9.6*10⁴ / t )
  
  Where i is the current, A is the conductor cross section in mm², and t is time. Per this equation, the fusing action of 6mm² wire is ~3.5*10⁶ A²s. Your discharge will probably have an action about 100x less than this. However, going back to the skin depth consideration, you will want to scale this fusing equation by the factor:
  
  (2d/r - d²/r²)²
  
  Where d is the skin depth from the previous equation and r is the wire radius, both in meters. Which still puts you well in the clear by this approach.

In reality you will not want the copper to get anywhere near its melting point of 1083 C so maybe a better thing to do is say we don't want its temperature to rise more than X degrees, for practical reasons like not starting a fire or melting its insulation (maybe 100-200 C is a safe limit). Per my second attachment (the TRM white paper) we get an equation that calculates the temperature rise of the wire:

• T_rise = 253(10^{8.9*10-6(i/A)2t} - 1)
  
  OR rearranged to give a maximum current for some pulse width t and an allowable T_rise:
  i_max = A*sqrt( log₁₀(T_rise/253 + 1) / (8.9*10^-6 t) )
  Again where T_rise is in degrees C and A is in mm²
  

There will be other considerations in specific situations such as the forces involved when conductors are in close proximity to each other (or themselves as in a coil of wire). In these situations the wire can fail mechanically well below its fusing current. All of this to say, your 6mm² wire will probably be totally fine for discharging a capacitor bank into random loads such as popping aluminum foil etc. but if you are trying to achieve another goal you may be better served with larger wire or even some form of bus bar like MRMILSTAR suggests. Let us know what your setup and use case are and we can advise further!

You all may be familiar with the “Ross relay” used widely in the world of pulsed power. I recently designed a low cost 3D printed version with a few upgrades. See my short video below summarizing it.

https://youtube.com/shorts/Em6C3439wSk?feature=share







I’ll update this post with more detail and links to the 3D models, BOM, and kicad files. Let me know if y’all have any questions or suggestions for upgrades!

-Ben

I will be receiving this book in a few days and plan to read through it. I will be interested to post some thoughts/questions that come up during my study.

The longevity in pulse applications has little to do with the size of the terminal, and a lot more to do with the construction of the attachment to the metalized film inside.

Fair point, although I am hoping that the end terminal, along with the general geometry of the capacitor, is somewhat of a proxy for:

1. The intended current
2. The construction method

The cylindrical shape and axial connections indicates a fairly direct connection from the terminals to the end spray on the metalized polypropylene roll inside. Which is preferred to something like this which would have more complex internal connections:


Like you say, the only real way to know is to test!

-Ben

Umar,

Interesting project idea! It sounds like you want it to have a bandwidth in the 10's of MHz, any specific range? Also if I understand correctly, it would be a capacitive divider probe and not suitable at low frequency or DC?

I will be interested to follow this and would like to help out if I can. I have access to a manual lathe and mill as well as ANSYS EM simulation software, let me know if there are any design or prototyping steps I can help with.

-Ben