Thanks for the help everyone, I ended up manually making the spreadsheet, with capacitors ranging from 7.5 to 82g and 16mm to 40mm diameter. Basically the higher voltage the better, within a capacitor family. Some capacitor families go up to 550V, but the most energy dense families only go up to 450V. The next largest factor is the connection style, in that snap-in capacitors are much lighter for a given capacity than either screw terminal or radial leaded capacitors. It also seems that smaller diameter capacitors had a higher energy density, but length had a fairly small effect. Manufacturer basically doesn't matter as their high end capacitors all have the same capacitance for a given case size and voltage.

Because of this, I ended up choosing the smallest diameter and longest snap-in capacitor available, the 22mm diameter, 50mm long, 400V 330uF United Chemi-Con ESMQ401VSN331MP50S, and am planning on putting 3 of them in parallel. They don't list the mass of their capacitors, but based on TDK's mass for the same size it is 2.66 J/g. The highest energy density I could find was 2.99 J/g, but that and several other capacitors at the highest energy density were not stocked anywhere.

Imagine a loose contact resistance to be welded (switch closing after a spot weld). The 1st weld is easy, Each subsequent weld current gets shared by each previous weld as the gap gets closer.

The Ni-Chrome wire does make it a little easier to make the resistant-weld significantly smaller than the inter-weld resistance.

Assumptions:

• Ni-Chrome end-to-end R= 200 mOhms, height = 1/4 Diameter or 50 mOhms
• weld contact surface area over height must be 100% otherwise there will be hot spots where current during operation has more resistance and less path to share.

This means the weld must be continuous along the height of the foil which involves a 90 deg wrap around the SS terminal wire.

Imagine only 10 spots, instead of 20 spots or 40 spots. In order for each weld to be lower resistance than the heater, it must be less than 50 mOhms/10 or 5 mOhms which needs to be achieved in 1mm² spot.

So what energy does it take to raise a spot of Ni-Chrome per mm³ well above 1400°C melting point to diffuse into SS with a similar melting point?

10 Joules? ( tiny spot weld) 100 Joules? 300 Joules?

Since Energy of a Cap is \$E=½CV²= I²ESR\$ and max current must be much greater than the average bond current has ESR which is falling with V so it is not simple I=V/R and is limited by Cap Array ESR. Rather the cap array must be far less than the spot weld ESR so as not to absorb much of the stored energy lost in heat.

Let's assume the caps must be explosion proof and must be plastic self-healing Y cap rated or better. What what is better high V or high C? That depends on ESR of each part of the system ( caps, SS, nichrome and existing spot welds)

Start with 100J or C = 2 x 100[J] / V² and assume CAP ESR< 5mΩ and T=ESR*C minimum

At 1V , C = 200 Farads with T = 1 second and I = 200A max = 1V/5mΩ

At 10V , C = 2 Farads with T = 10ms and I = 2,000A max

At 100V, C = 20mF with T = 100 us and I = 20,000A max ( no way on a small array)

If you can get tungsten electrodes and an array of L-ion cells in parallel to supply 200A for a few seconds, you might get some practical results. But ideally you want to maximize current yet have enough voltage to strike an arc. ( at 1kV/mm you need to have surface roughness < 1um to arc at 1V and not covered with carbon from 1st attempt.) 1um is unrealistic.

Therefore you want slightly higher voltage around 4V to get > 100A for > 1 second.

Others can contribute and compute volume of 1mm² metal and the energy to raise the temperature 1600'C.

Or decide if the resistance rise in the SS to 800% or so causes the heat to be localized for a continuous seam weld.

Anecdotal

But I still think this one is done with Ultrasonic welders. For 1 point Cap discharge, is easy. But seam weld, not so easy. In '79 I designed an instrument to monitor difussion bonding of a Zirconium shim inside a two Monel Steel tubes at ~10kA * 4V. It was water-jet cooled as the tube rolled around and power had to increase as R reduiced around the circumference.