https://www.youtube.com/watch?v=zr-eZ_pLTNI
Lights up an MH lamp using a Tesla coil, probably not on a ballast

Arcs start when the electric field exceeds what it takes to break down (ionize) the gas

Electrc field is basically voltage divided by distance. For example if there are 2 uniform flat conductors 2mm apart, with 1kV between them, the field is 500V/mm. When the conductors are not uniform, the field tends to be stronger around sharp edges or where the conductors (the surfaces which face the other pole conductor) have smaller surface area

The external Tesla coil applies very high voltage, this high voltage over the distances between it and the arc tube electrodes creates a region with high electric field, some of which happens to also be inside the arctube. If it have sufficient field strength, it will ionize the gas near the electrode

With initial ionization present, the discharge will quickly take over the path between the 2 main electrodes

I saw this video from styropyro
At 16:00 he uses a tesla coil gun to ignite a metal halide lamp that wasn't starting (i think the ignitor connected to the ballast failed)
How does this work?

@RRK
But isn't the whole point of LPS to have higher efficiency than HPS? Unless we are talking about the pre-HPS years here. I thought that was the whole LPS mission statement, to be the most efficient lamp. Were they still more efficient than HPS even when considering these high ballast losses?
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LPS started way before HPS, so yes, we practically are talking about "pre-HPS" years, when the main standards (how the lamps "are normally handled") were set. Then it was just the "It was always made this way" inertia in the industry.

New incandescent sports lighting fixtures in the late '70s is crazy!

I have read that some North American mercury vapor ball field fixtures used 1000W H36 mercury vapor lamps that were overdriven at 1500W on dedicated ballasts in order to provide the most light output possible before metal halide lamps were even a thing.

Update - I've since read this too. Running a 1,000W bulb in a 1,500W ballast would definitely severely reduce the lifespan, and as such sports facilities were probably the only place it made practical sense. I do wonder why there weren't explicit 1,500W MV bulbs like there are MH bulbs. Maybe they weren't cost effective to manufacture?

Construction metal wholesalers can cut sheet metal and bend it

The bending can be done along a line on any sheet metal part, but bent parts cannot be inserted into the machine again to bend along a line that crosses the 1st bend, only along parallel lines. They use it mostly to make gutters and brackets, in our case it is good for bending the spine, reflector and end bits

Then in the reflector you'll have to make cutouts for the lamp sockets. The construction metal places i know here don't generally have the correct machinery for this job, so you might either want to take it to a more complete metalworking shop (maybe laser), or try to make as much as you can.

In the drawing i show an option how it can be DIY'd. Cut from the edge with tin snips, fold the piece back with long/deep pliers exactly at the line, and fold it flat against the back of the reflector. Though this may make painting the reflector awkward. You may try to grind it off (with a grinder, from the back) after folding. Still do grind it only after folding to not leave a rough edge on the outside

See here for the construction of 90's Gaash 2800, on which you can base the design :

https://www.lighting-gallery.net/gallery/displayimage.php?album=2158&pos=52&pid=108528
https://www.lighting-gallery.net/gallery/displayimage.php?album=2158&pos=51&pid=108529

Use the 4064 reflector shape if you like it more, though for the 2800 based design you'll still want narrow cutouts exactly for each tombstone socket, not wide cutouts like the 4064 :

https://www.lighting-gallery.net/gallery/displayimage.php?album=2158&pos=22&pid=110735

The above strip lights (2800 based on 1600, and 4064/02 based on 5054/02) do have end parts that have precise rectangular cutouts for the tombstone sockets, and are installed in place by elaborate latching tabs. Unless you use laser cutting, you will want to avoid this in the design. (Gaash used press die for stamping it)

Instead, use the design from the early versions of Gaash 1600 with just simple bent parts, however this will require tombstones that can be mounted on a surface (generally the old ones with thick base) and not only pop through cutouts

In the original 1600 the pieces were connected by point welding. You can use whatever method including screws or rivets. (Electrode will burn a hole in so thin metal)

See drawing

Most CAD software packages have a sheet metal tool that's perfect for this. I believe Fusion 360 and OnShape have a free/reduced cost option for hobby/personal use. A striplight is fairly simple but you can also design more elaborate styles such as louvered fixtures or half pipers.

Some PEM nuts clinched into the sheet metal will make assembly a lot easier with screws and PEM studs clinched into the channel can be used to mount the ballast and as a grounding point.

Once you have your design you can generate drawings with all the measurements and either fabricate it yourself or take it to a sheet metal shop.

You may know that I have a Universal USB-1024-14 sign light ballast. Recently, I've decided I want to put it to use. The design is that of a basic industrial strip light, it'll be made of 1/16th in thick metal for the main body and reflector, although a separate flat piece made of 1/8th in thick metal will hold the ballast and hooks and will be connected to the rest of the fixture via mechanical means. I plan on having it operate 4 F36T12/HO lamps, using R17d lamp sockets. Any ideas or suggestions on making this become a reality? I will be designing and manufacturing it myself, but any idea on how to get the measurements right? I want to get the measurements right one the 1st or 2nd time in order to not spend a ton of money on prototypes.

Yeah it seemed like it would be fairly easy for a manufacturer to modify one of those designs for LPS, modifying the design to match the current of a LPS lamp and also modifying the wiring shouldn't be take too much effort.