I was given a 50w, S68 HPS lamp.  Anyone have ideas for lighting it with something other than the proper ballast, which I don't have? I'm thinking a pair of 14-22w preheat chokes in paralell, a F32T8 electronic ballast, or a 40w rapid start ballast, all with either a piezoelectric lighter ignitor or a starter from a capacitive LOA shoplight or something similar as the ignitor? Any other ideas or advice on what will/won't work? (At least somewhat, ie warms up partway then cycles?)

An instant-start F54T5HO ballast will drive a 50w HPS close to spec.   I have a generic (chinese) 1-lamp F54T5HO ballast thats instant start (most cheap chinese T5 ballasts are not programmed start). It takes forever (like 8 minutes) warmup time, the lamps stays in the low pressure sodium state for most of that time, but eventually reaches normal color and intensity. Also ive found the GE Lucalox lamp works best with this setup. I tried a 50w Philips on it and it had an ever so slight flicker

The S68 (a 52V arc) is designed to operate on a series choke fed by ~1A. So a parallel combination of preheat chokes to get the desired curent with a superimposed ignitor would work the best.
What may be more difficult is to get the ignitor, as as far as I know the superimposed ignitor style is not normally used in the 120V area.
You may try a "4..22W" starter (for those preheaters) in series with ~40..60W filament bulb, all that parallel to the lamp.

Or other option would be building one (I will use metric convention, I guess you would be able to figureout the gauges,...):
You will need an ignitor for an existing low voltage ballast (anything for the 55V 35..150W HPS lamps, they are practically all the same).
Then a pulse transformer on a ferrite core. That you may make by winding about 200 turns of about 0.5..0.7mm diameter magnet wire (I do not remember the gauge number), with a tap 10 turns from the end. The turns do not have to be exact, tolerances +/-30% on the overall number of turns and 15% on the ratio are still OK. Insulate the assembly well, remember for the~2kV pulse voltage between the ends.

The complete coil is connected between the lamp and ballast, in series with the lamp, the end with the 10 turns is connected towards the ballast.
The ignitor is connected by the "Lamp" terminal (the one normally connected to the lamp wire) to the tap on the coil,
by the "tap" terminal (the one normally connected to the tap of the ballast)
and by the "Neutral" to the lamp Neutral.

This way you made ~1.5..2.5kV superimposed ignitor, which could even work with remote ballast arrangement, the ignitor assembly (sothe coil plus the original pulser)should be placed close to the lamp.

OK interesting.  I like the idea of something lower-voltage since I don't have any pulse-rated sockets.  But I'll post results.

Don't use an electronic ballast - HID lamps don't like. Three 14/15/20 chokes in parallel will do the trick, or, if you happen to have one, an F24T12/HO ballast. A less-ideal setup like two chokes or an F40T12 ballast will work for a quick test, though - it just won't run up all the way.

Regarding an ignitor, a barbecue ignitor fired adjacent to the bulb might work, too.

The 2kV should be handled well with any 250V rated socket. However the sockets rated just 130V or so could be problematic...

Is it possible to ballast the 50w HPS with a 100w incandescent lamp? (Assuming that a method of starting the lamp was figured out).

Is it possible to ballast the 50w HPS with a 100w incandescent lamp? (Assuming that a method of starting the lamp was figured out).

I dont think so. The thing is, with low frequency ac the current has to drop to zero (twice per mains period), which in fact extinguishes the arc, so after the polarity changes, the arc has to be reignited again. For this reignition the ballast needs to provide an elevated voltage (compare to the arc voltage before the zero cross), to regenerate the ionization. The concept counts on quite substantial remaining ionization from the previous half cycle, as even without current the ionization decays with some time constant. But the longer the gap, the decay progresses further, so higher voltage is needed to restore it back the next half cycle.

With inductive ballast you have two things "playing into your cards": First due to the phase shift, the current zero cross happens when the mains voltage is near its maximum. So once the discharge stops, immediatelly the full mains peak is availableBecause it is immediatelly, the decay hadnt progressed that much. And even there, the full mains peak voltage makes the reignition very reliable. The second thing is, at the moment of the current dropping to zero, the wiring capacitances on the lamp net are charged to the normal arc voltage. With the mains at near the full peak of the opposite polarity, the coil inductance sees the sum of both. Because it is in fact an LC resonator, it swings back towards the mains voltage, hypothetically (when undamped) up tp the same sum of lam and mains peak, but added to the mains voltage. So the lamp would see double the mains plus the original arc voltage (so about 300V in the most optimistic case). So even way more voltage available for the arc reignition. The thing is, the concept of the inductor ballasted lamp counts on all this (although due to losses the swing back is way lower, but still it adds something).

The resistive ballast yileds rather long gap without any current around the zero cross (the part of the sinewave, where the mains voltage is below the lamp arc, so the current can not flow). As a result, the discharge need way higher voltage spike for reignition for the following halfwave. Again the resistive style has just the mains voltage for it (no ringing overshoot,...), plus you would have to wait till the sinewave top to het the mains voltage higher, what means even longer gap, so higher reignition voltage.
As a result, the arc wont be able just to sustain.

What about those self ballasted mercury lamps? They are in series with incandescent. There are also ones that use a halogen instead.

I imagine something could be done with HPS

What about those self ballasted mercury lamps? They are in series with incandescent. There are also ones that use a halogen instead.

I imagine something could be done with HPS

These (230V ones) use the auxiliary probe, which helps even with the zero cross restrike. The gap rowards its electrodec is small, so way lower voltage suffices to maintain the ionization. Then this ionization, plus the aid of its UV, then prime the main arc path so the ionization between the main electrodes gets restored immediately once the voltage reaches the equilibrium (voltage, when the collision multiplication equals the recombination decay of the ions in the arc stream).
With the 120V ones Im not exactly sure if there is some similar mechanism as well, or if these rely solely on the rather long ionization decay time of the mix used.
It could be the arc priming is with mercury (due to the long ionization decay) required only the few seconds after start, when electrodes are cold. Once hot, just the electron emission is enough to restore the full arc from the remaining ionization. Then because 120V are preheated before ignition, the starting probe wont be needed.

Sodium needs thin ceramic arctube, where is impossible to place anyrhing usable as the starting probe. So you need to use some electrical means to keep supplying the main arc path during the phase when the mins is too low in voltage, so you need some electronic around.
When DC arc supply is manageable (short discharge, so the diffusion can offset the electrolysis), a simple rectifier-multiplier with a series resistor can be connected parallel of the main rectifier output, so even when the main path does not carry current, rhe multiplier retains some ionization. And what you get is the GEs selfballasted MH briefly produced in the 70s.
 But when the feed has to be strictly AC (standard HPS,...), the circuit would become way more complicated (e.g. using HF for the mainraining ionization, but that needs an inductor in series with the main current path), so it becomes simpler to use the electronic as the main ballast and get rid of the ballasting resistor.
So nothing really simple enough to actually make sense (technical, as well as commercial) for anything but the mercury. In the last few decades the complete electronic ballast was possible to make so it fits to at least enlarged base, so few types of selfballasted MH reflectors were produced (their high cost was the strong factor blocking their use except high end display lighting). With HPS that was way too expensive (normal person reasoning: why to buy the icky yellow when the crisp white MH is just a tiny bit more expensive).
Only the simplicity of the mercury design actually made those somewhat comercially viable for quite long time (although only niche for most of the time).