I can tell you, these sparks are quite noisy! Keep you children (and yourself) at a safe distance!
Never attempt to energize such apparatus at your home!

With the given 0.5 mA supply, there is a spark every few seconds. Triggering is nice, and stage voltage reaches about 23-24 kV – the design limit.

Should you ever operate a Marx generator, make sure to properly ground and short it prior to approaching it any closer than a few feet!

Some boundary conditions:

(1) Stage voltage equals charge voltage – 20-25 kV range would be most suitable to fit an easy-to-build flyback transformer type supply.

(2) Discharge energy should be at least 10 Joules, otherwise, there is not enough noise and the thing doesn’t look and feel dangerous enough (you might as well use a piezo fire lighter to make some sparks…)

(3) Charge time should be reasonable, not more than a few seconds.

With 16 0.1 µF capacitors, rated for 1.6 kV and operated at 1.5 kV (24 kV per stage), a design was established that uses 10 stages – about 220-230 kV peak voltage. This results in about 20 Joules of discharge energy.
It was also found that there is no need to make the stage charging resistors very large (some sources suggest multiple Megaohms, 1 M is just fine for most of the designs relevant in this context). A value of about 8 M was determined for the charge resistor – mostly because of the 0.5 mA current limit of the power supply – you can use a lower value, if you want to put more current into the Marx. But remember that a high-value charge resistor will also protect the rectifier cascade of you power supply, so you might not want to take too big risks.

Detail view

For the spark gap – these are the approximate voltage for a gap mm:

Accordingly, the gaps were adjusted to about 8.5 mm using a plastic gauge (to avoid scratching of the spheres).
Note that the stage carrier plates have cut-outs at the spark gaps! This is to avoid unwanted discharge, but also to ensure line-of-sight contact of the spark gaps, which ensures stable triggering (because of UV radiation, emitted from one gap, lowering the spark cap threshold voltage of the next).

Full view

(in the back, you can see an earlier experimental model, using Wima FKP-1 capacitors – however, this design added a lot of inductance, and the adjustment of the spark gaps was not thought out very well).

What is a Marx generator – essentially, a device that lets you charge a set of capacitors in parallel (say, to 24 kV), and then discharge they in series, say, at 240 kV, if you have 10 capacitors. There is much more theory to it, all has been very well described elsewhere since the times of Mr. Marx, who first deviced such circuits, arguably, in 1923. If you need more explanation – please ask, I will be glad to explain it to you.

To build a nice Marx generator, you need a few parts:

(1) High voltage resistors – don’t assume this is the easy part – the resistors need to be able to withstand quite some voltage, several kV, and high discharge energy-changes in potential. Carbon composite resistors are best for such applications, but rate to find nowadays. You can get away with series connection of some high-value metal oxide layer transistors. I used some Vitrohm 1 M (Megaohm), 7.5 kV rated resistors obtained as NOS (now-old-stock; series 176 – could not find any data, but seem reasonably robust), some current/more widely available types that may be suitable: Vishay 0207 High Pulse Load Resistors (2 in series), or similar, successfully used for similar projects of more serious nature.

(2) Capacitors – also these must be not only be designed for high voltage, but also pulse rated. Best are especially made pulse discharge capacitors – but these often are oil-filled, rare, and too big for the given purpose. Best alternatives are PP type film capacitors, like the Wima FKP-1 or FKP-4. I used Vishay MKP1841, 0.1 µF 1.6 kV capacitors, metallized PP. The spec to look for is the maximal pulse rise time – the 1841s are not too bad, at least, good enough for this project, and a large bag could be sourced at low cost.

(3) Spark gaps – these need to trigger precisely, otherwise, the apparatus won’t work at full performance, or constantly misfire. Best use polished stainless steel spheres, about 15-20 mm diameter, readly available, already threaded, and easy to attach to the stages.

(4) Some hardware – isolating stand-offs, and some isolating sheet material for the stags – I used some FR4 glass fibre-epoxy boards (leftovers from failed printed circuits, with the copper fully stripped).

(5) A high voltage supply and a feed resistor (about 3-10 M, capable to withstanding at least 50 kV). A series of resistors, item 1, mounted along a plastic rod (Plexiglass, or the like) will do. For the supply, this needs to provide about 20-25 kV (make sure it doesn’t provide more, otherwise the capacitors will suffer!), about 0.5 mA. A fly-back transformer based supply. I’m use a regulated supply (TL494 switchmode regulator, flyback transformer), so the stage charge voltage can be adjusted precisely, and no risk to damage anything.

(6) A good ground connection (earth conductor). Never use plain mains ground, if you don’t want to damage your home electronics! Anything will do, like a water pipe (if fully metallic down to the inlet), or a heating pipe).

(7) Plenty of ground wires around that you can use to safely discharge the apparatus and to keep it shorted to ground if not in use. RISK OF ELECTRIC SHOCK! ALWAYS SHORT THIS APPARATUS WHEN NOT IN USE!