Making ultrastable high voltage supply

[ThaWookiees]

For a project, I need a power supply which can do 10-20kv at 300microAmps, but here's the real shocker: I need 0.1 ppm stability on the thing. For HV generation, I was initially thinking daisy-chained transformers to jump 110V mains to 1100V, then 11kvAC. I was also initially thinking of using high frequency AC @ 10khz to 1mhz to reduce variance that would show up when smoothing 60hz mains frequency. I then realized I could go down to Amazon, and get a painfully unstable, inaccurate 400kv dc to dc converter (that is only around 10kv) and add some components to reach the 0.1ppm I need. To achieve this, I had in mind several ferrites in series along with several HV ceramic caps, hoping that would take care of it. I purchased about 10lb of iron oxide in order to make my own ferrites, so in theory I have at my disposal almost infinite inductance. For ceramic caps, I found some 10 packs of several hundred pF 10-40kV capacitors. I later found a ZVS driver with flyback transformer deal which can achieve the same voltage but will give better control than the potted 400kv modules. Should I also use an inductor/capacitor bank from a 12V DC power supply I'll be using for the ZVS driver, along with the bank on the HV side of the supply? I was also thinking of using bulkier 18AWG copper wire (with appropriate insulation) in order to minimize instability from a thinner wire. Is this unnecessary? I think that since I'll be building one of these, I may as well use higher quality parts (ignoring the cheap high voltage generator). Is there an inverse relationship with ripple adjusting? Increasing capacitance on the cap bank decreases variance in the output? Increasing inductance and frequency of ripple decreases output ripple?
Thanks for your input!
(Please do not patronize me and talk about high voltage safety. )

[tautech]

Furnace ignition transformers will get you a good way to where you want to be, maybe 2 with secondaries in series.
But how to check you have the right phasing..........

[Brumby]

I'm not about to take you on about HV safety.  From what you have written, I think it's pretty clear you have a fair idea about the subject.

Regulating HV is something I know nothing about - however, the thing that catches my eye is the precision you are aiming for.

With the current requirement being so low, the impedance of the supply is going to be high - which, at those voltages, makes me wonder if atmospheric leakage will be a challenge - particularly with changes in humidity and particulates.

Or am I showing my ignorance?

[ThaWookiees]

Thanks for bringing up the environmental aspects of achieving stability- can I just immerse all of the electronics in a bath of mineral oil to reduce said effects? A pool of mineral oil with 4 wires sticking out- input 12V and output 10kV?

[Marco]

Generally you'd do this with a single transformer. How much is your time worth? You can buy a semi-regulated high voltage power supply pretty cheap (couple hundred bucks).

Then you can concentrate on the post regulator for your extreme stability goals ... which is probably going to involve a temperature controlled oil bath (don't put the pass transistor in the oil bath by the way).

[StillTrying]

For a project, I need a power supply which can do 10-20kv at 300microAmps, but here's the real shocker: I need 0.1 ppm stability on the thing.

Are you sure it's not 0.1 percent. I don't think 0.1ppm is possible or measurable.

[matseng]

This is a bit off topic here, but how would one even measure the 10KV at a 0.1ppm precision? Wouldn't the 0.1ppm require 6-7 digits and then 3 more digits to compensate for the voltage divider from 10kv down to something the meter wants?

[ThaWookiees]

Oops, probably should have clarified the specs a bit more. the 0.1ppm is for the ripple. The supply just needs to put out 10kv-20kv at any voltage, so long as that voltage does not vary by more than 0.1ppm in an hour. In order to maintain constant temperature regulated parts, I could do a distilled water ice-bath. I still need help with stabilization, I'll get the 10% stable high voltage converter, then how could I use a capacitor/inductor bank to smooth it?

[Marco]

This is a bit off topic here, but how would one even measure the 10KV at a 0.1ppm precision? Wouldn't the 0.1ppm require 6-7 digits and then 3 more digits to compensate for the voltage divider from 10kv down to something the meter wants?

You build several different methods to measure that voltage at 0.1 ppm (don't need INL at that level) which to the best of your knowledge have significantly better short term stability and then cross validate everything till no one important objects to your assertion of the short term stability any more. Or you just try to make it believable without having a way to validate it and assume.

That said, a HP3458A doesn't even have a 0.1 ppm transfer accuracy for an hour. So I won't believe it

[Brumby]

Oops, probably should have clarified the specs a bit more. the 0.1ppm is for the ripple.

OK - Ripple is one thing

but...

The supply just needs to put out 10kv-20kv at any voltage, so long as that voltage does not vary by more than 0.1ppm in an hour.

This is drift - which gets us right back to the fundamental of regulation.

I don't believe you will be able to rely on thermal stability, because even minor variations are going to be a factor ... and by this I mean a person walking near the thing or clouds overhead casting a shadow on the building.  This brings us back to active regulation.

I hadn't thought about it before aside from saying 'Wow' to myself, but 0.1ppm is an extraordinary requirement.  That's 1mV stability on a 10kV supply.  I, too, have to question this specification.

I am also curious as to what sort of application would demand such precision.

[tautech]

Thanks for bringing up the environmental aspects of achieving stability- can I just immerse all of the electronics in a bath of mineral oil to reduce said effects? A pool of mineral oil with 4 wires sticking out- input 12V and output 10kV?

Not just mineral oil: low dielectric oils, the most common being transformer oils.
http://www.electrical4u.com/transformer-insulating-oil-and-types-of-transformer-oil/

However there are vegetable oils substitutes too, Google will find them.

[ThaWookiees]

So sorry, I only need 10ppm. That's 3 orders of magnitude of additional ease. I found the spec here https://www.matsusada.com/pdf/sem.pdf for a SEM power supply. It really intrigued me as to how they'd achieve any parts per million stability in the first place! I am chiefly concerned with how I could go about making any supply more stable in the first place! I saw Dave's videos on PSUs and the different value capacitor bank output, and was curious how this would apply to HV. Do I go with a feedback circuit (kind of annoying and overcomplicated if I can go with passives)? Or can I just use passives (the capacitor/inductor method) to get good stability? Typically the instruments which use this kind of power supply are in their own climate controlled and seismically isolated rooms, so I would not be surprised if FEI, Hitachi, or JEOL have made 0.1ppm ripple/drift supplies.

[Marco]

Do I go with a feedback circuit

Is the current the load pulls stable to within 10 ppm? If not then yes.

My lay man's opinion, use a temperature controlled oil bath at 40+ degrees.

- LM399 voltage reference, with a opamp control loop which drives a current source
- Micro with DAC to set the control voltage
- Very large string of Stackpole RNCS resistors as a voltage divider (semi hermetic, keeps things relatively cheap)
- 4 transistor current mirror at the high side feeding current into the divider (with a parallel high voltage capacitor) as the high voltage reference
- Buffer with a NPN pass resistor and opamp, pass transistor not inside the oil bath.

Should probably have one extra level of preregulation in front of this just to be safe, but that can be a resistor, Zener and transistor. Opamps and transistors in the oil bath should probably have hermetic cases.

Unless some friend in a lab happens to have some very high precision high voltage measurement device, actually measuring the stability at high voltage is probably going to be costly.

[T3sl4co1l]

Let's see what kind of passives you'd need to filter something to 10ppm stability in 1 hour.

Suppose the output is noisy, on the order of 1% (10,000 ppm) variation (it might be worse than this, but we can simply adjust everything by the same factor).  You need 0.001% (10 ppm).

1 hour is a frequency around 0.28mHz (milli, not Mega).  For a factor of 1000 reduction (that's 60dB) of AC amplitude, we need a cutoff frequency about (1000)^(1/2) times below that, for a 2nd order LC filter, or 8.6uHz.

The nominal output voltage and current are 10kV and 0.3mA, so the filter's characteristic impedance should be on the order of Zo = 10kV/0.3mA or 33Mohms.  We might require that the amount of ripple the filter itself produces, due to varying load current, also be low; if it should be on the order of 10ppm, then we reduce Zo to 10ppm, or 330 ohms.

(Anyone familiar with filter design, should be begging to stop right now.  I shall persevere regardless...)

The cutoff frequency of the filter happens to be the frequency where the L/C reactances are equal to Zo, so we can calculate them easily:
L = (330 ohm) / (2*pi*(8.6uHz)) = 6.1MH
C = 1 / (2*pi*(330 ohm)*(8.6uHz)) = 56F

This filter will be poorly damped (assuming neither the source nor load has a lossy impedance around 330 ohms, and the inductor's DCR is much less than 330 ohms, which it will need to be in order to satisfy the ppm requirement at DC as well), so we should divide the capacitor about in half, and add ~330 ohms ESR to one half.

The supply may have a constant-current characteristic, in which case we should put a capacitor on that side, too.  We can save a bit on the total filter size, in that case, because a CLC filter is three poles, and only needs to be at about 1/10th the cutoff frequency.  (Both capacitors can be split with added ESR as suggested, or ESR added to just one, accepting the modest degradation in performance.)

So, 10kV 56F capacitors, right? Yeah, so there's probably a lesson in there...

(It'll also take about a year of continuous on-time before it stabilizes within the desired margin, too!)

You can throw stupid numbers at a filter design method, and get proportionally stupid responses from it!  GIGO.  You need to reality-check your inputs in the first place.

So, this is why you can't simply filter the thing.  The required cutoff frequency is absurdly low.  For time constants in the ~kHz, filtering is relatively trivial -- a series resistor and a pair of modest value (~nF) capacitors will do an excellent job!  For time constants in the ~Hz, you could maybe get away with some bigger parts, but, you'll be taking a long time charging them from the poor little power supply, and you'll be storing quite a lot of energy, which is expensive and much more hazardous.

For any longer time constant, you need a regulated control method.  And for 10ppm, you need a high gain error amplifier, with low offset and drift.  The amplifier itself will be operating at a couple of volts, so you need a precision (again, ~10ppm drift) resistor divider to sense the high voltage.  That puts the amp at a 1000:1 (or worse) disadvantage, so it needs to be good to microvolts.  Precision and high gain!  It doesn't need to be very fast, so a standard (~one buck) chopper amp will do the job.

The error amplifier output drives something that controls the high voltage power supply.  It might be a control input, it might be a pass transistor controlling the supply voltage, it might be a PWM modulator in a switching circuit, whatever.

And, that's basically it.  I don't know anything about those "400kV" modules, but I doubt they're all that consistent (or quiet, in the Hz range where filtering is difficult!), and you need some way to control them (maybe by varying the supply voltage).  You might be better off with a ZVS resonant or "chopper" oscillator on a flyback transformer, varying the supply to that.  You can at least do it for a modest price, but measuring and verifying that it's actually working correctly will cost you a lot in test equipment, if you don't have it already!

Which leads to the most salient question: how do you even know when it's out by 10ppm, and either 1. can it be used for verification (repeatably), or 2. can it be made tolerant of such changes, so that an expensive power supply design is not required?

Tim

[Alex Nikitin]

Let's be realistic (and I'm speaking from my first-hand experience as I did design this kind of HV supplies for a number of years) - it would be much cheaper and simpler to buy a ready made supply with good stability, like the SEM supply from your link. To make this kind of supply is a difficult task even if you have lots of experience with both HV and high stability but separately. Combined together, these requirements take the design complexity on a completely different level. Even the task of verifying the performance stated is a formidable one, as the measuring equipment should have the stability at least 3 times better than the DUT.

Cheers

Alex

[oldway]

For a project, I need a power supply which can do 10-20kv at 300microAmps...

This is juist what a color TV HV power supply did....!!!! With shunt regulation using a PD510 tube.
Reduce voltage from 24KV to 20KV ajusting polarisation of the shunt regulator.

You can improve voltage regulation by modification of the grid control of the PD510 tube.

See schematic here: http://elektrotanya.com/philips_k8_chassis_color_tv_englisch_sch.pdf/download.html
Wait "get manual".

Or buy a new one:
http://www.fug-elektronik.de/en/

NB: model HCE 7-20000

[Alex Nikitin]

For a project, I need a power supply which can do 10-20kv at 300microAmps...

This is juist what a color TV HV power supply did....!!!! With shunt regulation using a PD510 tube.
Reduce voltage from 24KV to 20KV ajusting polarisation of the shunt regulator.

You can improve voltage regulation by modification of the grid control of the PD510 tube.

See schematic here: http://elektrotanya.com/philips_k8_chassis_color_tv_englisch_sch.pdf/download.html
Wait "get manual".

There are many ways to generate and adjust the required HV voltage. To make it stable and low ripple is a completely different story.

Cheers

Alex

[oldway]

The right solution would be to buy it....but it seems that ThaWookiees need a cheap solution 

[Alex Nikitin]

The right solution would be to buy it....but it seems that ThaWookiees need a cheap solution 

To buy it is the cheapest solution  .

Cheers

Alex

[oldway]

What brand and what model you recommended?
How much is this power supply ?

[David Hess]

Alexander Smolyakov and Mihail Gurevich built a 100 kilovolt reference by stacking REF5010s to achieve a stability within +/- 5ppm.  Their work became a Texas Instruments application note:

http://www.ti.com/cn/lit/pdf/sbaa203

[Marco]

10k$ worth of REF5010s though.

[ThaWookiees]

Thanks for all of the great feedback,

So, this is why you can't simply filter the thing.  The required cutoff frequency is absurdly low.  For time constants in the ~kHz, filtering is relatively trivial -- a series resistor and a pair of modest value (~nF) capacitors will do an excellent job!  For time constants in the ~Hz, you could maybe get away with some bigger parts, but, you'll be taking a long time charging them from the poor little power supply, and you'll be storing quite a lot of energy, which is expensive and much more hazardous.

I really appreciate the figure of a 56F cap, at 10kV? No thanks! So, clearly the 60hz is out of the picture, do you believe (or mathematically know) that I can go with a few nanofarads at 1-2mhz? I will find a book on filter design to aid me further. For now in my electronics life, I will go with a passive solution because if I add enough inductance (hopefully not a mega henry) and enough capacitance (nanoFarads, if I go high frequency) then I won't have to measure, and I can assume 10% instability, and correct for it with the passive bank of filters!
Correct my understanding of filters- Those are things which smooth out signals, right? Or are they frequency selectors, as I've seen in radio gear?
Thanks for everybody being supportive and realistic at the same time!

[Molenaar]

....

Correct my understanding of filters- Those are things which smooth out signals, right? Or are they frequency selectors, as I've seen in radio gear?
Thanks for everybody being supportive and realistic at the same time!

In this case both, by selecting only frequencies that are lower than your ripple/drift, you smooth out your signal.

[Kilrah]

So, clearly the 60hz is out of the picture, do you believe (or mathematically know) that I can go with a few nanofarads at 1-2mhz

You can't just "go to 1-2MHz"... the frequency he based himself on is the one you specified your long term stability with by giving a stability spec over an hour. With the same approach (that is of course an example that can't work, the point was precisely to explain that it can't work) a filter specced at 1MHz frequency you'll only guarantee stability to the next microsecond

[Marco]

I will go with a passive solution because if I add enough inductance (hopefully not a mega henry) and enough capacitance (nanoFarads, if I go high frequency) then I won't have to measure, and I can assume 10% instability, and correct for it with the passive bank of filters!

You do realize you are going from asking for ppm specs to building something to ppk specs right?

Rectifying the output from a transformer, filtering it a little and relying solely on transformer action to regulate the output is not a precision power supply.

[T3sl4co1l]

For a project, I need a power supply which can do 10-20kv at 300microAmps...

This is juist what a color TV HV power supply did....!!!! With shunt regulation using a PD510 tube.
Reduce voltage from 24KV to 20KV ajusting polarisation of the shunt regulator.

You can improve voltage regulation by modification of the grid control of the PD510 tube.

Indeed, color sets were regulated -- such was necessary to ensure correct picture size, color, brightness and (most of all) convergence.

I think stability was a few percent.

Originally achieved with a 30W 30kV 1mA shunt regulator triode -- watch out for x-rays on that one!

Tim

[David Hess]

CRT deflection is largely dependent on cathode voltage so on oscilloscopes, this potential of about -3 kV has to be stable to better than about 1%.  In practice it is usually much more stable than that.  The reference, error amplifier, and high voltage output divider limit performance but there is considerable improvement which could be made with better parts.  I think the limiting factor will be the high voltage DC divider; high voltage thick film resistors just are not good enough for the proposed performance but a series string of precision resistors should work.  Watch out for voltage derating, self heating, and voltage coefficient of resistance though.

Oscilloscope high voltage inverters operate between 20 and 50 kHz making filtering relatively easy but the transformers are not trivial to wind.  Getting to a higher output voltage will be difficult; I would first try using transformers intended for LCD CFL backlight inverters with the primaries connected in parallel and the secondaries connected in series.  I would plan on vacuum potting the entire high voltage assembly.

An alternative would be to use one LCD CFL backlight transformer with a capacitor-diode voltage multiplier on the output but the 100 uA current requirement may be a little too much.  With care this could work without vacuum potting.

[oldway]

CRT deflection is largely dependent on cathode voltage so on oscilloscopes, this potential of about -3 kV has to be stable to better than about 1%.  In practice it is usually much more stable than that.  The reference, error amplifier, and high voltage output divider limit performance but there is considerable improvement which could be made with better parts. HV power supply of analog oscilloscope can't be used because current is too low (100 to 150µA) and also output voltage. (generaly between 10 and 16KV...Only Tektronix 7000 series have higher accelerating voltage) I think the limiting factor will be the high voltage DC divider; high voltage thick film resistors just are not good enough for the proposed performance but a series string of precision resistors should work. With 20 KV, this seems difficult. Buy a cheap High voltage probe of 30KV and use the high voltage resistors of this probe Watch out for voltage derating, self heating, and voltage coefficient of resistance though.

Oscilloscope high voltage inverters operate between 20 and 50 kHz making filtering relatively easy Filtering is made by the capacitance between internal graphite coating and external one. You need a 20KV condenser ! but the transformers are not trivial to wind.  Getting to a higher output voltage will be difficult; I would first try using transformers intended for LCD CFL backlight inverters with the primaries connected in parallel and the secondaries connected in series.  You can't do that because insulation between primary and secundary is not intended to witstand such a high voltage I would plan on vacuum potting the entire high voltage assembly.

An alternative would be to use one LCD CFL backlight transformer with a capacitor-diode voltage multiplier on the output but the 100 uA current requirement may be a little too much.  With care this could work without vacuum potting.

[David Hess]

HV power supply of analog oscilloscope can't be used because current is too low (100 to 150µA) and also output voltage. (generaly between 10 and 16KV...Only Tektronix 7000 series have higher accelerating voltage)

They used x7 multipliers (sometimes Tektronix marked this x14 in their documentation) to produce 21kV post deflection acceleration from the 3kV peak-to-peak transformer output starting with the 150 MHz 7704 which was available starting in 1969.  I am not suggesting to use that many voltage multiplier stages for the reason you identify but that means raising the secondary voltage.

With 20 KV, this seems difficult. Buy a cheap High voltage probe of 30KV and use the high voltage resistors of this probe.

The thick film resistors used in these probes are pretty good but will be less stable then an assembled precision resistor.

Filtering is made by the capacitance between internal graphite coating and external one. You need a 20KV condenser!

Oscilloscope CRTs do not have an external coating or at least none of the "modern" ones since the 1960s I have seen do.  The oldest ones used wall bands or a continuous coating and later ones used a wound helix terminated at the grounded field forming electrode.

The series stacked capacitance itself in the voltage multiplier provides filtering but so what?  High voltage capacitors are readily available.  It is too bad these guys do not sell the needed transformer:

http://hvstuff.com/high-voltage-capacitors

You can't do that because insulation between primary and secundary is not intended to witstand such a high voltage

Which is why I would plan on vacuum potting the entire high voltage assembly as I mentioned in my post.  Two transformers in a balanced configuration to produce a grounded center tap would be better (my neon sign transformer has a grounded center tapped secondary) but I doubt the application will allow it.

I was thinking of something along the lines of a higher voltage version of the laser power supply Jim Williams showed in figure 11 on page 7 of Linear Technology application note 61:

http://cds.linear.com/docs/en/application-note/an61fa.pdf

[botcrusher]

Thanks for bringing up the environmental aspects of achieving stability- can I just immerse all of the electronics in a bath of mineral oil to reduce said effects? A pool of mineral oil with 4 wires sticking out- input 12V and output 10kV?

Not just mineral oil: low dielectric oils, the most common being transformer oils.
http://www.electrical4u.com/transformer-insulating-oil-and-types-of-transformer-oil/

However there are vegetable oils substitutes too, Google will find them.

Time to crack out that old sealed vat of PCBs

[Marco]

With a HV350REG available for 250$ it hardly seems worth the trouble.

[David Hess]

With a HV350REG available for 250$ it hardly seems worth the trouble.

The HV350REG is not going to have even close to the required stability but a separate DC regulator could be added to its output.  I know a easy design such a regulator could take but this post is too small to contain it.

I am kidding.  Instead of trying to design a 10+ kilovolt voltage regulator, float the HV350REG with a regulated low voltage and use the high voltage resistor divider on the combined output.  I am dubious however that the HV350REG output is quiet enough however.

[Alex Eisenhut]

https://www.matsusada.com/pdf/sem.pdf

[oldway]

In an old scrap CRT color TV or CRT monitor, you can salvage all the components needed to make your own 20KV power supply project for nothing or very cheap. (ferrite flyback transformer, high voltage power transistor, voltage multiplier, high voltage capacitors, ...)

As this kind of power supply is current limited with high internal resistance, a shunt regulation would be very simple and should have a great stability.

[David Hess]

As this kind of power supply is current limited with high internal resistance, a shunt regulation would be very simple and should have a great stability.

What form does a 10 to 20 kilovolt shunt regulator take?  Could it use a series string of high voltage avalanche diodes for level shifting?

[oldway]

Triode Svetlana GP5, ED500, ED510, PD500, PD510, 6BK4,....

http://www.jogis-roehrenbude.de/Russian/GP5/GP5.pdf

http://www.ebay.fr/itm/3-x-Russian-GP5-GP-5-6BK4-Vintage-Vacuum-Triode-Tube-NOS-ED500-5-/181703232728

[saturation]

Spellman's MPS high stability modules could meet your specs.

http://www.spellmanhv.com/en/Products/Modules/3W-15W/MPS.aspx

[Marco]

Instead of trying to design a 10+ kilovolt voltage regulator, float the HV350REG with a regulated low voltage and use the high voltage resistor divider on the combined output.  I am dubious however that the HV350REG output is quiet enough however.

You're going to need a lot of passive filtering and output capacitance for that to work ... high voltage dividers tend to have poor high frequency response, unless you want to build one with RC segments (not trivial to keep the response flat).

[David Hess]

Instead of trying to design a 10+ kilovolt voltage regulator, float the HV350REG with a regulated low voltage and use the high voltage resistor divider on the combined output.  I am dubious however that the HV350REG output is quiet enough however.

You're going to need a lot of passive filtering and output capacitance for that to work ... high voltage dividers tend to have poor high frequency response, unless you want to build one with RC segments (not trivial to keep the response flat).

It is an interesting problem; use a fixed parallel high voltage capacitance across the series resistor and trim the capacitance on the low voltage shunt resistor for best response.  Flat response is not required and most designs will perform better with a little bit of lead compensation.

Running a transient response test on a power supply like this though is probably better imagined than performed or at least admired from a safe distance.  The last time I worked on something like this, the observation was made that it is amazing what becomes a conductor at high voltages.

I would worry that the high voltage power supply has so much noise and drift that the error amplifier cannot remove it.  That Spellman supply linked by saturation looks like just the thing to avoid designing and building something that will likely fail spectacularly a few times.

[Brumby]

.... it is amazing what becomes a conductor at high voltages.

 

[oldway]

Shunt regulator act as a filter....
Flyback (current generator) + shunt regulator.
How the control works ?
Angle of the flyback power supply is regulated to maintain 500µA as average cathode current of the high voltage triode.
Polarisation of the triode is regulated by opamp to obtain the required output HV voltage.
NB: at power up, a delay is needed for the warm up of the triode.

[Marco]

It is an interesting problem; use a fixed parallel high voltage capacitance across the series resistor and trim the capacitance on the low voltage shunt resistor for best response.  Flat response is not required and most designs will perform better with a little bit of lead compensation.

Actually it was the reverse of I was thinking, you don't want capacitance at all on the lower leg.

At a 1:1000 attenuation you'd need GHz+ GBW to get good ripple rejection at 10+ Khz, and it's not necessary. Just let attenuation approach 1x at frequencies above a couple Hz.

Funny, I've never understood how shunt regulators work it seems :/

[oldway]

If needed, there is a cheap solution to make a 20KV capacitor: the Leyden jar. 

[David Hess]

It is an interesting problem; use a fixed parallel high voltage capacitance across the series resistor and trim the capacitance on the low voltage shunt resistor for best response.  Flat response is not required and most designs will perform better with a little bit of lead compensation.

Actually it was the reverse of I was thinking, you don't want capacitance at all on the lower leg.

At a 1:1000 attenuation you'd need GHz+ GBW to get good ripple rejection at 10+ Khz, and it's not necessary. Just let attenuation approach 1x at frequencies above a couple Hz.

The reason I would do it this way is that it is easier and safer to have a grounded trimmer capacitor on the lower leg of the resistive divider and it allows trimming of the phase lead.  The fixed high voltage capacitor across the high voltage part of the divider swamps other parasitic effects which may change over time.

The other design I would consider uses a very high voltage level shift on the output of the low voltage error amplifier so the gain within the loop is 1.  This effectively becomes a high voltage emitter follower but getting this to work at 10+ kilovolts would be more difficult.

Funny, I've never understood how shunt regulators work it seems :/

I could design a high voltage shunt regulator using solid state devices but I was interested in what other solutions there are.  Somewhere I have a several amp 50+ kilovolt rectifier assembly which is interesting to study.  It uses fiberglass supports to hold an array of individual stud rectifiers mounted on printed circuit boards.

[Marco]

The reason I would do it this way is that it is easier and safer to have a grounded trimmer capacitor on the lower leg of the resistive divider and it allows trimming of the phase lead.

The design isn't sensitive to it at all. It's not a question of phase lead, the phase goes from 0 to near 90 and back to near 0 regardless. The upper leg capacitance sets the -3dB point and the combination of the upper and lower leg capacitances set the high frequency attenuation. Whether the -3 db point of the attenuator is at 2 Hz or 3 Hz doesn't matter. Whether the high frequency attenuation is 0.99 or 0.98 and the phase is 1 degree or 2 degree doesn't matter, that's just screwing around in the margins, has little effect on loop regulation.

So say a 1G string for the upper leg with 100 pF worth of high voltage capacitor and a lower leg of 1M is all that's necessary.