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Where I can find photos of nuclear explosions just after detonation (before 5-10 ms, the shorter the better)?

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No guarantee that they exist. Just getting the timing right is a challanging instrumentation problem under the best of circumstances. Not because timing to a few nanoseconds is hard but becuase understanding the time sequence of detonation to that level may not be easy and because closeups will have to contend with the destruction of the instrument itself and data speeds on cable or fiber on order of $.6 \mathrm{c}$. – dmckee♦ Jan 2 at 4:43
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@dmckee I upvoted your comment but am red in the face, because I googled, as you can see in my answer. – anna v Jan 2 at 5:01

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Never underestimate the power of googling.

I googled "high speed nuclear explosion photos" and got a large number of them. Here is one:

nuclear detonation

This image captures two common elements: the spikes (called "rope tricks") and an uneven surface shape

The duration of the exposure is typically 10 nanoseconds

At this stage of the detonation the surface of the fireball has a temperature of 20,000 degrees, three times hotter than the sun's surface. At such temperatures the amount of thermal radiation (light) given off is so enormous anything it touches is vaporized ahead of the expanding fireball. The three spikes in this image result from the guide wires supporting the tower on which the bomb was located absorbing enough heat to turn into light emitting plasma. Because thermal radiation travels faster than the fireball, the spikes extend out ahead of it.

p.s. I should have remembered one frame cameras, since I had been using "gun cameras" from WWII to get images of cosmic rays in spark chambers by triggering, back in 1967.

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Nice. There is a problem with the text that you quote however--$10\text{ ns}*\mathrm{c} \approx 10\text{ ft}$ --someone drop a order of magnitude somewhere. – dmckee♦ Jan 2 at 5:43
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@dmckee I am not good at "feet" – anna v Jan 2 at 5:52
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The picture below shows an explosion after about 1 ms. (source) It's called the "rope trick" image, because the explosion is taking place at the top of a tower and the spikes at the bottom are ropes being vaporised by the radiation travelling out from the explosion.

enter image description here

I found it by searching Wikimedia Commons for "nuclear detonation" and then scrolling down until I saw it, because I've seen the image before and knew what it looked like.

There is also the following photo (source), which is of a different explosion, taken after 16 ms:

enter image description here

I haven't seen many other pictures like this, so I suspect these are among the very few in existence.

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Even neglecting the rope tricks the structure in the earlier image is very interesting. – dmckee♦ Jan 2 at 5:44
@dmckee yes, I've often wondered what causes it. I suspect that it's due to fluctuations in the temperature, density and/or moisture content of the air making some regions get ionised more readily than others - but I'm not sure. – Nathaniel Jan 2 at 6:03
...which would make a good question for this site, come to think of it. I'll post one shortly. – Nathaniel Jan 2 at 6:07
@Nathaniel - the rope trick is because of material the cables are made of. The radiation from the explosion travels out at the speed of light and heats everything surrounding it. The cables absorb the radiation, heat up and emit light more than the air - you aren't seeing the speed down the cable so much as the rate the cable itself explodes. – Martin Beckett Feb 10 at 21:36
@MartinBeckett I know that - I've edited the answer to make it clearer. – Nathaniel Feb 11 at 0:49

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