How to create pulses which are 10ns long and 15kV/ 80A amplitude?
Your requirements of short, variable length pulses, high voltage, and high current are hard to achieve simultaneously. Needless to say, for high speed, high voltage, high current pulses, it is imperative to absolutely minimize any parasitic inductance or capacitance in the switching circuit, connections, or load.

The MOSFET cascode will get you to, I guess, 50ns pulses and 5kV into 200 ohms without too much difficulty. There is a limit to how many MOSFETs one can reasonably stack and still have good voltage-sharing and switching performance, so the MOSFETs will need to be overspecified and rise times will not be much better than 10ns. The cascode also cannot turn off rapidly, so if you want square pulses with well-controlled fall times you will probably have to use a push-pull design, although P-MOSFETs are slower to switch and hard to find with high breakdown voltages. Transformer-coupled gate drive is also possible, which could reduce the turn-off times for N-MOSFETs or enable half-H-bridge designs, but the design and construction of the transformers is not easy. See here for an example that achieves somewhat worse performance than you are interested in, or here for some discussion regarding the approach proposed in the article you link and why it is difficult to apply in practice.

Behlke makes many products of this general type, and although some of them can meet your other requirements, none can achieve pulses shorter than about 50-100ns. The on-state resistance is also a significant fraction of your load impedance, and obviously it becomes worse the more MOSFETs one places in series or the higher-voltage devices one chooses.

A Marx generator is good for high voltage, high current, fast-rising pulses, but the pulse length is not easily controllable, and as with all spark-gap-based devices, jitter could be rather large unless special effort is taken to minimize it.

Your only serious option may be something like a Blumlein transmission line or other transmission-line-based pulse multiplier. Here is a page describing it, and here and here are two papers describing voltage-multiplying Blumlein generators. The disadvantages are that varying the pulse duration requires changing the physical length of the transmission line, and the transmission line impedance has to be matched to the load. Triggering it is a problem in itself, although one possibility is a laser-triggered spark gap. These devices are large anyway, but especially a 200 ohm transmission line capable of carrying large currents and yielding pulse widths of up to 100ns will be rather bulky. Possibly you could use 50 ohm transmission lines and a 4:1 transmission line transformer, but achieving good wideband coupling while keeping leakage inductance and inter-winding capacitance small is not easy. One company that makes devices like this is Barth Electronics.

If you can relax the requirement for variable pulse widths, you could investigate commercial Pockels cell drivers or other electronically similar devices, which are based on solid-state Marx generators. These are often limited to providing 5-6kV negative pulses, because this is what Pockels cells require, and do not usually have fast fall times; however, there are exceptions.

One such exception that deserves special mention are those made by FID GmbH. This company makes several products similar to what you require, such as the FDS 20-10NKN5. They are based on a special avalanche-mode device, the fast ionization dynistor, that seems to be almost unique to this company, but which has some very impressive capabilities. It can produce a 10kV pulse with 20ps rise time, or a 1MV(!) pulse with 1ns rise time. I'm not aware of any other technology that comes anywhere close to this level of performance.