Hi Mason,

A couple of useful pages to get you started:

www.microwaves101.com/encyclopedias/power-handling
www.microwaves101.com/encyclopedias/atmospheric-breakdown
10 kW will cook some electronics, but for plausible arcing (e.g. the field is so strong that incoming weapons self-destruct as soon as they get close) consider bumping up your sources to MW levels. By way of comparison, using some example figures from the textbook Microwave Engineering, by D Pozar, coaxial cable breaks down at 520 kW and waveguide breaks down at around 2.3 MW.

From the charts on the power handling page linked above, it looks like you need a field strength of about 3 MV/m to cover a 100 mm gap at sea level (1 atmosphere). This drops with altitude, if the pressure was only 0.01 atmospheres then 30 kV/m would probably do it.

In terms of range, lets assume your shield is spherical around the spaceship. The relationship between field strength, power, and distance is:

E = sqrt(30*P)/r

Rearrange to solve for distance

r = sqrt(30*P)/E

So, to get 30 kV/m from a 10 kW source, you've got an effective range of 18 mm. Hmm, not much.

Bump up the source to 10 MW, the effective range is 577 mm. Still not great.

At 1 GW, the effective range is still only 5.77 m.

If it fits your story arc, it might be more plausible to suggest a smart system (more like your microwave laser) that sends a focused beam to each target. Give it a 50 dB gain antenna, which has around a degree beamwidth, and you can get that same 5.77 m range from a 10 kW source. A still plausible 10 MW source now gets you 180 m of range. 100 MW pushes that out to 577 m, and a 1 GW source with a 50 dB antenna will happily fry things at 1.8 km range.

Hope this is helpful, good luck with the story!