10s of kilowatts, not 10 kilowatts. And that's for a huge, delta-shaped blended wing aircraft. If you take the takeoff power of a 777 and distribute it over the entire cross-sectional area of the plane you'll end up with several hundred kilowatts per square meter.
Even rounding down to 100 megawatts and then assuming a 70m x 60m triangle (2100 m^2) you end up with about 50 kilowatts per square meter. Now consider that the power gathering equipment not only needs to be extremely efficient (as even 95% efficiency would dump enough heat into the plane's structure to cause it to melt fairly quickly) but also needs to be built extremely carefully as any imperfection that resulted in a drop in efficiency for any small part of the plane would result in catastrophe.
And, of course, as mentioned there would be the problems of bleed-over and so forth. You want to be able to fly planes over populated areas, most likely.
Even rounding down to 100 megawatts and then assuming a 70m x 60m triangle (2100 m^2) you end up with about 50 kilowatts per square meter. Now consider that the power gathering equipment not only needs to be extremely efficient (as even 95% efficiency would dump enough heat into the plane's structure to cause it to melt fairly quickly) but also needs to be built extremely carefully as any imperfection that resulted in a drop in efficiency for any small part of the plane would result in catastrophe.
And, of course, as mentioned there would be the problems of bleed-over and so forth. You want to be able to fly planes over populated areas, most likely.