Let's do the high level junior high school maths. (note, may take 30 seconds).
10 kw into 50 ohms = 14.142 amps + 707 Vrms (1 kv peak).
A simple dipole would suffice, ditto with a vertical, or a yagi.
No engineering degree in rocket science required here folks, it's all really old news.
Simple math for sure but not correctly applied. The issue is not at the 50 ohm feedpoint of the antenna, it is at the several thousand ohms of impedance near the ends of the antennas that you suggest.
- Glenn W9IQ
It's a non issue with 10 kw pep out, (1kv peak) even 20 kw pep out..(1414 V peak)..even with high humidity, fog, or rain. The corona problems at the tips starts up at a helluva lot higher peak V. Freq will also affect the corona. Simple Loops at the ends of wire dipole ants, or machined aluminum corona balls for the tips of DE (readily available for any tip OD) typ solve any corona issues..and in some cases, lower noise a bit on RX.
On a yagi, the DE will be the issue, not the parasitic els, but not always, depending on design. Another method used on DE yagi tips is 2-4" long, solid alum cylinders, with the exposed end machined into a 1/2 sphere. The hardcore eme folks will grind off the sharp edges of all the ele tips. The GE HV spray works superb too. Corona is just stripping electrons right out of the air, typ from sharp edges. Get rid of the sharp edges, or replace with a sphere, or 1/2 sphere usually works. The HV spray just insulates the tips from the air. Ele caps will also sometimes work. I don't like plugging the ends of eles on yagi's. Get water inside the ele, and it's retained inside...and freezes. Typ the ends of the else sag a bit, so water migrates towards the sealed tips. I used to use caps on each end of the booms...and when taking one yagi down, it had gallons of water inside the boom..go figure.
Even 1.5 kw = 390 V peak..at the feed point. At the tips of the ant, the peak V is sky high. With just 600 watts cxr..fed into my old 204BA, sitting on wooden saw horses, hold a 4' fluorescent light tube parallel to the DE tip, and it lights up like a searchlight...and that was at 12 noon in summer.
Theories abound, including NEC etc, on exactly how much peak V is at the tips of a full size DE, or a shortened (loaded) DE. I never found any consensus, since the results varied from A-Z. So have no real clue as to how much V is actually at the tips. I don't see too many issues on the tips of AM broadcast towers, and they typ use just tower sections.