Uh, Homer it's time to blow your nose. Once your nostrils are cleared, the letter "M" will no longer sound like a "B".
That's MILLION Watts, not Billion.
Just to start, they choose a frequency that will be most effectively absorbed at the time it's in use. Absorbed, NOT reflected. It aims nearly straight up. Not gonna get much "skip" from that angle, except straight back down. It says they can 'steer' the array up to 30 degrees off of vertical. Even at that angle, the 'skip' distance from Alaska isn't too terribly far.
The layer of the atmosphere that mostly absorbs those Megawatts is roughly 300 meters thick. The "spot" illuminated by the antenna is roughly 30 kilometers in diameter. So the VOLUME that they are heating up is 30,000 times 3.14 times 300, or twenty-eight million, 260 thousand cubic meters. 28,260,000 cubic meters is soaking up 3 Megawatts, which we can conveniently round off to 1 Watt for each ten cubic meters of upper atmosphere. Since one cubic meter is one million cubic centimeters, that one Watt is spread across ten million cubic centimeters. Trust me, the sunlight at those altitudes is a LOT more than one-tenth of a microwatt per cubic centimeter. Not sure of the exact number, but they mention that the VARIATION in solar UV absorbed up there is less that the HAARP energy, once it is spread across its whole target volume.
One tenth of a microwatt per cubic centimeter. Don't know the math right off, but think about illuminating a 30,000-seat football stadium with a 2-cell flashlight. Not sure how high above it you would have to go, maybe a thousand feet or so. Of course, if you hover just a thousand feet up above it with your flashlight, and do it on a clear, moonless night, the starlight falling on the stadium from behind you will be brighter. You get the idea, right?
Your cell phone's field strength across your skull is a WHOLE LOT more than one-tenth of a microwatt per cubic centimeter, holding it to your ear.
Kinda like air travel. You're a thousand-plus times more likely to die in a car going to or from the airport, than in an air crash. But since deaths from air travel are rare and spectacular, this fact gets lost in the hype. Don't worry about insurance for the flight, get some for the trip in the car.
Or, you could check out the countermeasures available, like
The Aluminum Foil Deflector Beanie
The math behind this isn't so different from the math that allows evolution to make sense. How many generations of "selective breeding" take place in a million years? Large numbers are what the universe is constructed from. They're just hard to get your arms (mind) around.
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