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Humans Accidentally Made a Space Cocoon For Ourselves Out of Radio Waves (vice.com)
An anonymous reader shares a Motherboard article: Humans have accidentally created a protective bubble around Earth by using very low frequency (VLF) radio transmissions to contact submarines in the ocean. It sounds nuts, but according to recent research published in Space Science Reviews, underwater communication through VLF channels has an outer space dimension. This video explainer, released by NASA on Wednesday, visualizes how radio waves wafting into space interact with the particles surrounding Earth, and influence their motion. Satellites in certain high-altitude orbits, such as NASA's particle-watching Van Allen Probes, have observed these VLF ripples creating an 'impenetrable boundary,' a phrase coined by study co-author Dan Baker, director of the University of Colorado's Laboratory for Atmospheric and Space Physics. This doesn't mean impenetrable to spacecraft or asteroids, per se, but rather to potentially harmful particle showers created by turbulent space weather.
Perhaps if we can emit VLF radiation at very high frequency
If we emit Very Low Frequency radiation at very high frequency it won't be very low frequency any more.
"That's the way to do it" - Punch
Peeked at TFA, sounds like it amplifies an existing Van Allen belt. Probably doesn't work surgically. Probably impossible to set up a belt on other planets with known tech, but I don't know belts and maybe a mild one can be synthesized, then amplified. I imagine the scale/distribution of radio emitters required isn't too impossible since we did it accidentally.
1) Don't worry about the core, it'll last. It's currently at ~5000K and will be at ~4950K in a billion years... which is about 300M years after the surface will be baked sterile by the Sun.
2) Even so... it would take a LONG time for the solar wind to strip our atmosphere away. And in fact, it turns out we were wrong about the effect of the Earth's magnetic field; it is actually helping the solar wind heat and strip the atmosphere. At current depletion rates, it's estimated to be good for another 4 billion years or so. That's more than 3 billion years after the planet is baked and around the time it'll be engulfed by the Sun.
We really don't need to worry about the core, its magnetic field, or the density of the planetary atmosphere.