magnetosphere

The lack of a magnetosphere is a problem on geological time scales (thousands to millions of years) after terraforming.

Because Mars has no magnetosphere all habitable structures will have to be well underground to protect against radiation.

Ganymede is the exception here, due to the fact that it is the only Jovian moon with it's own magnetosphere.

Aside from the obvious problems with keeping an atmosphere, can tidally locked planets have a magnetosphere?

The satellite lacks a magnetosphere, which not only leaves it exposed to radiation by Jupiter, but to the solar wind.

In the extreme long term, Mars may be a good place to try a planet-wide artificial magnetosphere, using high-temperature superconducting materials.

Earth, by contrast, has a magnetosphere that's much larger, and provides significant protection.

Earth's magnetosphere could disappear today, and whatever other chaos that causes, Earth's atmosphere would still deflect most charged and uncharged particles from space.

Does anyone know how Musk plans to address the lack of Mars' magnetosphere?

A spinning liquid metallic outer core, with a certain composition, but yes (we think.) Even Earth's magnetosphere isn't fully understood.

It's thought that the collision resulted in a larger metal core, increasing the strength of our magnetosphere and thus our protection from ionized solar particles.

I'd love to hear the sun's magnetosphere once, or radiation bursts from a quasar.

The key phrase there is "effective strength" so if you have a massive supply of energy at your fingertips, it may be feasible to divert some of it towards the creation of an artificial magnetosphere similar to Earth's own.