To be extra fair,in the book version the story unfolds at Saturn, not Jupiter. It was in the movie version of 2001 and subsequently 2010 (both book and movie) that the events take place at Jupiter. Furthermore, the book version of 2010 is a lot more interesting than the movie as it's a real race to Jupiter, with a Chinese spaceship being assembled officially as a space station, but then the space station takes off to Jupiter and arrives before the Americano-Russian team on the Leonov, only to be killed by local fauna and flora from under the ice of Europa while attempting to use the ice for refueling...
I don't have the radiation data on hand from Cassini for Saturn, but I'll try to find it out...
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From what I gather from the Wikipedia article on Saturn's magnetosphere, the radiation environment is much less severe than Jupiter, and even than Earth... Two zones are to be avoided however: 1) There is a main radiation belt between the outer large visible A-ring at 2.3 Rs (Saturn radii, or 138 000 km) out to Enceladus, at 3 Rs (180 000 km)... 2) Another "hazardous" zone is a plasma sheet limited to the equatorial plane (0 degree inclination orbits) from 6 Rs (360 000 km) out to 14 Rs (840 000 km).
However, contrary to Jupiter and Earth's magnetosphere, most of the atoms are in a neutral state instead of being ionized, so this helps a lot as far as ionizing radiation goes. Titan lies at 20 Rs (1 200 000 km), so radiation is not much of an issue there, except when it crosses the day-side magnetopause that can be pumped with ions by solar activity.
The cool thing about Saturn is that the rings and the moons actually reduce radiation levels, up to the point that the rings provide a "safe haven"...
Very interesting because Titan is the most interesting world after mars to colonise and explore
In Jupiter, the best world is Europe but it will be safe under tons of ice