"As I understand it, the Sun has a greater escape velocity than Earth and there are magnetic fields associated with the Sun, yet it is able to expel massive quantities of energetic particles into space . Why could this not happen on Earth?"
It could (see above- Earth isn't a source of high energy particles)
I thought that nuclear fission ‘DID’ contain high energy particles.

Certainly, it does. But this is a "problem" to do with degree and scale.
If we were continously by the hour exploding nukes in the atmosphere, then there would a significant amount of high energy particles being emitted by Earth (but not anywhere close to what being emitted by the Sun, but maybe close to number high energy particles are entering Earth from the Sun). In other words if you measured the high energy particles being emitting from the Earth, +99.9% would not be from anything humans did or even a significant level from "natural source" from the Earth. The source would be from the Sun and rest of the universe (exploding stellar objects) "bouncing off" the earth.

So in other words, the camel CAN carry one more straw?

No. That's not what I was talking about. Exploding a nuke in our atmosphere every hour, would certainly have serious health effect on human beings and all living creatures on Earth- the longer this was done the more serious the affect- until evenually it would make entire environment lethal. Nuclear reactor accidents can also serious health consequences and the health hazard can have a long term affect on all living creatures in contaminated area.
What I was addressing the "Earth isn't a source of high energy particles". Nor is the Moon, though you can detect high energy particles coming from the Moon and this was used to determine the Moon's chemical composition and confirmed there was water at the Lunar poles:
http://lunar.arc.nasa.gov/results/neutron.htm

"That is comforting to know. However. I am going to dig for more 'facts', such as 'how strong' is the 'camel' and how much of a load it is allready carrying. "
Fine, but I'm quite sure you will find that the entire Earth is not radiating more radiation now, then say 1000 year ago [but not saying you can't detect any effects from human use of nuclear technology (such as from high altitude nuclear tesing) ]
Though there are areas which have been contaminated by man made radiation. Try searching for info on the two atomic bombs dropped on Japan, Bikini atoll (hydrogen bomb testing), the armies' nuclear testing in Arizona, and the recent French nuclear test might have some useful info.
Oh, and also check out high altitude nuclear test explosions (which has been banned for a number of years by most countries), the Superfund clean-up, and stuff on nuclear waste storage at Yucca mountains.

Thank you for the responses it has been an enlightening experience. :-)

It's been fun:)