Another great post.
Unlike our own planet, Mars doesn't have the same internal dynamo in its core that generates a magnetic field, which means Mars is pretty defenseless from cosmic rays. That same field protects Earth's atmosphere from being stripped away by solar winds. Mars used to have a magnetic field, but after it deteriorated, most of the atmosphere was stripped away. Here is Mars' magnetosphere visualized and compared to Earth's.
It's basically non-existent.
It might sound scary, but our bodies are used to low levels of radiation. We have error correcting mechanisms that fix DNA and cells that repair. It's intense high level radiation that's dangerous because it overwhelms these processes and can cause morbidity rapidly.
RE: Radiation on our way to and on MARS - Colonization of MARS Series