Electrons in uniform magnetic field.

Hello.

So I was wondering that when you shoot an electron through an uniform magnetic field, obviously Lorenz force starts to skew the path to that corkscrew shape that we all know. But then there is an acceleration towards the center of the circle, and if the the velocity of the electron changes, isn't there supposed to be bremsstrahlung radiation then? I don't think that it happens because then the electron should radiate and the radii should decay. Right?

But why? What is the difference between this and an electron that has it's velocity changed due to a proton?