text: The total radiated power is
  where  (the velocity of the particle divided by the speed of light),  is the Lorentz factor,  is the vacuum permittivity,  signifies a time derivative of  and  is the charge of the particle.
  In the case where velocity is parallel to acceleration (i.e., linear motion), the expression reduces to
  where  is the acceleration. For the case of acceleration perpendicular to the velocity (), for example in synchrotrons, the total power is
  Power radiated in the two limiting cases is proportional to   or  . Since , we see that for particles with the same energy  the total radiated power goes as  or , which accounts for why electrons lose energy to bremsstrahlung radiation much more rapidly than heavier charged particles (e.g., muons, protons, alpha particles). This is the reason a TeV energy electron-positron collider (such as the proposed International Linear Collider) cannot use a circular tunnel (requiring constant acceleration), while a proton-proton collider (such as the Large Hadron Collider) can utilize a circular tunnel. The electrons lose energy due to bremsstrahlung at a rate  times higher than protons do.