Electron
Here are some usefull formulas to calculate the power radiated by an electron accelerated by a magnetic field perpendicular to the velocity and .[3]
where , is the perpendicular magnetic field, the electron mass.
Using the classical electron radius
where is the radius of curvature,
can also be derived from particle coordinates (using common 6D phase space coordinates system x,x',y,y',s,):
Note: The transverse magnetic field is often normalized using the magnet rigidity:
[4]
Field expansion (using Laurent_series): where is the transverse field expressed in [T], the multipole field strengths (skew and normal) expressed in , the particle position and the multipole order, k=0 for a dipole,k=1 for a quadrupole,k=2 for a sextupole, etc...