Beam Propagation in Misaligned Magnetic Elements: A MatLab ® Based Code

We present a method to calculate kinematical parameters of a beam subject to a misaligned magnetic element. The procedure consists in transforming the kinematical parameters of the beam to the reference frame in which the magnetic element is aligned, propagating the beam through the element, and transforming back to the original frame. This is done using rotation matrices around the X-, Y-, and Z-axes. These matrices are not Lorentz invariant, so the rotations must be relativiscally corrected. We describe the transformation matrices, present a MatLab ® based code that uses this method to propagate up to 1000 particles trough a misaligned quadrupole, and show some graphical outputs of the code.