First quadrupole built by PBPL. 
First quadrupole built by PBPL.
Using quadrupole magnets is one of the most efficient way to keep the beam focused throughout the transport and, more generally, to control the twiss parameters of the beam. If the quadrupole poles are of the perfect shape (hyperbolic), it generates constant magnetic field gradient B', which acts as a focusing lens in x and defocusing in y, or vice versa.
For the thin (L<<f) quadrupole magnet of the magnetic length L the focal length f is given by
