A number of particles with given initial conditions can be tracked through a beam-line or a ring. The particles can be tracked either for a single passage or for many turns.
While MAD-X [a] is keeping most of the functionality of its predecessor MAD-8, the trajectory tracking in MAD-X is considerably modified comparing to MAD-8 . The reason is that in MAD8 the thick lens tracking is inherently not symplectic, which implies that the phase space volume is not preserved during the tracking, i.e. contrary to the real particle the tracked particle amplitude is either growing or decreasing.
The non-symplectic tracking as in MAD-8 has been completely excluded from MAD-X by taking out the thick lens part from the tracking modules. Instead two types of tracking modules (both symplectic) are implemented into MAD-X.
The first part of this design decision is the thin-lens tracking module (thintrack) which tracks symplecticly through drifts and kicks and by replacing the end effects by their symplectic part in form of an additional kick on either end of the element. This method demands a preliminary conversion of a sequence with thick elements into one composed entirely of thin elements (see the MAKETHIN command). The details of its usage are given on the page "thintrack".
The second part of this design decision is to produce a thick lens tracking module based on the PTC code [b] that allows a symplectic treatment of all accelerator elements giving the user full control over the precision (number of steps and integration type) and exactness (full or extended Hamiltonian) of the results.
The first PTC thick-lens tracking module is named ptc_track. It has the same features as the thin-lens tracking code (thintrack) except it treats thick-lenses in a symplectic manner.
There is a second PTC tracking module called the line tracking module (ptc_track_line). It is meant for tracking particles in CLIC, in fact it treats beam-lines containing traveling-wave cavities and includes a beam acceleration.