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The result should be a consistent set of parameters fulfilling the design requirements. They are the basis for the design of machine elements.
Depending on the complexity of the problem, different techniques are in use
for optics codes. The majority of these codes rely on the description of machine
elements using maps, which can be of higher order for non-linear elements. In
the simplest case for the description of linear machines the maps become matrices
and are therefore often referred to as “matrix codes” [54]). The concatenation of
the matrices provide a matrix for the entire ring and its analysis gives the optical
parameters, closed orbit etc.
Another technique is to follow the particles through the accelerator, i.e. integrating the equation of motion in the electromagnetic fields of the machine elements.
The analysis of the results of these “tracking programs” provides the required
parameters and information about the stability of the machine (for some details see
[54]).
Dealing with complex machines, other considerations may become important
such as e.g.:
• Definition of an input language which can be used by other programs. This input
language defines the sequence of elements, i.e. the ring or a beam line, as well
as the properties of the elements such as e.g. their types (dipole, quadrupole,..),
lengths and strengths.
• For large machines with a large number of elements the interface to a data base
may be required. Large machines such as the LHC or future colliders have several
thousand elements.
• An interface to the control system for on-line modelling is desirable
6.6.4 Single Particle Tracking Codes
To evaluate the performance of accelerators, in particular multi pass, i.e. circular
machines, one has to deal with complex iterative processes. The standard perturbation theories can fail to correctly describe the behaviour beyond leading orders.
Single particle tracking codes are successfully used when analytical methods fail
to describe the effect of non-linear forces on the stability of the particles. Many
tracking codes have been developed together with the necessary tools to analyse
the results and from the simulation point of view the treatment of non-linear effects
is well established. Conceptually, in a tracking code the equation of motion of a
particle in an accelerator element is solved and the phase space coordinates of the
particle are followed through all elements of the accelerator or beam line. To obtain
the desired information, it may be necessary to repeat this process for up to 10 7 turns
which require appropriate algorithms and techniques to avoid numerical problems.
Similar problems exist and some of these techniques have been developped for
celestial mechanics. In order to draw conclusions from the tracking data it is
necessary to provide tools to allow a qualitative and quantitative understanding of
B. J. Holzer et al.
The result should be a consistent set of parameters fulfilling the design requirements. They are the basis for the design of machine elements.
Depending on the complexity of the problem, different techniques are in use
for optics codes. The majority of these codes rely on the description of machine
elements using maps, which can be of higher order for non-linear elements. In
the simplest case for the description of linear machines the maps become matrices
and are therefore often referred to as “matrix codes” [54]). The concatenation of
the matrices provide a matrix for the entire ring and its analysis gives the optical
parameters, closed orbit etc.
Another technique is to follow the particles through the accelerator, i.e. integrating the equation of motion in the electromagnetic fields of the machine elements.
The analysis of the results of these “tracking programs” provides the required
parameters and information about the stability of the machine (for some details see
[54]).
Dealing with complex machines, other considerations may become important
such as e.g.:
• Definition of an input language which can be used by other programs. This input
language defines the sequence of elements, i.e. the ring or a beam line, as well
as the properties of the elements such as e.g. their types (dipole, quadrupole,..),
lengths and strengths.
• For large machines with a large number of elements the interface to a data base
may be required. Large machines such as the LHC or future colliders have several
thousand elements.
• An interface to the control system for on-line modelling is desirable
6.6.4 Single Particle Tracking Codes
To evaluate the performance of accelerators, in particular multi pass, i.e. circular
machines, one has to deal with complex iterative processes. The standard perturbation theories can fail to correctly describe the behaviour beyond leading orders.
Single particle tracking codes are successfully used when analytical methods fail
to describe the effect of non-linear forces on the stability of the particles. Many
tracking codes have been developed together with the necessary tools to analyse
the results and from the simulation point of view the treatment of non-linear effects
is well established. Conceptually, in a tracking code the equation of motion of a
particle in an accelerator element is solved and the phase space coordinates of the
particle are followed through all elements of the accelerator or beam line. To obtain
the desired information, it may be necessary to repeat this process for up to 10 7 turns
which require appropriate algorithms and techniques to avoid numerical problems.
Similar problems exist and some of these techniques have been developped for
celestial mechanics. In order to draw conclusions from the tracking data it is
necessary to provide tools to allow a qualitative and quantitative understanding of