Accelerator physics

Accelerator physics deals with the problems of building and operating particle accelerators.

The experiments conducted with particle accelerators are not regarded as part of accelerator physics. These belong (according to the objectives of the experiments) to particle physics, nuclear physics, condensed matter physics, materials physics, etc. as well as to other sciences and technical fields. The types of experiments done at a particular accelerator and/or its other uses are largely constrained by the characteristics of the accelerator itself, such as energy (per particle), types of particles, beam intensity, beam quality, etc.

Accelerator physics itself is the study of the motion of the particle beam through the machine, control and manipulation of the beam, interaction with the machine itself, and measurements of the various parameters associated with particle beams.

Equations of motion

The motion of charged particles through an accelerator is controlled using applied electro-magnetic fields, and the equations of motion may be derived from (or, since in many cases a general solution is not possible, approximated from) relativistic Hamiltonian mechanics. Typically, a separate Hamiltonian is written down for each element (e.g. for a single quadrupole magnet, or accelerating structure) to allow the equations of motion to be solved for this one element. Once this has been done for each element encountered in the machine, the full trajectory of each particle may be calculated for the entire machine.

In many cases a general solution of the full Hamiltonian is not possible, so it is necessary to make approximations. This may take the form of the Paraxial approximation (a Taylor series in the dynamical variables, truncated to low order), however, even in the cases of strongly non-linear magnetic fields, a Lie transform may be used to construct an integrator with a high degree of accuracy, and the paraxial approximation is not necessary.
Diagnostics

A vital component of any accelerator are the diagnostic devices that allow various properties of the particle bunches to be measured.

A typical machine may use many different types of measurement device in order to measure different properties. These include (but are not limited to) Beam Position Monitors (BPMs) to measure the position of the bunch, screens (fluorescent screens, Optical Transition Radiation (OTR) devices) to image the profile of the bunch, wire-scanners to measure its cross-section, and toroids or ICTs to measure the bunch charge (i.e. the number of particles per bunch).

While many of these devices rely on well understood technology, designing a device capable of measuring a beam for a particular machine is a complex task requiring much expertise. Not only is a full understanding of the physics of the operation of the device necessary, but it is also necessary to ensure that the device is capable of measuring the expected parameters of the machine under consideration.

Success of the full range of beam diagnostics often underpins the success of the machine as a whole.

Machine tolerances

Errors in the alignment of components, field strength, etc., are inevitable in machines of this scale, so it is important to consider the tolerances under which a machine may operate.

Engineers will provide the physicists with expected tolerances for the alignment and manufacture of each component to allow full physics simulations of the expected behaviour of the machine under these conditions. In many cases it will be found that the performance is degraded to an unacceptable level, requiring either re-engineering of the components, or the invention of algorithms that allow the machine performance to be 'tuned' back to the design level.

This may require many simulations of different error conditions in order to determine the relative success of each tuning algorithm, and to allow recommendations for the collection of algorithms to be deployed on the real machine.

Interactions between the beam and the machine

Due to the strong electro-magnetic fields that follow the beam, it is possible for it to interact with any electrical impedance in the walls of the beam pipe. This may be in the form of a resistive impedance (i.e. the finite resistivity of the beam pipe material) or an inductive/capacitive impedance (due to the geometric changes in the beam pipe's cross section).

These impedances will induce so called 'wake-fields' (a strong warping of the electromagnetic field of the beam) that can interact with later particles. Since this interaction may have a negative effect, it must be studied to determine its magnitude, and to determine any actions that may be taken to mitigate it.

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