A Brief Introduction to Beam Position Monitors for Charged Particle Accelerators

While charged particle accelerators have their origin in the research related to fundamental and high-energy physics, they expanded their applications to many other fields of applied research in physics, material science, biology, chemistry, and medical science, including the treatment of patients, to name some. However, in all types of accelerators assembles of charged particles, e.g., electrons, protons, ions, sometimes their antimatter partners positrons or p-bars (anti-protons) are accelerated to a desired energy, typically in an evacuated, metallic tube, called beam pipe. The acceleration is performed by providing an electric field of high gradient to the charged particle assemble in the direction of motion. In most cases this is performed by resonant radio-frequency (RF) cavities, which are fed by a high-power RF source. However, new acceleration schemes using high power lasers, plasma wakefields, etc. are also studied these days. A guide-field along the accelerator, typically provided by sets of different types of magnets, ensures the charged particles stay within the transverse boundaries of the beam pipe, near its center, travelling on the wanted trajectory. Accelerating elementary particles, like electrons, or quasi-elementary particles, like protons, to very high energies (GeV range) results their velocity $v$ to be close to speed-of-light $c$ , typically expressed as relative velocity $\beta=v/c\approx 1$ , and any further acceleration manifests in a gain of momentum $p=\gamma m_{0}v$ , with $\gamma=1/\sqrt{1-\beta^{2}}$ being the Lorentz factor and $m_{0}$ being the mass of the particle at rest, 0.511 MeV and 938.26 MeV for electron and proton, respectively. The use of resonant RF cavities for the acceleration, causes the particles to form bunches, which fill a longitudinal range of typically a few millimeters up to some meters, depending on $f_{RF}, \gamma$ and other factors. This means, the large number of charged particles in the accelerator are not uniformly distributed along the beam-line but appear in bunches of typical $N=10^{8}-10^{11}$ particles per bunch, and the minimum space between the center of those bunches is defined by the RF bucket length, given by the wavelength $\lambda_{RF}=v/f_{RF}$ of the RF system.