*G. Barr, R. Devenish, R. Walczak, and T. Weidberg*

- Published in print:
- 2016
- Published Online:
- March 2016
- ISBN:
- 9780198748557
- eISBN:
- 9780191811203
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198748557.003.0003
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter gives an introduction to accelerator physics, concentrating on synchrotrons. Accelerating cavities for standing and travelling radiofrequency (RF) waves, the synchronicity requirement, ...
More

This chapter gives an introduction to accelerator physics, concentrating on synchrotrons. Accelerating cavities for standing and travelling radiofrequency (RF) waves, the synchronicity requirement, and the beam bunch structure are explained, as well as the energy loss due to synchrotron radiation. The beam emittance and the amplitude β function are introduced to describe the ensemble of beam trajectories. Dipole and quadrupole magnets, which act as the most important elements of so-called beam optics, are described. The LHC superconducting dipole magnets are described in some detail as an example. Colliders and fixed-target accelerators are then compared in terms of the centre-of-mass energy and the luminosity. As an important example, antiproton–proton colliders, including the use of stochastic cooling, are described and the chapter concludes with the outlook for accelerator developments in future decades.Less

This chapter gives an introduction to accelerator physics, concentrating on synchrotrons. Accelerating cavities for standing and travelling radiofrequency (RF) waves, the synchronicity requirement, and the beam bunch structure are explained, as well as the energy loss due to synchrotron radiation. The beam emittance and the amplitude *β* function are introduced to describe the ensemble of beam trajectories. Dipole and quadrupole magnets, which act as the most important elements of so-called beam optics, are described. The LHC superconducting dipole magnets are described in some detail as an example. Colliders and fixed-target accelerators are then compared in terms of the centre-of-mass energy and the luminosity. As an important example, antiproton–proton colliders, including the use of stochastic cooling, are described and the chapter concludes with the outlook for accelerator developments in future decades.

*E. J. N. Wilson*

- Published in print:
- 2001
- Published Online:
- January 2010
- ISBN:
- 9780198508298
- eISBN:
- 9780191706363
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508298.003.0003
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

The lattice described in the chapter is the periodic pattern of focusing and bending magnets that a particle experiences on each turn. Hills Equation describes the vertical and horizontal transverse ...
More

The lattice described in the chapter is the periodic pattern of focusing and bending magnets that a particle experiences on each turn. Hills Equation describes the vertical and horizontal transverse oscillations of the particle. Its solution is a modified form of the harmonic oscillator. The square of the local amplitude is the product of the beam emittance and the betatron function, beta, which depends on the lattice pattern alone. Beta links to the rate of phase advance of the motion. Two-by-two transport matrices for one turn of the ring have elements that depend on the Twiss parameters, which are the beta amplitude and its derivatives together with the phase advance. They may be computed numerically by multiplying a chain of individual matrices—one for each magnetic element in the ring. The trace of the matrix defines the number of oscillations per turn, Q, which must be real for stability.Less

The lattice described in the chapter is the periodic pattern of focusing and bending magnets that a particle experiences on each turn. Hills Equation describes the vertical and horizontal transverse oscillations of the particle. Its solution is a modified form of the harmonic oscillator. The square of the local amplitude is the product of the beam emittance and the betatron function, beta, which depends on the lattice pattern alone. Beta links to the rate of phase advance of the motion. Two-by-two transport matrices for one turn of the ring have elements that depend on the Twiss parameters, which are the beta amplitude and its derivatives together with the phase advance. They may be computed numerically by multiplying a chain of individual matrices—one for each magnetic element in the ring. The trace of the matrix defines the number of oscillations per turn, Q, which must be real for stability.