Accelerator Physics

Within the Thermal Wave Model framework a comparison among Wigner function, Husimi function, and the phase-space distribution given by a particle tracking code is made for a particle beam travelling through a linear lens with small aberrations. The results show that the quantum-like approach seems to be very promising.

Most present and future electron accelerators require bright sources. Invented less than ten years ago, the photo-injector the principle of which is briefly recalled, has already demonstrated that it can provide very bright beams. In this paper, the most advanced photo-injector projects are reviewed, their specific features are outlined, and their major issues are examined. The state-of-the-art in photocathode and laser technologies is presented. Beam dynamics issues are also considered since they are essential in the production of bright beams. Finally, the question of the maturity of photo-injector technology is addressed.

A method for calculating coupling impedances and power losses for off-axis beams is developed. It is applied to calculate impedances of small localized discontinuities like holes and slots, as well as the impedance due to a finite resistivity of chamber walls, in homogeneous chambers with an arbitrary shape of the chamber cross section. The approach requires to solve a two-dimensional electrostatic problem, which can be easily done numerically in the general case, while for some particular cases analytical solutions are obtained.

This paper defines the beta function and other linear orbit parameters using the exact equations of motion. The orbit functions are redefined using the exact equations. Expressions are found for the transfer matrix and the emittances. Differential equations are found for the beta function and the eta function. New relationships between the linear orbit parameters are found.

It will be shown that starting from a coordinate system where the 6 phase space coordinates are linearly coupled, one can go to a new coordinate system where the motion is uncoupled by means of a linear transformation. The original coupled coordinates and the new uncoupled coordinates are related by a 6x6 matrix, R. R will be called the decoupling matrix. It will be shown that of the 36 elements of the 6x6 decoupling matrix R, only 12 elements are independent. This may be contrasted with the results for motion in 4-dimensional phase space, where R has 4 independent elements. A set of equations is given from which the 12 elements of R can be computed from the one period transfer matrix.This set of equations also allows the linear parameters for the uncoupled coordinates to be computed from the one period transfer matrix. An alternative procedure for computing the linear parameters and the 12 independent elements of the decoupling matrix R is also given which depends on computing the eigenvectors of the one period transfer matrix. These results can be used in a tracking program, where the one period transfer matrix can be computed by multiplying the transfer matrices of all the elements in a period, to compute the linear parameters and the elements of the decoupling matrix R.

Muon production requirements for a muon collider are presented. Production of muons from pion decay is studied. Lithium lenses and solenoids are considered for focussing pions from a target, and for matching the pions into a decay channel. Pion decay channels of alternating quadrupoles and long solenoids are compared. Monte Carlo simulations are presented for production of π→μ by protons over a wide energy range, and criteria for choosing the best proton energy are discussed.

Muon Colliders have unique technical and physics advantages and disadvantages when compared with both hadron and electron machines. They should thus be regarded as complementary. Parameters are given of 4 TeV and 0.5 TeV high luminosity \mu^+ \mu^- colliders, and of a 0.5 TeV lower luminosity demonstration machine. We discuss the various systems in such muon colliders, starting from the proton accelerator needed to generate the muons and proceeding through muon cooling, acceleration and storage in a collider ring. Detector background, polarization, and nonstandard operating conditions are discussed.

Muon Colliders have unique technical and physics advantages and disadvantages when compared with both hadron and electron machines. They should thus be regarded as complementary. Parameters are given of 4 TeV and 0.5 TeV high luminosity \mumu colliders, and of a 0.5 TeV lower luminosity demonstration machine. We discuss the various systems in such muon colliders, starting from the proton accelerator needed to generate the muons and proceeding through muon cooling, acceleration and storage in a collider ring. Problems of detector background are also discussed.

Transverse ionization cooling of muons is modeled as a Brownian motion of the muon beam as it traverses a Li or Be rod. A Langevin like equation is written for the free particle case (no external transverse magnetic field) and for the case of a harmonically bound beam in the presence of a focusing magnetic field. We demonstrate that the well known muon cooling equations for short-absorbers can be extrapolated to the useful case of a long absorber rod with a focusing magnetic field present.

The motion of a particle in 6-dimensional phase space in the presence of linear coupling can be written as the sum of 3 normal modes. A cubic equation is found for the tune of the normal modes, which allows the normal mode tunes to be computed from the 6x6 one turn transfer matrix. This result is similar to the quadratic equation found for the normal mode tunes for the motion of a particle in 4-dimensional phase space. These results are useful in tracking programs where the one turn transfer matrix can be computed by multiplying the transfer matrices of each element of the lattice. The tunes of the 3 normal modes, for motion in 6-dimensional phase space, can then be found by solving the cubic equation. Explicit solutions of the cubic equation for the tune are given in terms of the elements of the 6x6 one turn transfer matrix.