Accelerator Physics

The Radio-Frequency Quadrupole (RFQ) has a FODO lattice and Drift-Tube-Linacs (DTL) in general also have FODO lattices. Therefore the natural solution for the matching between these is a FODO lattice. For matching in all three planes one then needs sixteen degrees of freedom. However, different requirements, depending on the applications, may change this solution. For example, in the production environment (like medical and industrial applications), one needs fixed current and fixed beam quality. On the other hand, in the research environment one not only needs all degrees of freedom, but may also want to chop of beam pulse. This paper discusses matching solutions for these different requirements.

On the basis of the recently proposed {\it Thermal Wave Model (TWM) for particle beams}, we give a description of the longitudinal charge particle dynamics in circular accelerating machines by taking into account both radiation damping and quantum excitation (stochastic effect), in presence of a RF potential well. The longitudinal dynamics is governed by a 1-D Schrödinger-like equation for a complex wave function whose squared modulus gives the longitudinal bunch density profile. In this framework, the appropriate {\it r.m.s. emittance} scaling law, due to the damping effect, is naturally recovered, and the asymptotic equilibrium condition for the bunch length, due to the competition between quantum excitation (QE) and radiation damping (RD), is found. This result opens the possibility to apply the TWM, already tested for protons, to electrons, for which QE and RD are very important.

Nonlinear dynamics of the one-dimensional ultrarelativistic bunch of electrons,moving in cold plasma,is considered in multiple scales perturbative approach. A square root of the inverse Lorentz factor of the bunch electrons is taken as a small parameter. Bunch electrons momenta is changed in the first this http URL the underdense plasma and for the model example of the combined bunch the selfacceleration of the bunch electrons can be remarkable.

A novel diagnostic method for detecting ordering in one-dimensional ion beams is presented. The ions are excited by a pulsed laser at two different positions along the beam and fluorescence is observed by a group of four photomultipliers. Correlation in fluorescence signals is firm indication that the ion beam has an ordered structure.

A recently developed method for the calculation of Lyapunov exponents of dynamical systems is described. The method is applicable whenever the linearized dynamics is Hamiltonian. By utilizing the exponential representation of symplectic matrices, this approach avoids the renormalization and reorthogonalization procedures necessary in usual techniques. It is also easily extendible to damped systems. The method is illustrated by considering two examples of physical interest: a model system that describes the beam halo in charged particle beams and the driven van der Pol oscillator.

It has been shown that a small discontinuity such as an enlargement or a hole on circular waveguides can produce trapped electromagnetic modes with frequencies slightly below the waveguide cutoff. The trapped modes due to multiple discontinuities can lead to high narrow-band contributions to the beam-chamber coupling impedance, especially when the wall conductivity is high enough. To make more reliable estimates of these contributions for real machines, an analytical theory of the trapped modes is developed in this paper for a general case of the vacuum chamber with an arbitrary single-connected cross section. The resonant frequencies and coupling impedances due to trapped modes are calculated, and simple explicit expressions are given for circular and rectangular cross sections. The estimates for the LHC are presented.

A novel diagnostic method to detect ordering within one-dimensional ion beams in a storage ring is presented. The ions are simultaneously excited by a ultrashort pulsed laser ( ≃1 ps) at two different locations along the beam and fluorescence is detected by a group of four photo-multipliers. Correlation in fluorescence signals is a firm indication that the ion beam has an ordered structure.