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At least 19 recordsLinked to original sources

arXiv1994

Symplectic Computation of Lyapunov Exponents

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.

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arXiv1994

Order $\hbar$ Corrections to the Classical Dynamics of a Particle with Intrinsic Spin Moving in a Constant Magnetic Field

$O(\hbar)$ effects that modify the classical orbit of a charged particle are described for the case of a classical spin-1/2 particle moving in a constant magnetic field, using a manifestly covariant formalism reported previously. It is found that the coupling between the momentum and spin gives rise to a shift in the cyclotron frequency, which is explicitly calculated. In addition the orbit is found to exhibit $O(\hbar)$ oscillations along the axis of the uniform static magnetic field whenever the gyromagnetic ratio $g$ of the particle is not 2. This oscillation is found to occur at a frequency $\propto$ $\frac{g}{2} - 1$, and is an observable source of electric dipole radiation.

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arXiv1994

Candela Photo-Injector Experimental Results

The CANDELA photo-injector is a two cell S-band photo-injector. The copper cathode is illuminated by a 500 fs Ti:sapphire laser. This paper presents energy spectrum measurements of the dark current and intense electron emission that occurs when the laser power density is very high.

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arXiv1995

Finding matched rms envelopes in rf linacs: A Hamiltonian approach

We present a new method for obtaining matched solutions of the rms envelope equations. In this approach, the envelope equations are first expressed in Hamiltonian form. The Hamiltonian defines a nonlinear mapping, $\cal M$, and for periodic transport systems the fixed points of the one-period map are the matched envelopes. Expanding the Hamiltonian around a fiducial trajectory one obtains a linear map, $M$, that describes trajectories (rms envelopes) near the fiducial trajectory. Using $\cal M$ and $M$ we construct a contraction mapping that can be used to obtain the matched envelopes. The algorithm is quadratically convergent. Using the zero-current matched parameters as starting values, the contraction mapping typically converges in a few to several iterations. Since our approach uses numerical integration to obtain all the mappings, it includes the effects of nonidealized, $z$-dependent transverse and longitudinal focusing fields. We present numerical examples including finding a matched beam in a quadrupole channel with rf bunchers.

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arXiv1995

Coupling Impedances and Heating due to Slots in the KEK B-factory

The longitudinal and transverse coupling impedances produced by the long slots in the Low Energy Ring of KEK B-factory are calculated. The power dissipated inside the vacuum chamber due to the fields scattered by the slots is evaluated using results for the real part of the coupling impedance. Estimates are made for the power flow through the slots to the pumping chamber.

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arXiv1995

Beam Dynamics problems in a muon collider

We discuss the various beam dynamics problems in muon collider systems, starting from the proton accelerator needed to generate the muon beams and proceeding through the muon storage ring.

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arXiv1995

Trapped Modes in the Vacuum Chamber of an Arbitrary Cross Section

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.

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arXiv1995

Polarizabilities of an Annular Cut and Coupling Impedances of Button-Type Beam Position Monitors

The longitudinal and transverse coupling impedances of a small discontinuity on the accelerator chamber wall can be expressed in terms of the electric and magnetic polarizabilities of the discontinuity. The polarizabilities are geometrical factors and can be found by solving a static (electric or magnetic) problem. However, they are known in the explicit analytical form only for a few simple-shaped discontinuities, for example, for an elliptic hole in a thin wall. In the present paper the polarizabilities of a ring-shaped cut in the wall are obtained. The results are applied to calculate the coupling impedances of button-type beam position monitors.

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arXiv1995

RFQ-DRL MATCHING SOLUTIONS FOR DIFFERENT REQUIREMENTS

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.

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arXiv1995

Normal Mode Tunes for Linear Coupled Motion in Six Dimensional Phase Space

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.

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arXiv1995

Coaxial Ring Cyclotron as a Perspective Nuclear Power Engineering Machine

The circuit arrangement of the proposed coaxial ring cyclotron (CRC) is described, and its main advantages, such as simple injection technique, several injected beams summation option, high efficiency, are considered. The proposed proton accelerator is a perspective machine for the solution of the main problems of the present day nuclear power engineering as well as for the next-generation nuclear power plants, representing a combination of subcritical reactors and particle accelerators. The possibility of installation of CRCs into ring accelerators with an average diameter from 60 to $100m$, e.g., the Yerevan electron synchrotron, is considered.

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arXiv1995

Linear Orbit Parameters for the Exact Equations of Motion

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.

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arXiv1995

Construction of Nonlinear Symplectic Six-Dimensional Thin-Lens Maps by Exponentiation

The aim of this paper is to construct six-dimensional symplectic thin-lens transport maps for the tracking program SIXTRACK, continuing an earlier report by using another method which consistes in applying Lie series and exponentiation as described by W. Groebner and for canonical systems by A.J. Dragt. We firstly use an approximate Hamiltonian obtained by a series expansion of the square root. Furthermore, nonlinear crossing terms due to the curvature in bending magnets are neglected. An improved Hamiltonian, excluding solenoids, is introduced in Appendix A by using the unexpanded square root mentioned above, but neglecting again nonlinear crossing terms...

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arXiv1995

Linear Parameters and the Decoupling Matrix for Linearly Coupled Motion in 6 Dimensional Phase Space

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.

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arXiv1995

Particle Motion in the Stable Region Near an Edge of a Linear Half-Integer Stopband

This paper studies the motion of a particle whose tune is inside and near a linear half-integer stopband. Results are found for the tune and beta functions in the stable region close to an edge of the stopband. It is shown that the eigenvalues and the eigenfunctions of the transfer matrix are real inside the stopband. All the results found are also valid for small accelerators where the large accelerator approximation is not used.

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arXiv1996

Particle Motion in the Stable Region Near an Edge of a Linear Sum Resonance Stopband

This paper studies the particle motion when the tune is in the stable region close to the edge of linear sum resonance stopband. Results are found for the tune and the beta functions. Results are also found for the two solutions of the equations of motion. The results found are shown to be also valid for small accelerators where the large accelerator approximation may not be used.

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arXiv1996

Final Focus System for a Muon Collider: A Test Model

The present scenario for a high luminosity 4 TeV on center of mass muon collider requires a beta function =3 mm at the interaction point. We discuss a test model of a basic layout which satisfies the requirements although it is not fully realistic.

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arXiv1996

On the Problem of the Coupled Cavity Chain Characteristic Calculations

This paper presents the results of studies in elaboration of a mathematical model of the cavity-chain slow wave structures. Considered is the problem of coupling of an infinitely long cylindrical cavity chain coupled through centerholes in the dividing walls of finite thickness without the assumption about smallness of any parameters. On the basis of a rigorous electrodynamic approach it is shown that the cavity chain can be described by a set of equations that describe the coupling of an infinite number of similar-type modes of short-circuit cavities. At the same time the coupling coefficients are determined by solving the basic sets of linear algebraic equations which describe the coupling the tangential electric fields on the right and left cylindrical hole cross-sections of the disks. The results are given of numerical simulations of the dependence of electrodynamic characteristics on the number of connections between the modes taken into account. Based on these calculations for different cavity dimensions, the number of coupling connections that give the sufficient accuracy of the description was determined.

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