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50
INVARIANTS OF BETATRON MOTION AND DYNAMICAL APERTURE
"... In this contribution the approximate limiting stable amplitude for the nonlinear betatron motion in circular accelerators containing sextupoles is derived for the purely one dimensional case of the horizontal motion. Using as input the beta functions, the sextupole positions as well as the sextupol ..."
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in the case of a FODOlattice with two families of sextupoles and a more general examole of a LEPtype structure with insertions is good. 2. Generalized. The differential equation of from Ref. [I.] and reads as: x " + Q * x $ K'(o where K ' and 8 are the invariants betatronmotion is taken cs
ORBIT HAMILTONIAN, SYNCHROTRON OSCILLATIONS AND SYNCHROBETATRON COUPLING
"... Abstract We develop a Hamiltonian formalism for synchrobetatron coupling using the orbit length as an independent variable. We start from a basic Hamiltonian in the curvilinear coordinate system and obtain symplectic equations of synchrobetatron coupled motin. This paper is an addition to a previo ..."
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Abstract We develop a Hamiltonian formalism for synchrobetatron coupling using the orbit length as an independent variable. We start from a basic Hamiltonian in the curvilinear coordinate system and obtain symplectic equations of synchrobetatron coupled motin. This paper is an addition to a
ANALYTICAL DESCRIPTION OF BETATRON OSCILLATIONS IN LINEAR MACHINES
"... As pointed out by Wiedemann, there are three basic periodic lattices using usually in storage rings [1,2]. Among these are the FODO, ChasmanGreen lattice and triplet. They have not sextupole and octopole lenses and define socalled linear machines. To facilitate the calculations the consideration i ..."
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is restricted only to systems with quadrupole magnets. The equations of small deviations are derived in linear approximation. It is established that these expressions are specific differential equations with periodic coefficients and small parameter of the highest derivative. The Hill equations with a formula
Betatron xray production in mixed gases
"... Betatron xrays with multikeV photon energies have been observed from a GeVclass laserplasma accelerator. The experiment was performed using the 200 TW Callisto laser system at LLNL to produce and simultaneously observe GeVclass electron beams and keV Betatron xrays. The laser was focused with ..."
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. Electron spectra were measured on large image plates with the twoscreen method after being deflected by a large 0.42 Tesla magnet spectrometer. Betatron oscillations observed on the electron spectra can be benchmarked against a simple analytical model (RungeKutta algorithm solving the equation of motion
ANALYTIC CALCULATION OF THE DYNAMICAL APERTURE FOR THE TWO DIMENSIONAL BETATRON MOTION IN STORAGE RIN&S
"... In this contribution we study the onmomentum nonlinear equations of motion for the coupled transverse motion of a single charged particle in a storage ring. We seek for the maximum initial linear ..."
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In this contribution we study the onmomentum nonlinear equations of motion for the coupled transverse motion of a single charged particle in a storage ring. We seek for the maximum initial linear
KINETIC STABILITY PROPERTIES OF AN INTENSE RELATIVISTIC ELECTRON RING IN A HIGHCURRENT BETATRON ACCELERATOR
, 1985
"... The kinetic stability properties of an intense relativistic electron ring located at the midplane of an externally applied betatron field are investigated within the framework of the linearized VlasovMaxwell equations, including the important influence of electromagnetic effects and surfacewave pe ..."
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The kinetic stability properties of an intense relativistic electron ring located at the midplane of an externally applied betatron field are investigated within the framework of the linearized VlasovMaxwell equations, including the important influence of electromagnetic effects and surface
Renormalization Group Reduction of the Henon Map and Application to the Transverse Betatron Motion in Cyclic Accelerators
, 2003
"... The renormalization group method is applied to the study of discrete dynamical systems. As a particular example, the Henon map is considered as applied to describe the transverse betatron oscillations in a cyclic accelerator or storage ring possessing a FODOcell structure with a single thin sextupo ..."
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The renormalization group method is applied to the study of discrete dynamical systems. As a particular example, the Henon map is considered as applied to describe the transverse betatron oscillations in a cyclic accelerator or storage ring possessing a FODOcell structure with a single thin
Summary
"... The coupling mechanisms of synchrotron and betatron motion have been intensively studied in the past by various authors. Piwinski and Wrulich [I] analysed firstly the coupling effect caused by a nonvanishing dispersion in the accelerating cavities. They also found that not only the betatron motion ..."
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the coupled nonlinear differential equations for the vertical betatron motion and the synchrotron motion is not only valid in the neighbourhood of resonances but for any values of the synchrotron and betatron tunes. After introducing the coupled equations we succeed to decouple the synchrotron equation from
DISPERSION IN THE PRESENCE OF STRONG TRANSVERSE WAKEFIELDS
"... To minimize emittance growth in a long linac, it is necessary to control the wakefields by correcting the beam orbit excursions. In addition, the particle energy is made to vary along the length of the bunch to introduce a damping, known as the BNS damping, to the beam breakup effect. In this paper ..."
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to the beam dynamics in long linacs with strong wakefields like SLC. 1 WAKE INDUCED DISPERSION (TWOPARTICLE MODEL) Consider a linac with uniform betatron focusing and no acceleration. Introduce an orbit kick at s =0. The betatron equation of motion for a particle with relative energy error
SOLUTION OF RMS ENVELOPE EQUATION IN LAMINAR FLOW
"... An approach to the envelope description of laminar nonrelativistic particle beams is presented, which describes a new kind of equilibrium flow for strongly space charge dominated proton beams subject to acceleration in RF Linacs. The analysis is based on the extension of the invariant envelope conc ..."
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concept, recently introduced in the field of RF photoinjectors[1], to nonrelativistic particle beams whose envelope is dominated by coherent plasma oscillations instead of incoherent betatron motion associated to thermal rms emittance. An exact analytical solution of the rms envelope equation
Results 1  10
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50