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We will present a method of chromaticity correction for a high brilliant SR ring. This method has been successfully applied to a low emittance ring, the VUV and soft x‐ray ring, which is one of the future plans of the Photon Factory. As a result, we have obtained a sufficiently wide dynamic aperture, more than 40 mm in both transverse directions.

This article presents a missing-bending-magnet scheme for PEP as a modification that could be considered if PEP were available as a fully dedicated synchrotron radiation source. The scheme can be applied to one or more PEP sextants without changing the rest. By removing some bending magnets, rearranging the remaining magnets, and adding two quadrupoles, ten additional straight sections per sextant can be created, each 5 m or more in length, for insertion devices. Beam lines therefrom, plus possible beam lines from bending magnets would enter a continuous experimental hall instead of individual tunnels and halls for each beam line. This should result in construction cost savings and increased operations efficiency. The ideal beam orbit is unchanged at the two ends and the middle of the sextant. At the end of the curved part of the sextant the lattice functions match those of the long interaction region straight section in the low emittance configuration of PEP. The electron beam characteristics in the newly created straight sections are described, including the enlargement of the horizontal beam size due to the nonzero dispersion. Some disadvantages of the scheme are increased operations complexity due to the need for nine new quadrupole families, increased beam emittance (by 14.5% if one sextant is modified), and reduced dynamic aperture. However, the dynamic aperture is still about as large as the physical aperture and should be adequate for good beam lifetime and injection.

A very low‐emittance 1.3‐GeV storage ring has been designed. Modified TBA lattice is used in order to achieve as low emittance as possible and the beam tracking is also carried out to find lattice parameters, which make the dynamic aperture as large as possible. High‐emittance operation is also considered for obtaining large irradiation fields. Moreover, a high‐gain single‐pass FEL undulator which lases around 1000 A is to be installed. For the biochemical and medical applications, a 5‐T wiggler will be inserted in one of four of 6‐m‐long straight sections. The obtained emittance is ∼1.6×10−8 π mrad and the circumference of the storage ring is 126.0 m.

A new magnetic lattice is proposed for a 6 GeV electron storage ring specifically designed for utilization of high brightness undulator and wiggler radiation sources. The basic cell is an achromatic arc with three combined function dipoles, having a vertical focusing gradient. With this arrangement it is possible to achieve an electron beam emittance of ∼ 6 × 10 −9 m·rad at 6 GeV, moderately low chromaticity and good dynamic aperture.

We have proposed a new operation scheme to ease the small dynamic aperture problem at beam injections into low emittance storage rings. Electron beams are injected into the storage ring in a high emittance mode. Then the operation mode is transferred into a low emittance mode, while keeping the betatron tunes constant. The new operation scheme facilitates enlargement of the dynamic aperture during beam injections. A very large dynamic aperture is not necessary in the low emittance storage mode. The new operation scheme can realize a storage ring with an emittance lower than the conventional one.

We present PyZgoubi, a framework that has been developed based on the tracking engine Zgoubi to model, optimise and visualise the dynamics in particle accelerators, especially fixed-field alternating-gradient (FFAG) accelerators. We show that PyZgoubi abstracts Zgoubi by wrapping it in an easy-to-use Python framework in order to allow simple construction, parameterisation, visualisation and optimisation of FFAG accelerator lattices. Its object oriented design gives it the flexibility and extensibility required for current novel FFAG design. We apply PyZgoubi to two example FFAGs; this includes determining the dynamic aperture of the PAMELA medical FFAG in the presence of magnet misalignments, and illustrating how PyZgoubi may be used to optimise FFAGs. We also discuss a robust definition of dynamic aperture in an FFAG and show its implementation in PyZgoubi.

SuperKEKB is a major upgrade of the asymmetric B-factory collider, KEKB, to provide 40 times higher luminosity than that achieved at KEKB. The design of SuperKEKB adopts the nano-beam scheme for the collision of two beams, which was originally proposed for the Italian SuperB project. The nano-beam scheme is realized with low-emittance optics, a very small β-function, and a large crossing angle at the collision point. For the low-emittance design, a substantial part of the positron ring (LER) was reconstructed. All dipole magnets in the LER were replaced with longer ones. The beam pipes in the LER were redesigned to mitigate the electron cloud problem. Around the interaction point, about 300 m of both rings were completely redesigned for the new collision scheme. The commissioning of SuperKEKB is divided into three phases. Phase 1 is used for vacuum scrubbing of new beam pipes without the Belle-II detector and the final focus magnets. The final focus magnets and Belle-II are installed in Phase 2. However, the central vertex detector (VXD) of Belle-II is not installed. Phase 2 is devoted to background studies and collision tuning. After the installation of VXD, Phase 3 starts for the new luminosity frontier. The construction of SuperKEKB for Phase 1 is nearing completion. The preparation of hardware for Phase 2 and Phase 3 is in steady progress. From various aspects, the nano-beam scheme SuperKEKB is a challenging accelerator. The tolerances for the hardware to realize nano-scale beam sizes and to keep the collision are very tight. The optics design is still being optimized to maximize the dynamic aperture. It is hard to predict how the commissioning will proceed.

Double magnets share common laminations without magnetic coupling. Single layer coils of rectangular conductor are dry wound on extruded bore tubes. Magnet construction requires no molding or prestress. Absence of superconducting (SC) magnetization fields in the aperture results in very large dynamic range. The coil is wound continuously across the midplane to give unusually large dynamic aperture. Above ~2.2 T saturation is corrected by simple sextupole windings with no inductive coupling to the dipole. Ultrastable design requires no internal quench protection. A quadrupole pair of novel design gives excellent field quality to B > 2 T without corrections, with no SC magnetization. Experience shows magnets are accurate enough for the assembly to take place at its final location. No training is required. Test procedures (measurements with search coils or with the beam) and cooldown properties are discussed.

In large accelerators and low beta colliding beam storage rings, the strong sextupoles, which are required to correct the chromatic effects, produce strong nonlinear forces which act on particles in the beam. In addition in large hadron storage rings the superconducting magnets have significant nonlinear fields. To understand the effects of these nonlinearities on the particle motion there is currently a large theoretical effort using both analytic techniques and computer tracking. This effort is focused on the determination of the 'dynamic aperture' (the stable acceptance) of both present and future accelerators and storage rings. A great deal of progress has been made in understanding nonlinear particle motion, but very little experimental verification of the theoretical results is available. In this paper we describe 'dynamic tracking', a method being studied at the SPEAR storage ring, which can be used to obtain experimental results which are in a convenient form to be compared with the theoretical predictions.

The dynamic aperture and its determination emerged from the SSC reference design study as the single most important accelerator physics issue pertinent to the SSC. Beside the fundamental need of a finite dynamic aperture for any accelerator, it was considered to be a useful criterion for the magnet selection. An aperture workshop organized in November 1984 at LBL served the purpose to identify the various aspects of the aperture question and to organize the aperture task force accordingly. It was recognized that numerical models had to play an important role and the qualifications of several tracking codes were investigated. None of the existing codes could meet all of the criteria for an ideal tracking code and substantial program development became unavoidable. It was therefore decided to begin tracking SSC test lattices, which were provided by the aperture task force's lattice group and are described in an other paper to this conference, with existing tracking programs. 6 refs., 5 figs., 2 tabs.

This paper outlines the status of a 6‐GeV synchrotron radiation designed at RIKEN. This facility consists of a main storage ring, a booster synchrotron, a 1.5‐GeV preinjector linac, positron injection linacs, and others. The electronan GeV. The storage ring has a circumference of 1069.2 m and 7‐m‐long straight sections for insertion devices. The lattice of the main ring is a Chasman–Green‐type one and has 36 periodicity. The low emittance (ex=8.2 nm rad) and large dynamic aperture are expected even with field errors and misalignments of magnetic elements. Three years of a preconstruction research and development period and 5 years of construction period are scheduled.This paper outlines the status of a 6‐GeV synchrotron radiation designed at RIKEN. This facility consists of a main storage ring, a booster synchrotron, a 1.5‐GeV preinjector linac, positron injection linacs, and others. The electronan GeV. The storage ring has a circumference of 1069.2 m and 7‐m‐long straight sections for insertion devices. The lattice of the main ring is a Chasman–Green‐type one and has 36 periodicity. The low emittance (ex=8.2 nm rad) and large dynamic aperture are expected even with field errors and misalignments of magnetic elements. Three years of a preconstruction research and development period and 5 years of construction period are scheduled.

Tracking studies including the effects of random multipoles resulting from construction errors have been made for RHIC with two independent tracking programs at three different tunes. The studies were made using ten different sets of random errors for each of the programs. The aperture was defined as the worst case, and the results of the two programs are in good agreement. A second set of studies was made for which the number of dipoles was doubled to determine whether doubling the number of independent random errors results in a reduction of the effects or random multipoles. The results for the two cases, one dipole per half cell and two dipoles per half cell, indicate there is little difference in dynamic aperture.

The quality of synchrotron radiation beams from SPEAR, in particular the brilliance of undulator radiation, can be improved significantly by reducing the emittance of the stored electron beam. A reduction of the horizontal emittance by a factor of 3.5 to a value of 130 nanometer-radians (nm-r) at 3 GeV has been achieved by using stronger focussing, mainly in the horizontal plane. The low emittance configuration also reduces the dispersion and vertical beta functions in the straight sections, making them more suitable for wigglers. The higher betatron tunes lead to a larger phase advance between the two kickers, which has to be corrected during injection by shunting current from some quadrupoles. The configuration was optimized within SPEAR hardware limitations and tested for dynamic aperture with the tracking program PATRICIA. After implementation of this scheme, beam was successfully injected and accumulated. The measured emittance of the stored beam was in agreement with calculations. Presently the configuration is being made operational.

The PATRICIA particle tracking program has been used to study chromatic effects in the Brookhaven CBA (Colliding Beam Accelerator). The short term behavior of particles in the CBA has been followed for particle histories of 300 turns. Contributions from magnet multipoles characteristic of superconducting magnets and closed orbit errors have been included in determining the dynamic aperture of the CBA for on and off momentum particles. The width of the third integer stopband produced by the temperature dependence of magnetization induced sextupoles in the CBA cable dipoles is evaluated for helium distribution systems having periodicity of one and six. The stopband width at a tune of 68/3 is naturally zero for the system having a periodicity of six and is ~10-4 for the system having a periodicity of one. Results from theory are compared with results obtained with PATRICIA; the results agree within a factor of slightly more than two.

For an accelerator lattice containing non-linear elements, particle amplitudes outside a "dynamic aperture" are unstable. In this paper an analytic procedure for estimating this aperture not depending on resonance assumptions is described. The amplitude x(N) after N iterations is expanded in powers of the initial amplitude x0. Low order coefficients are obtained using the symbolic algebraic manipulation program REDUCE. For intermediate values of N (e.g., 100) these terms give an asymptotic description which, by particle tracking, is shown to be valid. This leads to an estimate of the dynamic aperture and to its possible enlargement.

A comparison between the predicted stability region and the results of tracking for the 7-GeV Advanced Photon Source CDR lattice is given. The tracking results are obtained by searching for the limit of stability in N{sub y} for a fixed value for N{sub x}. (Negative N{sub x} is understood to mean cos {phi}{sub xo} = {minus}1.) The limits of the stable region for this lattice are caused by the chromaticity correcting sextupoles and the predominance of the integral resonance for v{sub x} = 0.88 per period.

A damping ring with very high horizontal tune is analyzed. The dynamic aperture is determined using the tracking program TEAPOT and is found to be marginally satisfactory, depending on the required beam emittance reduction factor. Synchrobetatron resonances due to the centrifugal space charge force are analyzed and found to be not serious at the beam current levels suggested in a damping ring design of Palmer. Much of the paper is devoted to re‐calculating the properties of such a ring with the results largely corroborating Palmer’s, except that an appreciably greater beam emittance is found.

This note is intended to describe our current thinking and to show interconnections of various subtasks. The discussed topics are: (1) Storage Ring Group - A. Refinement of lattices to include: photons from bending magnets, dynamic aperture studies, refinement of accelerator physics straight section, B. Non-standard lattice, C. Touschek lifetime, D. Gas scattering lifetime, E. BBI (bunched beam instabilities), F. Magnet error considerations, G. tracking of particles, H. Orthogonal adjustments of beam positions and angles, (2) Injector Group, (3) Linac Group, (4) RF Group, (5) Alignment and stability, (6) Technical Components, (7) Vacuum, (8) Diagnostics, and (9) Control System.

On-going beam dynamics studies at LBL are performed in connection with the 1-2 GeV Advanced Light Source (ALS), the SSC, Collider Physics (Novel Power Sources) and Heavy Ion Fusion Accelerator Research (HIFAR). Exploratory activities include generic research on (a) high-brightness, low-emittance storage rings and linacs for the TeV-scale future linear colliders, b{bar b} facilities, etc., (b) beam dynamics and optics of incoherent and coherent undulator radiation, (c) Free Electron Laser Studies, (d) development of a high-brightness laser-driven RF photocathode electron source for the LBL-LLNL-SLAC collaboration on Relativistic Klystrons and (e) new methods of acceleration. The major physics issues being studied in connection with the ALS are the effects of undulators and wigglers on storage ring beam dynamics (nonlinear stability and stable dynamic aperture), short bunch-length collective phenomena and multi-loop high-fidelity orbit and photon beam feedback for stability of the radiation source. In connection with the first issue, detailed nonlinear behavior of the electron beam in presence of insertion devices in an otherwise symmetric low-emittance lattice are being pursued and various compensation schemes are being investigated. We held a workshop on this specialized topic May 17-20, 1988 at LBL, where participants from international laboratories such as Sincrotrone Trieste, KEK, SLAC, BNL,more » ANL, etc., participated. Contributions will soon be published as proceedings to this workshop. Considerable insight into the physics of short bunches has been gained through a similar workshop last year on the 'Impedance Beyond Cutoff' at LBL, where a realistic picture of the impedance spectrum at high frequencies corresponding to short bunch lengths emerged. The focus at the moment is on the nature of coherent instabilities potentially driven by this high-frequency impedance. Securing a stable photon beam against vibrations and other noise sources simultaneously at several beam lines in a synchrotron radiation source is nontrivial and requires multi-loop orbit feedback system with accompanying cross-talk. A possible control algorithm is under investigation. In other matters, experimental study of dynamic effects with undulators is being planned at BESSY and other laboratories; impedance measurement test facility; instrumentation and feedback, advanced accelerator control systems and optics of synchrotron radiation are being pursued actively. Possibilities of infra-red and XUV FEL's as upgrades to the ALS are also being considered. Collaboration with LLNL and SLAC for the Relativistic Klystron is an ongoing activity. This promising power-source is being actively investigated both theoretically and experimentally with a goal towards a 1 GeV test experiment in late 1989. In this connection, studies of a conceptual design of a bright injector for the test experiment has been undertaken at Berkeley. The Conceptual Design Report will be completed in October, 1988. The design utilizes a high-brightness laser-driven RF photocathode electron gun, similar to the LANL early experiments, together with achromatic magnetic bunching and transport systems and diagnostics. The design is performed with attention to possible use in an FEL as well. Heteroenergetic collision optics for a possible b{bar b} facility based on 12 GeV PEP and a 2 GeV high-brightness ring has been obtained. The possible implications of collective effects is under study presently.« less

It is the author’s hope that this document will help provide the novice with both an understanding of what dynamic aperture is and some insight as to why it is limited. In addition, we hope that this paper will provide information as to the analytical and numerical methods available for the study of dynamic aperture. Finally, we wish to present some interpretations and applications of these concepts and tools by means of examples. Those factors having an impact on the dynamic aperture of circular machines and storage rings will be discussed; applications to two types of machine of current popular interest (namely, large hadron colliders and synchrotron radiation electron storage rings) will be made in order to illustrate the ideas that are presented.

A set of eight test lattices for the SSC have been devised for such purposes as the investigation of the dependences of chromatic properties and dynamic aperture on the type, field, physical aperture and errors of the magnets, on the sextupole correction scheme, on the tunes and on the cell phase advances. They are distinguished from realistic lattices in that certain features of the latter are missing - most notably the crossing magnets that bring the two counter-rotating proton beams into collision at the interaction points, and the utility insertions, which are the sites for the injection, beam abort, and radiofrequency systems. Furthermore the placement of magnets in the cells is simplified. 7 refs., 9 figs., 2 tabs.

Experience gained with existing e+e- storage rings and the accumulation of understanding derived from theory and simulation allow more accurate prediction of the performance of future machines like LEP. We describe the relation of luminosity to other quantities of interest to the machine users, such as energy spread, beam sizes or polarization. For example, the maximum event rate on a narrow resonance may not correspond to the condition of maximum luminosity. Partial control of beam parameters is available through damping partition number variation, coupling adjustment, wigglers, etc. but a proper estimation of the necessary operating conditions must include a self-consistent, realistic treatment of the beam-beam effects which also determine performance. The established correlation between theory and simulation of the beam-beam effect in several regimes has been exploited in the search for good working points. Single particle stability (dynamic aperture) has been improved at the same time.

Eight three-block dipole wigglers will be used in LEP to maximize luminosity and control other beam parameters such as emittance, damping rates at injection, energy spread and polarization. The excitation law for constant emittance (chosen, for example, to fill the dynamic aperture) and damping partition numbers is given. In contrast to conventional wigglers where orbit perturbation is avoided by means of a series of equal fields of alternate polarity, the LEP wigglers will use unequal fields and pole lengths. This allows one to retain a high potential asymptotic polarisation level together with an increased polarisation rate. The choice of the degree of field asymmetry is imposed by limitations on the transverse dimensions of the magnets and field levels, by polarisation requirements and by cost. A practical design of the proposed wiggler is presented.

Electron storage rings are the most effective sources of synchrotron radiation. The required extremely low beam emittance makes a very careful design of the beam optics necessary including the chromatic corrections. This adds nonlinear magnetic fields reducing the dynamic aperture for the beam. An example of low emittance optics is the modified Chasman-Green lattice of the ESRF. Synchrotron radiation with extremely high brilliance is produced by undulators and wigglers. These devices require special straight insertions.

This note will address a proposed method for specifying the multipole tolerance for the design and production of APS quadrupole magnets. The tolerances for the multipole components for the quadrupole magnets will be set to that level which reduces the dynamic aperture by about 10--15% from the ideal machine dynamic aperture (as specified in CDR-87). This level may appear rather stringent, especially compared to the 50--60% reduction resulting from quad placement errors. However, when all tolerances are taken together, the residual dynamic aperture would be prohibitively small and commissioning would be difficult if these tolerances were at twice this level. The dynamic aperture was determined using the numerical tracking program RACETRACK.

A design of a 90° bending magnet for a synchrotron radiation source with a characteristic wavelength of 0.2 nm is presented which involves a multilayer coil with circular cross-section optionally surrounded by a C-shaped cold iron shielding, and a cold bore. The usefulness of this design is checked by dynamic aperture calculations including nonlinear effects through 3rd order for the lattice of the proposed synchrotron radiation source at Karlsruhe.

The N30 lattice discussed in a previous note showed that a nearly matched lattice could be produced by separating four of the present quadrupole from their present power supplies and powering them separately. Although having significantly higher dynamic aperture, less closed orbit distortion and improved natural emittance compared to the present Aladdin lattice, the proximity of the {nu}{sub x} = 5.24 tune was felt to be too close to the 3{nu}{sub x} = 16 (a structure resonance) and the tune should be raised. In order to demonstrate the tunability of this modified lattice, Yang Cho found a new tune ({nu}{sub x} = 6.27, {nu}{sub y} = 6.23), hereafter called L2V2 lattice. This lattice, although not as nicely matched as the N30 lattice, has a 10% lower natural emittance and considerably more dynamic aperture. The L2V2 lattice has not been fully optimized, but is sufficient to demonstrate the advantages of this modified Aladdin lattice.

One of the uncomfortable features of the Chasman-Green lattice is that the chromaticity-correcting sextupoles are all very strong compared with those in the FODO-type lattice. Because of their strengths, when their arrangement creates certain harmonic components, the dynamic aperture is severely reduced and on is forced to add more sextupoles to eliminate harmful harmonic components.During the course of design studies, S. Kramer has made many computer runs to investigate tune shifts resulting from horizontal orbit deviations in sextupoles. An interesting observation is that the average tune shift is definitely related to the dependence of tunes on the betatron oscillation amplitudes (or, equivalently, the transverse emittances). This note is an ``attempt`` to explain the connection at least qualitatively. It is no more than an attempt since the explanation is not yet quantitative and it may even be somewhat inconsistent.

A key issue for improving the performance of third generation light sources like the ESRF storage ring is the identification and correction of resonances that have a detrimental effect in the machine performance. Frequency analysis of experimental data, recorded on BPMs around the ring, is a powerful tool for studying the non-linear dynamics of an accelerator in operation. In a series of experiments, experimental frequency maps were produced using the 1000-turns measurement system. These maps revealed the resonance structure in the vicinity of the nominal working point which was limiting the dynamic aperture. Their comparison with maps produced by simulations was used as a guide for understanding the storage ring non-linear model. The possibility of using the quasi-periodic approximations of the experimental data for testing the efficiency of resonance correction schemes was finally investigated

We present PyZgoubi, a framework that has been developed based on the tracking engine Zgoubi to model, optimise and visualise the dynamics in particle accelerators, especially fixed-field alternating-gradient (FFAG) accelerators. We show that PyZgoubi abstracts Zgoubi by wrapping it in an easy-to-use Python framework in order to allow simple construction, parameterisation, visualisation and optimisation of FFAG accelerator lattices. Its object oriented design gives it the flexibility and extensibility required for current novel FFAG design. We apply PyZgoubi to two example FFAGs; this includes determining the dynamic aperture of the PAMELA medical FFAG in the presence of magnet misalignments, and illustrating how PyZgoubi may be used to optimise FFAGs. We also discuss a robust definition of dynamic aperture in an FFAG and show its implementation in PyZgoubi.

Single particle dynamics in the storage ring can be significantly influenced by strong nonlinearities from long and strong-field insertion devices. This paper reports our preliminary results on the dynamics impact of the 24 m long OK5 FEL in the Duke ring. Initial studies are performed using an intermediate lattice with two OK5 wigglers. The dynamic aperture is computed using a recently developed symplectic wiggler integrator and the frequency map technique, NAFF We have observed significant dynamic aperture reduction due to OK5 wigglers at lower beam energies. We also report our preliminary findings on the means to improve beam dynamics with wigglers.

The 1 GeV Duke FEL storage ring is dedicated to drive UV and VUV free electron laser devices. The high brightness and low emittance electron beams needed for these devices demand high performance and tight tolerances on the storage ring magnet lattice. Tight tolerances include close spacing of magnetic elements. We show how combined function magnets are used to eliminate discrete elements and odd shaped end pieces which cause magnetic coupling, saturation and severe undesirable field nonlinearities. Using this scheme we are able to achieve desirable ring dynamic aperture with only minor modification of existing hardware. Also included is a discussion of a non-standard septum magnet with stray field compensation which will be employed by this storage ring. The design, testing procedures, and preliminary results are outlined for this magnet. >

After the installation of 32 additional RF cavities in the 1997-1998 shutdown LEP was operated at a beam energy of 94.5 GeV. The total integrated luminosity for the year 1998 clearly surpassed its target and reached 198 pb/sup -1/. Vertical beam-beam tuneshifts of more than 0.07 were obtained. The performance did not seem to be beam-beam limited, but the total beam current was limited by power dissipation problems to around 6 mA. A high phase advance optics (102/spl deg/, 90/spl deg/), with a smaller natural emittance, was used for regular operation in 1998. This contributed to the excellent performance of LEP, together with the further reduction of both the horizontal and vertical beta function at the interaction points. No dynamic aperture problems were encountered.

A beam optics scheme has been designed [ 1 ] for the Future Circular Collider- e + e − (FCC-ee). The main characteristics of the design are: beam energy 45 to 175 GeV, 100 km circumference with two interaction points (IPs) per ring, horizontal crossing angle of 30 mrad at the IP and the crab-waist scheme [ 2 ] with local chromaticity correction. The crab-waist scheme is implemented within the local chromaticity correction system without additional sextupoles, by reducing the strength of one of the two sextupoles for vertical chromatic correction at each side of the IP. So- called “tapering" of the magnets is applied, which scales all fields of the magnets according to the local beam energy to compensate for the effect of synchrotron radiation (SR) loss along the ring. An asymmetric layout near the interaction region reduces the critical energy of SR photons on the incoming side of the IP to values below 100 keV, while matching the geometry to the beam line of the FCC proton collider (FCC-hh) [ 3 ] as closely as possible. Sufficient transverse/longitudinal dy- namic aperture (DA) has been obtained, including major dynamical effects, to assure an adequate beam lifetime in the presence of beamstrahlung and top-up injection. In particular, a momentum acceptance larger than ± 2% has been obtained, which is better than the momentum acceptance of typical collider rings by about a factor of 2. The effects of the detector solenoids including their compensation elements are taken into account as well as synchrotron radiation in all magnets. The optics presented in this paper is a step toward a full conceptual design for the collider. A number of issues have been identified for further study.

By introduction of an optical gating beam on a semiconductor wafer, near-field terahertz (THz) imaging with a dynamic aperture has been realized. The spatial resolution is determined by the focus size of the optical gating bean and the near-field diffraction effect. THz imaging with subwavelength spatial resolution (better than 50 µm) is demonstrated.

A high-energy (0.5-3.0 TeV centre of mass) electron-positron Compact Linear Collider (CLIC) is being studied at CERN as a new physics facility. The design study has been optimized for 3 TeV centre-of-mass energy. Intense bunches injected into the main linac must have unprecedentedly small emittances to achieve the design luminosity 1035cm-2s-1 required for the physics experiments. The positron and electron bunch trains will be provided by the CLIC injection complex. This thesis describes an optics design and performance of a positron damping ring developed for producing such ultra-low emittance beam. The linear optics of the CLIC damping ring is optimized by taking into account the combined action of radiation damping, quantum excitation and intrabeam scattering. The required beam emittance is obtained by using a TME (Theoretical Minimum Emittance) lattice with compact arcs and short period wiggler magnets located in dispersion-free regions. The damping ring beam energy is chosen as 2.42 GeV. The lattice features small values of the optical functions, a large number of compact TME cells, and a large number of wiggler magnets. Strong sextupole magnets are needed for the chromatic correction which introduces significant nonlinearities, decreasing the dynamic aperture. The nonlinear optimization of the lattice is described. An appropriate scheme of chromaticity correction is determined that gives reasonable dynamic aperture and zero chromaticity. The nonlinearities induced by the short period wiggler magnets and their influence on the beam dynamics are also studied. In addition, approaches for absorption of synchrotron radiation power produced by the wigglers are discussed. Realistic misalignments of magnets and monitors increase the equilibrium emittance. The sensitivity of the CLIC damping ring to various kinds of alignment errors is studied. Without any correction, fairly small vertical misalignments of the quadrupoles and, in particular, the sextupoles, introduce unacceptable distortions of the closed orbit as well as intolerable spurious vertical dispersion and coupling due to the strong focusing optics of the damping ring. A sophisticated beam-based correction scheme has been developed in order to bring the design target emittances and the dynamic aperture back to the ideal value. The correction using dipolar correctors and several skew quadrupole correctors allows a minimization of the closed-orbit distortion, the cross-talk between vertical and horizontal closed orbits, the residual vertical dispersion and the betatron tune coupling. The small emittance, short bunch length, and high current in the CLIC damping ring could give rise to collective effects which degrade the quality of the extracted beam. A number of possible instabilities and an estimate of their impact on the ring performance are briefly surveyed. The effects considered include fast beam-ion instability, coherent synchrotron radiation, Touschek scattering, intrabeam scattering, resistive-wall wake fields, and electron cloud.

Wiggler insertions are expected to occupy a significant portion of the lattice of the Next Linear Collider (NLC) Main Damping Rings (MDR) and have a noticeable impact on the single-particle beam dynamics. Starting from a realistic 3D representation of the magnetic fields we calculate the transfer maps for the wigglers, accounting for linear and nonlinear effects, and we study the beam dynamics with particular attention paid to the Dynamic Aperture(DA). A DA reduction is observed but appears to remain within acceptable limits.

Nonlinear beam dynamics studies of the 2.5 GeV dedicated SR source SIBERIA-2 are described. The effect of chromatic sextupoles and measured multipole field errors are taken into account. The influence of high order resonances is considered. The technique for finding the alternative operation point with an extended nonlinear stable region is described. >

In 1997 LEP will enter its third phase and will be operated at energies well above 90 GeV. In order to reach the required luminosities at these higher energies, i.e., to reach the maximum beam-beam tune-shift parameter, an optics with a small horizontal emittance is desirable. Such a lattice must have a dynamic aperture sufficient to guarantee the beam life time. Several lattices with different phase advances per cell have been developed for this purpose and the reasons for these particular choices are explained. The relative merits of these different solutions as well as the experience gained both in dedicated experiments and in using these lattices in regular operation during 1996 are discussed.

Detailed studies of the SNS ring lattice optics have been conducted. The horizontal and vertical tuning ranges for matched solutions with well-behaved lattice functions were determined and the power supply margin verified. Using stability criteria, potential working points have been identified and studied in detail. Studies, focused on behavior of the lattice functions under increasingly complex assumptions, included chromatic effects and sextupoles, and lattice perturbations due to the injection chicane and to dynamic bumps for painting. Results are being used in determining injection painting schemes, in dynamic aperture studies, and in validating collimator settings.

The general layout of ISI-800, a low emittance third generation machine consisting of a linac injector (120 MeV), a storage ring with 4-period TEA lattice, and intended for research and industrial applications, is presented together with a discussion of most important design considerations. Design features of magnet, vacuum, injection RF systems are described. Three straight sections are available for wigglers and undulators, and up to 24 photon beam lines may ultimately emanate from dipole magnets, The emittance is 27 nm. The dynamic aperture is sufficiently large for the injection and the stable storage of the beam.

A technique for assessing the dynamic aperture performance of high speed analogue-digital convertors is proposed which treats the test unit as a black box. Details of data processing and analysis are included which give a performance measure in terms of effective convertor resolution.

A beamformer for evaluation of dynamic aperture control to maximize lateral resolution of an ultrasonic phased array is under development at The Applied Research Laboratory of The Pennsylvania State University. For echocardiographic applications, the beamformer offers the advantages of fast scanning with good lateral resolution at all ranges. Techniques for improving lateral resolution at unlimited depth of field over that obtainable by a fixed focus system include the farfield variable aperture and previously reported dynamic focusing approaches. The relative performance limits and the effects of these techniques on beam‐former complexity are compared. An electronic beamformer configuration for implementing the less complex variable aperture approach is described. The ultrasonic array and packaging concepts are presented along with acoustic performance data relating to the individual array elements. Measurements of damping and cross coupling and analyses of predicted performance have been made and are in...