The high brightness electron beam required by a short wavelength self-amplified spontaneous emission free-electron laser (FEL) may be reached only with an accurate design of the beam dynamics from the generation in the rf injector up to the undulator. The beam dynamics is affected by strong self-consistent effects at injection, in the compression stage, and during the FEL process. The support of numerical simulations is extensively used in the predictions of the beam behavior in these nonlinear dynamical conditions. I present a review of available simulation techniques, currently exploited in the design of short wavelength free-electron lasers.

Theoretical and experimental work has been carried out to study the longitudinal space-charge effects in a retarding field energy analyzer. A one-dimensional, steady state model for both a monoenergetic beam and a thermal beam has been developed for this purpose. Potential improvements of using two-dimensional and time-dependent solutions are also briefly discussed. The study shows that, if the current density inside the device is higher than a critical value, the longitudinal space-charge effect and the formation of a potential minimum similar to the virtual cathode formation in an electron gun will distort the measured energy spectrum. The measured FWHM and the rms energy spread will be affected. The measured mean energy will also be shifted toward the low-energy side. By using a two-dimensional correction, the theoretical model also qualitatively explains the appearance of a visible tail at the high-energy side of the spectrum, as observed in experiments. According to the theory, to avoid this measurement distortion due to the longitudinal space charge, care has to be taken to limit the current density inside the device.

Frequency map analysis [J. Laskar, Icarus 88, 266 (1990)] is used here to analyze the transverse dynamics of four third generation synchrotron light sources: the ALS, the ESRF, the SOLEIL project, and Super-ACO. Time variations of the betatron tunes give additional information for the global dynamics of the beam. The main resonances are revealed; a one-to-one correspondence between the configuration space and the frequency space can be performed. We stress that the frequency maps, and therefore the dynamics optimization, are highly sensitive to sextupolar strengths and vary in a large amount from one machine to another. The frequency maps can thus be used to characterize the different machines.

A study of round-to-flat configurations, and vice versa, of angular-momentum-dominated beams is presented. The beam propagation in an axial magnetic field is described in terms of the familiar Courant-Snyder formalism by using a rotating coordinate system. The discussion of the beam transformation is based on the general properties of a cylindrically symmetric beam matrix and the existence of two invariants for a symplectic transformation in 4D phase space.

Coherent synchrotron radiation (CSR) can play an important role by not only increasing the energy spread and emittance of a beam, but also leading to a potential instability. Previous studies of the CSR induced longitudinal instability were carried out for the CSR impedance due to dipole magnets. However, many storage rings include long wigglers where a large fraction of the synchrotron radiation is emitted. This includes high-luminosity factories such as DAPHNE, PEP-II, KEK-B, and CESR-C as well as the damping rings of future linear colliders. In this paper, the instability due to the CSR impedance from a wiggler is studied assuming a large wiggler parameter $K$. The primary consideration is a low-frequency microwavelike instability, which arises near the pipe cutoff frequency. Detailed results are presented on the growth rate and threshold for the damping rings of several linear collider designs. The different scaling between the wiggler CSR impedance and the dipole CSR impedance suggests an optimization for the damping ring design.

At the interaction point of a storage ring collider each beam is subject to perturbations due to the electromagnetic field of the counterrotating beam. For flat beams, a well-known approximation models the beam by a current sheet which is uniform in the horizontal plane, restricting the particle motion to the vertical direction. In this classical model a water-bag beam distribution has been used to find working points and beam-beam tune shift parameters which lead to a stable beam distribution. We investigate the stability of a more realistic Gaussian equilibrium distribution. A linearized Vlasov equation written in action-angle variables is used to compute the radial and angular modes of a perturbation in two-dimensional phase space to first order in the displacement from the design trajectory. We find that the radial modes, which are often neglected, can have a stabilizing effect on the beam motion.

Phase advance and $\beta$ function are basic lattice functions characterizing the linear properties of an accelerator lattice. Accurate and efficient measurements of these quantities are important for commissioning and operating a machine. For rings with little coupling, we report a new method to measure these lattice functions based on the model-independent analysis technique, which uses beam histories of excited betatron oscillations measured simultaneously at a large number of beam position monitors. It is simple, fast, accurate, and robust. Measurements done at the storage ring of the Advanced Photon Source are reported. Comparisons among various methods are made.

Bunch shortening causes an electron-cooled beam to be space charge dominated at low energies. Instability during the bunch shortening has been studied using a particle-tracking program where the 3D space-charge field due to the beam is calculated with a simplifying model.

A novel rf shield structure for bellows chambers or gate valves in high-current accelerators is proposed. The rf shield has no thin fingers, but nested comb teeth instead at the inner surface of the beam duct. The comb-type rf shield has a higher thermal strength structurally than the conventional finger-type one. A simulation also indicates its lower impedance. Especially, the leak of a TE modelike higher order mode through the axial slits, which causes mainly heating of these components, is almost suppressed due to thick teeth. An abrasion test in a vacuum using a test piece of the comb-type rf shield shows less dust generation compared to the finger type. Another preliminary test transmitting 508 MHz microwaves through a prototype rf shield in the atmosphere found no abnormal heating or arcing. A trial model of bellows chambers with the comb-type rf shield will be installed and tested using a real beam in the KEK $B$-factory positron ring this year.

The booster ionization profile monitor (IPM) obtains transverse beam profiles by measuring the distribution of ions resulting from interaction of the proton beam with background gas in the beam chamber. The challenge of the IPM operation is that the measured ion distribution is not an exact representation of the beam distribution, since the ion trajectories are influenced by the electromagnetic field of the beam. We have developed a new model for the dependence of the IPM measurement on the beam parameters, assuming a Gaussian beam distribution. Our model of the ion dynamics in the detector was constrained by making independent measurements of the horizontal beamwidth at injection and extraction and comparing these to data taken from the IPM at the same time. Our calibration results in the formula ${\sigma }_{\mathrm{measured}}={\sigma }_{\mathrm{real}}+C_{1}N{\sigma }_{\mathrm{real}}^{p_1}$, where $N$ is the number of protons in the machine, in units of ${10}^{12}$, $C_1=(1.13\pm 0.06)\times {10}^{-5}$, in units of $(\mathrm{meters}{)}^{1-p_1}/{10}^{12}$, and $p_1=-0.615\pm 0.013$; the subscript “measured” indicates the raw IPM measurement, the subscript “real” the true beamwidth. This result is the first detailed calibration of the response of the booster IPM based on experimental data.

The linearized Vlasov-Maxwell equations are used to investigate detailed properties of the wall-impedance-driven instability for a long charge bunch ($\mathrm{\text{bunch}}\mathrm{\text{length}}{\ell }_b\gg \mathrm{\text{bunch}}\mathrm{\text{radius}}{r}_b$) propagating through a cylindrical pipe with radius $r_w$ and wall impedance $\tilde{Z}(\omega )$. The stability analysis is carried out for perturbations about a cylindrical Kapchinskij-Vladimirskij beam equilibrium with a flattop density profile in the smooth-focusing approximation. The perturbations are assumed to be of the form $\delta \psi (\mathbf{x},t)=\delta {\psi }^{\ell }(r)\exp (i\ell \theta +i{k}_{z}z-i\omega t)$, where $(r,\theta )$ are the radial and azimuthal coordinates in the transverse direction, and $z$ is the coordinate in the longitudinal direction. Here, $\ell =1,2,\dots$ is the azimuthal mode number of the perturbation in the transverse direction, $k_z$ is the wave number in the longitudinal direction, and $\omega$ is the oscillation frequency. As an example, detailed stability properties are determined for dipole-mode perturbations $(\ell =1)$ assuming negligibly small axial momentum spread of the beam particles. The stability analysis is valid for a general value of the normalized beam intensity $s_b={\widehat{\omega }}_{pb}^2/2{\gamma }_b^2{\omega }_{\beta \perp }^2$ in the interval $0<s_b<1$, where ${\widehat{\omega }}_{pb}=(4\pi {\widehat{n}}_b{e}_b^2/{\gamma }_b{m}_b{)}^{1/2}$ is the relativistic plasma frequency and ${\omega }_{\beta \perp }$ is the applied focusing frequency.

We study a nonlinear integral equation that is a necessary condition on the equilibrium phase-space distribution function of stored, colliding electron beams. It is analogous to the Haïssinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. The equation is analyzed for the case of the Chao-Ruth model of the beam-beam interaction in 1 degree of freedom, a so-called strong-strong model with nonlinear beam-beam force. We prove the existence of a unique solution, for sufficiently small beam current, by an application of the implicit function theorem. We have not yet proved that this solution is positive, as would be required to establish existence of an equilibrium. There is, however, numerical evidence of a positive solution. We expect that our analysis can be extended to more realistic models.

Photonic crystals provide a method of confining a synchronous speed-of-light mode in an all-dielectric structure, likely a necessary feature in any optical accelerator. We explore computationally a class of photonic crystal structures with translational symmetry in a direction transverse to the electron beam. We demonstrate synchronous waveguide modes and discuss relevant parameters of such modes. We then explore how accelerator parameters vary as the geometry of the structure is changed and consider trade-offs inherent in the design of an accelerator of this type.

Finding self-consistent distributions of beam particles interacting with each other via the space charge force is one of the challenges of accelerator physics. Exactly solvable models are used for simulation benchmarks, instability threshold calculations, etc. Since such distributions have been found only in one and two dimensions (Kapchinsky-Vladimirsky distribution), it is not possible to apply them to a general three dimensional motion. This paper shows how to construct new sets of self-consistent distributions, extending even to the three dimensional case.

Resonance-driven collective instabilities of charged-particle beams were extensively studied in connection with high-current transport systems, leading to restrictions imposed on the zero-current phase advance. In this paper, we discuss application of such parametric instabilities to circular machines. This effect is directly related to the space-charge limit in rings and its understanding is of crucial importance. Its relation to the coherent resonance condition of an integer type is explained. Practical application of such resonant responses to both structural and imperfection driven harmonics is addressed.

We present the measurement results of electron beam emittance in the Accelerator Test Facility damping ring operated in multibunch modes. The measurements were carried out with an upgraded laser wire beam profile monitor. The monitor has now a vertical wire as well as a horizontal one and is able to make much faster measurements thanks to an increased effective laser power inside the cavity. The measured emittance shows no large bunch-to-bunch dependence in either the horizontal or vertical directions. The values of the vertical emittance are similar to those obtained in the single-bunch operation. The present results are an important step toward the realization of a high-energy linear collider.

The characteristics of the electron-photon showers initiated by 2 to 10 GeV electrons aligned along the $⟨111⟩$ axis of tungsten crystals are compared with those for the amorphous tungsten. In this energy range, as known, the positron yield at the optimal target thicknesses is larger in a crystal case only by several percent. However, the amount of the energy deposition in a crystal turns out to be considerably (by 20%–50%) lower than in an amorphous target providing the same positron yield, while the peak energy-deposition density is approximately of the same magnitude in both cases.

For damping rings of future linear colliders, extremely low vertical emittance will be required. In an electron circular accelerator, the dominant sources of the vertical emittance are the vertical dispersion in arc sections and the $x\mathrm{\text{−}}y$ orbit coupling, caused by various errors. A systematic method to correct the vertical dispersion and the orbit coupling based on beam position measurement has been developed. In this paper, simulation studies assuming realistic misalignments, performances of monitors, and correctors of the Accelerator Test Facility damping ring at KEK are presented.

Linear collider designs foresee some bends of about 5–10 mrad. The spin precession angle of 1 TeV electrons on a 10 mrad bend is 23.2 rad and it changes proportional to the energy. Measurement of the spin direction using Compton scattering of laser light on electrons before and after the bend allows determining the beam energy with an accuracy of about ${10}^{-5}$. In this paper the principle of the method, the procedure of the measurement, and possible errors are discussed. Some remarks about the importance of plasma focusing effects in the method of beam energy measurement using Moller scattering are given.