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.

In the proximity of a nonlinear resonance $\nu \approx \frac{m}{n}$, the beam distribution in a storage ring is distorted depending on how close is the resonance and how strong is the resonance strength. In the 1-dimensional case, it is well known that the particle motion near the resonance can be described in a smooth approximation by a Hamiltonian of the form $(\nu -\frac{m}{n})J+D_{\nu }(J)+f_1(\phi ,J)$, where $(\phi ,J)$ are the phase space angle and action variables, $D_{\nu }$ is the detuning function, and $f_1$ is an oscillating resonance term. In a proton storage ring, the equilibrium beam distribution is readily solved to be any function exclusively of the Hamiltonian. For an electron beam, this is not true and the equilibrium distribution is more complicated. This paper solves the Fokker-Planck equation near a single resonance for an electron beam in a storage ring. The result is then applied to obtain the quantum lifetime of an electron beam in the presence of this resonance. Resonances due to multipole fields and due to the beam-beam force are considered as examples.

Transverse beam combining is a cost-saving option employed in many designs for heavy ion fusion drivers. However, the resultant transverse phase space dilution must be minimized so as not to sacrifice focusability at the target. A prototype combining experiment has been completed employing four 3-mA ${\mathrm{Cs}}^{+}$ beams injected at 160 keV. The focusing elements upstream of the merge consist of four quadrupoles and a final combined-function element (quadrupole and dipole). Following the merge, the resultant single beam is transported in a single alternating gradient channel where the subsequent evolution of the distribution function is diagnosed. The results are in fair agreement with particle-in-cell simulations. They indicate that for some heavy ion fusion driver designs, the phase space dilution from merging is acceptable.

Based on the requirements from a conceptual design of a polarized positron beam for future linear colliders, we constructed a special collision system with a short focal length of 150 mm of the laser beams so as to produce $\gamma$ rays through inverse Compton scattering. In order to achieve efficient laser-electron collisions, we created a special optics to produce very small $e^{-}$-beam sizes of ${\sigma }_{e_{x0}}=7.6\mu \mathrm{m}$ and ${\sigma }_{e_{y0}}=5.4\mu \mathrm{m}$ in the horizontal and vertical directions at the collision point. Using laser light with a wavelength of 532 nm and an $e^{-}$ beam of 1.28 GeV, provided from the ATF-damping ring at KEK, we generated $2\times {10}^5$ $\gamma$ rays with a time duration of 26 ps in rms, leading to a peak brightness of $1.7\times {10}^{18}/({\mathrm{mrad}}^2{\mathrm{mm}}^{2}0.1\%\mathrm{bandwidth}\mathrm{s}$) near to the maximum energy of 56 MeV.

We explore the rf characteristics of pipe cooled superconducting cavities versus bath cooled ones, using different pipe configurations and different liquid helium temperatures. Pipe cooled cavities can perform nearly as well as bath cooled ones, provided a suitable pipe configuration and cavity wall thickness is chosen. Pure thermal estimates and fits with experimental data show that pipe cooling is a viable solution for future cavities.

An analytical formalism for the solution of cumulative beam breakup in linear accelerators with arbitrary time dependence of beam current is presented, and a closed-form expression for the time and position dependence of the transverse displacement is obtained. It is applied to the behavior of a single bunch and to the steady-state and transient behavior of dc beams and beams composed of pointlike and finite-length bunches. This formalism is also applied to the problem of cumulative beam breakup in the presence of random displacement of cavities and focusing elements, and a general solution is presented.

The applicability of superconducting TEM-class spoke cavities to high-energy ion linacs is discussed, and detailed designs for two TEM-class, triple-spoke-loaded superconducting niobium resonant cavities are presented. The 345 MHz cavities have a velocity range of $0.4<\beta <0.75$ and a beam aperture of 4 cm. Spoke-loaded cavities offer several advantages compared with the higher-frequency elliptical-cell cavities that are currently being developed for this range of particle velocities. The proposed triple-spoke cavities can provide broader velocity acceptance, more accelerating voltage per cavity, reduced heat-load operation at 4.2 K, and increased longitudinal acceptance through the high-energy section. Application to the proposed U.S. rare-isotope accelerator driver linac is discussed in detail.

The interaction between a low-density electron cloud in a circular particle accelerator with a circulating charged particle beam is considered. The particle beam’s space charge attracts the cloud, enhancing the cloud density near the beam axis. It is shown that this enhanced charge and the image charges associated with the cloud charge and the conducting wall of the accelerator may have important consequences for the dynamics of the beam propagation. The tune shift due to the electron cloud is obtained analytically and compared to a new numerical model (QuickPIC) that is described here. Sample numerical results are presented and their significance for current and planned experiments is discussed.

In plasmas with strongly anisotropic distribution functions $(T_{\parallel b}/T_{\perp b}\ll 1)$ a Harris-like collective instability may develop if there is sufficient coupling between the transverse and longitudinal degrees of freedom. Such anisotropies develop naturally in accelerators and may lead to a deterioration of beam quality. This paper extends previous numerical studies [E. A. Startsev, R. C. Davidson, and H. Qin, Phys. Plasmas 9, 3138 (2002)] of the stability properties of intense non-neutral charged particle beams with large temperature anisotropy $(T_{\perp b}\gg T_{\parallel b})$ to allow for nonaxisymmetric perturbations with $\partial /\partial \theta \ne 0$. The most unstable modes are identified, and their eigenfrequencies, radial mode structure, and nonlinear dynamics are determined. The simulation results clearly show that moderately intense beams with $s_b={\widehat{\omega }}_{pb}^2/2{\gamma }_b^2{\omega }_{\beta \perp }^2\gtrsim 0.5$ are linearly unstable to short-wavelength perturbations with $k_z^2{r}_b^2\gtrsim 1$, provided the ratio of longitudinal and transverse temperatures is smaller than some threshold value. Here, ${\widehat{\omega }}_{pb}^2=4\pi {\widehat{n}}_b{e}_b^2/{\gamma }_b{m}_b$ is the relativistic plasma frequency squared, and ${\omega }_{\beta \perp }$ is the betatron frequency associated with the applied smooth-focusing field. A theoretical model is developed based on the Vlasov-Maxwell equations which describes the essential features of the linear stages of instability. Both the simulations and the analytical theory predict that the dipole mode (azimuthal mode number $m=1$) is the most unstable mode. In the nonlinear stage, tails develop in the longitudinal momentum distribution function, and the kinetic instability saturates due to resonant wave-particle interactions.