A simple particle-core model for circular accelerators has been constructed assuming that dispersion effects are relatively weak. This model is applicable to a large class of high-intensity rings designed for modest density applications such as spallation neutron sources. Applying this model to isotropic beams in a smooth ring, halo formation processes in the presence of dispersion are investigated. In the analysis, it is found that dispersion matching is essential to suppress horizontal beam widening in injection if momentum spread is larger than a certain threshold. Even if the beam widening due to dispersion mismatch is suppressed, a halo can be formed in the same mechanism as in a linac, namely, parametric resonance between oscillating core and single particles. The width of halos formed by the particle-core resonance in modest-density rings is found to be a little narrower than that in a straight channel, and typically 1.6 to 1.8 times the maximum core width.

First results are reported from time resolved measurements of ion currents extracted from the Frankfurt 14 GHz Electron Cyclotron Resonance Ion Source with pulsed biased-disk voltage. It was found that the ion currents react promptly to changes of the bias. From the experimental results it is concluded that the biased disk effect is mainly due to improvements of the extraction conditions for the source and/or an enhanced transport of ions into the extraction area. By pulsing the disk voltage, short current pulses of highly charged ions can be generated with amplitudes significantly higher than the currents obtained in continuous mode.

A free electron can temporarily gain a very significant amount of energy if it is overrun by an intense electromagnetic wave. In principle, this process would permit large enhancements in the center-of-mass energy of electron-electron, electron-positron, and electron-photon interactions if these take place in the presence of an intense laser beam. Practical considerations severely limit the utility of this concept for contemporary lasers incident on relativistic electrons. A more accessible laboratory phenomenon is electron-positron production via an intense laser beam incident on a gas. Intense electromagnetic pulses of astrophysical origin can lead to very energetic photons via bremsstrahlung of temporarily accelerated electrons.

A method that measures the transverse profile (emittance) of the bunch by detecting radiation arising at the scattering of the bunch on scanning wire is widely used. In this work information about bunch scattering is obtained by measuring the oscillation frequency of the tightened scanning wire. In such a way, the system of radiation (or secondary particles) extraction and measurement can be removed. The entire unit consists of a compact fork with tightened wire and a scanning system. Normal oscillation frequency of a wire depends on wire tension, its geometric parameters, and, in a second approximation, its elastic characteristics. Normal oscillations are generated by interaction of an alternating current through the wire with magnetic field of a permanent magnet. In this case, it is suggested that the magnetic field of the accelerator (field of dipole magnets or quadrupole magnets) be used for excitation of oscillations. The dependence of oscillation frequency on beam scattering is determined by several factors, including changes of wire tension caused by transverse force of the beam and influence of beam self-field. Preliminary calculations show that the influence of wire heating will dominate. We have studied strain gauges on the basis of vibrating wire from various materials (tungsten, beryl bronze, and niobium zirconium alloys). A scheme of normal oscillation generation by alternating current in autogeneration circuit with automatic frequency adjustment was selected. A special method of wire fixation and elimination of transverse degrees of freedom allows us to achieve relative stability better than ${10}^{-5\mathrm{}}$ during several days at a relative resolution of ${10}^{-6\mathrm{}}$. Experimental results and estimates of wire heating of existing scanners show that the wire heats up to a few hundred grades, which is enough for measurements. The usage of wire of micrometer thickness diminishes the problem of wire thermalization speed during the scanning of the bunch.

In the framework of the modified Bethe's diffraction theory, we study the energy lost by a relativistic particle beam traveling in a coaxial liner with many holes, including the effect of attenuation in the coaxial region. The interference among the holes is the main source of losses and is affected by the attenuation in the coaxial only over sufficiently long distances. We derive analytical formulas for all the interesting quantities and particular attention is given to clarifying the physical meaning of the results; numerical examples are considered using LHC-like parameters.

Uncontrolled beam losses due to space-charge-induced halo generation are a concern in high intensity rings, which are characterized by high beam intensities and low uncontrolled beam loss requirements. It is therefore important to investigate the dynamics of space charge in high intensity rings. We report here the results of extensive calculations using a particle-tracking approach with a self-consistent particle-in-cell model and alternatively with a particle core model. We find that the inclusion of space charge forces provides agreement between calculated and experimentally observed beam profile shapes in the high intensity proton storage ring. We also confirm computationally the extension to rings of the accepted dynamics of halo generation with rms beam mismatch exciting the parametric resonance. In addition, we propose a new two-stage mechanism for halo production in rings in which space-charge-driven lattice resonances generate beam mismatch that excites the parametric resonance. Because of its dependence on lattice resonances, this mechanism is peculiar to rings and is capable of generating halo even from initially matched beams. It is also very sensitive to the operating point in tune space, as we show in the results of a vertical tune scan simulating injection into the Spallation Neutron Source accumulator ring. Our results extend and enhance the understanding of fundamental space charge physics, which has been developed for linear accelerators, to rings.

The present analysis considers an intense non-neutral ion beam with characteristic axial velocity $V_b={\beta }_{b}c$ and directed kinetic energy $({\gamma }_b-1\mathrm{})m_b{c}^2$ propagating in the $z$ direction through an applied focusing field which produces a transverse focusing force ${\mathbf{F}}_{\mathrm{foc}}=-{\gamma }_b{m}_b{\omega }_{\beta b}^2(x{\hat{\mathbf{e}}}_x+y{\hat{\mathbf{e}}}_y)$ on a beam ion (smooth focusing approximation). For a thermal equilibrium distribution function $F_b\left(H_{\perp }^0\right)=\mathrm{const}\times \exp (-H_{\perp }^0/T_b)$, it is shown that the normalized radial density profile $\pi r_b^2{n}_b^0\left(r\right)/N_b$, plotted as a function of $r/r_b$, depends on a single dimensionless parameter, ${\delta }_b=N_b{Z}_b^2{e}^2/2{\gamma }_b^2{T}_b$, which is a measure of the normalized beam intensity. Here, $N_b\equiv \int \mathrm{dxdy}{n}_b^0\left(r\right)$ is the number of beam ions per unit axial length and $r_b^2\equiv N_b^{-1\mathrm{}}\int \mathrm{dxdy}{r}^2{n}_b^0\left(r\right)$ is the mean-square beam radius. “Universal” profiles for the beam density are presented for a wide range of system parameters. The present results are readily extended to the case of a cylindrical non-neutral plasma column confined by a uniform axial magnetic field $B_0{\hat{\mathbf{e}}}_z$.

So far, polarized proton beams have never been accelerated to energies higher than 25 GeV. During the acceleration process, the beam polarization is quite undisturbed, when the accelerator is well adjusted, except at first-order depolarizing spin orbit resonances. At some accelerators other effects have been observed but first-order resonances have always been dominant. At these resonances the spin tune plus or minus one of the orbit tunes is an integer. These beams have usually been investigated by theories which correspondingly lead to an undisturbed polarization during acceleration, except at such resonances. Therefore we speak of “first-order theories.” The first frequently used first-order theory is the single resonance model, which is usually used for simulating the acceleration process. Here the equation of spin motion is simplified drastically by dropping all but the dominant Fourier component of the driving term of that differential equation. The second frequently used first-order theory, the linearized spin-orbit motion theory, is also quite crude. It is based on a linearization of the spin and orbit equation of motion with respect to the phase space coordinates and two suitably chosen spin coordinates. Because of linearization this method cannot be used close to resonances but at fixed energies it is a useful tool. It will be shown that the validity of these first-order theories is restricted at Hadron Electron Ring Accelerator (HERA) energies of up to 820 GeV. An overview of the available theories which go beyond the first-order resonances is given and we explain which of these approaches are applicable for the analysis of polarization in the HERA proton ring. Since these theories include more than one Fourier harmonic in the driving term of the equation of motion, we refer to them as “non-first-order” or “higher-order” theories. Finally, the higher-order effects observed while simulating polarized beams in HERA with these advanced methods are illustrated.

The DARHT-2 accelerator under construction at Los Alamos National Laboratory requires a long flattop ($2\mu \mathrm{s}$) 2–4 kA, 3.5 MV, low-emittance electron beam source. The injector is being constructed at Lawrence Berkeley National Laboratory and consists of a large-area thermionic cathode mounted atop a vertical column. The 90° bend between the horizontally emitted beam and the column produces dipole and higher-pole fields which must be corrected. In addition, the fast rise of the current flowing into the vacuum tank excites rf modes which cause transverse oscillations of the beam centroid. We have modeled these effects with the 3D electromagnetic code LSP. The code has models for pulsed power transmission lines, space-charge-limited emission and transport of charged particles, externally applied magnetic fields, and frequency-dependent absorption of rf. We calculate the transverse displacement of the beam as a function of time during the current pulse, and the positioning and thickness of ferrite absorber needed to damp the rf modes. The numerical results are compared to analytic calculations.

A method is described that provides a solution to the long-standing problem of stray radiation-induced signals on photoemission-based x-ray beam position monitors (BPMs) located on insertion device x-ray beam lines. The method involves the introduction of a chicane into the accelerator lattice that directs unwanted x radiation away from the photosensitive x-ray BPM blades. This technique has been implemented at the Advanced Photon Source, and experimental confirmation of the technique is provided.

A method is presented to simulate the transport of a dc charged particle beam strongly influenced by its self-fields. If the initial phase space of the beam is chosen to be a Kapchinskij-Vladimirskij distribution, the simulation is in agreement with the Kapchinskij-Vladimirskij envelope equations. The simulation was initialized with a Gaussian transverse momentum distribution to investigate the origin of current profiles measured in a 130 keV, 635 mA plasma-focused electron beam.

The flip-flop effect with the linearized beam-beam force is formulated through self-consistent $\beta$ functions and equilibrium emittances which are both affected by collision. We give the results of two models of emittance dependence. The effect of finite bunch length is also discussed.

A weak-strong simulation code is used to study the single-particle stability in the presence of triplet field errors, head-on collisions, and long-range beam-beam interactions at the Large Hadron Collider. We present the dependence of the simulated transverse diffusion rate on various parameters, such as starting amplitude, working point in tune diagram, crossing angle, beta function at the interaction points (IPs), beam current, triplet nonlinearities, tune modulation, and a transverse offset at one of two IPs. For several examples, we perform a frequency map analysis à la Laskar, to obtain tune footprints and the tune variation in time. A cursory look at the effect of a Möbius lattice is also reported.

This paper will explore the possibility of the formation of localized modes in the coupled transverse oscillations of bunches in an accelerator. Such modes are characterized by a large amplitude excitation of one of the bunches, with little or no excitation of the other bunches. They are very similar to intrinsic localized modes predicted to appear in lattice excitations of anharmonic condensed matter systems. The existence of the phenomenon in accelerators requires long-range coupling between the bunches, and quartic terms in the effective potential experienced by the bunches. The discussion in this paper considers the specific cases of a long-range coupling due to the resistive wall impedance, and nonlinearities in the transverse force caused by octupoles. The general equations for the localized mode frequencies and amplitudes are derived. The equations are applied to the specific cases of 9 and 21 equally spaced, equally populated bunches in the Cornell electron storage ring. For both cases, with the currently available octupole strength, and with currents of 8 mA per bunch, localized modes with amplitudes of about 2 mm, and with frequency shifts of $50–100\mathrm{s}{}^{-1\mathrm{}}$ relative to the linear coupled-bunch mode frequencies, may be possible.

Single bunch instabilities for the $50\mathrm{GeV}\times 50\mathrm{GeV}$ muon collider are discussed. An impedance budget of the collider is estimated. A phase-slip factor of $|\eta |=1\mathrm{}\times {10}^{-6\mathrm{}}$ is desired to avoid excessive rf systems. Potential-well distortion of a smooth bunch can be compensated by rf cavities. Accumulated growth in energy due to imperfections and noises in the muon bunch can be reduced by smoothing the bunch distribution before injection. The growth due longitudinal microwave instability is small because of the compensated rf cavities, the finite lifetime of the muons, and the choice of a small $|\eta |$. Beamloadings in the compensating rf cavities are large and suitable feed-forward cancellation is required. Transverse microwave instability can be damped by chromaticities and octupoles. Beam breakup can be cured by Balakin-Novokhatsky-Smirnov damping in principle, but is nontrivial in practice. When beam breakup is small, it can possibly be damped by a betatron tune spread in the beam.

Space charge debunching is a major issue for future high-gradient, high-frequency accelerator techniques. Space charge will set limits on the maximum six-dimensional phase space density obtainable in optical or plasma based accelerators. These accelerators will have short microbunches a fraction of an optical wavelength, in which space charge debunching is unmitigated by two-dimensional effects. The element of an accelerator system most vulnerable to space charge is the drift space between the prebuncher and the acceleration sections. A self-consistent model coupling the energy and phase modulation in the drift space is developed. It is shown that both space charge effects and coherent energy spread can be offset by adjusting the prebuncher and beam optics parameters. In the accelerator sections, the large relativistically corrected inertia together with two-dimensional effects combine to make space charge debunching unimportant. The analytical results compare well with PARMELA code simulations.

We describe an instability diagnostic that exploits the information contained in the angular evolution of coupled-bunch oscillations in phase space. In addition to enabling measurement of coherent tunes and bunch tunes with accuracy of a few hertz, phase space tracking allows new kinds of comparisons between instability theory and experiment. Phase space evolution of bunches participating in a low-threshold vertical instability in the high energy ring of the Stanford Linear Accelerator Center B factory (PEP-II) is used to distinguish between the fast beam-ion instability and conventional instabilities. Tracking of longitudinal instabilities at the LBNL Advanced Light Source and PEP-II is used to measure coherent tunes and gain new insights into uneven-fill instabilities.

The status of the research on muon colliders is discussed and plans are outlined for future theoretical and experimental studies. Besides work on the parameters of a 3–4 and 0.5 TeV center-of-mass (COM) energy collider, many studies are now concentrating on a machine near 0.1 TeV (COM) that could be a factory for the $s$-channel production of Higgs particles. We discuss the research on the various components in such muon colliders, starting from the proton accelerator needed to generate pions from a heavy-$Z$ target and proceeding through the phase rotation and decay ($\pi \to \mu {\nu }_{\mu }$) channel, muon cooling, acceleration, storage in a collider ring, and the collider detector. We also present theoretical and experimental R&D plans for the next several years that should lead to a better understanding of the design and feasibility issues for all of the components. This report is an update of the progress on the research and development since the feasibility study of muon colliders presented at the Snowmass '96 Workshop [R. B. Palmer, A. Sessler, and A. Tollestrup, Proceedings of the 1996 DPF/DPB Summer Study on High-Energy Physics (Stanford Linear Accelerator Center, Menlo Park, CA, 1997)].

The beam-beam interaction in the Tevatron collider sets limits on bunch intensity and luminosity. These limits are caused by a tune spread in each bunch which is mostly due to head-on collisions, but there is also a bunch-to-bunch tune spread due to parasitic collisions in multibunch operation. We propose to compensate these effects with the use of a countertraveling electron beam, and we present general considerations and physics limitations of this technique.

This paper considers an intense non-neutral ion beam propagating in the $z$ direction through a periodic-focusing quadrupole or solenoidal field with transverse focusing force, $-\left[{\kappa }_x\right(s)x{\hat{\mathbf{e}}}_x+{\kappa }_y(s\left)y{\hat{\mathbf{e}}}_y\right]$, on the beam ions. Here, $s={\beta }_b\mathrm{ct}$ is the axial coordinate, $({\gamma }_b-1\mathrm{})m_b{c}^2$ is the directed axial kinetic energy of the beam ions, and the (oscillatory) lattice coefficients satisfy ${\kappa }_x(s+S)={\kappa }_x\left(s\right)$ and ${\kappa }_y(s+S)={\kappa }_y\left(s\right)$, where $S=\mathrm{const}$ is the periodicity length of the focusing field. The theoretical model employs the Vlasov-Maxwell equations to describe the nonlinear evolution of the distribution function $f_b({x,y,x}^{\prime }{,y}^{\prime },s)$ and the (normalized) self-field potential $\psi (x,y,s)$ in the transverse laboratory-frame phase space $\left({x,y,x}^{\prime }{,y}^{\prime }\right)$. Here, $\hat{H}({x,y,x}^{\prime },y^{\prime },s)=\left(1/2\right)\left(x^{\prime 2}{+y}^{\prime 2}\right)+\left(1/2\right)\left[{\kappa }_x\right(s)x^2+{\kappa }_y(s\left)y^2\right]+\psi (x,y,s)$ is the (dimensionless) Hamiltonian for particle motion in the applied field plus self-field configurations, where $(x,y)$ and $\left(x^{\prime }{,y}^{\prime }\right)$ are the transverse displacement and velocity components, respectively, and $\psi (x,y,s)$ is the self-field potential. The Hamiltonian is formally assumed to be of order $\epsilon$, a small dimensionless parameter proportional to the characteristic strength of the focusing field as measured by the lattice coefficients ${\kappa }_x\left(s\right)$ and ${\kappa }_y\left(s\right)$. Using a third-order Hamiltonian averaging technique developed by P. J. Channell [Phys. Plasmas 6, 982 (1999)], a canonical transformation is employed that utilizes an expanded generating function that transforms away the rapidly oscillating terms. This leads to a Hamiltonian, $H(\tilde{X},\tilde{Y},{\tilde{X}}^{\prime },{\tilde{Y}}^{\prime },s)=\left(1/2\right)({\tilde{X}}^{\prime 2}+{\tilde{Y}}^{\prime 2})+\left(1/2\right){\kappa }_f({\tilde{X}}^2+{\tilde{Y}}^2)+\psi (\tilde{X},\tilde{Y},s)$, correct to order ${\epsilon }^3$ in the “slow” transformed variables $(\tilde{X},\tilde{Y},{\tilde{X}}^{\prime },{\tilde{Y}}^{\prime })$. Here, the transverse focusing coefficient in the transformed variables satisfies ${\kappa }_f=\mathrm{const}$, and the asymptotic expansion procedure is expected to be valid for a sufficiently small phase advance ($\sigma <\pi /3=60°$, say). Properties of axisymmetric beam equilibrium distribution functions, $F_b^0\left(H^0\right)$, with $\partial /\partial s=0=\partial /\partial \Theta$, are calculated in the transformed variables, and the results are transformed back to the laboratory frame. Corresponding properties of the periodically focused distribution function $f_b({x,y,x}^{\prime }{,y}^{\prime },s)$ are calculated correct to order ${\epsilon }^3$ in the laboratory frame, including statistical averages such as the mean-square beam dimensions, $〈x^2〉\left(s\right)$ and $〈y^2〉\left(s\right)$, the unnormalized transverse beam emittances, ${\epsilon }_x\left(s\right)$ and ${\epsilon }_y\left(s\right)$, the self-field potential, $\psi (x,y,s)$, the number density of beam particles, $n_b(x,y,s)$, and the transverse flow velocity, ${\mathbf{V}}_b(x,y,s)$. As expected, the beam cross section in the laboratory frame is a pulsating ellipse for the case of a periodic-focusing quadrupole field or a pulsating circular cross section for the case of a periodic-focusing solenoidal field.