Several ideas have been proposed to “condition” an electron beam prior to the undulator of a free-electron laser (FEL) by increasing each particle’s energy in proportion to the square of its transverse betatron amplitude. This conditioning enhances FEL gain by reducing the axial velocity spread within the electron bunch. We demonstrate that for symplectic beam lines, and independent of the method, this conditioning is always accompanied by a large head-tail focusing variation which, for short-wavelength FELs, is so severe as to make conditioning completely impractical. We furthermore find that any system added to correct the head-tail focusing variation will also remove the conditioning. As an example, a new method for conditioning is presented and shown to generate exactly the same head-tail focusing problems as in previously published work.

We develop a new approach to the calculation of the synchrotron radiation in a toroidal vacuum chamber. Using a small parameter $ϵ=\sqrt{a/R}$, where $a$ is the characteristic size of the cross section of the toroid and $R$ is the bending radius, we simplify Maxwell’s equations assuming that the characteristic frequency of the modes $\omega \sim c/aϵ$ and neglect terms of higher order in $ϵ$. For a rectangular cross section of the waveguide, we find an analytical solution of the equations and analyze their asymptotics at very high frequency. We then obtain an equation which gives radiation into each synchronous mode. We demonstrate the flexibility of the new method by calculating the frequencies and the loss factors for the lowest modes in square and round waveguides.

The theory and simulation of coherent resonant coupling due to space charge in coasting or bunched anisotropic equilibrium beams is presented. Our work confirms that analytical results on coherent oscillations and instabilities of anisotropic KV (Kapchinskij-Vladimirskij) distributions are a valid tool to interpret the findings from 2D and 3D self-consistent particle-in-cell simulations for both KV and waterbag distributions. With reference to rings we discuss space charge coherent tune shifts up to fourth order and introduce a coherent coupled mode coefficient, which enables us to resolve the issue of KV anomalies by relating them to negative energy modes. The second emphasis of this study is with reference to linacs and a detailed discussion of “stability charts” describing resonant regions where approach to equipartition may occur.

An intense charged particle beam with directed kinetic energy $({\gamma }_b-1)m_b{c}^2$ propagates in the $z$ direction through an applied focusing field with transverse focusing force modeled by ${\mathbf{F}}_{\mathrm{foc}}=-{\gamma }_b{m}_b{\omega }_{\beta \perp }^2{\mathbf{x}}_{\perp }$ in the smooth-focusing approximation. This paper examines properties of the axisymmetric, truncated thermal equilibrium distribution $F_b(r,{\mathbf{p}}_{\perp })=A\exp (-H_{\perp }/{\widehat{T}}_{\perp b})\oplus (H_{\perp }-E_b)$, where $A$, ${\widehat{T}}_{\perp b}$, and $E_b$ are positive constants, and $H_{\perp }$ is the Hamiltonian for transverse particle motion. The equilibrium profiles for beam number density, $n_b(r)=\int d^{2}p{F}_b(r,{\mathbf{p}}_{\perp })$, and transverse temperature, $T_{\perp b}(r)=[n_b(r){]}^{-1}\int d^{2}p(p_{\perp }^2/2{\gamma }_b{m}_b)F_b(r,{\mathbf{p}}_{\perp })$, are calculated self-consistently including space-charge effects. Several properties of the equilibrium profiles are noteworthy. For example, the beam has a sharp outer edge radius $r_b$ with $n_b(r\ge r_b)=0$, where $r_b$ depends on the value of $E_b/{\widehat{T}}_{\perp b}$. In addition, unlike the choice of a semi-Gaussian distribution, $F_b^{\mathrm{SG}}=A\exp (-p_{\perp }^2/2{\gamma }_b{m}_b{\widehat{T}}_{\perp b})\oplus (r-r_b)$, the truncated thermal equilibrium distribution $F_b(r,\mathbf{p})$ depends on $(r,\mathbf{p})$ only through the single-particle constant of the motion $H_{\perp }$ and is therefore a true steady-state solution $(\partial /\partial t=0)$ of the nonlinear Vlasov-Maxwell equations.

We consider the impedance of a structure with rectangular, periodic corrugations on two opposing sides of a rectangular beam tube. Using the method of field matching, we find the modes in such a structure. We then limit ourselves to the case of small corrugations, but where the depth of corrugation is not small compared to the period. For such a structure we generate analytical approximate solutions for the wave number $k$, group velocity $v_g$, and loss factor $\kappa$ for the lowest (the dominant) mode which, when compared with the results of the complete numerical solution, agreed well. We find if $w\sim a$, where $w$ is the beam pipe width and $a$ is the beam pipe half-height, then one mode dominates the impedance, with $k\sim 1/\sqrt{w\delta }$ ($\delta$ is the depth of corrugation), $(1-v_g/c)\sim \delta$, and $\kappa \sim 1/(aw)$, which (when replacing $w$ by $a$) is the same scaling as was found for small corrugations in a round beam pipe. Our results disagree in an important way with a recent paper of Mostacci et al. [A. Mostacci et al., Phys. Rev. ST Accel. Beams 5, 044401 (2002)], where, for the rectangular structure, the authors obtained a synchronous mode with the same frequency $k$, but with $\kappa \sim \delta$. Finally, we find that if $w$ is large compared to $a$ then many nearby modes contribute to the impedance, resulting in a wakefield that Landau damps.

The subject of high-energy density (HED) in matter is of considerable interest to many branches of physics. Intense beams of energetic heavy ions are a promising tool for creating large samples of HED matter which can be used to study the equation-of-state properties of such exotic states of matter experimentally. The Gesellschaft für Schwerionenforschung (GSI), Darmstadt, is a unique laboratory worldwide which has a heavy ion synchrotron facility, SIS18 (with a magnetic rigidity of 18 Tm), that delivers intense heavy ion beams. Using the beams generated at this present facility, interesting experimental work has been carried out in the field of HED matter [D. H. H. Hoffmann et al., Nucl. Instrum. Methods Phys. Res., Sect. B 161–162, 9 (2000)]. The GSI is planning to significantly expand its accelerator capabilities with construction of a new synchrotron ring, SIS100, which will have a magnetic rigidity of 100 Tm. This new facility will deliver a uranium beam which will have orders of magnitude higher intensity than the existing facility and will also have the possibility of multibeam acceleration. This paper presents two-dimensional hydrodynamic simulations of different target geometries including solid as well as hollow cylinders that are irradiated with beams having different shapes of the focal spot which will be available at the SIS100 facility. These include a circular focal spot, an annular focal spot, and an elliptic focal spot, respectively. The purpose of this study is to determine the region of the physical parameters including density, temperature, and pressure that can be accessed using the SIS100 beam. This information, we hope, will be useful for designing experiments on the studies of thermophysical properties of matter including the designing of appropriate diagnostic tools.

We employ Abel’s transform to derive an analytic expression for filtering an equilibrium distribution function from its longitudinal beam profile. The result can be applied to a large class of Hamiltonians that are quadratic in the momentum coordinate.

The longitudinal dynamics and its coupling with the transverse dynamics of bunched beams with strong space charge are analyzed. We introduce a self-consistent Vlasov description for the longitudinal phase space similar to the familiar description for the transverse phase space using a Kapchinskij-Vladimirskij distribution. A longitudinal beam envelope equation is derived. An exact solution is then obtained when coupling to the transverse dynamics is ignored. This longitudinal envelope equation is coupled to the transverse envelope equation to form a set of coupled dynamical equations, which is then solved numerically. This analysis is prompted by the surprising results of recent experiments which showed that by driving an intense laser pulse into matter, which in turn creates a plasma, short bright relativistic electron bunches are produced, surprisingly narrowly focused. We find that because the space charge forces weaken with increasing transverse and longitudinal phase space, both the transverse and longitudinal emittance blowouts anticipated of bright compact bunches are mitigated by this coupling. It should be possible to capture these bunches into an rf cavity to accelerate to higher energies.

Two-stream instabilities in intense charged particle beams, described self-consistently by the nonlinear Vlasov-Maxwell equations, are studied using a 3D multispecies perturbative particle simulation method. The recently developed Beam Equilibrium, Stability and Transport code is used to simulate the linear and nonlinear properties of the electron-proton ($e\mathrm{\text{−}}p$) two-stream instability observed in the Proton Storage Ring (PSR) experiment for a long, coasting beam. Simulations in a parameter regime characteristic of the PSR experiment show that the $e\mathrm{\text{−}}p$ instability has a dipole-mode structure, and that the growth rate is an increasing function of beam intensity, but a decreasing function of the longitudinal momentum spread. It is also shown that the instability threshold decreases with increasing fractional charge neutralization and increases with increasing axial momentum spread of the beam particles. In the nonlinear phase, the simulations show that the proton density perturbation first saturates at a relatively low level and subsequently grows to a higher level. Finally, the nonlinear space-charge-induced transverse tune spread, which introduces a major growth-rate reduction effect on the $e\mathrm{\text{−}}p$ instability, is studied for self-consistent equilibrium populations of protons and electrons.

Longitudinal ballistic and collective beam echoes with diffusion effects are investigated theoretically. In the presence of the space-charge impedance, the collective echo amplitude is obtained as a closed form expression. In contrast to the ballistic case, the collective echo amplitude consists of one maximum at time $t_{\mathrm{echo}}$. The echo amplitude grows up and damps down with a rate proportional to the Landau damping rate of space-charge waves. The effect of weak diffusion is found to modify the ballistic and the collective echo amplitudes in the same manner. This effect of diffusion was confirmed using a “noiseless,” grid-based simulation code. As a first application the amount of numerical diffusion in our simulation code was determined using the echo effect.

This paper presents an analytical investigation of the transverse electron-proton ($e\mathrm{\text{−}}p$) two-stream instability in a proton bunch propagating through a stationary electron background. The equations of motion, including damping effects, are derived for the centroids of the proton beam and the electron cloud by considering Lorentzian and Gaussian frequency spreads for the particles. For a Lorentzian frequency distribution, we derive the asymptotic solution of the coupled linear centroid equations in the time domain and study the $e\mathrm{\text{−}}p$ instability in proton bunches with nonuniform line densities. Examples are given for both uniform and parabolic proton line densities.

Electron cloud instabilities in the Los Alamos Proton Storage Ring and those foreseen for the Oak Ridge Spallation Neutron Source are examined theoretically, numerically, and experimentally.

In preparation for the heavy ion program of the Large Hadron Collider at CERN, accumulation and cooling tests with lead ion beams have been performed in the Low Energy Antiproton Ring. These tests have revealed that due to the unexpected large outgassing of the vacuum system, the dynamic pressure of the ring could not be maintained low enough to reach the required beam intensities. To determine the actions necessary to lower the dynamic pressure rise, an experimental program has been initiated for measuring the molecular desorption yields of stainless steel vacuum chambers by the impact of $4.2\mathrm{MeV}/\mathrm{u}$ lead ions with the charge states $+27$ and $+53$. The test chambers were exposed either at grazing or at perpendicular incidence. Different surface treatments (glow discharges, nonevaporable getter coating) are reported in terms of the molecular desorption yields for ${\mathrm{H}}_{\mathrm{2}}$, $\mathrm{C}{\mathrm{H}}_{\mathrm{4}}$, CO, Ar, and $\mathrm{C}{\mathrm{O}}_{\mathrm{2}}$. Unexpected large values of molecular yields per incident ion up to $2\times {10}^4$ $\mathrm{\text{molecules}}/\mathrm{\text{ion}}$ have been observed. The reduction of the ion-induced desorption yield due to continuous bombardment with lead ions (beam cleaning) has been investigated for five different stainless steel vacuum chambers. The implications of these results for the vacuum system of the future Low Energy Ion Ring and possible remedies to reduce the vacuum degradation are discussed.

In a number of papers an attractive method of laser polarization of electrons (positrons) at storage rings or linear colliders has been proposed. We show that these suggestions are incorrect and based on errors in the simulation of multiple Compton scattering and in the calculation of the Compton spin-flip cross sections. We argue that the equilibrium polarization in this method is zero.

A transformer model of ferrite kicker magnets is presented in this paper. Based on this model, an equivalent circuit is derived for which the elements can be obtained by bench measurements or by estimates from the magnet geometry. Improved formulas for the transverse coupling impedance of lumped and traveling wave kicker magnets are derived from the model and the equivalent circuit. The formulas differ from the corresponding handbook results in their dependence on the external termination or aperture aspect, respectively. The effect of ferrite properties on the transverse coupling impedance is analyzed. The model was confirmed by bench measurements with the twin-wire technique made on the full-size and half-size prototypes of the extraction kicker of the SNS accumulator ring. The application of this model to the design of the kickers allowed a significant reduction of the SNS transverse coupling impedance budget.

A helical quadrupole focusing channel has continuous field symmetry and a stronger focusing power compared with a conventional FODO focusing channel. The good field symmetry allowed us to construct an explicit transfer matrix under the paraxial approximation. In the present paper, we report the paraxial analysis of the helical quadrupole focusing channel and compare its characteristics with those of a conventional FODO focusing channel.

A multibeamlet approach to a high current ion injector, whereby a large number of beamlets are accelerated and then merged to form a single beam, offers a number of potential advantages over a monolithic single beam injector. These advantages include a smaller transverse footprint, more control over the shaping and aiming of the beam, and more flexibility in the choice of ion sources. A potential drawback, however, is a larger emittance. In this paper, we seek to understand the merging of the beamlets and how it determines the emittance. When the constraints imposed by beam propagation physics and practical engineering issues are included, the design is reduced to a few free parameters. We describe the physics design of a multibeamlet injector and produce a design for an example set of parameters. Extensive use of 2D and 3D particle simulations was made in understanding the injector. Design tolerances and sensitivities are discussed in general and in relation to the example.

Experimental observations on the electron cloud have been collected at the CERN Proton Synchrotron machine throughout the last two years. At the same time, an intense campaign of simulations has been carried out to understand the observed electron cloud buildup and the related instability. In this paper, the results of the numerical simulations are presented and discussed.

The root-mean-squared (rms) envelope equations are derived and analyzed for an unbunched intense charged-particle beam in an alternating-gradient focusing field and a cylindrical conducting pipe. All higher-order image-charge effects from the cylindrical pipe are expressed in terms of so-called multiple moment factors in the rms beam envelope equations, and the multiple moment factors are evaluated. Numerical results show that for vacuum phase advance ${\sigma }_v<{90}^{\circ }$, the image-charge effects on the matched and slightly mismatched beam envelopes are negligibly small, at all orders, for all beams with arbitrary beam density profiles (including hollow density profiles) as well as for arbitrary small apertures (including beams with large aspect ratios). However, the main unstable region for the envelope evolution with image-charge effects, which occurs for ${90}^{\circ }<{\sigma }_v<{270}^{\circ }$, depending on the value of the normalized beam intensity $SK/\epsilon$, is found to be narrower than its counterpart without image-charge effects.