Space Charge Forces Research Articles

Particle tracking study of the injection process with field interferences in a rapid cycling synchrotron

The large-bore magnets in the injection system of a high-intensity proton synchrotron are placed close to each other as compared to their bore sizes. In such cases, the magnetic cores interfere with the fringe fields of adjacent magnets. Moreover, the incoming beam passes through several kinds of time-varying fields along the injection line and the nonlinear field region of the ring quadrupole magnet. The beam behavior under these conditions is analyzed by using the Runge-Kutta method. Although the interference of the magnetic fields does not result in emittance growth, it produces a closed-orbit distortion. Field fluctuations of the time-varying field cause an emittance growth and the nonlinear field deforms the beam profile in phase space of the incoming beam. These effects lead to the modification of the injection scheme. This study focuses on the particle tracking with magnetic field interferences during the early stage of beam commissioning, when the space charge force is not important.

Analysis of slice transverse emittance evolution in a photocathode RF gun

The slice transverse emittance of an electron beam is of critical significance for an X-ray FEL. In a photocathode RF gun, the slice transverse emittance is not only determined by the emission process, but also influenced strongly by the nonlinear space charge effect. In this paper, we study the slice transverse emittance evolution in a photocathode RF gun using a simple model that includes effects of RF acceleration, focusing, and space charge force. The results are compared with IMPACT-T space charge simulations and may be used to understand the development of the slice emittance in an RF gun.

Dynamically self-optimized beam distributions at the UCLA Pegasus laboratory: Linearity of transverse and longitudinal phase spaces

In this paper we present preliminary experimental results of the recently proposed idea to generate ideal uniformly filled ellipsoidal beam distributions in an rf photoinjector by cathode illumination with a very short laser pulse (∼35 fs rms) and subsequent expansion under the beam's own space-charge forces. The great interest for uniformly filled ellipsoidal beam shapes derives from the electromagnetic fields associated with such charge distributions, which depend linearly on the bunch coordinates, thus allowing a perfectly linear, emittance-growth free transport. At the UCLA Pegasus laboratory, where the experiment was performed, we used an X-band deflecting cavity as an electron streak camera to visualize directly on a fluorescent screen the longitudinal beam profiles and verify the space-charge-dominated beam expansion. The transverse quality of the bunch was then characterized by a pepper-pot technique, yielding emittance values close to the thermal limits. The measured phase spaces, both transverse (reconstructed from the emittance measurement) and longitudinal (directly measured using the deflecting cavity on a dispersion screen), are also presented.

Efficient temporal shaping of electron distributions for high-brightness photoemission electron guns

To achieve the lowest emittance electron bunches from photoemission electron guns, it is essential to limit the uncorrelated emittance growth due to space charge forces acting on the bunch in the vicinity of the photocathode through appropriate temporal shaping of the optical pulses illuminating the photocathode. We present measurements of the temporal profile of electron bunches from a bulk crystal GaAs photocathode illuminated with 520 nm wavelength pulses from a frequency-doubled Yb-fiber laser. A transverse deflecting rf cavity was used to make these measurements. The measured laser pulse temporal profile and the corresponding electron beam temporal profile have about 30 ps FWHM duration, with rise and fall times of a few ps. GaAs illuminated by 520 nm optical pulses is a prompt emitter within our measurement uncertainty of $\ensuremath{\sim}1\text{ }\text{ }\mathrm{ps}\text{ }\mathrm{rms}$. Combined with the low thermal emittance of negative electron affinity photocathodes, GaAs is a very suitable photocathode for high-brightness photoinjectors. We also report measurements of the photoemission response time for GaAsP, which show a strong dependence on the quantum efficiency of the photocathode.

Analytical analysis of longitudinal space charge effects for a bunched beam with radial dependence

The longitudinal space-charge (LSC) force can be a major cause of the microbunching instability in the linac for an x-ray free-electron laser. In this paper, the LSC-induced beam modulation is studied using an integral equation approach that takes into account the transverse (radial) variation of the LSC field for both the coasting-beam limit and a bunched beam. Variation of the beam energy and the transverse beam size is also incorporated. We discuss the validity of this approach and compare it with other analytical analyses as well as numerical simulations.

Experimental studies of compensation of beam–beam effects with Tevatron electron lenses

Applying the space-charge forces of a low-energy electron beam can lead to a significant improvement of the beam-particle lifetime limit arising from the beam–beam interaction in a high-energy collider [1]. In this paper, we present the results of various beam experiments with ‘electron lenses’, novel instruments developed for the beam–beam compensation at the Tevatron, which collides 980 GeV proton and antiproton beams. We study the dependencies of the particle betatron tunes on the electron beam current, energy and position; we explore the effects of electron-beam imperfections and noises; and we quantify the improvements of the high-energy beam intensity and the collider luminosity lifetime obtained by the action of the Tevatron electron lenses.

Time-dependent imaging of space-charge dominated electron beams

When considered as non-neutral plasmas, space-charge dominated charged particle beams have significantly smaller Debye lengths than their beam sizes. Therefore, collective effects due to space-charge forces are very important to the beam dynamics. As an example, density perturbations generated in a space-charge dominated charge particle beam will stimulate longitudinally space-charge waves. To study the modification of transverse beam distributions by longitudinal beam dynamics, experimental studies of low-energy electron beams, with and without longitudinal density perturbations, have been undertaken at the University of Maryland’s electron ring and the Long Solenoid Experiment (LSE). We have taken time-resolved beam images on these machines using two different diagnostics: Optical transition radiation, produced from an intercepting aluminized silicon screen, and a fast (<3ns decay time) phosphor screen. Results from both techniques show that both the transverse size and transverse particle distribution of a space-charge dominated beam are affected by the longitudinal dynamics of the beam. In addition to the fast imaging measurements, longitudinal mean energy profiles of different beams have also been measured at different locations in the LSE system.

Lie algebraic analysis for the nonlinear transport of intense bunched beam in electrostatic quadrupoles**Supported by National Natural Science Foundation of China (1057009)

In this paper, the nonlinear transport of intense bunched beams in electrostatic quadrupoles is analyzed using the Lie algebraic method, and the results are briefly presented of the linear matrix approximation and the second order correction of particle trajectory in the state space. Beam having K-V distribution and Gaussian distribution approximation are respectively considered. A brief discussion is also given of the total effects of the quadrupole and the space charge forces on the evolution of the beam envelope.

Generating a Quasiellipsoidal Electron Beam by 3D Laser-Pulse Shaping

A generic 3D laser-pulse-shaping scheme is proposed towards the generation of a uniform ellipsoidal particle distribution, an ideal distribution due to the linear dependence of the space-charge force on the particle position. The shaping is accomplished via spatiotemporal coupling of the laser dynamics via chromatic aberration in an optical lens. Particle tracking simulations show that the electron beam initiated by such a laser pulse in a high-gradient radio-frequency photoinjector delivers very low emittance, ideal for beam-based light sources such as the x-ray free-electron laser.

Experimental evidences for emittance degradation by space charge effect when using a focusing solenoid below an electron cyclotron resonance ion source

Solenoids are widely used to provide initial focusing of beams extracted from an ion source. However, in the case of an electron cyclotron resonance (ECR) ion source, the extracted beam will usually include different ion species and for each of them a wide distribution of charge states. When such a multicomponent beam is focused by a solenoid, the ions with a Q/A larger than the beam of interest are overfocused and usually go through a waist before reaching the analyzing magnet. If the beam currents obtained for these ions are sufficient, the resulting space charge forces can significantly degrade the emittance of the beam components with a lower Q/A and result for those in a hollow beam. Using a beam viewer and an emittance-measuring device, this paper reports on experimental findings that confirm the existence of such an effect for low charge states of argon. Moreover, by changing the experimental conditions of the ECR plasma in order to modify the charge state distribution of the extracted ion beam, it is shown that the threshold where this space charge effect starts to be significant can be changed.

Stability of transverse dipole modes in coasting ion beams with nonlinear space charge, octupoles, and chromaticity

The influence of the nonlinear space-charge force, which causes an amplitude-dependent tune shift, on the transverse stability of a coasting beam with impedances is investigated. In particular, the interplay of nonlinear space charge with a cubic lattice nonlinearity (octupoles) and with linear chromatic effects is considered. For each case, the stability diagram obtained from a dispersion relation with two-dimensional tune spread is compared with results from a simulation scan. For the latter, a 3D particle tracking code is used, with self-consistent 2D space charge, coupling to transverse impedances, chromaticity, and nonlinear lattice effects. The validity of non-self-consistent space-charge models in analytical and in numerical approaches is examined. We reconfirm that, although nonlinear space charge does not provide Landau damping of its own, it modifies strongly the stability properties and must be taken into account in an analysis of Landau damping induced by external (octupole or chromaticity) effects. It is demonstrated that non-self-consistent approaches for space charge are not always applicable.

Experimental Demonstration of Colliding-Beam-Lifetime Improvement by Electron Lenses

We report the successful application of space-charge forces of a low-energy electron beam for improvement of particle lifetime determined by beam-beam interaction at a high-energy collider. In our experiments, an electron lens, a novel instrument developed for the beam-beam compensation, was set on a 980-GeV proton bunch at the Fermilab Tevatron proton-antiproton collider. The proton-bunch losses due to its interaction with the antiproton beam were reduced by a factor of 2 when the electron lens was operating. We describe the principle of electron lens operation and present experimental results.

Criteria for emittance compensation in high-brightness photoinjectors

A critical process in high-brightness photoinjectors is emittance compensation, which brings under control the correlated transverse emittance growth due to the linear space-charge force. Although emittance compensation has been used and studied for almost two decades, the exact criteria to achieve emittance compensation is not as clear as it should be. In this paper, a perturbative analysis of slice envelopes and emittance evolution close to any reference envelope is developed, via which space-charge and chromatic effects are investigated. A new criterion for emittance compensation is found, which is complementary to the well-known matching condition for the invariant envelope and agrees very well with simulations.

EMITTANCE DEGRADATION DUE TO WAKE FIELDS IN A HIGH BRIGHTNESS PHOTOINJECTOR

Wake fields effects in addition to space charge forces may have an important impact during the emittance compensation process in a high brightness photo-injector. To study this effect we developed an upgraded version of the Homdyn code including off axis beam dynamics and wake fields. Homdyn describes a bunch as a uniformly charged cylinder, divided in cylindrical slices; in the upgraded version each slice's centroid can be transversally displaced from the nominal axis thus inducing wake fields. When the bunch is short as compared to the beam pipe radius, wake fields for a single cavity are calculated using methods of diffraction theory; instead we use, for a periodic collection of cavities, an asymptotic wake field obtained numerically at SLAC and then fitted to a simple function. As a first application we studied and verified a correction scheme for the SPARC photo-injector to control the bunch trajectory and angle at the entrance of the undulator. The correction scheme consists of a number of steering magnets and beam position monitors placed along the photo-injector. Two different steering approaches are analyzed and the emittance degradation is studied. The code demonstrates the steering positions and number do correct the bunch's orbit and angle and gives good results concerning the emittance degradation. The emittance and energy spread degradation due to wake fields in the emittance meter experiment is also discussed.

SCALED MODELS: SPACE-CHARGE DOMINATED ELECTRON STORAGE RINGS

New coherent radiation sources in the hard X-ray and Terahertz regimes promise exciting new developments in science, as previously dark areas of the spectrum are brightly illuminated. Ultra-short, ultra-bright radiation packets can probe the structure of matter, and image chemical and biological processes well beyond the present state of the art. Production of this coherent radiation, however, places an unprecedented challenge on the production and acceleration of high-quality electron beams. To deliver a nano-Coulomb of charge with an emittance of less than one micron, while transporting the beam through long sections of acceleration and compression, is the prerequisite for unlocking the gates of this promising new science. Using a low-energy electron storage ring, we deliberately enhance the space charge force while slowing down the time-scale to easily measurable levels so as to maximize our understanding of the particle dynamics necessary for producing bright beams.

DESIGN OF A 2 kA, 30 fs RF-PHOTOINJECTOR FOR WATERBAG COMPRESSION

Because uniformly filled ellipsoidal ‘waterbag’ bunches have linear self-fields in all dimensions, they do not suffer from space-charge induced brightness degradation. This in turn allows very efficient longitudinal compression of high-brightness bunches at sub or mildly relativistic energies, a parameter regime inaccessible up to now due to detrimental effects of non-linear space-charge forces. To demonstrate the feasibility of this approach, we investigate ballistic bunching of 1 MeV, 100 pC waterbag electron bunches, created in a half-cell rf-photogun, by means of a two-cell booster-compressor. Detailed GPT simulations of this table-top set-up are presented, including realistic fields, 3D space-charge effects, path-length differences and image charges at the cathode. It is shown that with a single 10MW S-band klystron and fields of 100 MV/m, 2kA peak current is attainable with a pulse duration of only 30 fs at a transverse normalized emittance of 1.5 μm.

Space charge compensation studies of hydrogen ion beams in a drift section

Demands of high intensity beams are increasing for material science and engineering applications. To control the high intensity beam dynamics, the nonlinear space charge forces, produced by the beam and the residual plasma at low energy, have to be carefully studied. Interactions between the beam and the residual gas tend to neutralize the beam space charge. The temporal and spatial evolutions of these interactions complicate the beam dynamics, even into a drift section. A 1.5D ($xy$ for motion, $r$ for space charge) PIC code, CARTAGO, has been written in order to simulate the beam dynamics in a low energy beam transport line including the space charge compensation effects. This paper relates the structure and the numerical methods used in the code and shows studies of the space charge compensation regime for ${\mathrm{H}}^{+}$ and ${\mathrm{H}}^{\ensuremath{-}}$ beams in a drift section.

COMPASS, the COMmunity petascale project for accelerator science and simulation, a broad computational accelerator physics initiative

Accelerators are the largest and most costly scientific instruments of the Department of Energy, with uses across a broad range of science, including colliders for particle physics and nuclear science and light sources and neutron sources for materials studies. COMPASS, the Community Petascale Project for Accelerator Science and Simulation, is a broad, four-office (HEP, NP, BES, ASCR) effort to develop computational tools for the prediction and performance enhancement of accelerators. The tools being developed can be used to predict the dynamics of beams in the presence of optical elements and space charge forces, the calculation of electromagnetic modes and wake fields of cavities, the cooling induced by comoving beams, and the acceleration of beams by intense fields in plasmas generated by beams or lasers. In SciDAC-1, the computational tools had multiple successes in predicting the dynamics of beams and beam generation. In SciDAC-2 these tools will be petascale enabled to allow the inclusion of an unprecedented level of physics for detailed prediction.

Nonlinearδfparticle simulations of collective excitations and energy-anisotropy instabilities in high-intensity bunched beams

Collective effects with strong coupling between the longitudinal and transverse dynamics are of fundamental importance for applications of high-intensity bunched beams. The self-consistent Vlasov-Maxwell equations are applied to high-intensity finite-length charge bunches, and a generalized particle simulation algorithm is developed for bunched beams with or without energy anisotropy. The nonlinear method exhibits minimal noise and accuracy problems in comparison with standard particle-in-cell simulations. Systematic studies are carried out under conditions corresponding to strong 3D nonlinear space-charge forces in the beam frame. For charge bunches with isotropic energy, finite bunch-length effects are clearly evident by the fact that the spectra for an infinitely long coasting beam and a nearly spherical charge bunch have strong similarities, whereas the spectra have distinctly different features when the bunch length is varied between these two limiting cases. For bunched beams with anisotropic energy, there exists no exact kinetic equilibrium because the particle dynamics do not conserve transverse energy and longitudinal energy separately. A reference state in approximate dynamic equilibrium has been constructed theoretically, and a quasi-steady state has been established in the simulations for the anisotropic case. Collective excitations relative to the reference state have been simulated using the generalized algorithm. In particular, the electrostatic Harris instability driven by strong energy anisotropy is investigated for a finite-length charge bunch. The observed growth rates are larger than those obtained for infinitely long coasting beams. However, the growth rate decreases for increasing bunch length to a value similar to the case of a long coasting beam. For long bunches, the instability is axially localized symmetrically relative to the beam center, and the characteristic wavelength in the longitudinal direction is comparable to the transverse dimension of the beam.

Three-dimensional particle-in-cell simulations of 300GHz reflex klystrons

Three-dimensional (3D) particle-in-cell simulations of 300GHz reflex klystrons are presented. 300GHz electromagnetic wave generation in a resonant cavity is analyzed by using a 3D simulation model in which all the geometric parameters (such as the grid thickness, repeller shape, beam radius, etc.) are described. When an electron beam of an energy of 1.0keV and a net current of 8.9mA is used, the maximum electronic efficiency of energy transfer is observed when the gap transit angle is 0.7πrad, and the efficiency saturates when the beam current is over 10mA. Space charge forces produce a shift in the optimum repeller voltage. It is also shown that the effect of the beam temperature is not critical, even though the bunching wavelength of the electron beam is several times smaller than that in conventional vacuum electron devices. Our simulation results show that a microfabricated 300GHz reflex klystron can directly generate electromagnetic waves with output power levels of several tens of milliwatts.