Space Charge Forces Research Articles

Space-charge effects in ionization beam profile monitors

Ionization profile monitors (IPMs) are widely used in accelerators for non-destructive and fast diagnostics of high energy particle beams. At high beam intensities, the space-charge forces make the measured IPM profiles significantly different from those of the beams. We analyze dynamics of the secondaries in IPMs and develop an effective algorithm to reconstruct the beam sizes from the measured IPM profiles. Efficiency of the developed theory is illustrated in application to the Fermilab 8 GeV proton Booster IPMs.

Rapidly converging chaos indicator for studying dynamic aperture in a storage ring with space charge

The determination of dynamic aperture in storage rings and colliders is a numerically intensive procedure. When realistic space-charge forces come into consideration, the numerical load becomes even heavier. Furthermore, dynamic aperture estimation using chaos indicators like frequency map analysis (FMA) raises reliability issues when the dynamical system has a time-dependent perturbation like the space-charge force. In this article, we apply a rapidly converging chaos indicator called reversibility error method (REM) to study the space-charge contribution to the dynamic aperture of the integrable optics test accelerator (IOTA) storage ring at a small value of the space charge tune shift. The strength of REM is addressed through examples, including a particle-core model of halo formation. We also develop a toy model of the IOTA lattice to further reduce the computing time required to estimate the dynamic aperture, and we compare this model with a realistic space-charge simulation for verification.

Evolution of bunch envelope and emittance in photo-injectors with application to the AWAKE experiment

We investigate on time evolution of envelopes and emittance of bunched beams in photo-injectors. We carry out a detailed beam dynamic study with focus on calculations of space charge forces. We take the average of the forces over the whole ensemble of particles. This results in space charge coefficients that are largely independent of the bunch distribution. By implementing these coefficients in the beam envelope equations we find a set of modified equations as a model for describing the evolution of the bunch envelope. Our equations crucially decrease the consumed time in particle-in-cell codes for designing today’s photo-injectors. The feasibility and accuracy of the model have been benchmarked against the simulation results from existing particle-in-cell codes with very good agreement. We apply our model for the design of the ultra-short bunch photo-injector of the AWAKE experiment. Moreover, by using assumption of linear external fields we develop the governing equations of the bunch emittances in photo-injectors. These equations allow us to partly quantitatively and partly qualitatively study the effects of external and space charge fields on emittance growth phenomena.

Understanding beam distributions in hadron linacs in the presence of space charge

Space charge forces are a significant contribution to the beam dynamics in high intensity hadron linacs, often causing beam halo that results in beam loss. Currently, there is limited success in modeling beam distributions in high intensity hadron linacs at the RMS level, and no demonstrated capability for measuring or modeling distributions at the level of beam halo. This article discusses the current state of the art capability in this area, and explores next steps in both simulation and beam instrumentation that will enable measurement and modeling of beam halo in high intensity hadron linacs.

Choice of Linac parameters to minimize the space-charge effects

In high-intensity linear accelerators, the tune spreads induced by the space-charge forces in the radial and longitudinal planes are key parameters for halo formation and beam losses. For matched beams, they are the parameters governing the number of resonances (including coupling resonances), which affect the beam and determine the respective sizes of the stable and halo areas in phase space. The number and strength of the resonances excited in mismatched beams leading to even higher amplitude halos are also directly linked to the tune spreads. In this paper, the equations making the link between the basic linac parameters (rf frequency, zero-current phase advances, beam intensity and emittances) and the tune spreads are given. The analysis of the way these linac parameters can be chosen to minimize the tune spreads is presented. The ESS linac parameters are used as an example for this study.

Multitube Helical-Waveguide Gyrotron Traveling-Wave Amplifier: Device Concept and Electron-Optical System Modeling

A multitube configuration for a gyrotron traveling-wave amplifier (gyro-TWA) that is based on the use of one multibeam electron gun and several parallel helically corrugated interaction waveguides operating with axis-encircling-like electron beamlets at the second cyclotron harmonic is proposed. This new gyro-TWA concept, similar to that for multibeam or clustered linear-beam klystrons, can provide a multifold decrease in the thermal loading and increase in the RF breakdown strength for each tube at the same average or pulse output powers or a significant increase in the output power at a moderate level of the mentioned factors. It is shown that the multibeam electron flow appropriate for such a multitube gyro-TWA can be formed by a single magnetron-injection gun (MIG) using selectively emitting regions on the cathode. In some cases, such a gun can be less sensitive to the influence of space-charge forces and other disturbing factors and generate a beam of better quality than a single-beam cusp gun. In particular, a gun for the ten-tube ${W}$ -band gyro-TWA, which ensures generation of a beam with a total power of about 1.3 MW, a pitch factor from 1.2 to 1.5, and a root-mean-square (rms) transverse velocity spread of about 8%, was designed and numerically modeled.

Design and experiment of X-band high-repetition rate high-power multi-beam relativistic klystron amplifier

The relativistic klystron amplifier (RKA) is a very important kind of high power microwave device, which has the advantages of high power, high efficiency, stable output phase and amplitude. The development of multi-injection RKA toward engineering and practical application needs to further improve operating frequency and output power of klystron amplifier, while the RKA of conventional circular waveguide drift tubes is restricted by the physical factors such as geometric size, space charge force and high-voltage breakdown. The multi-beam RKA based on the technology of multiple electron beams can work at low voltage and guiding magnetic field, and can also possess high electron beam current and diversion coefficient. The physical limitation of conventional structure RKA is overcome, and the working frequency and the output power are improved. In the experiment, the X-band GW level power of microwave is obtained. The multi-beam RKA needs to further improve its working frequency and working life. In the experiment, the power conversion efficiency of multi-beam RKA is about 35%, and most of the remaining electron energy will accumulate on the collection pole at the end. If the heat dissipation of the collector is not designed appropriately, the collection will be seriously ablated when working at high heavy frequency. Thus a large quantity of plasma and secondary electrons are generated, which affects the stability of the device. To solve the problem of electron reflux bombarding the output cavity after electron beam exchanging energy in the gap of output cavity, the reflux process of relativistic electron beam in the device is analyzed in this paper. On this basis, a coaxial extraction structure with four-gap extension interaction is designed to avoid electron reflux and reduce the gap electric field, thus improving the working life of the device. At the same time, in order to solve the problem that the conventional water cooling channel can affect the output microwave mode in a high-frequency over-mode device, a mode transformation structure of coaxial TEM mode-fan-shaped TE<sub>10</sub> mode-coaxial TEM mode-circular waveguide TM<sub>01</sub> mode is designed. The mode conversion efficiency is greater than 99.9%, and the influence of collecting polar water cooling channel on the output microwave mode is avoided. The stable operation of multi-beam RKA in the X-band with a repetition rate of 45 Hz is realized experimentally, while the output power is over 1 GW and the microwave pulse width is over 100 ns. At present, the multi-beam RKA runs about 10000 times in total, and the output microwave parameters do not decrease significantly.

Space Charge Driven Resonances in the CERN PS

In the CERN Proton Synchrotron space charge driven resonances are excited around the operational working point due to the periodicity of the optics functions. In this paper, the resonances are studied using analytical methods, i.e. the evaluation of the resonance driving terms connected to the space charge potential of Gaussian distributions. Furthermore, the resonances are characterized in measurements and simulations for various beams. The beams considered are different in terms of brightness, in order to study the dependence of the resonance strength on the space charge force.

Suppression of Microbunching Instability Through Dispersive Lattice

The microbunching instability from the initial small modulation such as shot-noise can be amplified by longitudinal space-charge force and causes significant electron beam quality degradation at the exit of accelerator for the next generation x-ray free electron laser. In the paper, we present analytical and numerical simulation studies of a novel method using dispersion leakage from a quadrupole inside a bunch compressor chicane.

Envelope dynamics and stability with non-linear space-charge forces

We developed a model to calculate the stability of Gaussian beam distributions with non-linear space-charge forces in the presence of random and skew-quadrupole errors. The effect of the space-charge force on the beam matrix is calculated analytically including full cross-plane coupling in 4D phase space, which allows us to perform fast parameter studies. For stability analysis, we find the fixed points of the beam including the space-charge forces and construct a Jacobi-matrix by slightly perturbing the periodic solution. The stability of envelope oscillations is inferred by eigenvalue analysis. Furthermore, we employ envelope tracking as a complementary method and compare the results of the eigenvalue analysis with FFT data from the tracked envelope. The non-linearity of the space-charge force in combination with lattice errors and beam coupling opens up for envelope-lattice resonances and envelope coupling resonances. Hitting these resonances leads to envelope blow-up, causing an effective beam mismatch. Therefore, we finally examine the effect of beam mismatch on the envelope tune-shift and its stability.

Transport of intense beams with current-dependent initial conditions in linearly tapered solenoid channels

AbstractIn electron beams where space charge plays an important role in the beam transport, the beams’ transverse and longitudinal properties will become coupled. One example of this is the transverse–longitudinal correlation produced in a current-modulated beam generated in a DC electron gun, formed through the competition between the time-dependent radial space charge force and the time-independent radial focusing force. This correlation will cause both the slice radius and divergence of the beam extracted from the gun to depend on the slice current. Here we consider the transport of such a beam in a linearly tapered solenoid focusing channel. Transport performance was generally improved with longer taper lengths, minimal initial correlation between slice divergence and slice current, and moderate degrees of initial correlation between initial slice radius and slice current. Performance was also generally improved with lower slice emittances, although surprisingly transport was improved by slightly increasing the assumed slice emittance in certain limited circumstances.

Analytical modeling of longitudinal beam dynamics in an RF-gun: From almost zero to relativistic velocities

We develop and test a model for the longitudinal beam dynamics in an RF-gun consisting in a single and fully analytical transfer matrix. This model deals with the main difficulty of beam dynamics in an RF-gun, which is the velocity variation from almost zero to relativistic one along the beam path, by splitting the gun into two zones. A first one, close to the photocathode, where the accelerating field is assumed to be electrostatic. A second one, farther away from the photocathode, where the electron beam is assumed to be ultra-relativistic. We investigate the capability of the model through comparisons with ASTRA simulations, and measurements performed on the PITZ and PHIL facilities. These comparisons show that the agreement with the analytical model is globally good for the cases where the electron bunch has a low density, and is deteriorated when this density increases due to the growing effect of space-charge forces. The agreement with the analytical model is also found to be dependent on the type of RF-gun considered. The comparisons we made also reveal some limitations of the model, for most of which we propose simple practical solutions.

Limitations on Currents in Cylindrical Drift Tubes of Millimeter-Wave Vacuum Electronic Devices

The conditions providing the equilibrium stationary state of high-density solid and annular electron beams, transported in cylindrical drift tubes and focused by a homogeneous magnetic field, have been investigated. An efficient numerical model is proposed to determine the distributions of the electrostatic potential, charge density, and electron velocities in the stationary state of these beams, with allowance for the space-charge forces. The results of the numerical calculations for the limiting currents, determined by the longitudinal deceleration (caused by space-charge forces) and conditions for equilibrium transverse magnetic focusing for transported beams of different configurations on the length of a klystrontype vacuum electronic device, are presented. The limitations on the device working length, related to the excitation of diocotron instability, are estimated. The calculation results are compared with the data obtained using the quasi-three-dimensional program “Arsenal-MSU” and analytical formulas suggested by other researchers.

Properties of THz coherent undulator radiation generated from a compact accelerator source at Kyoto University

A compact accelerator-base source of THz Coherent Undulator Radiation (THz-CUR) at the Kyoto University has been developed with the purpose of providing intense quasimonochromatic and tunable THz-CUR at frequencies below 1 THz. The source is driven by a compact accelerator using a photocathode RF gun, which emits an electron beam with a fixed energy of 4.6 MeV and high bunch charge. The THz-CUR from our source can be generated when a compressed electron bunch passes through a planar undulator. In this study, we investigate the properties of this radiation, including the total radiation energy, spatial distribution, and power spectrum. With an electron beam of 160 pC bunch charge, the total radiation energy of THz-CUR at 0.16 THz was 1.2 µJ in the micropulse. The THz-CUR covering the frequency range from 0.16 THz to 0.65 THz could be produced by changing the magnetic field of the undulator at a 60 pC bunch charge. Due to the influence of the space charge forces causing the degradation of electron beam qualities, saturation of the radiation energy occurred, and the radiation power spectrum at a frequency of 0.65 THz could not be observed in the high charge condition (160 pC). The effects of bunch lengthening, energy spread, and emittance growth and the influence of the phase error on the generation of THz radiation are also discussed in this paper. This opens up the possibility of understanding the generation of THz-CUR and sheds further light on the enhancement of the radiation power.

Beam matching with space charge in energy recovery linacs

Abstract Matching with space charge of an Energy-Recovery Linac (ERL) arc into the subsequent RF structure is essential to preserve beam quality. We show how to match beam envelopes and dispersion along the bends and recirculation arcs of an ERL, including space charge forces, in order to adjust the beam to the parameters of the subsequent RF structure. For a qualitative analysis, we show that one can use a beam matrix approach together with the smooth focusing approximation but with longitudinal–transverse coupling. It is also shown that the space-charge-modified dispersion plays a key role for the adjustment of the momentum compaction R 56 required for both the isochronous and the non-isochronous recirculation mode of an ERL. In this work, a simple coupled transverse–longitudinal beam matrix approach for matching with space charge is employed and compared with particle tracking simulations using ELEGANT. As an example case, we use the 5 MeV low-energy, 18 0 ° injection arc, which also works as a bunch compressor, and matched to the subsequent first RF structure of the projected multi-turn Mainz Energy-recovering Superconducting Accelerator (MESA).

To the theory of gyrotrons with confocal resonators

In recent years, in addition to the development of traditional gyrotrons with an axially symmetric interaction space, there has been strong interest in developing gyrotrons, whose interaction space is not axially symmetric (e.g., gyrotrons with confocal resonators). The theory of such gyrotrons is presented in this paper. First, equations describing such gyrotrons in the cold-cavity approximation are formulated. Then, the linear theory is developed, which is followed by a simple, single-mode, nonlinear theory. After that, the theory describing the mode interaction in such gyrotrons is presented. Then, an alternative concept of gyrotrons with single and multicavity confocal resonators and sheet electron beams is proposed. This paper also includes the analysis of diffractive losses in confocal resonators and the estimates for curling of the ends of sheet beams of gyrating electrons caused by the space charge forces.

A study of coherent and incoherent resonances in high intensity beams using a linear Paul trap

In this paper we present the first quantitative measurement of the change in frequency (tune) with intensity of four transverse resonances in a high intensity Gaussian beam. Due to the nonlinear space charge forces present in high intensity beams, particle motion cannot be analytically described. Instead we use the simulator of particle orbit dynamics and the intense beam experiment, two linear Paul traps (LPTs), to replicate the system experimentally. In high intensity beams a coherent resonant response to both space charge and external field driven perturbations is possible, these coherent resonances are excited at a tune that differs by a factor Cm from that of the incoherent resonance. By increasing the number of ions stored in the LPT and studying the location of four different resonances we extract provisional values describing the change in tune of the resonance with intensity. These values are then compared to the Cm factors for coherent resonances. We find that the Cm factors do not accurately predict the location of resonances in high intensity Gaussian beams. Further insight into the experiment was gained through simulation using Warp, a particle-in-cell code.

Suppression of beam halo in an RF linac using a hollow electron beam

AbstractHigh-intensity electron linacs have severe space-charge effects that lead to the production of beam halo which degrade the beam quality. For a given charge per bunch, hollow beams have a weaker nonlinear space-charge force. In this paper, we have investigated the possibility of using hollow beam to control halo growth in linacs. We simulate the dynamics of such a beam in a 17 MeV radio frequency linac using ASTRA beam dynamics code and show that it experiences a smaller emittance growth as well as reduced beam halo. The results suggest that using a hollow beam, high charge per bunch could be propagated and accelerated in a radio frequency linac.

Permanent-magnet quadrupoles for an interdigital H -mode drift tube linear accelerator: Optimization code and adjustable magnet design

Magnets to be used for the internal quadrupoles of an interdigital $H$-mode drift tube linear accelerator (IH-DTL) using KONUS beam dynamics should be both compact in size and high in focusing field gradient. Permanent magnets are an attractive solution, but then the ability to adjust the field strength is lost. We investigated two different solutions to this problem: the first using external adjustable electromagnets; the second using internal adjustable permanent magnets. The first method moves the variability out of the resonant cavity, using adjustable electromagnet quadrupole doublets before entry into the IH-DTL to compensate for the lack of internal variability. We carried out optimization simulations with custom code that ran many instances of the lorasr beam dynamics simulation software, using different values of field strength for the external doublets. By optimizing the magnet settings for different values of input current, we were able to compensate for the space-charge forces involved in accelerating a high-intensity continuous-wave (CW) deuteron beam. Second, we designed some novel adjustable permanent-magnet quadrupoles to be used inside the cavity, which combine the advantages of small cross-section and variable field gradient. This allows much more control over the beam, and even other ion species with differing charge-to-mass ratios can be accommodated within the same accelerator design. We developed two adjustable permanent-magnet designs: one with an electromagnetic component, and the other with two concentric moving rings of Halbach-array quadrupoles.

Injection of a self-consistent beam with linear space charge force into a ring

One major concern in the design and operation of high-intensity rings is beam loss due to beam halo. Another issue of importance in applications involving fixed targets is the uniformity of the beam energy deposition on the target. Both of these issues could be favorably addressed by a hard-edged beam with uniform transverse density. This paper presents a detailed feasibility study for painting such a beam into a high-intensity proton ring. For the purposes of this paper, we define self-consistent beams to be ellipsoidal, or elliptical in 2D, distributions that have uniform density and linear space charge force and that retain these properties under all linear transformations. Because of their linear space charge forces and linear transport properties, self-consistent distributions may undergo very little halo formation if realized in practice. Because of their uniform density, they would have smaller maximum space charge tune shifts than peaked density distributions, and they would be attractive for high-intensity fixed target applications. Self-consistent distributions involve very special relationships between the phase space coordinates, making them singular in some respects and difficult to realize experimentally. The most famous self-consistent distribution is the Kapchinsky-Vladimirsky distribution, but now many other self-consistent distributions have been discovered. One such, the 2D rotating distribution, can be painted as a coasting beam into a ring having an appropriately designed and tuned lattice. For bunched beams, if the bunch length is sufficiently long, it is expected that the coasting beam assumption will be a good approximation during painting. However, it is unknown how robust self-consistent distributions will be under real world transport in the presence of nonlinearities and collective effects. This paper studies these issues for a particular case of interest by applying realistic detailed computational models to the simulation of painting a self-consistent rotating beam into the Spallation Neutron Source (SNS) ring. As a result, we propose a case that can be carried out with only a minor modification of the SNS hardware.