Nonlinear Space-charge Effects Research Articles

Differentiable self-consistent space-charge simulation for accelerator design

The nonlinear space-charge effects in a high intensity or high brightness accelerator can have a significant impact on the beam properties through the accelerator. These effects are included in the accelerator design via self-consistent multi-particle tracking simulations. In order to study the sensitivity of the final beam's properties with respect to the accelerator design parameters, one has to carry out the time-consuming space-charge simulation multiple times. In this paper, we propose a differentiable self-consistent space-charge simulation model that enables the study of the beam sensitivity through only one simulation. Such a model can also be used with gradient-based numerical optimizers for accelerator design optimizations including the self-consistent space-charge effects.

Wave–particle interactions in a long traveling wave tube with upgraded helix

We investigate the interaction of electromagnetic waves and electron beams in a 4 m long traveling wave tube (TWT). The device is specifically designed to simulate beam-plasma experiments without appreciable noise. This TWT presents an upgraded slow wave structure (SWS) that results in more precise measurements and makes new experiments possible. We introduce a theoretical model describing wave propagation through the SWS and validated by the experimental dispersion relation, impedance, and phase and group velocities. We analyze nonlinear effects arising from the beam–wave interaction, such as the modulation of the electron beam and the wave growth and saturation process. When the beam current is low, the wave growth coefficient and saturation amplitude follow the linear theory predictions. However, for high values of current, nonlinear space charge effects become important and these parameters deviate from the linear predictions, tending to a constant value. After saturation, we also observe trapping of the beam electrons, which alters the wave amplitude along the TWT.

Advances in the simulation of space-charge effects

The nonlinear space-charge effects are an important topic in high intensity accelerator beam dynamics and have been extensively studied using macroparticle tracking simulations. In this paper, we report on recent advances in the simulation of space-charge effects using a symplectic multiparticle space-charge model. The transverse space-charge limit was explored for a periodic focusing and defocusing lattice. The artificial numerical emittance growth in the macroparticle space-charge simulation was analyzed using a one-dimensional model.

On Long-Term Space-Charge Tracking Simulation

The nonlinear space-charge effects in high intensity accelerator can degrade beam quality and cause particle losses. Self-consistent macroparticle tracking simulations have been widely used to study these space-charge effects. However, it is computationally challenging for long-term tracking simulation of these effects. In this paper, we study a fully symplectic self-consistent particle-in-cell model and numerical methods to mitigate numerical emittance growth. We also discuss about a fast alternative frozen space-charge model that has a potential to improve computational speed significantly.

Theoretical Estimation and Multiparticle Simulation on Evolution of Longitudinal and Transverse Temperatures During Pulse Compression in Compact Simulator for Heavy Ion Inertial Fusion

Kinetic energy exchange in the longitudinal and transverse directions of a charged particle beam during longitudinal pulse compression is discussed through a compact beam simulator for heavy ion inertial fusion. With the goal of understanding the beam behavior in a compact beam simulator experiment, the evolution of the transverse and longitudinal thermal spreads is evaluated using theoretical estimation and numerical simulation. The multiparticle simulation results show the longitudinal and transverse coupling motions via the space charge effect during the longitudinal pulse compression. The ratio of effective temperatures in the longitudinal and transverse directions derived from numerical results is higher than that evaluated from theoretical estimation. It is implied that the discrepancy is caused by the nonlinear space charge effect during the longitudinal bunch compression.

Envelope instability and the fourth order resonance

The well-known envelope instability or the second order even collective mode [I. Hofmann, Phys. Rev. E 57, 4 (1998)] and the fourth order resonance $4\ensuremath{\sigma}=360\ifmmode^\circ\else\textdegree\fi{}$ due to the nonlinear space charge effect in high intensity beams have been studied previously. A wide stop band around 15\ifmmode^\circ\else\textdegree\fi{} is found in a pure periodic focusing channel. In addition, it is illustrated that the fourth order resonance dominates over the envelope instability and practically replaces it in the stop band [D. Jeon et al., Phys. Rev. ST Accel. Beams 12, 054204 (2009)]. In this paper, for a continuous beam with remarkable space charge, our 2D self-consistent particle-in-cell simulation work with the code topopic shows these two kinds of effects respectively in a periodic focusing defocusing (FD) channel. For a fixed tune depression $\ensuremath{\eta}=0.8$, a stop band with a width of almost 15\ifmmode^\circ\else\textdegree\fi{} is also demonstrated. Moreover, it is confirmed that analytical results of the rms envelope instability diagram are a valid tool to interpret the width of the stop band. Emittance growth rates in stop band are also well explained. It is found that, for a nearly rms matched beam, the emittance growth in the stop band is almost proportional to the saturation time of the nonlinear instability of the envelope, which happens in a quick manner and takes only a few FD cells. In contrast, the fourth order resonance is independent of rms matching and will be accompanied by beam evolution as ``a long term effect'' once the related mechanism is excited.

Echo-enabled tunable terahertz radiation generation with a laser-modulated relativistic electron beam

A new scheme to generate narrow-band tunable terahertz (THz) radiation using a variant of the echo-enabled harmonic generation is analyzed. We show that by using an energy chirped beam, THz density modulation in the beam phase space can be produced with two lasers having the same wavelength. This removes the need for an optical parametric amplifier system to provide a wavelength-tunable laser to vary the central frequency of the THz radiation. The practical feasibility and applications of this scheme are demonstrated numerically with a start-to-end simulation using the beam parameters at the Shanghai Deep Ultraviolet Free-Electron Laser facility (SDUV). The central frequency of the density modulation can be continuously tuned by either varying the chirp of the beam or the momentum compactions of the chicanes. The influence of nonlinear rf chirp and longitudinal space charge effect have also been studied in our article. The methods to generate the THz radiation in SDUV with the new scheme and the estimation of the radiation power are also discussed briefly.

Self-consistent simulation of the space charge dominated beams in an elliptical solenoid magnet

The behaviour of a space charge dominated beam has been studied through an elliptical solenoid which is used for making a planar beam as well as for matching an axisymmetric beam to a system needing unequal beam sizes in the two transverse planes. We have first developed an envelope model based on the canonical description of the motion and derived ten independent first order differential equations for the beam sigma matrix elements by assuming canonically transformed Kapchinskij-Vladimirskij (KV) like distribution of the beam. In order to investigate the nonlinear space charge effect a 2D particle-in-cell method has been used. Five types of phase space distributions for the initial beam have been utilized to study the evolutions of envelope and emittance as a function of beam current for different initial beam conditions as the beam passes through the elliptical solenoid. It is shown that the evolution of beam sizes depends weakly on the form of initial distributions whereas the projected emittances in the two transverse planes strongly depend on the initial beam conditions and type of distributions.

Longitudinal emittance growth due to nonlinear space charge effect

Emittance posts limits on the key requirements of final pulse length and spot size on target in heavy ion fusion drivers. In this paper, we show studies on the effect of nonlinear space charge on longitudinal emittance growth in the drift compression section. We perform simulations, using the 3D PIC code WARP, for a high current beam under conditions of bends and longitudinal compression. The linear growth rate for longitudinal emittance turns out to depend only on the peak line charge density, and is independent of pulse length, velocity tilt, and/or the pipe and beam size. This surprisingly simple result is confirmed by simulations and analytic calculations.

Envelope equations for cylindrically symmetric space charge dominated multi species beam

We have derived differential equations for the beam envelope of a cylindrically symmetric space charge dominated multi-species beam. The major contribution here is the inclusion of the emittance growth of each species of the beam resulting from the nonlinear space charge effect of the other species which arises if the beam radius of that particular species is greater than the other species. In addition, we have also discussed the beam selection using slits and considered only the effective values of the current and emittance of each species after the slit for further transport in case the beam size of any species is larger than the slit size or the finite aperture of the beam pipe. Finally, we have studied the transport of proton from 2.45 GHz microwave ion source in the presence of H2+, H3+ species to demonstrate the application of these results. Numerical results are presented for various values of the total beam current and different fractions of p, H2+, and H3+ species.

Studies of emittance growth and halo particle production in intense charged particle beams using the Paul Trap Simulator Experiment

The Paul Trap Simulator Experiment (PTSX) is a compact laboratory experiment that places the physicist in the frame-of-reference of a long, charged-particle bunch coasting through a kilometers-long magnetic alternating-gradient (AG) transport system. The transverse dynamics of particles in both systems are described by the same set of equations, including nonlinear space-charge effects. The time-dependent voltages applied to the PTSX quadrupole electrodes in the laboratory frame are equivalent to the spatially periodic magnetic fields applied in the AG system. The transverse emittance of the charge bunch, which is a measure of the area in the transverse phase space that the beam distribution occupies, is an important metric of beam quality. Maintaining low emittance is an important goal when defining AG system tolerances and when designing AG systems to perform beam manipulations such as transverse beam compression. Results are reviewed from experiments in which white noise and colored noise of various amplitudes and durations have been applied to the PTSX electrodes. This noise is observed to drive continuous emittance growth and increase in root-mean-square beam radius over hundreds of lattice periods. Additional results are reviewed from experiments that determine the conditions necessary to adiabatically reduce the charge bunch’s transverse size and simultaneously maintain high beam quality. During adiabatic transitions, there is no change in the transverse emittance. The transverse compression can be achieved either by a gradual change in the PTSX voltage waveform amplitude or frequency. Results are presented from experiments in which low emittance is achieved by using focusing-off-defocusing-off waveforms.

Recent advances in the physics of collective excitations in the Paul trap simulator experiment

The Paul trap simulator experiment (PTSX) is a compact laboratory linear Paul trap that simulates the transverse dynamics of a long charged-particle bunch propagating through a magnetic alternating-gradient (AG) transport system. The transverse dynamics of particles in the AG system in the beam's frame-of-reference and those of particles in PTSX are described by the same sets of equations, including all nonlinear space–charge effects. Initial experimental results are presented in which the collective transverse symmetric mode ( m = 0 ) and quadrupole mode ( m = 2 ) have been observed in pure-barium-ion plasmas in PTSX, with a depressed-tune ν / ν 0 ∼ 0.9 , with the intent of identifying collective modes whose signature will serve as a robust diagnostic for key properties of the beam, such as line density and transverse emittance. The results of particle-in-cell simulations performed with the WARP code are compared to the experimental data.

Analytical treatment of the nonlinear electron cloud effect and the combined effects with beam-beam and space charge nonlinear forces in storage rings

In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC II. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations.

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.

Transverse beam compression on the Paul trap simulator experiment

The Paul trap simulator experiment is a compact laboratory Paul trap that simulates a long, thin charged-particle bunch coasting through a kilometers-long magnetic alternating-gradient (AG) transport system by putting the physicist in the beam’s frame of reference. The transverse dynamics of particles in both systems are described by similar equations, including all nonlinear space-charge effects. The timedependent quadrupolar electric fields created by the confinement electrodes of a linear Paul trap correspond to the axially dependent magnetic fields applied in the AG system. Results are presented for experiments in which the lattice period and strength are changed over the course of the experiment to transversely compress a beam with an initial depressed tune of 0.9. Instantaneous and smooth changes are considered. Emphasis is placed on determining the conditions that minimize the emittance growth and the number of halo particles produced by the beam compression process. Both the results of particle-in-cell simulations performed with the warp code and envelope equation solutions agree well with the experimental data.

Conditions for minimization of halo particle production during transverse compression of intense ion charge bunches in the Paul Trap Simulator Experiment (PTSX)

The Paul Trap Simulator Experiment (PTSX) is a compact laboratory Paul trap that simulates propagation of a long, thin charged-particle bunch coasting through a multi-kilometer-long magnetic alternating-gradient (AG) transport system by putting the physicist in the frame-of-reference of the beam. The transverse dynamics of particles in both systems are described by the same sets of equations—including all nonlinear space-charge effects. The time-dependent quadrupolar voltages applied to the PTSX confinement electrodes correspond to the axially dependent magnetic fields applied in the AG system. This paper presents the results of experiments in which the amplitude of the applied confining voltage is changed over the course of the experiment in order to transversely compress a beam with an initial depressed tune ν/ ν 0∼0.9. Both instantaneous and smooth changes are considered. Particular emphasis is placed on determining the conditions that minimize the emittance growth and, generally, the number of particles that are found at large radius (so-called halo particles) after the beam compression. The experimental data are also compared with the results of particle-in-cell (PIC) simulations performed with the WARP code.

Experimental simulations of beam propagation over large distances in a compact linear Paul trap

The Paul Trap Simulator Experiment (PTSX) is a compact laboratory experiment that places the physicist in the frame of reference of a long, charged-particle bunch coasting through a kilometers-long magnetic alternating-gradient (AG) transport system. The transverse dynamics of particles in both systems are described by similar equations, including nonlinear space-charge effects. The time-dependent voltages applied to the PTSX quadrupole electrodes are equivalent to the axially oscillating magnetic fields applied in the AG system. Experiments concerning the quiescent propagation of intense beams over large distances can then be performed in a compact and flexible facility. An understanding and characterization of the conditions required for quiescent beam transport, minimum halo particle generation, and precise beam compression and manipulation techniques, are essential, as accelerators and transport systems demand that ever-increasing amounts of space charge be transported. Application areas include ion-beam-driven high energy density physics, high energy and nuclear physics accelerator systems, etc. One-component cesium plasmas have been trapped in PTSX that correspond to normalized beam intensities, ŝ=ωp2(0)∕2ωq2, up to 80% of the space-charge limit where self-electric forces balance the applied focusing force. Here, ωp(0)=[nb(0)eb2∕mbϵ0]1∕2 is the on-axis plasma frequency, and ωq is the smooth-focusing frequency associated with the applied focusing field. Plasmas in PTSX with values of ŝ that are 20% of the limit have been trapped for times corresponding to equivalent beam propagation over 10km. Results are presented for experiments in which the amplitude of the quadrupole focusing lattice is modified as a function of time. It is found that instantaneous changes in lattice amplitude can be detrimental to transverse confinement of the charge bunch.

High current transport experiment for heavy ion inertial fusion

The High Current Experiment (HCX) at Lawrence Berkeley National Laboratory is part of the US program to explore heavy-ion beam transport at a scale representative of the low-energy end of an induction linac driver for fusion energy production. The primary mission of this experiment is to investigate aperture fill factors acceptable for the transport of space-charge-dominated heavy-ion beams at high space-charge intensity (line-charge density /spl sim/ 0.2 /spl mu/C/m) over long pulse durations (>4 /spl mu/s) in alternating gradient electrostatic and magnetic quadrupoles. This experiment is testing - at driver-relevant scale - transport issues resulting from nonlinear space-charge effects and collective modes, beam centroid alignment and beam steering, matching, image charges, halo, electron cloud effects, and longitudinal bunch control. We present the results for a coasting 1 MeV K/sup +/ ion beam transported through the first ten electrostatic transport quadrupoles, measured with beam-imaging and phase-space diagnostics. The latest additions to the experiment include measurements of the secondary ion, electron and atom coefficients due to halo ions scraping the wall, and four magnetic quadrupoles to explore similar issues in magnetic channels.

Experimental study of the transport limits of intense heavy ion beams in the HCX

The High Current Experiment (HCX) at Lawrence Berkeley National Laboratory is part of the US program to explore heavy-ion beam transport at a scale representative of the low-energy end of an induction linac driver for fusion energy production. The primary mission of this experiment is to investigate aperture fill factors acceptable for the transport of space-charge-dominated heavy-ion beams at high space-charge intensity (line charge density up to ∼0.2 μC/m) over long pulse durations (4 μs) in alternating gradient focusing lattices of electrostatic or magnetic quadrupoles. The experiment also contributes to the practical baseline knowledge of intense beam manipulations necessary for the design, construction and operation of a heavy ion driver for inertial fusion. This experiment tests transport issues resulting from nonlinear space-charge effects and collective modes, beam centroid alignment and beam steering, matching, image charges, halo, electron cloud effects, and longitudinal bunch control. We first present the results for a coasting 1 MeV K + ion beam transported through the first ten electrostatic transport quadrupoles, measured with optical beam-imaging and double-slit phase-space diagnostics. This includes studies at two different radial fill factors (60% and 80%), for which the beam transverse distribution was characterized in detail. Additionally, beam energy measurements will be shown. We then discuss the first results of beam transport through four pulsed room-temperature magnetic quadrupoles (located downstream of the electrostatic quadrupoles), where the beam dynamics become more sensitive to the presence of secondary electrons.

Nonlinear electrostatic emittance compensation in kA, fs electron bunches.

Nonlinear space-charge effects play an important role in emittance growth in the production of kA electron bunches with a bunch length much smaller than the bunch diameter. We propose a scheme employing the radial third-order component of an electrostatic acceleration field, to fully compensate the nonlinear space-charge effects. This results in minimal transverse root-mean-square emittance. The principle is demonstrated using our design simulations of a device for the production of high-quality, high-current, subpicosecond electron bunches using electrostatic acceleration in a 1 GV/m field. Simulations using the GPT code produce a bunch of 100 pC and 73 fs full width at half maximum pulse width, resulting in a peak current of about 1.2 kA at an energy of 2 MeV. The compensation scheme reduces the root-mean-square emittance by 34% to 0.4pi mm mrad.