Horizontal Phase Space Research Articles

Steady-state solutions of split beams in electron storage rings

Recently, a novel operation method for synchrotron light sources with transversely split beams has been explored to fulfill the rising demand for flexible and high-throughput X-ray sources required in such diverse fields as time-resolved X-ray spectroscopy, molecular chemistry in organic cells, high-resolution medical imaging, quantum materials science or sustainable energy research. Within that novel operation mode, additional stable regions are produced in the horizontal phase space by operating an electron storage ring on a resonance that is driven by the nonlinear sextupole or octupole magnets. In the longitudinal phase space, a similar split can be produced by introducing an oscillation of the synchrotron phase via a modulation of the phase of the radiofrequency resonator. Strong radiation damping in electron storage rings, however, has to be overcome before additional regions in phase space can become populated by particles and form stable islands. This damping mechanism changes the dynamics of the system and causes diffusion between the different islands in phase space, raising the question what kind of equilibrium state exists in the asymptotic temporal limit. In this paper, a finite-differences approximation in rotating action-angle coordinates is used to solve the Vlasov–Fokker–Planck equation and to study the obtained equilibrium states for the longitudinal as well as the transverse case. The number of solution vectors and the magnitude of the corresponding singular values of the matrix of the underlying finite-differences equation are used as abstract indicators to define the required parameter set that provides stable additional beamlets. As a consequence, the beamlets have a stability that is close to that of the main beam in terms of diffusion caused by the radiation damping and quantum excitation.

4D transverse phase space tomography of an operational hydrogen ion beam via noninvasive 2D measurements using laser wires

Utilizing noninvasive 2D scans with laser wires, we tomographically reconstructed the 4D transverse phase space distribution of a 1-GeV hydrogen ion (i.e., ${\mathrm{H}}^{\ensuremath{-}}$) beam during operation. The 4D tomography is based on two new advances. First, we extended the formulation of maximum entropy phase space tomography to take 2D projections as input and derived theoretical results relevant to our application. Second, we introduced the method of ``perpendicular scans'' to obtain cross-plane information from a laser wire emittance scanner. Perpendicular scans are two unconventional 2D measurements performed with perpendicular front and back wires. In contrast, only parallel front and back wires (i.e., ``parallel scans'') are utilized in ordinary measurements of the horizontal and vertical 2D phase space distributions. When we applied the technique to the laser emittance station in the high-energy beam transport of the Spallation Neutron Source, experimental results showed that perpendicular scans can provide significant new information to the reconstructed 4D phase space distribution.

A novel non-adiabatic approach to transition crossing in a circular hadron accelerator

Crossing the transition energy is always a delicate process, representing a potential source of strong perturbations of the dynamics of charged particle beams in a hadron circular accelerator. Since the first generation of multi-GeV rings, intense studies have been devoted to understanding the possible harmful mechanisms involved in transition crossing and to devise mitigation measures. Nowadays, several circular particle accelerators are successfully operating across the transition energy and this process is well mastered. In a completely different context, stable resonances of the traverse phase space have been proposed as new means of manipulating charged particle beams. While the original aim of such a proposal was multi-turn extraction from the CERN Proton Synchrotron to the Super Proton Synchrotron, many more applications have been proposed and studied in detail. In this paper, the two topics, i.e. transition crossing and stable resonances, have been brought together with the goal of providing a novel and non-adiabatic approach to perform a clean transition crossing. The idea presented here is that by judiciously using sextupoles and octupoles it is possible to generate stable islands of the horizontal phase space. These islands represent a second closed orbit whose properties can be selected independently of those of the standard, i.e. central, closed orbit. This provides a means of performing a non-adiabatic change of the transition energy experienced by the charged particles by displacing the beam between the two closed orbits.

Design and Experimental Validation of High-Resolution Single-Shot Emittance Diagnostics for Heavy-Ion Beams

A pepper-pot diagnostic device was developed to accurately and robustly retrieve particle distribution in horizontal and vertical phase spaces by single-shot emittance measurements. Two masks that differ in both composition and manufacturing method were fabricated: one made of phosphor bronze by an optical lithography process and another made of stainless steel (SUS) by laser cutting. Scanning electron microscope (SEM) measurements of the two masks revealed that the former is superior in terms of regularity and shape of the mask holes and is therefore more suitable to use. A new image-processing algorithm, namely, cluster noise removal method, was developed which improves the resolution of the phase-space distribution measurements over traditional methods. The device was tested in experiments with low-energy argon beams generated by an electron-cyclotron resonance (ECR) ion source at Korea Institute of Fusion Energy (KFE), Daejeon, South Korea. The results show that the diagnostics can robustly and reliably retrieve the four-dimensional (4-D) phase-space distribution of ion beams with a single-shot measurement.

Two-plane painting injection scheme for BRing of HIAF

The high-intensity heavy-ion accelerator facility (HIAF) is under design at the Institute of Modern Physics (IMP) and will provide an intense ion beam for nuclear physics, atomic mass measurement research, and other applications. As the main ring of HIAF, the BRing accumulates beams to high intensity and accelerates them to high energy. To achieve high intensities up to $$1\times 10^{11}$$ ( $$^{238}$$ U $$^{34+}$$ ), the injection gain of the BRing must be as high as 88. However, multiple multiturn injection supported by the electron cooling system takes a long time, causing substantial beam loss under a strong space charge effect. Hence, a two-plane painting injection scheme is proposed for beam accumulation in the BRing. This scheme uses a tilted injection septum and horizontal and vertical bump magnets to paint the beam into horizontal and vertical phase space simultaneously. In this paper, the two-plane painting injection parameters are optimized, and the resulting injection process is simulated using the Objective Ring Beam Injection and Tracking (ORBIT) code. An injection gain of up to 110.3 with a loss rate of $$2.3\%$$ is achieved, meeting the requirements of BRing.

Development of a Rapid Beam Emittance Measurement System using a Real-Time Beam Profile Monitor

We have developed a rapid beam emittance measurement system for the K140 AVF cyclotron at Research Center for Nuclear Physics (RCNP). So far, an emittance monitor of conventional type section of a medium energy beam transport (MEBT) system to analyze the quality of the injected beam to the K400 ring cyclotron. Two kinds of emittance monitors were supplemented in the low energy beam line for evaluation of ion beams from ion sources. One of them is a conventional type consisting of position-variable slits and a three-wire profile monitor (TPM), similar to the one installed in the MEBT system of the AVF cyclotron. It takes about 30 minutes to get emittances in both the horizontal and vertical planes. For quick emittance measurements, we have developed a new system equipped with a fast moving slit with a fixed gap and a real time beam profile monitor (BPM83) with a rotating helical wire made of tungsten. The wire rotating speed is 18 rps. The BPM83 is controlled by a driver module BPM-FP3A. With this system the measurement time was considerably reduced to 70 seconds for both the horizontal and vertical emittances. The fast moving slits consist of two collimation blocks made of brass, and are inserted into the beam path at an angle of 45 degrees. The slits are scanned in the vertical plane at first, and then in the horizontal plane. The slits gap is variable, but at present it is fixed to 2 mm. A stepping motor for the slit is driven by a PLC system, and it takes only 70 seconds for a full stroke within 290 mm. The slit position is detected by a linear potentiometer. While moving the slits, the beam profile output from BPM-FP3A and the voltage of potentiometer are recorded at every position step simultaneously. The data acquisition system uses CAMAC and trigger signals generated by BPM-FP3A and NIM modules are provided for production of each beam profile at a frequency of 18 Hz, with 4.5 kHz sampling rate. A DAQ program runs on CC/NET (crate controller of CAMAC). When data acquisition finished, the data file is uploaded to a LINUX computer and analyzed automatically. First we calculate the slit position for each profile, then average profiles at every second millimeters. Time scale of the measured profile is converted into wire position. From the slit and the wire positions, we calculate the angle from a beam line axis. The measured slit position, the angle of the beam direction and a current density of the moment provides two dimensional beam current density distribution in phase space for estimation of emittance. Data analysis program is written by C, and the output is represented by gnuplot. Data analysis takes about 1 second. In total the horizontal and vertical phase space plots can be completed within 75 seconds from starting the first program. This rapid emittance measurement system will definitely make it easier to optimize parameters of ion sources and the beam transport system.

Sub-fs electron bunch generation with sub-10-fs bunch arrival-time jitter via bunch slicing in a magnetic chicane

The generation of ultrashort electron bunches with ultrasmall bunch arrival-time jitter is of vital importance for laser-plasma wakefield acceleration with external injection. We study the production of 100-MeV electron bunches with bunch durations of subfemtosecond (fs) and bunch arrival-time jitters of less than 10 fs, in an S-band photoinjector by using a weak magnetic chicane with a slit collimator. The beam dynamics inside the chicane is simulated by using two codes with different self-force models. The first code separates the self-force into a three-dimensional (3D) quasistatic space-charge model and a one-dimensional coherent synchrotron radiation (CSR) model, while the other one starts from the first principle with a so-called 3D sub-bunch method. The simulations indicate that the CSR effect dominates the horizontal emittance growth and the 1D CSR model underestimates the final bunch duration and emittance because of the very large transverse-to-longitudinal aspect ratio of the sub-fs bunch. Particularly, the CSR effect is also strongly affected by the vertical bunch size. Due to the coupling between the horizontal and longitudinal phase spaces, the bunch duration at the entrance of the last dipole magnet of the chicane is still significantly longer than that at the exit of the chicane, which considerably mitigates the impact of space charge and CSR effects on the beam quality. Exploiting this effect, a bunch charge of up to 4.8 pC in a sub-fs bunch could be simulated. In addition, we analytically and numerically investigate the impact of different jitter sources on the bunch arrival-time jitter downstream of the chicane, and define the tolerance budgets assuming realistic values of the stability of the linac for different bunch charges and compression schemes.

Novel technique for injecting and extracting beams in a circular hadron accelerator without using septum magnets

With a few exceptions, all on-axis injection and extraction schemes implemented in circular particle accelerators, synchrotrons, and storage rings, make use of magnetic and electrostatic septa with systems of slow-pulsing dipoles acting on tens of thousands of turns and fast-pulsing dipoles on just a few. The dipoles create a closed orbit deformation around the septa, usually referred to as an orbit bump. A new approach is presented which obviates the need for the septum deflectors. Fast-pulsing elements are still required, but their strength can be minimized by choosing appropriate local accelerator optics. This technique should increase the beam clearance and reduce the usually high radiation levels found around the septa and also reduce the machine impedance introduced by the fast-pulsing dipoles. The basis of the technique is the creation of stable islands around stable fixed points in horizontal phase space. The trajectories of these islands may then be adjusted to match the position and angle of the incoming or outgoing beam.

Tomography of Horizontal Phase Space Distribution of a Slow Extracted Proton Beam in the MedAustron High Energy Beam Transfer Line

MedAustron is a synchrotron based hadron therapy and research center in Wiener Neustadt, Austria, which currently is under commissioning for the first patient treatment. The High Energy Beam Transfer Line (HEBT) consists of multiple functional modules amongst which the phase-shifterstepper PSS is the most important module located where the dispersion from the synchrotron is zero and upstream of the switching magnet to the first irradiation room. The PSS is used to control the beam size for the downstream modules and for this scope rotates the beam in horizontal phase space by adjusting the phase advance. This functionality is used in this study to measure beam profiles for multiple phase space angles which act as input for a tomographic reconstruction. Simulation and measurement results are presented.

Transverse coupling property of beam from ECR ion sources

Experimental evidence of the property of transverse coupling of beam from Electron Cyclotron Resonance (ECR) ion source is presented. It is especially of interest for an ECR ion source, where the cross section of extracted beam is not round along transport path due to the magnetic confinement configuration. When the ions are extracted and accelerated through the descending axial magnetic field at the extraction region, the horizontal and vertical phase space strongly coupled. In this study, the coupling configuration between the transverse phase spaces of the beam from ECR ion source is achieved by beam back-tracking simulation based on the measurements. The reasonability of this coupling configuration has been proven by a series of subsequent simulations.

Demonstration of low emittance in the Cornell energy recovery linac injector prototype

We present a detailed study of the six-dimensional phase space of the electron beam produced by the Cornell Energy Recovery Linac Photoinjector, a high-brightness, high repetition rate (1.3 GHz) DC photoemission source designed to drive a hard x-ray energy recovery linac (ERL). A complete simulation model of the injector has been constructed, verified by measurement, and optimized. Both the horizontal and vertical 2D transverse phase spaces, as well as the time-resolved (sliced) horizontal phase space, were simulated and directly measured at the end of the injector for 19 and 77 pC bunches at roughly 8 MeV. These bunch charges were chosen because they correspond to 25 and 100 mA average current if operating at the full 1.3 GHz repetition rate. The resulting 90% normalized transverse emittances for $19\text{ }(77)\text{ }\text{ }\mathrm{pC}/\mathrm{bunch}$ were $0.23\ifmmode\pm\else\textpm\fi{}0.02$ $(0.51\ifmmode\pm\else\textpm\fi{}0.04)\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ in the horizontal plane, and $0.14\ifmmode\pm\else\textpm\fi{}0.01$ $(0.29\ifmmode\pm\else\textpm\fi{}0.02)\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ in the vertical plane, respectively. These emittances were measured with a corresponding bunch length of $2.1\ifmmode\pm\else\textpm\fi{}0.1$ $(3.0\ifmmode\pm\else\textpm\fi{}0.2)\text{ }\text{ }\mathrm{ps}$, respectively. In each case the rms momentum spread was determined to be on the order of ${10}^{\ensuremath{-}3}$. Excellent overall agreement between measurement and simulation has been demonstrated. Using the emittances and bunch length measured at $19\text{ }\text{ }\mathrm{pC}/\mathrm{bunch}$, we estimate the electron beam quality in a 1.3 GHz, 5 GeV hard x-ray ERL to be at least a factor of 20 times better than that of existing storage rings when the rms energy spread of each device is considered. These results represent a milestone for the field of high-brightness, high-current photoinjectors.

Single-knob beam line for transverse emittance partitioning

Flat beams feature unequal emittances in the horizontal and vertical phase space. Such beams were created successfully in electron machines by applying effective stand-alone solenoid fringe fields in the electron gun. Extension of this method to ion beams was proposed conceptually. The present paper is on the decoupling capabilities of an ion beam emittance transfer line. The proposed beam line provides a single-knob tool to partition the horizontal and vertical rms emittances, while keeping the product of the two emittances constant as well as the transverse rms Twiss parameters (αx,y and βx,y) in both planes. It is shown that this single knob is the solenoid field strength.

Tracking protons in an FFAG and a synchrotron with tiny arcs

We study a ray tracing method that uses tiny arcs to track a proton through a magnetic field. We show how to apply this to an FFAG and a synchrotron that are designed for cancer therapy. Assuming that the field traversed by a proton is uniform over each time step, the required equations and a simple scheme for treating a lattice are developed. We compare the computation time with the code Zgoubi for a FODO lattice. To test its usefulness, it is applied to the spiral FFAG, designed in the RACCAM project, to find the horizontal phase space trajectories. It is also applied to a compact synchrotron, designed in Japan, to determine the phase space trajectories during slow extraction of the proton beam.

Using an emittance exchanger as a bunch compressor

A general architecture of an emittance exchanger (EEX) is considered, where the horizontal and longitudinal phase spaces are exchanged. A family of designs is described which can lead to extremely short final longitudinal lengths, even subfemtosecond. Using higher-order particle simulations, a preferred configuration is found, which has better compression capability and less emittance growth than the standard EEX design at high beam energy. An alternative design is also found which eliminates any final energy-phase coupling. Features of compression using an EEX are significantly different than with a chicane because the final longitudinal phase space is decoupled from the initial longitudinal phase space. Advantages of using an EEX for compression include less susceptibility to the coherent synchrotron radiation (CSR) microbunch instability, less susceptibility to bunch length broadening from CSR effects, and elimination of the initial energy-phase correlation that is needed for compression using a chicane as well as any residual energy-phase correlation after compression. A key disadvantage of using an EEX is that the final horizontal emittance tends to strongly depend on the initial bunch length and beam energy.

Progresses in the studies of adiabatic splitting of charged particle beams by crossing nonlinear resonances

The multiturn extraction from a circular particle accelerator is performed by trapping the beam inside stable islands of the horizontal phase space. In general, by crossing a resonance of order $n$, $n+1$ beamlets are created whenever the resonance is stable, whereas if the resonance is unstable the beam is split in $n$ parts. Islands are generated by nonlinear magnetic fields, whereas the trapping is realized by means of a given tune variation so to cross adiabatically a resonance. Experiments at the CERN Proton Synchrotron carried out in 2007 gave the evidence of protons trapped in stable islands while crossing the one-third and one-fifth resonances. Dedicated experiments were also carried out to study the trapping process and its reversibility properties. The results of these measurement campaigns are presented and discussed in this paper.

Principle and analysis of multiturn injection using stable islands of transverse phase space

By applying a time reversal to the multiturn extraction method recently proposed, a novel approach to perform multiturn injection is described. It is based on the use of stable islands of the horizontal phase space generated by means of sextupoles and octupoles. A particle beam can be injected into stable islands of phase space, and then a slow tune variation allows merging the beam trapped inside the islands. The results of numerical simulations will be presented and discussed in detail, showing how to use the proposed approach to generate hollow bunches in the transverse phase space, and how different resonances can be used. The dependence of the final beam parameters on the key quantities of the proposed approach, such as emittance of the initial beam and the way the resonance is crossed, is investigated. Furthermore, a comparison of the proposed approach against the classical multiturn injection without the use of stable islands is carried out.

Compensation of the asymmetric phase–space distribution for a slowly extracted beam from a synchrotron

In ion beam cancer therapy, it is generally essential for a scanning-irradiation method and a rotating gantry system to deliver a circular beam profile with a Gaussian distribution. A slow beam extraction method utilized in a synchrotron ring, however, cannot deliver a beam with a Gaussian distribution in the horizontal phase space, because of its extraction mechanism. Furthermore, normally, the size of the horizontal emittance is much smaller than that of the vertical one. Thus, we have proposed a thin scatterer method in order to compensate for the phase–space distribution of a slowly extracted beam, although the emittance is slightly enlarged by scattering. As a result of particle tracking, we verified that the proposed method could change an asymmetric distribution to a Gaussian one in the horizontal phase space and realize a symmetric beam condition for the rotating gantry.

Coulomb Coupling Constant for Spatially Confined Single-Species Plasmas

where 2d is the average interparticle distance, T is the plasma temperature, and kB is the Boltzmann constant. This parameter has been employed even for the characterization of a nonneutral system consisting of a single species of particles. Such nonneutral plasmas are spatially localized by artificial electromagnetic forces that overcome internal Coulomb repulsion. In a Paul trap, for instance, a radiofrequency (rf) quadrupole field is utilized to confine a large number of particular ions. Charged-particle beams traveling in accelerators can also be regarded as a sort of nonneutral plasma focused by discrete electromagnetic elements; observing a beam from the rest frame, we actually see that it is almost equivalent to a single-species plasma in a Paul trap. The purpose of this note is to show that the conventional definition of the coupling constant is not relevant to these plasmas confined by time-dependent forces. As demonstrated below, the application of a non-static confinement field causes the plasma to ‘‘breathe’’, which can considerably reduce the magnitude of . In what follows, we consider, as an example, a single-species plasma column confined in a typical Paul trap. For the sake of simplicity, we only look at the transverse degrees of freedom, assuming that the plasma is longitudinally uniform. The transverse kinetic energy of a plasma is calculated from kBT 1⁄4 ðhpxi þ hpyiÞ=2m where ðpx; pyÞ are the horizontal and vertical kinetic momenta, m is the rest mass of the particle, and hAi stands for the average of the quantity ‘‘A’’ over the whole phase space. Since the plasma temperature is usually high according to this definition, the coupling constant is much less than unity, which means that the plasma is in a gaseous phase. In order to enhance the Coulomb coupling, we have to ‘‘cool’’ the plasma through dissipative interactions. It is said that is typically on the order of 1 to 10 in a liquid phase and, if it goes beyond 170, the plasma will be Coulomb crystallized. This argument relies on the plausible expectation that the average kinetic energy can be made arbitrarily low, at least, in theory. We, however, readily understand that the transverse momenta of off-axis particles never vanish as long as the external restoring force depends on time. Even after a perfect crystalline state is reached, kBT is always finite unless all particles are aligned exactly along the trap axis. The concept of temperature T must, therefore, be somewhat generalized in the present case so that the simple definition in eq. (1) remains appropriate. A possible way to avoid the ambiguity of T is the use of the emittance, i.e., the -space volume occupied by the plasma. This concept is quite popular in the particle accelerator community and has been used as a measure of beam quality. The root-mean-squared (rms) emittance projected on the horizontal phase space can be introduced as

Correction multipoles for the high current operation of the Heavy Ion Synchrotron SIS

An upgrade program is under way to fill the Heavy Ion Synchrotron SIS up to the space charge limit at injection energy (e.g., 2/spl middot/10/sup 11/ Ne/sup 10+/ ions and 4/spl middot/10/sup 10/ U/sup 73+/ ions). One part of the program entails the construction of corrector multipoles for fine tuning of the synchrotron. Four normal quadrupoles are foreseen to compensate gradient errors of the 36 main quadrupoles in the ring, while eight skew quadrupoles will be used for the correction of tilt errors of the main quadrupoles. The skew quadrupoles will also be used to improve the multiturn injection efficiency, by linear coupling of the horizontal and vertical phase spaces. Two skew sextupoles will be provided to compensate sextupole components of the short, large aperture vertical steering magnets in the ring. Two technical restrictions had to be fulfilled. First, the space occupied by the correctors must be minimal. Therefore, the correction magnets will be constructed with a number of concentrically arranged multipole correction windings in the same magnet housing. Second, these magnets must be mounted around the beam line vacuum chamber, to avoid breaking the vacuum during their installation. Different possible configurations were investigated by computer simulation with respect to their field quality. Installation of the magnets is planned for the winter shut down of 2001/2002.

Emittance growth and energy loss due to coherent synchrotron radiation in a bunch compressor

Electron bunches of high charge (up to 10 nC) are compressed in length in the Compact Linear Collider Test Facility magnetic chicane to less than 0.4 mm rms. The short bunches radiate coherently in the chicane magnetic field, and the horizontal and longitudinal phase space density distributions are affected. This paper reports the results of beam emittance and momentum measurements. Horizontal and vertical emittances and momentum spectra were measured for different bunch compression factors and bunch charges. In particular, for 10 nC bunches, the mean beam momentum decreased by about 5% while the rms momentum spread increased from 2% to 8%. The experimental results are compared with simulations made with the code TraFiC4.