Courant-Snyder Parameters Research Articles

Generating high quality ultrarelativistic electron beams using an evolving electron beam driver

A new method of controllable injection to generate high quality electron bunches in the nonlinear blowout regime driven by electron beams is proposed and demonstrated using particle-in-cell simulations. Injection is facilitated by decreasing the wake phase velocity through varying the spot size of the drive beam and can be tuned through the Courant-Snyder (CS) parameters. Two regimes are examined. In the first, the spot size is focused according to the vacuum CS beta function, while in the second, it is focused by the plasma ion column. The effects of the driver intensity and vacuum CS parameters on the wake velocity and injected beam parameters are examined via theory and simulations. For plasma densities of $\sim 10^{19} ~\text{cm}^{-3}$, particle-in-cell (PIC) simulations demonstrate that peak normalized brightnesses $\gtrsim 10^{20}~\text{A}/\text{m}^2/\text{rad}^2$ can be obtained with projected energy spreads of $\lesssim 1\%$ within the middle section of the injected beam, and with normalized slice emittances as low as $\sim 10 ~\text{nm}$.

Longitudinal Bunch Size Measurements with an RF Deflector at J-PARC LINAC

We have measured the longitudinal bunch size of beams from the radio-frequency quadrupole linac (RFQ) at the Japan Proton Accelerator Research Complex (J-PARC). The radio-frequency deflector (RFD) is installed in the medium-energy beam transport section (MEBT1) between the RFQ and the drift-tube linac (DTL). The RFD, which is usually used to produce a macro pulse configuration for the 3-GeV rapid-cycling synchrotron, is utilized to produce a different deflecting angle depending on the bunch arrival phase. Transverse beam profiles were measured after the RFD with and without deflection to extract the longitudinal bunch size. The Courant-Snyder parameters in the longitudinal direction were estimated by measurements for different strength of the upstream buncher. These measurements are one of the important steps to understand the longitudinal beam properties at a high beam current.

Spin polarization and production rate studies of surface muons in a novel solenoid capture system based on CSNS

A novel surface muon capture system with a large acceptance was proposed based on the China spallation neutron source (CSNS). This system was designed using a superconducting solenoid where a long graphite target was put inside it. Firstly, the spin polarization evolution was studied in a constant uniform magnetic field. As the magnetic field can interact with the spin of the surface muon, both the spin polarization and production rate of the surface muons collected by the new capture system were calculated by the G4beamline. Simulation results showed that the surface muons could still keep a high spin polarization (>90%) with different magnetic fields (0–10 T), and the larger magnetic field is, the more surface muons can be captured. Finally, the proton phase space, Courant–Snyder parameters, and intensities of surface muons of different beam fractions were given with magnetic fields of 0 and 5 T. The solenoid capture system can focus proton and surface muon beams and collect \(\pi ^{\pm }\) and \(\mu ^{\pm }\) particles. It can also provide an intense energetic positron source.

Analytical approach to chromatic correction in the final focus system of circular colliders

A conventional final focus system in particle accelerators is systematically analyzed. We find simple relations between the parameters of two focus modules in the final telescope. Using the relations, we derive the chromatic Courant-Snyder parameters for the telescope. The parameters are scaled approximately according to $({L}^{*}/{\ensuremath{\beta}}_{y}^{*})\ensuremath{\delta}$, where ${L}^{*}$ is the distance from the interaction point to the first quadrupole, ${\ensuremath{\beta}}_{y}^{*}$ the vertical beta function at the interaction point, and $\ensuremath{\delta}$ the relative momentum deviation. Most importantly, we show how to compensate its chromaticity order by order in $\ensuremath{\delta}$ by a traditional correction module flanked by an asymmetric pair of harmonic multipoles. The method enables a circular Higgs collider with 2% momentum aperture and illuminates a path forward to 4% in the future.

Characterizing a proton beam with two different methods in beam halo experiments

In beam halo experiments, it is very important to correctly characterize the RFQ output proton beam. In order to simulate the beam dynamics properly, we must first know the correct initial beam parameters. We have used two different methods, quadrupole scans and multi-wire scanners to determine the transverse phase-space properties of the proton beam. The experimental data were analyzed by fitting to the 3-D nonlinear simulation code IMPACT. For the quadrupole scan method, we found that the RMS beam radius and the measured beam-core profiles agreed very well with the simulations. For the multi-wire scanner method, we choose the case of a matched beam. By fitting the IMPACT simulation results to the measured data, we obtained the Courant-Snyder parameters and the emittance of the beam. The difference between the two methods is about eight percent, which is acceptable in our experiments.

Reconstruction of lattice parameters and beam momentum distribution from turn-by-turn beam position monitor readings in circular accelerators

In high chromaticity circular accelerators, rapid decoherence of the betatron motion of a particle beam can make the measurement of lattice and bunch values, such as Courant-Snyder parameters and betatron amplitude, difficult. A method for reconstructing the momentum distribution of a beam from beam position measurements is presented. Further analysis of the same beam position monitor data allows estimates to be made of the Courant-Snyder parameters and the amplitude of coherent betatron oscillation of the beam. The methods are tested through application to data taken on the linear nonscaling fixed field alternating gradient accelerator, EMMA.

Cancellation of Coherent Synchrotron Radiation Kicks with Optics Balance

Minimizing transverse emittance is essential in linear accelerators designed to deliver very high brightness electron beams. Emission of coherent synchrotron radiation (CSR), as a contributing factor to emittance degradation, is an important phenomenon to this respect. A manner in which to cancel this perturbation by imposing certain symmetric conditions on the electron transport system has been suggested.We first expand on this idea by quantitatively relating the beam Courant-Snyder parameters to the emittance growth and by providing a general scheme of CSR suppression with asymmetric optics, provided it is properly balanced along the line. We present the first experimental evidence of this cancellation with the resultant optics balance of multiple CSR kicks: the transverse emittance of a 500 pC, sub-picosecond, high brightness electron beam is being preserved after the passage through the achromatic transfer line of the FERMI@Elettra free electron laser, and emittance growth is observed when the optics balance is intentionally broken. We finally show the agreement between the theoretical model and the experimental results. This study holds the promise of compact dispersive lines with relatively large bending angles, thus reducing costs for future electron facilities.

Courant-Snyder invariant density screening method for emittance analysis

Emittance is an important characteristic of describing charged particle beams. In hadron accelerators, we often meet irregular beam distributions that are not appropriately described by a single rms emittance or 95% emittance or total emittance. In this paper, it is pointed out that in many cases a beam halo should be described with very different Courant-Snyder parameters from the ones used for the beam core. A new method — the Courant-Snyder invariant density screening method — is introduced for analyzing emittance data clearly and accurately. The method treats the emittance data from both measurements and numerical simulations. The method uses the statistical distribution of the beam around each particle in phase space to mark its local density parameter, and then uses the density distribution to calculate the beam parameters such as the Courant-Snyder parameters and emittance for different beam boundary definitions. The method has been used in the calculations for beams from different sources, and shows its advantages over other methods. An application code based on the method including the graphic interface has also been designed.

Parametrization of the driven betatron oscillation

An AC dipole is a magnet which produces a sinusoidally oscillating dipole field and excites coherent transverse beam oscillations in a synchrotron. By observing this driven coherent oscillation, the linear optical parameters can be directly measured at locations of the beam position monitors. The driven oscillations induced by an AC dipole will generate a phase space ellipse which differs from that of free oscillations. If not properly accounted for, this difference can lead to misinterpretations of the actual optical parameters, for instance, 6% or more in the cases of the Tevatron, RHIC, or LHC. This paper shows that the effect of an AC dipole on the observed linear optics is identical to that of a thin lens quadrupole. By introducing a new amplitude function to describe this new phase space ellipse, the motion produced by an AC dipole becomes easier to interpret. The introduction of this new amplitude function also helps measurements of the normal Courant-Snyder parameters based on beam position data taken under the influence of an AC dipole. This new parametrization of driven oscillations is presented and is used to interpret data taken in the FNAL Tevatron using an AC dipole.

Magnet lattice design of the SSRF electron-beam transfer lines

Under three-dimensional plane geometrical constraints ( X, Y, θ), with two asymmetric achromatic sections, the combined three-section structural FODO-like magnet lattice design is adopted and finely optimized in the SSRF electron-beam transfer lines. The magnet lattice has high flexibility and robustness, and the Courant-Snyder parameters can be easily adjusted within a wide range to meet the requirements of transmission and injection for different operation modes of the linear accelerator, booster synchrotron, and storage ring. In this article, the main parameters of the linear optics design of the SSRF electron-beam transfer lines are described, involving the physical design criteria, the total geometrical layout, the magnet lattice, and the beam Courant-Snyder parameters matching. The studies of the variant beam dynamic simulation program calculations show that the design purpose of the efficient beam transmission and injection will be basically achieved.

Macroparticle simulation studies of a proton beam halo experiment

We report macroparticle simulations for comparison with measured results from a proton beam halo experiment in a 52-quadrupole periodic-focusing channel. An important issue is that the input phase-space distribution is not experimentally known. Three different initial distributions with different shapes predict different beam profiles in the transport system. Simulations have been fairly successful in reproducing the core of the measured matched-beam profiles and the trend of emittance growth as a function of the mismatch factor, but underestimate the growth rate of halo and emittance for mismatched beams. In this study, we find that knowledge of the Courant-Snyder parameters and emittances of the input beam is not sufficient for reliable prediction of the halo. Input distributions with greater population in the tails produce larger rates of emittance growth, a result that is qualitatively consistent with the particle-core model of halo formation in mismatched beams.