Longitudinal Phase Space Research Articles

Reverse-bend FODO lattice applied to damping ring for SuperKEKB

SuperKEKB, which is a plan for upgrading KEKB to a higher luminosity of 5 × 10 35 cm 2 s - 1 , requires a beam currents of 9.4 A for LER (3.5 GeV-electrons) and 4.1 A for HER (8 GeV-positrons). In order to supply HER with a positron beam, which is currently injected to LER, the field gradient of the injector linac has to be increased. To meet this requirement, the S-band accelerating structures in the linac are to be replaced with C-band structures. A damping ring (DR) is indispensable, since the aperture of the C-band structure is much smaller than the beam emittance. In this paper, we describe the lattice design of DR. We adopt a new cell structure: FODO cell with alternating bends, where one of two bends in a cell is reversed. One of advantages of the proposed lattice is that a very small, even negative, momentum compaction factor is easily achieved by properly choosing the bend-angle ratio of the reverse bend to the main bend. A tracking simulation for the proposed DR has shown that it has a very large dynamic aperture in both the transverse and longitudinal phase space, for a very wide tune space.

Design and RF measurements of an X-band accelerating structure for linearizing the longitudinal emittance at SPARC

The paper presents the design of an X-band accelerating section for linearizing the longitudinal phase space in the Frascati Linac Coherent Light Source (SPARC). The nine cells structure, operating on the π standing wave mode, is fed by a central coupler and has been designed to obtain a 42 MV/m accelerating gradient. The two-dimensional (2D) profile has been obtained using the electromagnetic codes Superfish and Oscar-2D while the coupler has been designed using HFSS. Bead-pull measurements made on a copper prototype have been performed and the results are illustrated and compared with the numerical predictions. Mechanical details of the realized prototype and RF properties of the structure as a function of the assembly characteristics are also discussed.

Sextupole correction of the longitudinal transport of relativistic beams in dispersionless translating sections

We examine the use of sextupole magnets to correct nonlinearities in the longitudinal phase space transformation of a relativistic beam of charged particles in a dispersionless translating section, or dogleg. Through heuristic analytical arguments and examples derived from recent experimental efforts, augmented by simulations using the particle tracking codes PARMELA and ELEGANT, sextupole corrections are found to be effective in optimizing the use of such structures for beam compression or for shaping the current profile of the beam, by manipulation of the second-order longitudinal dispersion. Recent experimental evidence of the use of sextupoles to manipulate second-order horizontal and longitudinal dispersion of the beam is presented. The theoretical and experimental results indicate that these manipulations can be used to create an electron bunch with a current profile having a long ramp followed by a sharp cutoff, which is optimal for driving large-amplitude wake fields in a plasma wake field accelerator.

Contribution of synchrotron oscillation to spill ripple in RF-knockout slow-extraction

We have studied the effect of synchrotron oscillations on the spill ripple in RF-knockout extraction, in order to investigate the ripple component of the synchrotron-oscillation frequency and to suppress this component. By using a simplified model of RF-knockout extraction and the simulation, it was found that the following conditions are essential for suppressing the spill ripple including the component of the synchrotron-oscillation frequency: (1) sufficient amplitude of the synchrotron oscillation and (2) uniform distribution in longitudinal phase-space. In the experiment at the Heavy Ion Medical Accelerator in Chiba (HIMAC) synchrotron, the debunch–recapture was carried out before the extraction to obtain the larger oscillation amplitude and the uniform distribution in the longitudinal phase-space. In this article, the contribution of the synchrotron oscillation to the spill ripple is described in detail.

Experimental characterization of a space charge induced modulation in high-brightness electron beam

We present the experimental investigation of a collective effect driving strong modulation in the longitudinal phase space of a high-brightness electron beam. The measured beam energy spectrum was analyzed in order to reveal the main parameters of modulation. The experimental results were compared with a model of space-charge oscillations in the beam longitudinal phase space. The measurements and analysis allowed us to determine the range of the parameters of the observed effect on the modulation dynamics and illustrate its potential impact on short-wavelength free electron laser performance.

Beam-envelope theory of ionization cooling

Linear beam-envelope theory of ionization cooling in 6D phase space has been systematically established in the past few years. In this paper, we briefly review the general formalism as well as the specific theories for a quadrupole channel and a bent-solenoidal channel with symmetric focusing. These channels play important roles in the design of cooling channels for the envisioned neutrino factories and muon colliders. The analytical solutions of these channels are relatively simple yet provide good understanding of cooling and heating mechanisms in both transverse and longitudinal phase spaces. Furthermore, the resulting formulae can be used to evaluate cooling channel designs the same way as the radiation integrals are used in storage ring designs.

Three-dimensional time and frequency-domain theory of femtosecond x-ray pulse generation through Thomson scattering

The generation of high intensity, ultrashort x-ray pulses enables exciting new experimental capabilities, such as femtosecond pump-probe experiments used to temporally resolve material structural dynamics on atomic time scales. Thomson backscattering of a high intensity laser pulse with a bright relativistic electron bunch is a promising method for producing such high-brightness x-ray pulses in the 10--100 keV range within a compact facility. While a variety of methods for producing subpicosecond x-ray bursts by Thomson scattering exist, including compression of the electron bunch to subpicosecond bunch lengths and/or colliding a subpicosecond laser pulse in a side-on geometry to minimize the interaction time, a promising alternative approach to achieving this goal while maintaining ultrahigh brightness is the production of a time-correlated (or chirped) x-ray pulse in conjunction with pulse slicing or compression. We present the results of a complete analysis of this process using a recently developed 3D time and frequency-domain code for analyzing the spatial, temporal, and spectral properties an x-ray beam produced by relativistic Thomson scattering. Based on the relativistic differential cross section, this code has the capability to calculate time and space dependent spectra of the x-ray photons produced from linear Thomson scattering for both bandwidth-limited and chirped incident laser pulses. Spectral broadening of the scattered x-ray pulse resulting from the incident laser bandwidth, laser focus, and the transverse and longitudinal phase space of the electron beam were examined. Simulations of chirped x-ray pulse production using both a chirped electron beam and a chirped laser pulse are presented. Required electron beam and laser parameters are summarized by investigating the effects of beam emittance, energy spread, and laser bandwidth on the scattered x-ray spectrum. It is shown that sufficient temporal correlation in the scattered x-ray spectrum to produce sub-100 fs temporal slice resolution can be produced from state-of-the-art, high-brightness electron beams without the need to perform longitudinal compression on the electron bunch.

Experimental characterization of an ultrafast Thomson scattering x-ray source with three-dimensional time and frequency-domain analysis

We present a detailed comparison of the measured characteristics of Thomson backscattered x rays produced at the Picosecond Laser-Electron Interaction for the Dynamic Evaluation of Structures facility at Lawrence Livermore National Laboratory to predicted results from a newly developed, fully three-dimensional time and frequency-domain code. Based on the relativistic differential cross section, this code has the capability to calculate time and space dependent spectra of the x-ray photons produced from linear Thomson scattering for both bandwidth-limited and chirped incident laser pulses. Spectral broadening of the scattered x-ray pulse resulting from the incident laser bandwidth, perpendicular wave vector components in the laser focus, and the transverse and longitudinal phase spaces of the electron beam are included. Electron beam energy, energy spread, and transverse phase space measurements of the electron beam at the interaction point are presented, and the corresponding predicted x-ray characteristics are determined. In addition, time-integrated measurements of the x rays produced from the interaction are presented and shown to agree well with the simulations.

Methods of electron beam bunching

A review of electron beam-bunching methods is presented. A method to create trains of short electron microbunches by creating an electron multilayer mirror in the longitudinal phase space and then rotating it in fields of radiofrequency accelerators or Free-Electron Laser amplifiers is proposed.

Experiments with electron beam modulation at the DUVFEL accelerator

Recently strong modulation of the electron bunch longitudinal phase space was obtained in the DUVFEL accelerator at NSLS. The chirped beam energy spectra exhibit a spiky structure with a subpicosecond spike separation. A model based on the longitudinal space-charge effect has been suggested as an explanation of the observed effect. For characterization of the structure and comparison with the model we performed several experiments. In this paper we present experimental data and discuss them in relation to the model.

A two-Frequency RF Photocathode Gun

In this paper we resurrect an idea originally proposed by Serafini (Nucl. Instr. and Meth. A 318 (1992) 301) in 1992 for an RF photocathode gun capable of operating simultaneously at the fundamental frequency and a higher frequency harmonic. Driving the gun at two frequencies with the proper field ratio and relative phase produces a beam with essentially no RF emittance and a linear longitudinal phase space distribution. Such a gun allows a completely new range of operating parameters for controlling space charge emittance growth. In addition, the linear longitudinal phase space distribution aids in bunch compression. This paper will compare results of simulations for the two-frequency gun with the standard RF gun and the unique properties of the two-frequency gun will be discussed.

Longitudinal phase space tomography at the SLAC gun test facility and the BNL DUV-FEL

The Gun Test Facility and the accelerator at the DUV-FEL facility are operated as sources for high brightness electron beams; the first for the Linac Coherent Light Source project and the latter driving an FEL using High Gain Harmonic Generation in the UV. For both accelerators, projections of the longitudinal phase space on the energy coordinate were obtained by varying the phase of an accelerating structure after the gun and measured with a downstream spectrometer dipole. Using an algebraic reconstruction technique, the longitudinal phase space at the entrance to the varied accelerating structure could be reconstructed over a large range of charge from 15 to 600 pC .

Longitudinal phase space tomography at the SLAC gun test facility and the BNL DUV-FEL

The Gun Test Facility and the accelerator at the DUV-FEL facility are operated as sources for high brightness electron beams ; the first for the Linac Coherent Light Source project and the latter driving an FEL using High Gain Harmonic Generation in the UV. For both accelerators, projections of the longitudinal phase space on the energy coordinate were obtained by varying the phase of an accelerating structure after the gun and measured with a downstream spectrometer dipole. Using an algebraic reconstruction technique, the longitudinal phase space at the entrance to the varied accelerating structure could be reconstructed over a large range of charge from 15 to 600 pC .

Methods of electron beam bunching

A review of electron beam-bunching methods is presented. A method to create trains of short electron microbunches by creating an electron multilayer mirror in the longitudinal phase space and then rotating it in fields of radiofrequency accelerators or Free-Electron Laser amplifiers is proposed.

A two-Frequency RF Photocathode Gun

In this paper we resurrect an idea originally proposed by Serafini (Nucl. Instr. and Meth. A 318 (1992) 301) in 1992 for an RF photocathode gun capable of operating simultaneously at the fundamental frequency and a higher frequency harmonic. Driving the gun at two frequencies with the proper field ratio and relative phase produces a beam with essentially no RF emittance and a linear longitudinal phase space distribution. Such a gun allows a completely new range of operating parameters for controlling space charge emittance growth. In addition, the linear longitudinal phase space distribution aids in bunch compression. This paper will compare results of simulations for the two-frequency gun with the standard RF gun and the unique properties of the two-frequency gun will be discussed.

Flattop acceleration system in the RIKEN AVF cyclotron

A flattop acceleration system has been developed and installed in the RIKEN Azimuthally Varying Field (AVF) cyclotron in order to improve the transmission efficiency and energy spread of beams. The flattop accelerating voltage is generated by a superposition of voltages of the fundamental and third harmonics on the dee, by attaching an additional resonator capacitively coupled to the main resonator. The flattop voltage could be generated from 36 to 63 MHz corresponding to the third harmonic of the operating frequency range of 12–21 MHz. A beam acceleration test was carried out and beam emittance in the longitudinal phase space was measured using a spectrometer. With this flattop system, the single-turn extraction was achieved more easily and the momentum spread was reduced to one-third. The beam transmission efficiency through the AVF cyclotron as well as the RIKEN Ring Cyclotron (RRC) has also been improved.

Superconducting linac beam dynamics with high-order maps for RF resonators

The arbitrary-order map beam optics code COSY Infinity has recently been adapted to calculate accurate high-order ion-optical maps for electrostatic and radio-frequency accelerating structures. The beam dynamics of the superconducting low-velocity positive-ion injector linac for the ATLAS accelerator at Argonne National Lab is used to demonstrate some advantages of the new simulation capability. The injector linac involves four different types of superconducting accelerating structures and has a total of 18 resonators. The detailed geometry for each of the accelerating cavities is included, allowing an accurate representation of the on- and off-axis electric fields. The fields are obtained within the code from a Poisson-solver for cylindrically symmetric electrodes of arbitrary geometry. The transverse focusing is done with superconducting solenoids. A detailed comparison of the transverse and longitudinal phase space is made with the conventional ray-tracing code LINRAY. The two codes are evaluated for ease of optimization, with particular attention to higher-order effects, and future applications are discussed.

Free-electron laser without inversion in the high gain regime

A ‘phased’ optical klystron drift region developed to obtain free-electron lasing (FEL) without inversion in the small-gain small-signal regime is here applied to the high-gain regime. Numerical simulations show improvement in the gain and the tolerance to electron beam energy spread compared to conventional FEL. Longitudinal phase space dynamics has been studied to show the effect of the drift region on the electron beam.

Horizontal phase-space distortions arising from magnetic pulse compression of an intense, relativistic electron beam.

We report detailed measurements of the transverse phase space distortions induced by magnetic chicane compression of a high brightness, relativistic electron beam to subpicosecond length. A strong bifurcation in the phase space is observed when the beam is strongly compressed. This effect is analyzed using several computational models and is correlated to the folding of longitudinal phase space. The impact of these results on current research in collective beam effects in bending systems and implications for future short wavelength free-electron lasers and linear colliders are discussed.

Development of muon ring coolers, neutrino factories and supersymmetric Higgs factory

Over the past few years or so a key new development is the invention of ring coolers for muon cooling. In particular, these rings demonstrate robust cooling of the longitudinal phase space. We discuss the quadrupole or UCLA ring cooler and the prospects to make this a final cooler to reduce the transceiver emittance to the value required for a μ+μ− collider. This will lead to a Higgs factory for the A0/H0 in supersymmetry models.