Longitudinal Phase Space Research Articles

Tomographic measurements of longitudinal phase space density

Tomography — the reconstruction of a two-dimensional image from a series of its one-dimensional projections — is now a very broad topic with a wealth of algorithms for the reconstructions of both qualitative and quantitative images. One of the simplest algorithms has been modified to take into account the nonlinearity of large-amplitude synchrotron motion in a particle accelerator. This permits the accurate reconstruction of longitudinal phase space density from one-dimensional bunch profile data. The algorithm was developed in Mathematica™ in order to exploit the extensive built-in functions and graphics. Subsequently, it has been recoded in Fortran 90 with the aim of reducing the execution time by at least a factor of one hundred. The choice of Fortran 90 was governed by the desire ultimately to exploit parallel architectures, but sequential compilation and execution have already largely yielded the required gain in speed. The use of the method to produce longitudinal phase space plots, animated sequences of the evolution of phase space density and to estimate accelerator parameters is presented. More generally, the new algorithm constitutes an extension of computerized tomography which carers for nonrigid bodies whose projections cannot be measured simultaneously.

Statistical model analysis of multiparticle correlations ine+e−annihilation

A new statistical model for multiparticle production in $e^+e^-$ annihilation is proposed based on the idea of the longitudinal phase space with limited transverse momentum. The longitudinal rapidity space is divided into cells of equal size in order to take into account the Bose-Einstein correlations(BEC) with a finite correlation length $\delta y$. The maximum entropy method is used to determine the probability distributions of the final state pions (or $\rho$ mesons) for a given mean multiplicity, mean transverse momentum and mean total energy. Event simulation based on our model is performed in two extreme cases, a $\pi$-model and a $\rho$-model. The $\pi$-model assumes that only pions are produced directly. On the other hand, the $\rho$-model assumes that only $\rho$ mesons are produced directly and they decay into pions. A good overall fit to experimental data from PETRA to LEP energy regions is obtained for $\delta y$ ranging from 0.6 to 1.2 in the $\pi$-model. We found that the BEC plays a very important role to reproduce various correlation data. In some correlation data, resonance effect and conservation laws are also important.

Characteristics of the cyclotron beam in the longitudinal phase space

The determination of particle beam emittance and density distribution in the longitudinal phase-space projection is discussed and the experimental results are compared with the Gaussian distribution. Analysis of the data clearly shows the decomposition of the beam into three components. The orientation of the phase ellipse indicates a marginal improvement in the time resolution with the energy analysis of the beam. The effect of various machine parameters on the time structure is studied and stability limits of some of the parameters are determined experimentally.

Scaling in energy dependence of relative particle production rates and peak position of ξ distributions in e+e− annihilations

Abstract With the production rates, 〈 n part 〉, of the K 0 , K + , p and Λ and average charged particle multiplicities, 〈 n ch 〉, recently measured at LEP1.5–LEP2, scaling of the relative particle production rates 〈 n part 〉/〈 n ch 〉 is seen in a broad center of mass energy range from s = 29–35 to 183 GeV. The quantity ξ 0 /〈 n ch 〉 1/2 , where ξ 0 is the position of the maximum of the ξ=− ln (2p/ s ) distribution and p is the particle momentum, also scales from 14 to 183 GeV. It is shown that the gaussian shape of the ξ distribution is a simple consequence of longitudinal phase space. The slope parameter in the logarithmic increase of ξ 0 with the center of mass energy must be smaller than 1, as observed experimentally, but this does not necessary imply a manifestation of coherence.

THE HEAVY QUARK FRAGMENTATION FUNCTION AND THE MULTIPLICITY DIFFERENCE BETWEEN HEAVY AND LIGHT QUARK HADRONIC EVENTS IN e+e- ANNIHILATION IN THE LONGITUDINAL PHASE SPACE MODEL

The heavy quark fragmentation function and the multiplicity difference between heavy and light quark hadronic events are explained in a unified framework, namely the longitudinal phase space model. Good agreement of the predictions with data has been achieved.

Precise measurement of a subpicosecond electron single bunch by the femtosecond streak camera

Precise measurement of a subpicosecond electron single bunch by the femtosecond streak camera is presented. The subpicosecond electron single bunch of energy 35 MeV was generated by the achromatic magnetic pulse compressor at the S-band linear accelerator of Nuclear Engineering Research Laboratory (NERL), University of Tokyo. The electric charge per bunch and beam size are 0.5 nC and the horizontal and vertical beam sizes are 3.3 and 5.5 mm (full width at half maximum; FWHM), respectively. Pulse shape of the electron single bunch is measured via Cherenkov radiation emitted in air by the femtosecond streak camera. Optical parameters of the optical measurement system were optimized based on much experiment and numerical analysis in order to achieve a subpicosecond time resolution. By using the optimized optical measurement system, the subpicosecond pulse shape, its variation for the differents rf phases in the accelerating tube, the jitter of the total system and the correlation between measured streak images and calculated longitudinal phase space distributions were precisely evaluated. This measurement system is going to be utilized in several subpicosecond analyses for radiation physics and chemistry.

“White-light” Laser Cooling of a Fast Stored Ion Beam

We report the experimental demonstration of ``white-light'' cooling of a high-velocity ${}^{7}{\mathrm{Li}}^{+}$ ion beam stored at 6.4% of the speed of light in a storage ring. In a direct comparison with single-mode laser cooling, we show that white-light cooling is much more efficient to counteract strong intrabeam heating and leads to lower longitudinal beam temperatures at higher ion densities, i.e., much higher densities in longitudinal phase space.

BUNCHED LASER COOLING OF A STORED WEAK 7LI+ ION BEAM IN A PURE TRIPLET STATE

A preparation scheme for a 7Li+ ion beam in a storage ring is presented which provides ions in the metastable triplet states with well controlled longitudinal phase space properties. For both state selective preparation and beam cooling, laser- and electron-cooler forces are applied. The spatial- and momentum distributions of the ions are directly detected by a time resolved measurement of the fluorescence light. At low beam intensities, the remaining heating rate of such a beam is completely determined by residual gas scattering.

Space-charge effects on bunching of electrons in the CEBAF injector

The main injector for the 4 GeV CEBAF accelerator at Thomas Jefferson National Accelerator Facility was designed to deliver simultaneously three CW electron beams for nuclear physics research. The maximum design current for a single beam from the injector is 100 μA, or 0.2 pC per microbunch at a repetition rate of 499 MHz. It was found through computer simulation that space charge even at a subpicocoulomb level can spoil the bunching of electrons significantly, and some unexpected phenomena observed experimentally could be explained accordingly. This problem arises because of the low-momentum tilt allowed for bunching to preserve low-momentum spread. In this paper, we analyze in detail the space-charge effects on bunching of electrons with the CEBAF injector as an example. Conditions for effective matching of longitudinal phase space in the presence of space charge are discussed.

Observation of space-charge driven beam instabilities in a radio frequency photoinjector

This article describes an experimental determination of the correlated, longitudinal phase-space electron distribution produced by a radio frequency photoinjector. Measurements of the electron beam energy spectra and pulse shapes are analyzed to deduce the longitudinal phase space at the exit of the photoinjector rf cavity. Data were obtained for micro-pulse charges of 0.5, 1.0, 2.0, 3.0, 4.0, and 5.0 nC, and show different phenomena in the low-charge and high-charge regimes. At low beam charge, the uncorrelated energy spread increases with increasing charge density, while rf bunching appears to cancel any pulse-length elongation due to the space-charge forces. At high beam charge, the data show that the micro-pulse separates into three distinct sub-pulses of nearly equal charge, and with a temporal separation proportional to the relativistic plasma frequency. These effects are compared with the space-charge generated instabilities and virtual-cathode phenomena observed in lower voltage devices. The implications that these results have upon the fundamental limits of beam brightness and magnetic pulse compression limitations are discussed.

A μ+μ- Quantum Collider using Novel Crystal-Based Accelerator Components

We outline a concept of a 250 × 250 GeV μ+ μ- collider that uses bent crystals for beam confinement and steering instead of conventional magnets. The collider ring is based on a novel bending-focusing crystal cell. Beam optics of the proposed model cell has all the features of the alterating gradient FODO cell. Furthermore, alternating (horizontal-vertical) focusing provides unique betatron phase stability in both planes, while bending of particle trajectories due to crystal curvature is fully achromatic. We also explore the ionization energy loss of channeling muons interacting with the electron gas in a crystal channel as a possible cooling mechanism. Finally, a use of low Z binary crystals (such as LiF) for final focus at the interaction point is proposed. Bringing the μ+μ- into collision inside a crystal channel results in quantum confinement at the collision point. For such a collider the number of required μ± may be very low (~108μ per pulse), so that this collider has few problems from μ → e backgrounds or heating, which is a virtue of paramount importance. A low intensity hadronic μ± source (p + A → π → μ) can be utilized provided that an effective method of fast muon cooling is used. For example, the use of frictional cooling for low energy μ± beams could initially reduce the longitudinal phase–space, before the final transverse cooling is applied. Here, we outline such a "crystal cooler" that explores ionization energy loss in the ultrastrong focusing environment of a crystal channel. Employing all the above-mentioned novel crystal-based accelerator components, a possible luminosity of about 1032 cm-2 sec-1, is estimated for the proposed quantum collider. We also discuss a list of problems one needs to solve in order to make such a collider a real possibility.

Fluctuations in hadronic and nuclear collisions

We investigate several fluctuation effects in high-energy hadronic and nuclear collisions through the analysis of different observables. To introduce fluctuations in the initial stage of collisions, we use the Interacting Gluon Model (IGM) modified by the inclusion of the impact parameter. The inelasticity and leading-particle distributions follow directly from this model. The fluctuation effects on rapidity distributions are then studied by using Landau's Hydrodynamic Model in one dimension. To investigate further the effects of the multiplicity fluctuation, we use the Longitudinal Phase-Space Model, with the multiplicity distribution calculated within the hydrodynamic model, and the initial conditions given by the IGM. Forward-backward correlation is obtained in this way.

Heavy-ion injection in synchrotrons and storage rings

A survey of methods for injection of heavy ions in synchrotrons and storage rings is given. The three main injection methods—stacking in the transverse phase space, stacking in the longitudinal phase space, and ion stripping—are described in detail. Combinations of multiturn injection with linear coupling, beam cooling, and rf stacking are represented. Many examples and original results of the author on the simulation of the injection in the Nuclotron booster are given.

Interaction of relativistic electrons with ultrashort laser pulses: generation of femtosecond X-rays and microprobing of electron beams

The interaction of relativistic electrons with terawatt femtosecond laser pulses is reviewed with emphasis on how the scattering process can be used as a source of ultrashort X-ray pulses and as a time-resolved diagnostic for measuring transverse and longitudinal phase space distributions of an electron beam with microns spatial and subpicosecond temporal resolution. Recent experimental results are presented in which 90/spl deg/ Thomson scattering was utilized to generate 300 fs duration pulses of X-rays with peak energy of 30 keV. It is shown that, through analysis of the scattered X-ray beam properties, transverse and longitudinal distributions of the electron beam can be obtained.

Particle production in nuclear collisions from LBNL/SIS to SPS energies

Nucleon-nucleon and symmetric nucleus-nucleus collisions are studied in a wide range of centre-of-mass energies. Phase space distributions of pions and kaons are characterized by the widths of the rapidity distributions and their average transverse momenta. The shapes of the rapidity distributions are found to dependent rather on the energy than the mass of the projectiles. At a given energy it is independent of the longitudinal phase space distribution of the participant nucleons in the final state of the collision. The average transverse momenta of pions are insensitive to projectile energy above s of 10 GeV and increase only by a few percent when going from nucleon-nucleon to central nucleus-nucleus collisions. The average transverse momenta of heavy particles produced in hadronic interactions saturate only at higher beam energies. Their system size dependence is considerable. In central nuclear collisions at s of 20 GeV mean transverse momenta in excess of what has been obtained in p+ p at s of 630 GeV are found. In central A + A collisions the inelasticity rises with beam energy in contrast to an approximate invariance in nucleon-nucleon interactions. The fraction of energy in strange particles increases with energy up to s of 5 GeV and saturates beyond. A similar behaviour is seen as function of projectile size. A strong increase of the energy fraction in strange particles from nucleon-nucleon to central collisions between light nuclei like sulphur contrasts with a minor increase when comparing light with heavy nuclei.

Nonlinear subpicosecond electron-bunch compressor

The minimum bunch length achievable using a magnetic bunch compression system is related to the nonlinear dispersion of the compressor and the nonlinear energy-phase correlation of the bunch's longitudinal phase space. For electron bunches with medium or high charge (on the order of 1 nC, or higher), the longitudinal wakefields in the accelerating structure cause a large nonlinearity in the initial energy-phase correlation. Specific nonlinearities in the dispersion of the bunch compressor must then be introduced in order to maximally compress the bunch length, which is done by a chicane-style compressor by increasing the bend angle. This nonlinear dispersion actually decreases the rms longitudinal-beam emittance, by compensating for the nonlinearities in the beam's energy-phase correlation. In this paper, we report on the compression theory, design, and operation of such a compressor. For this compressor, introducing nonlinear dispersion reduced the minimum compressed bunch length by about a factor of 5, resulting in measured FWHM bunch lengths of 2 3 ps for bunch charges as large as 1 nC.

Longitudinal phase space experiments on the ELSA photoinjector

Abstract The excellent beam quality produced by RF photocathode injectors is well-established, and has been verified by numerous measurements of the transverse emittance. However, there are few experimental determinations of the longitudinal phase space. This paper reports on experiments performed at the ELSA FEL facility to measure the longitudinal phase space distribution at the exit of the 144 MHz photoinjector cavity. Phase spaces were determined by the analysis of beam energy spectra and pulse shapes at 17.5 MeV for micropulse charges between 0.5 and 5 nC. Additional data has been obtained at lower beam charges but with higher peak current densities at the photocathode. A simple ray tracing model was used to transform the injector phase space through the accelerator and around a 180°, three dipole, non-isochronous bend. The phase space parameters at the injector exit are varied to fit the data at 17.5 MeV. The data analysis shows the energy spread of the beam at the injector exit increases for peak current densities up to 600 A/cm 2 , while the pulse length remains essentially unchanged. The increased energy spread is explained by additional acceleration produced by the space charge electric field. At 800 to 1400 A/cm 2 , the pulse dissociates into multiple pulses separated by 40 to 90 ps. The paper argues the multiple pulses result from a combination of pulse length elongation and the formation of a “virtual cathode”. This is the first observation of these effects in an RF photoinjector.

The Boeing photocathode accelerator magnetic pulse compression and energy recovery experiment

Abstract An 18 MeV photocathode accelerator, consisting of a two-cell RF photocathode injector (previously operated at 27 MHz micropulse repetition frequency, 5 nC micropulse charge, and 25% duty factor [D.H. Dowell et al., Appl. Phys. Lett. 63 (1993) 2035]) followed by four new multicell cavities, all operating at 433 MHz, is currently being tested for FEL applications. In the present experiment, the inclusion of a third harmonic RF linearizer (operating at 1300 MHz) will allow tailoring of flat-topped micropulse shapes with high peak current. This pulse shaping leads to optimal FEL efficiency and is discussed in another contribution to this conference [J.L. Adamski et al.]. The 1300 MHz structure can also be used in a simple experiment to investigate energy recovery for high power and high efficiency FELs. In this case, proper RF phasing of the drive laser micropulses will allow the 1300 MHz accelerator section to simultaneously accelerate and decelerate alternate micropulses. Longitudinal phase space preparation for both experimental modes is discussed.

Proposed visible FEL facility at Boeing

The design for a potential free electron laser (FEL), driven by a 120-MeV linac capable of generating 0.1-A macropulse average current beams at a duty factor of 0.6%, is described. The accelerator will employ a photo-injected, 18-MeV, 433-MHz linac as an injector [T.D. Hayward et al., Proc. 1995 Particle Accelerator Conf., Dallas, TX, USA (1995)], followed by a 1300-MHz longitudinal phase space “linearizer” a magnetic buncher, and seven sections of 1300-MHz, pulsed traveling wave linac structure. Pulse lengths of 7 ps will be attained with minimal distortion of the pulse profile and normalized 90% emittance of 30 ± 10 πmm mr. The wiggler and magnets used to transport the beam will be reclaimed from previous FEL demonstration experiments.

The determination of an electron beam's longitudinal phase space distribution through the use of phase-energy measurements

Abstract We have been able to measure the longitudinal phase space distribution of the Stanford Superconducting Accelerator's (SCA) electron beam by applying tomographic techniques to energy spectra taken as a function of the relative phase between the beam and the accelerating field. The temporal profile of the beam obtained by projecting the distribution onto the time axis is compared with that obtained from interferometric transition radiation measurements.