Momentum Compaction Research Articles

Longitudinal beam dynamics and FEL interaction on a negative momentum compaction storage ring

A simulation study for longitudinal phase space of the electron bunch including effects of potential-well distortion and FEL interaction has been performed for both positive and negative momentum compaction factors on a storage ring. The trend of the bunch lengthening is well interpreted by the wake field due to inductive impedance. In spite of large energy spread in the case of the negative momentum compaction, FEL oscillation may be possible. The peak power of Q-switched lasing is higher than that in positive momentum compaction. There was, however, no significant difference in FEL power and particle distribution in the longitudinal phase space at the equilibrated state.

Analysis of the longitudinal collective behavior in a50GeV×50GeVmuon collider ring

Simulations of the longitudinal instability in the $50\mathrm{GeV}\ifmmode\times\else\texttimes\fi{}50\mathrm{GeV}$ muon collider ring have been performed. Operation of the ring close to the slippage factor ${\ensuremath{\eta}}_{1}\ensuremath{\simeq}{10}^{\ensuremath{-}6}$, such that synchrotron motion is frozen, minimizes the need for rf to maintain the bunch length. However, there is still an energy spread due to the bunch wake. For design parameters of the ring, this induced energy is too large and must be controlled. This paper demonstrates that the bunch wake may be compensated for by two rf cavities with low rf voltages. These studies were made at the nominal design point, and sensitivities to errors were explored. It is seen that the small energy spread of the beam ($\ensuremath{\delta}E/E=3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$) in the $50\mathrm{GeV}\ifmmode\times\else\texttimes\fi{}50\mathrm{GeV}$ muon collider ring can be maintained during the 1000 turn lifetime of the muons. Controlled beam dynamics requires proper choice of rf parameters (rf voltage, rf frequency, and phase offset) for two cavities; these parameters depend on the ring design through the impedance, beam pipe radius, and momentum compaction. The simulation also shows that the computation of wake field using bins of variable width (each with a constant number of macroparticles in each bin) gives an accurate wake and also yields reduced computing time compared to an evaluation of the wake as the direct sum over the wakes of all preceding macroparticles.

Differential algebraic determination of high-order off-energy closed orbits, chromaticities, and momentum compactions

Abstract For some modern particle accelerators, including the planned muon collider, the accurate analysis of non-linear time-of-flight effects in the form of momentum compactions is critical for the preservation of bunch structure. A Differential Algebra-based (DA) method is presented that allows the determination of off-energy closed orbits and chromaticities to any order. By performing a coordinate transformation to the off-energy closed orbit, it is possible to compute momentum compactions analytically. This method has been implemented in the code COSY INFINITY and is tested for two cases where analytical solutions can be obtained by hand; agreement to machine precision is found. By contrast, comparisons are made with several codes that use conventional numerical methods for the determination of momentum compaction, and it is found that these approaches sometimes yield rather inaccurate results, especially for higher orders.

Single-bunch beam property for FEL on the UVSOR storage ring

Single-bunch beam properties such as bunch lengthening and instability that are very important factors to develop storage ring free electron lasers (SRFEL) have been investigated on the UVSOR electron storage ring. Data were analyzed based on a model of potential-well distortion due to the impedance of the vacuum pipe. The inductive impedance was obtained to be 40 nH which is approximately 10 times larger than that of a newly constructed 3rd generation light source. In an operation with negative momentum compaction factor, the bunch shortening was observed which is also explained by which the inductive impedance dominates the single bunch property on the UVSOR ring.

Correction of dispersion and the betatron functions in the CEBAF accelerator

During commissioning of the CEBAF accelerator, correcting dispersion, momentum compaction and betatron beam envelopes was essential for robust operation. To speed up the diagnostic process we developed a method which allows one to track and correct the machine optics on-line. The method is based on measuring the propagation of 30 Hz modulated betatron oscillations. Compared to the usual methods of dispersion or difference orbit measurement, synchronous detection of the beam displacement, as measured by beam position monitors, offers significantly improved speed and accuracy. The beam optics of the accelerator was altered to decrease lattice sensitivity at critical points and to simplify control of the betatron function match. The calculation of the Courant–Snyder invariant from signals of each pair of beam position monitors was used for a correction of the betatron functions.

Study of beam property on a storage ring operated with negative momentum compaction factor

To investigate variations of the bunch length and the energy spread of the electron beam on a storage ring, which are very important beam properties for storage ring free electron lasers, we have measured longitudinal electron distributions and spectra of spontaneous radiation from an optical klystron on the UVSOR storage ring operated with both signs of negative and positive momentum compaction factors. Significant differences in the bunch lengthening and the increase of the energy spread with the beam current have been found between two operations. In a case of the negative momentum compaction, a threshold beam current for the longitudinal microwave instability was observed to be very low, meanwhile “the bunch shortening” was observed.

Quasi-isochronous buckets in storage rings

In order to maintain a reasonable r.f. system, it may be necessary for a collider with ultra-short bunches to operate with a small slippage factor, for example, η < 1 × 10 −6 for all the particles in the bunches. The buckets dominated by the zeroth order, first order, or second order of η are examined, and the required r.f. voltages are computed. The problem of microwave instability is addressed. The reliability of computing higher-order momentum-compaction factor using lattice codes is examined.

Measurement of storage-ring lattice functions: Application to the Pohang Light Source

Measurement of the lattice functions was carried out in the storage ring for the light source. The measurement includes β, dispersion functions, phase advances, tunes, momentum compaction, chromaticities, and linear coupling. Two methods were used for the β measurement; a quadrupole-tweaking method and a method using a sensitivity matrix. Using the sensitivity-matrix method gives additional information on the phase between monitors and correctors, as well as the fractional part of the tunes. The linear-coupling constant was obtained by driving the tunes across the coupling resonance and measuring the minimum tune separation. It is also shown that by using four skew-quadrupole circuits, the coupling constant can be varied arbitrarily. In this article, a detailed method for the lattice-function measurement is presented, and the result applied to the storage ring of the Pohang Light Source is given. The measured results are compared with the design values and shown to be in good agreement.

Emittance manipulation by first- and second-order lattice control

The lattice of the MAX-I electron storage ring has been investigated and tuned towards small momentum compaction values. By measurements of the synchrotron frequency, bunch length, horizontal beam size and beam movement, the beam has been found to behave in reasonable agreement with the predictions of the lattice model up to second order in energy deviation. Both longitudinal and horizontal emittance could be varied within a relatively large range with lattice changes and/or controlled beam energy changes.

Design of the muon collider lattice: Present status

The last component of a muon collider facility, as presently envisioned, is a colliding-beam storage ring. Design studies on various problems for this ring have been in progress over the past year. In this paper we discuss the current status of the design. The projected muon currents require very low beta values at the IP, {beta}* = 3 mm, in order to achieve the design luminosity of L = 10{sup 35} cm{sup -2} s{sup -1}. The beta values in the final-focus quadrupoles are roughly 400 km. To cancel the corresponding chromaticities, sextupole schemes for local correction have been included in the optics of the experimental insertion. The hour-glass effect constraints the bunch length to be comparable too. To obtain such short bunches with reasonable rf voltage requires a very small value of the momentum compaction a, which can be obtained by using flexible momentum compaction (FMC) modules in the arcs. A preliminary design of a complete collider ring has now been made; it uses an experimental insertion and arc modules as well as a utility insertion. The layout of this ring is shown schematically, and its parameters are summarized. Though some engineering features are unrealistic, and the beam performance needsmore » some improvement, we believe that this study can serve as the basis for a workable collider design. The remaining sections of the paper will describe the lattice, show beam behaviour, and discuss future design studies.« less

Quasi-isochronous experiments with the Super-ACO storage ring

The aim of these experiments was to produce short light pulses by reducing the momentum compaction factor. These experiments show that the correction of the second-order term, using sextupole magnets, is essential in order to successfully reduce the momentum compaction by a large factor. By this technique, a factor of 100 reduction was obtained. However, most measurements were performed at a reduction factor of 13. Good agreement was obtained between experimental results and theoretical predictions.

Quasi-isochronous storage ring for enhanced FEL performance

Abstract A compact storage ring is designed to be used as driver for a free electron laser (FEL). This ring can be operated very close to zero momentum compaction factor (α) to increase the electron density and thus the gain of the FEL. In order to control α with zero dispersion in the straight sections we use an inverted dipole located between the bending magnets and 4 families of quadrupoles. By using 3 families of sextupoles we can control the 2 transverse chromaticities and 2nd order momentum compaction. We find that the ring has sufficient dynamic aperture for good performance.

Performance of SRRC 1.3 GeV electron booster synchrotron

The characteristics and the performance of SRRC 1.3 GeV electron booster synchrotron are described in this report. Operation parameters, such as synchrotron tune, betatron tune, momentum compaction factor, betatron function, chromaticity etc. were measured at injection energy, 50 MeV, DC mode; and compared with calculated results at a tune of v x = 4.40, v y = 2.43. The tune drift and the bunch length variation of accelerated beam have been studied. The energy spread and the beam emittance variation during ramping were derived. The diagnostics instrumentation used in this experiment was described. Comparison between experimental results and theoretical expectations is presented.

The isochronous storage ring free electron laser

The concept of an isochronous storage ring free electron laser is studied using a simple model based on the longitudinal moments of the stored electron distribution. Laser performance is given as a function of machine parameters including momentum compaction and current density. Altogether, using the model presented we are able to calculate laser rise time, saturation characteristics, output power, and the time-dependent longitudinal profile of the optical laser pulses.

Minimizing dispersion in flexible-momentum-compaction lattices.

Medium-energy accelerators are often confronted with problems during transition energy crossing, such as longitudinal microwave instability and nonlinear synchrotron motion. These problems can be avoided by an accelerator having a negative momentum-compaction factor. A modular method for designing a lattice with adjustable momentum-compaction factor is presented. The dispersion excursion of the basic flexible momentum compaction module can be minimized to less than the maximum dispersion of the focusing-defocusing (FODO) lattice containing the same FODO cells. The phase advance of the module can be adjusted to be an odd multiple of quarter betatron waves. We found that a lattice composed of such modules possesses excellent chromatic properties with excellent tunability, smaller systematic stop-band widths, and smaller sextupole distortion functions.

Control of the bunch length on an electron storage ring

We report on an experiment to control bunch length by means of changing the momentum compaction factor on the UVSOR storage ring. The momentum compaction factor was varied by changing the dispersion function, and reduced to be approximately one hundredth of the ordinary value. The shortest bunch length estimated from the synchrotron oscillation frequency was 25 ps, which is one tenth of the ordinary value. Correction for the second order momentum compaction factor was found to be essential for operation with the extremely low momentum compaction factor. The results of measurement of the momentum compaction factor and the bunch length are presented.

Second order single particle dynamics in quasi-isochronous storage rings and its application to the LNLS-UVX ring

We analyze the second order single particle longitudinal dynamics in a quasi-isochronous storage ring. We expand the momentum compaction factor to include the effects of second order terms taking sextupoles into account and of transverse betatron oscillations. The introduction of nonlinearities due to higher order terms results in a second stability region for longitudinal phase oscillations, in addition to the well known linear stable operation point. The conditions for this new solution to fall within the energy acceptance of the storage ring are presented. Inclusion of transverse motion coupling may lead to either a reduction or an enhancement of the stable longitudinal phase-space regions. The analysis is applied to the LNLS 1.15 GeV UVX electron storage ring, indicating that it should be possible to operate this ring in a quasi-isochronous mode.

Measurement of the Bunch Length on the UVSOR Storage Ring

We have measured the bunch length in single-bunch operation of the UVSOR (Ultraviolet Synchrotron Orbital Radiation) storage ring in a beam current region from 0.1 to 70 mA at energies ranging from 500 to 750 MeV. The momentum compaction factor of the present operation point is determined experimentally from the bunch length and the synchrotron oscillation frequency measured simultaneously at a low beam current. The bunch length increases gradually as the beam current increases, and bunch lengthening is larger when the beam energy is lower. This behavior of bunch lengthening agrees well with a prediction of the potential-well distortion theory. Based on the theory, the effective longitudinal coupling impedance is estimated as a function of bunch length.

Quasi-isochronous storage ring

We study the single particle and collective dynamics of a storage ring where the momentum compaction is made small to make it nearly isochronous, to reduce the bunch length and increase the peak current. We find that a quasi-isochronous ring makes it possible to obtain a bunch length in the millimeter range and to increase the beam longitudinal brilliance by more than one order of magnitude.

Beam dynamics in high-current cyclic electron accelerators

The physical processes affecting the transport and acceleration of high-power, high-quality electron beams in cyclic accelerators are reviewed. A distinction is made between those effects that are unique to recirculating geometries and those that also occur in linacs. Among the former are included the phenomena of momentum compaction, orbital resonances, and the negative mass instability; among the latter are the beam break-up and other microwave instabilities, the effects of image forces, and the problem of matching an incoming beam envelope to a transport line. All have played prominent roles in the design and operation of existing and planned cyclic machines. These dynamical effects and some experimental approaches to controlling them are discussed.