Microwave Instability Research Articles

Vlasov simulation of the microwave instability

Advanced storage ring concepts for intense ion beams often require operation far outside the stability boundaries provided by Landau damping. Whether a machine can be operated in such a regime depends on the phase space dilution after saturation of the microwave instability. A Vlasov simulation model is employed to analyze the saturation mechanisms in space charge dominated coasting and bunched beams.

Correlations and coherence in the microwave instability

We expand upon the solvable model for the microwave instability in an electron storage ring as proposed in Wang (Phys. Rev. E 58 (1998) 984). The Vlasov–Maxwell equations are reduced to an integral eigenvalue problem similar to that which arises in the Karhunen–Loéve expansion theory for stochastic processes (Goodman, Statistical Optics, Wiley, New York, 1985). We derive first- and second-order correlation functions for the electron beam line density for the microwave instability. Using a set of coherent modes the correlation functions are diagonalized. A relationship between the first- and second-order correlation functions is obtained and it is shown to be similar to that of the Hanbury-Brown Twiss experiment (Born and Wolf, Principles of Optics, 6th Edition, Pergamon press, New York, 1980; Loudon, The Quantum Theory of Light, Clarendon press, Oxford, 1983). We obtain an expression for the Wigner distribution in terms of the first-order correlation function and relate this to the power in the electric field. We introduce an entropy-like quantity to characterize the coherence of the instability.

Vlasov simulation of the microwave instability in space charge dominated coasting ion beams

Advanced storage ring concepts for intense ion beams often require operation far outside the stability boundaries provided by Landau damping. Whether a machine can be operated in such a regime depends on the phase space dilution after saturation of the microwave instability. A Vlasov simulation model is employed to analyze the saturation mechanisms in space charge dominated coasting beams. The stabilizing effect of space charge [I. Hofmann, Laser Part. Beams 3, 1 (1985)] is addressed to fluidlike mode coupling effects.

Microwave instability in electron storage rings

Tracking simulations, with the aim of studying the microwave regime with short and intense bunches, suggest different instability mechanisms, according to the impedance model. In order to get a better insight of the source of the instability, i.e. azimuthal or radial mode coupling, we choose to follow the Sacherer (IEEE Trans. Nucl. Sci. NS-24, 1977 1393) approach to investigate the stability of the stationnary solution. The generalized Sacherer's integral, including mode coupling and potential well distortion, is then solved by using the “step function technique” for the expansion of the radial function, as proposed by Oide and Yokoya (KEK Preprint-90-10, April, 1990). For illustration, the effect of the resonant frequency of a broadband resonator in the SOLEIL storage ring is studied. When the resonator frequency is much higher than the bunch spectrum width, azimuthal mode coupling can occur before radial mode coupling. When the resonator frequency is lower, radial mode coupling comes usually first, but two or more bunchlets are produced at relatively low current. The diffusion process between the bunchlets, which leads to the well-known “saw-tooth” behavior, originates actually from a fast-growing microwave instability. Lastly, the beneficial effect of an harmonic cavity on the microwave instability is estimated and discussed.

Beam instability issues of the50GeV×50GeVmuon collider ring

Single bunch instabilities for the $50\mathrm{GeV}\ifmmode\times\else\texttimes\fi{}50\mathrm{GeV}$ muon collider are discussed. An impedance budget of the collider is estimated. A phase-slip factor of $|\ensuremath{\eta}|=1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ is desired to avoid excessive rf systems. Potential-well distortion of a smooth bunch can be compensated by rf cavities. Accumulated growth in energy due to imperfections and noises in the muon bunch can be reduced by smoothing the bunch distribution before injection. The growth due longitudinal microwave instability is small because of the compensated rf cavities, the finite lifetime of the muons, and the choice of a small $|\ensuremath{\eta}|$. Beamloadings in the compensating rf cavities are large and suitable feed-forward cancellation is required. Transverse microwave instability can be damped by chromaticities and octupoles. Beam breakup can be cured by Balakin-Novokhatsky-Smirnov damping in principle, but is nontrivial in practice. When beam breakup is small, it can possibly be damped by a betatron tune spread in the beam.

Single bunch behavior and microwave instability

The performance of the new generation of storage rings can be seriously limited by the microwave instability, an effect which causes increase of energy spread and consequent bunch lengthening. Although it is commonly present in storage rings, it still remains not completely understood. In this contribution the different methods used to study the microwave instabilities and the behavior of the bunch in such a regime are reviewed.

Storage ring free electron laser amplifiers and microwave instability

This work is aimed at investigating the storage ring free electron laser longitudinal dynamics. In particular we analyze the effects of the free electron laser interaction on the turbulent anomalous bunch lengthening due to the microwave instability. It is shown that the free electron laser interaction can counteract the microwave instability by simultaneously heating the e-beam, and by modifying the machine characteristic damping times.

Storage ring saw-tooth and microwave instability and free electron laser

An umber of theoretical and experimental investigations have suggested that the Free Electron Laser operating with Storage Rings produce effects which inhibit various type of beam instabilities. We exploit simple arguments, based on well-known heuristic criteria, to derive the critical intracavity power necessary to switch off longitudinal instabilities of the microwave and saw-tooth type. The dynamics of the instability is described by exploiting a couple of equations which account for the evolution of the instability growth rate and for the consequent e-beam energy spread enhancement. These equations, implicitly containing the Boussard criterion, are combined to the Free electron laser rate equations model, to study the dynamical interplay between the laser growth and the mechanisms which lead to the instability suppression and to precise the conditions under which this effect occurs.

Microwave instability as a coherent light source

We suggest that the coherent radiation observed recently at SURF II and the National Snychrotron Light Source vacuum ultraviolet ring is due to coherent microwave instability or, equivalently, to {open_quotes}microbunching{close_quotes} of the electron beams in the storage rings. We formulate in this paper the problem of microwave instability in the time domain. A linear homogeneous integro-differential equation for the perturbed current distribution is derived to describe the microwave coherent motion inside the electron bunch. For a specific band-limited high-frequency impedance, the equation can be diagonalized analytically and the eigensolution manifests explicitly the characteristics of microbunching. Coherent radiation power is also calculated for this solvable model, assuming the instability to be initiated by the shot noise inherent in the electron beam. {copyright} {ital 1998} {ital The American Physical Society}

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.

Dynamics of a storage-ring FEL oscillator with the inclusion of the microwave instability

We present an analysis of the dynamical behavior of a storage-ring FEL oscillator with the inclusion of the microwave longitudinal instability. We prove that the FEL interaction provides a damping mechanism for this type of instability and we discuss the relevant physical interpretation. We also show that the numerical model, exploited to include the microwave instability effects, reproduces the relevant phenomenology and yields a dynamical basis for the Boussard criterion.

Observations of bunch-lengthening effects in the APS 7-GeV storage ring

Measurements of the bunch length and horizontal beam size at a bending magnet source point in the lattice versus single-bunch current have been done on the Advanced Photon Source (APS) 7-GeV storage ring. These data are relevant to issues (limits) of obtaining higher volume charge densities for storage-ring-based FELs. Bunch lengths from σ τ ∼ 25 to 70 ps were measured using a Hamamatsu C5680 dual-sweep streak camera. Additional complementary data on energy spread deduced from horizontal beam size at a dispersive point in the lattice were also tracked versus single-bunch current. Both optical synchrotron radiation (OSR) and X-ray synchrotron radiation (XSR) techniques were used. The significant bunch lengthening observed without a comparable horizontal size change ( ΔE growth) is consistent with the potential-well distortion model rather than the predictions of a microwave instability calculation. With higher RF gap voltage, peak currents up to 400 A were observed.

Nonlinear dynamics of microwave instability in accelerators

We develop a nonlinear theory of the weak single bunch instability in electron and positron circular accelerators and damping rings. A nonlinear equation is derived that governs the evolution of the amplitude of unstable oscillations with account of quantum diffusion effects due to the synchrotron radiation. Numerical solutions to this equation show a large variety of nonlinear regimes depending on the growth rate of the instability and the diffusion coefficient. Comparison with the observation in the Stanford Linear Collider Damping Ring at the Stanford Linear Accelerator Center shows qualitative agreement with the patterns observed in the experiment. {copyright} {ital 1997} {ital The American Physical Society}

Microwave Instability at Transition Crossing: Experiments and a Proton-Klystron Model

Longitudinal bunch shapes in the KEK proton synchrotron were measured by a fast bunch-monitor system, which showed the rapid growth of the instability at the frequency of {approximately}1GHz and significant beam loss just after transition energy. Temporal evolution of the microwave instability is explained for the first time with a proton-klystron model. {copyright} {ital 1997} {ital The American Physical Society}

Storage-ring free-electron-laser amplifiers and the microwave instability

We discuss the storage-ring longitudinal dynamics by including the contributions from a free-electron-laser amplifier and from the microwave instability. We show that the two effects exhibit a mutual interplay that leads, under certain conditions, to the inhibition of the start up of the microwave instability and/or to a reduction of the electron-beam heating due to the free-electron laser. The agreement with the experimental results is also discussed.

Microwave instability beyond threshold.

Stability of the steady-state bunch distribution described by the Haissinski solution [J. Haissinski, Nuovo Cimento {bold 18B}, 72 (1973)] is studied above the threshold of microwave instability. It is shown that instability may lead to a new self-consistent state corresponding to particles trapped in a separatrix of an unstable mode. The free energies of the two solutions are compared. The relaxation oscillations between the new and Haissinski solutions are possible and may be related to the sawtooth instability observed recently in the experiments [P. Krejcik {ital et} {ital al}., (unpublished)]. {copyright} {ital 1996 The American Physical Society.}

Dynamical aspects of FEL interaction in single passage and storage ring devices

The dynamical behaviour of the free-electron lasers is investigated by using appropriate scaling relations valid for devices operating in the low and high gain regimes, including saturation. The analysis is applied to both single passage and storage ring configurations. In the latter case the interplay between the interaction of the electron beam with the laser field and with the accelerator environment is investigated. In particular we discuss the effect of FEL interaction on the microwave instability.

Some aspects of the design study on a fourth-generation-like VUV/SXR light source

Some aspects of the design study on a fourth-generation-like [1] vacuum ultraviolet/soft X-ray (VUV/SXR) light source are summarized. A storage ring lattice adopting a seven-bend achromat (SBA) [2] structure is presented. High brightness and coherence of SR light are emphasized. The natural electron beam emittance reaches as low as 0.25 nm.rad at 2 GeV. The ring circumference is 473.68 m. Eight 7-m long and four 18-m long dispersion-free straights are available for installation of insertion devices (IDs) and other kinds of equiqment. Sources based on long undulators placed in long straights would be able to provide SR spectra with a photon beam brightness up to 10 21 photons/s/mrad 2/mm 2/0.1%BW. The Touschek lifetime, which is reputed as one of the most crucial issues for design of such low energy (2–4 GeV), low emittance (in the 10 −10 m.rad range) light sources, has been studied by taking into account the bunch lengthening and intra-beam scattering effects. We find that at lower energies (around 2 GeV) both the bunch length and momentum spread increase by a factor of 2.7 due to the longitudinal microwave instability, and the emittance blows up by factors of 2.7–4.4, corresponding to coupling ratios of 10%-1%, caused by the intra-beam scattering; however, at the higher energies (around 4 GeV), there are no remarkable changes for these parameters (an average bunch current of 1 mA is assumed throughout the calculation). Thus, the energy dependence of the Touschek lifetime is modified correspondingly, and the Touschek lifetime issue becomes less serious at the cost of the bunch lengthening and widening and the emittance blowup at the low energy range.

Space-charge-dominated bunched beams in the frequency domain.

The effect of space charge on high-phase-space-density bunched beams in an ion storage ring with electron cooling is investigated in the frequency domain for bunches in the vicinity of the local microwave instability threshold. Space charge causes a splitting of synchrotron satellites into incoherent and coherent lines. Results of measurements of the splitting and shift are compared with analytical formulas as well as with simulation of the noise spectra by multiparticle computer simulation. Coherent frequencies of the quadrupole and sextupole modes of Gaussian bunches are found to deviate slightly from the analytical mode frequencies. Consequences for the interaction with narrow-band impedances and on the possible accuracy of \ensuremath{\Delta}p/p momentum-spread measurements for high-phase-space-density bunches are briefly discussed. \textcopyright{} 1996 The American Physical Society.