Gaussian Bunch Research Articles

Density distributions of tune shifts from space charge or beam-beam interactions in Gaussian bunches

Density distributions of tune shifts from space charge or beam-beam interactions in Gaussian bunches

Beam-beam interaction in a dielectric laser accelerator electron-positron collider

We examine through numerical calculation the collision of counter-propagating trains of optically spaced electron or positron microbunches in a 1 TeV collider scenario for a dielectric laser accelerator. A time-dependent envelope equation is derived for arbitrary number of bunches in the classical limit, with inclusion of the radiation reaction force. Example parameters are examined based on a constrained luminosity relation that takes into account the bunch charge for optimal efficiency, material damage limits, and power constraints. We find that for initially identical counter-propagating Gaussian bunch trains, the periodic temporal structure leads to a peak in luminosity with number of bunches. For longer bunch trains, the enhancement then decreases inversely with number of bunches. The corresponding fractional energy loss of the beam is found to be of order 1.75%, which is reduced to 0.35% when the nonlinear radial dependence of the transverse force is included, with an average beamstrahlung parameter of 0.075, an important result considering that beamstrahlung losses are a critical concern for future TeV colliders.

Noninvasive bunch length measurements exploiting Cherenkov diffraction radiation

We present the observation and the detailed investigation of coherent Cherenkov diffraction radiation (CChDR) in terms of spectral-angular characteristics. Electromagnetic simulations have been performed to optimize the design of a prismatic dielectric radiator and the performance of a detection system with the aim of providing longitudinal beam diagnostics. Successful experimental validations have been organized on the CLEAR and the CLARA facilities based at CERN and Daresbury laboratory respectively. With ps to sub-ps long electron bunches, the emitted radiation spectra extend up to the THz frequency range. Bunch length measurements based on CChDR have been compared to longitudinal bunch profiles obtained using a radio frequency deflecting cavity or coherent transition radiation (CTR). The retrieval of the temporal profile of both Gaussian and non-Gaussian bunches has also been demonstrated. The proposed detection scheme paves the way to a new kind of beam instrumentation, simple and compact for monitoring short bunches of charged particles, particularly well-adapted to novel accelerator technologies, such as dielectric and plasma accelerators. Finally, CChDR could be used for generating intense THz radiation pulses at the MW level in existing radiation facilities, providing broader opportunities for the user community.

Probability of radiation of twisted photons by axially symmetric bunches of particles

The effect of a finite width of a particle bunch on radiation of twisted photons is studied. The general formulas connecting the radiation probability distribution of twisted photons produced by bunches of identical particles with the radiation probability distribution of twisted photons generated by one particle are obtained for axially symmetric bunches. The bunch is called axially symmetric if it is axially symmetric with respect to the detector axis at some instant of time and all the particles in the bunch move along parallel trajectories. The general sum rules for the probability of radiation of twisted photons by axially symmetric bunches are established. In particular, we prove that the projection of the average total angular momentum of radiated twisted photons per particle in the bunch does not depend on the radial profile of the bunch. The uniform, Gaussian, and exponential radial bunch profiles are considered in detail. The radiation of axially symmetric bunches in ordinary and crystalline undulators is investigated. The selection rules for radiation of twisted photons by one particle in undulators are violated when the finite width of the particle bunch is taken into account. We find the condition when this violation is marginal. The form of the radiation probability distribution of twisted photons becomes universal for wide incoherent axially symmetric particle bunches. We completely describe these universal distributions.

Radiation field of an ideal thin Gaussian bunch moving in a periodic conducting wire structure

A theoretical approach for describing the electromagnetic radiation produced by prolonged electron bunch propagating in the lattice of metallic wires of finite length is presented. This approach is based on vibrator antenna theory and involves approximate solving of Hallen's integral equation. For a single wire, it is also supposed that a wire is sufficiently thin and charge motion is relativistic. For many-wire structures, the approximation similar to kinematic approach of parametric X-ray radiation (PXR) theory is additionally applied. The validity of the method is verified by numerical simulations with COMSOL Multiphysics. Possible applications of interaction between charged particle bunches and artificial wire structures are discussed.

Cherenkov radiation of a charge exiting open-ended waveguide with dielectric filling

We consider a semi-infinite open-ended cylindrical waveguide with uniform dielectric filling placed into collinear infinite vacuum waveguide with larger radius. Electromagnetic field produced by a point charge or Gaussian bunch moving along structure's axis from the dielectric waveguide into the vacuum one is investigated. We utilize the modified residue-calculus technique and obtain rigorous analytical solution of the problem by determining coefficients of mode excitation in each subarea of the structure. Numerical simulations in CST Particle Studio are also performed and an excellent agreement between analytical and simulated results is shown. The main attention is paid to analysis of Cherenkov radiation generated in the inner dielectric waveguide and penetrated into vacuum regions of the outer waveguide. The discussed structure can be used for generation of Terahertz radiation by modulated bunches (bunch trains) by means of high-order Cherenkov modes. In this case, numerical simulations becomes difficult while the developed analytical technique allows for efficient calculation of the radiation characteristics.

Wakefield acceleration in multilayer dielectric waveguide with usage of ring beam

In this paper, we simulated the process of wakefield acceleration of electron Gaussian bunch by electron ring beam. The beam dynamics of ring uniform is discussed in detail. Calculation results show that wakefield accelerating scheme is more effective compared to the scheme with one-layer dielectric waveguide excited by gaussian bunch.

Bunch length scaling due to broadband impedance as a parameter for transverse feedback application

This paper investigates the possibility for suppression of the head–tail instability in an electron storage ring using a bunch-by-bunch transverse feedback system. General conditions are found whereby the Gaussian bunch profile may be modeled by a two-particle system which interacts with the vacuum chamber broadband impedance. We choose the kick factor received by a Gaussian bunch with the rms bunch length σt, from a broadband impedance with the resonance frequency ωr and quality factor Qr, as the relevant parameter and explain why the kick factor depends on ωrσt∕Qr. Finally, we demonstrate that a Gaussian bunch can be modeled by a two-particle system when the parameter ωrσt∕Qr is sufficiently small.

Optimization of electron bunch injection in dielectric laser acceleration

Dielectric laser acceleration (DLA) is new cheap and miniature laser acceleration scheme for acceleration of charged particles in the vicinity of the dielectric grating. In this paper injection characteristics of the electron bunch in a single fused silica grating based-structure with period λg = 260 nm is analyzed. Optimum aspect ratios of the grating width d/λg and height h/λg are obtained for the first surface mode harmonic. Simulation results of the injected electron dynamics show that there are two lateral positions (y = 1.75 and y = 2.6 μm) that the final electron energy is maximized. Existence of these two lateral positions increases flexibility of the injection process. In other words, injection can be made in the range of 1.4 < y(μm)<2.8 with two peaks of energy. Finally, injection of Gaussian electron bunch at each two optimum transverse positions is investigated by a numerical simulation. The initial momentum distribution is assumed to be Gaussian around the mean resonance velocity (β = λg/λ = 0.33). The initial longitudinal and transverse emittance of the electron bunch are selected as ε|| = (δE/E) = 0.01 and, ε⊥ = 3μmmrad respectively. The net energy gain in the fifty grating periods is 2.03 keV (2.225 keV) and acceleration gradient for each injection position is about 160 MeV/m.

Bunch radiation from a semi-infinite waveguide with dielectric filling inside a waveguide with larger radius

We consider a point charge and Gaussian bunch of charged particles moving along the axis of a circular perfectly conducting pipe with uniform dielectric filling and open end. It is supposed that this semi-infinite waveguide is located in collinear infinite vacuum pipe with perfectly conducting walls and larger diameter. We deal with two cases corresponding to the open end of the inner waveguide with and without flange. Radiation produced by a charge or bunch flying from dielectric part to wide vacuum part is analyzed. We use modified residue-calculus technique and construct rigorous analytical theory describing scattered field in each sub-area of the structure. Cherenkov radiation generated in the dielectric waveguide and penetrating into the vacuum regions of the structure is of main interest throughout the present paper. We show that this part of radiation can be easily analyzed using the presented formalism. We also perform numerical simulation in CST PS code and verify the analytical results.

Проходження гауссового пучка крізь квадратично-неоднорідну призму

Проходження гауссового пучка крізь квадратично-неоднорідну призму

Radiation of a Charge Intersecting a Boundary Between a Bilayer Area and a Homogeneous One in a Circular Waveguide

This paper is devoted to the analysis of electromagnetic field excited by a charge moving in a circular waveguide, which consists of two semi-infinite parts. The charge moves with a constant velocity along the waveguide axis from the partially dielectric section into the homogeneous one. It is assumed that Cherenkov radiation is generated in the bilayer section. The total field is represented as a sum of a known forced field that is the field of the charge in the infinite regular waveguide and a free field resulting from the presence of the transverse boundary. The infinite system of algebraic equations for amplitudes of the free-field modes is derived. The further analysis is conducted using numerical calculations. Special attention is given to the study of the so-called Cherenkov-transition radiation (CTR) within the homogeneous part of the waveguide volume. Typical distributions of CTR over frequencies and modes are presented for the case when the channel and the homogeneous area are free of medium. Analytical results obtained for the point charge are generalized for the charged bunch with an arbitrary profile and verified using direct simulations for the case of Gaussian bunch.

Optimized stability of a modulated driver in a plasma wakefield accelerator

AbstractWe analyze the transverse stability for a configuration of multiple Gaussian bunches subject to the self-generated plasma wakefield. Through a semi-analytical approach we first study the equilibrium configuration for the modulated beam and then we investigate the evolution of the equilibrium configuration due to the emittance-driven expansion of the beam front that results in a rigid backward shift. The rear-directed shift brings the modulated beam out of the equilibrium, with the possibility for some of the bunch particles to be lost with a consequent deterioration of the driver. We look therefore for the proper position of the single bunches that maximize the stability without severely affecting the accelerating field behind the driver. We then compare the results with three-dimensional particle in cell simulations.

Transformer ratio saturation in a beam-driven wakefield accelerator

We show that for beam-driven wakefield acceleration, the linearly ramped, equally spaced train of bunches typically considered to optimise the transformer ratio only works for flat-top bunches. Through theory and simulation, we explain that this behaviour is due to the unique properties of the plasma response to a flat-top density profile. Calculations of the optimal scaling for a train of Gaussian bunches show diminishing returns with increasing bunch number, tending towards saturation. For a periodic bunch train, a transformer ratio of 23 was achieved for 50 bunches, rising to 40 for a fully optimised beam.

Multibunch and multiparticle simulation code with an alternative approach to wakefield effects

The simulation of beam dynamics in the presence of collective effects requires a strong computational effort to take into account, in a self-consistent way, the wakefield acting on a given charge and produced by all the others. Generally this is done by means of a convolution integral or sum. Moreover, if the electromagnetic fields consist of resonant modes with high quality factors, responsible, for example, for coupled bunch instabilities, a charge is also affected by itself in previous turns, and a very long record of wakefield must be properly taken into account. In this paper we present a new simulation code for the longitudinal beam dynamics in a circular accelerator, which exploits an alternative approach to the currently used convolution sum, reducing the computing time and avoiding the issues related to the length of wakefield for coupled bunch instabilities. With this approach it is possible to simulate, without the need for large computing power, simultaneously, the single and multibunch beam dynamics including intrabunch motion. Moreover, for a given machine, generally both the coupling impedance and the wake potential of a short Gaussian bunch are known. However, a classical simulation code needs in input the so-called ``Green'' function, that is the wakefield produced by a point charge, making necessary some manipulations to use the wake potential instead of the Green function. The method that we propose does not need the wakefield as input, but a particular fitting of the coupling impedance requiring the use of the resonator impedance model, thus avoiding issues related to the knowledge of the Green function. The same approach can also be applied to the transverse case and to linear accelerators as well.

Analytic calculation of the electric field of a coherent THz pulse

Accelerators can serve as sources for intense THz radiation by producing sub-ps long electron bunches, which generate synchrotron radiation coherently in the THz regime. In this paper, we present an analytic method to calculate the electric field pulse emitted by an electron bunch with arbitrary bunch shape. Our method is applied to a Gaussian bunch as well as a complex bunch profile resulting from a nonlinear beam dynamics simulation.

Quasineutral plasma expansion into infinite vacuum as a model for parallel ELM transport

An analytic solution for the expansion of a plasma into vacuum is assessed for its relevance to the parallel transport of edge localized mode (ELM) filaments along field lines. This solution solves the 1D1V Vlasov–Poisson equations for the adiabatic (instantaneous source), collisionless expansion of a Gaussian plasma bunch into an infinite space in the quasineutral limit. The quasineutral assumption is found to hold as long as λD0/σ0 ≲ 0.01 (where λD0 is the initial Debye length at peak density and σ0 is the parallel length of the Gaussian filament), a condition that is physically realistic. The inclusion of a boundary at x = L and consequent formation of a target sheath is found to have a negligible effect when L/σ0 ≳ 5, a condition that is physically plausible. Under the same condition, the target flux densities predicted by the analytic solution are well approximated by the ‘free-streaming’ equations used in previous experimental studies, strengthening the notion that these simple equations are physically reasonable. Importantly, the analytic solution predicts a zero heat flux density so that a fluid approach to the problem can be used equally well, at least when the source is instantaneous. It is found that, even for JET-like pedestal parameters, collisions can affect the expansion dynamics via electron temperature isotropization, although this is probably a secondary effect. Finally, the effect of a finite duration, τsrc, for the plasma source is investigated. As is found for an instantaneous source, when L/σ0 ≳ 5 the presence of a target sheath has a negligible effect, at least up to the explored range of τsrc = L/cs (where cs is the sound speed at the initial temperature).

Cherenkov-transition radiation in a waveguide with a dielectric-vacuum boundary

We analyze the electromagnetic field of a charged particle moving uniformly in a circular waveguide and crossing the boundary between a dielectric and a vacuum. Our study focuses on the case when Cherenkov radiation is generated in the dielectric. Analytical and numerical investigation of the waveguide modes is performed. We show that a large radiation can be excited in the vacuum area. The mode amplitudes in the vacuum can be greater than those in the dielectric. The field from a Gaussian bunch is also studied. We note that the effect under consideration can be used to generate a large quasimonochromatic or multimode radiation.

Transverse modes and instabilities of a bunched beam with space charge and resistive wall impedance

Transverse instability of a bunched beam is investigated with synchrotron oscillations, space charge tune shift, and resistive wall wakefield taken into account. A boxcar model is used for a general analysis, and truncated Gaussian distribution is invoked for details. The beam spectrum, instability growth rate, and effects of chromaticity are studied in a wide range of parameters, both with head-tail and collective bunch interactions included. Influence of internal bunch oscillations on the collective instabilities is investigated thoroughly. Landau damping caused by the space charge tune spread is discussed, and the instability thresholds of different modes of truncated Gaussian bunch are estimated.

Radiation of a charge moving in wire metamaterial perpendicularly to the main axis

We consider electromagnetic radiation of a charge which moves in a volume structure consisting of thin parallel wires and having small period. The structure is described by the permittivity tensor. The charge velocity is directed perpendicularly to the wires. Analytical and numerical investigations are performed for the case of point charge. Some unusual properties of radiation are noted. In particular, it is shown that radiation propagates along the wires and concentrates nearby certain "rays" behind the charge. The wave field doesn't decrease with increase in distance along these "rays". The cases of Gaussian and rectangular bunches with negligible thickness are considered as well. Prospects of use of structure under consideration for diagnostics of bunches are noted.