Large Piwinski Angle Research Articles

Strong–strong beam–beam simulations with lattices of circular e+e- colliders

Strong–strong beam–beam simulations for circular colliders are very time-consuming. Thus far, such simulations have predominantly utilized a linear transfer matrix to represent the full nonlinear lattice. Otherwise, when nonlinear lattices were included, beam–beam interactions were usually studied by using weak–strong or quasi-strong–strong numerical models. The next-generation circular colliders, including FCC-ee at CERN, CEPC in China, and the Super Tau-Charm Factories in China and Russia, will leverage the crab waist collision scheme with a large Piwinski angle. This scheme has already been employed in the two currently operational colliders, DAFNE and SuperKEKB. Accurate predictions of the performance of such colliders call for strong–strong beam–beam simulations, taking into account the interplay of the beam–beam interaction with lattice nonlinearities, impedances, and other collective effects. To answer this call, a novel code APES-T that allows integrating the direct strong–strong beam–beam simulations with element-by-element nonlinear tracking has been developed. To overcome the limitations in computing time, APES-T employs parallelization techniques. Specifically, the beam–beam module is parallelized using MPI programming, while the element-by-element tracking modules are parallelized using GPU programming. In this paper, we present the development of the APES-T code, its benchmark against the SAD code, and its application to the CEPC in investigating the interplay between beam–beam interaction, beamstrahlung, and lattices.

Combined phenomenon of transverse impedance and beam-beam interaction with large Piwinski angle

Combined phenomenon of transverse impedance and beam-beam interaction with large Piwinski angle

Coupling effects of beam-beam interaction and longitudinal impedance

Recent studies have shown a novel coherent head-tail instability induced by beam-beam interaction with a large Piwinski angle. The instability has become an important issue during the designs of CEPC and FCC-ee. Simulations have further revealed that the longitudinal impedance has a strong impact on the beam stability, squeezing the horizontal stable tune area seriously. The cross-wake force has been introduced to represent beam-beam interaction. A mode coupling theory based on the localized wake (impedance) force has been developed to explain the instability. However, the theory did not consider the effects of longitudinal impedance. In this paper, we develop a new transverse mode coupling analysis method that could be used to study the beam-beam instability with and without longitudinal impedance. The result shows that the distortion of longitudinal phase space trajectory and the incoherent synchrotron tune shift induced by longitudinal impedance would reduce the stable tune area.

How to increase the physics output per MW.h for FCC-ee?

The efficiency of colliders for physics is largely determined by their luminosity, while most of the energy consumed by high-energy e^+e^- colliders is proportional to the total beam current. Thus, the energy efficiency is mainly determined by the specific luminosity that needs to be maximized. One of the most effective ways to achieve this is by using the Crab waist collision scheme, which implies a large Piwinski angle (LPA). A distinctive feature of the FCC-ee is the great influence of beamstrahlung (radiation in the field of an opposite bunch) on beam dynamics. At low energies, this manifests itself in a significant increase in the energy spread and bunch length, at high energies, in a limitation of the beam lifetime. The collision of intense bunches with LPA and beamstrahlung can also lead to various kinds of instabilities limiting the luminosity. Here, we discuss the main aspects to consider when optimizing the parameters of the FCC-ee collider at different energies and explain the choice of basic parameters such as RF voltage, lattice functions at IP, bunch intensity, etc. We will also pay attention to open issues requiring further study and identify some key points for the next phase of this project.

An interplay between beam–beam and beam coupling impedance effects in the Future Circular e$$^+$$e$$^-$$ Collider

In order to reach high luminosity, the Future Circular e\(^+\)e\(^-\) Collider will need very intense beams with small emittances and small beta functions in the interaction points. This is achieved with a large Piwinski angle combined with the crab waist collision scheme. Under these conditions, the luminosity and the beam–beam tune shifts are strongly influenced by the bunch length. On the other hand, in this machine, the beamstrahlung effect is dominant too, leading to an increase of bunch length and energy spread. Moreover, due to the extreme beam parameters, new important beam–beam instabilities have been found, such as the so-called coherent X-Z instability. Finally, the bunch length and energy spread are also affected by collective effects. In this paper, we study the beam–beam interaction, by focusing on the X-Z instability for FCC-ee, in the lowest energy configuration (45.6 Gev, Z-resonance), by taking into account, self-consistently, the combined effects of beamstrahlung and the machine impedance model that has been evaluated so far. Finally, we also discuss some possible mitigation methods.

FCC-ee: the synthesis of a long history of e+e- circular colliders

The design of FCC-ee is relying on the accumulated experience of mathrm {e^{+}e^{-}} colliders that have been designed, constructed and operated in the past 40 years. FCC-ee will surpass the 26.7 km long Large Electron Positron collider LEP by a factor 4 in size. Like for LEP the large size is justified by the need to control the synchrotron radiation losses that for both machines reach a few percent per turn. To that end LEP had the first large super-conducting (SC) RF system with around 3.8 GV of accelerating voltage. LEP achieved for the first time very large beam-beam parameters of around 0.08, and it relied on transversely polarized beams to determine accurately the beam energy for the experiments. The DAvarPhi NE collider, together with PEP II and KEKB split the two beams into separate vacuum chambers to reach much higher Ampere-level beam currents. To overcome beam-beam lifetime and performance issues DAvarPhi NE used for the first time the Crab Waist concept for the interaction region (IR) optics. The B-factories, PEP-II and KEKB have verified the double-ring mathrm {e^{+}e^{-}} collider with multi-ampere stored currents for over 1000 bunches, small beta ^*, top-up injection, and achieved then-highest luminosity. KEKB has applied 22-mrad crossing angle at the IP with crab crossing. Both machines inherited accelerator techniques from their predecessors, PEP and TRISTAN, which was a small-scale LEP. Currently the next generation SuperKEKB collider is starting up. It has already achieved some milestones required for FCC-ee such as small beta ^* (0.8 mm) and virtual crab-waist scheme with a large Piwinski angle (>10).

Combined Effect of Beam-Beam Interaction and Beam Coupling Impedance in Future Circular Colliders

The future large scale electron-positron colliders, such as FCC-ee in Europe and CEPC in China, will rely on the crab waist collision scheme with a large Piwinski angle. Differently from the past generation colliders both luminosity and beam-beam tune shifts depend on the bunch length in such a collision scheme. In addition, for the future circular colliders with extreme beam parameters in collision several new effects become important such as beamstrahlung, coherent X-Z instability and 3D flip-flop. For all these effects the longitudinal beam dynamics plays an essential role and should be taken into account for the collider luminosity optimization. In this paper we discuss an impact of the longitudinal beam coupling impedance on the collider performance.

Design of beam optics for a Super Tau-Charm Factory

Beam optics design for a Super Tau-Charm Factory (STCF) that planning in China is presented in this paper. This STCF is an electron-positron circular collider characterized with high luminosity, wide energy ranges as well as high longitudinally polarized electron beam. In order to achieve high luminosity, the recently proposed collision scheme based on large Piwinski angle and crab waist sextupole will be adopted. In this paper, the beam optical parameters and their design basis for the STCF storage ring lattice are given. In addition, the preliminary dynamic aperture and beam-beam simulation are studied to get a luminosity more than 0.5 × 1035 cm-2 s-1 at the optimized energy 2 GeV.

Self-consistent simulations of beam-beam interaction in future e+e− circular colliders including beamstrahlung and longitudinal coupling impedance

For the past generation ${e}^{+}{e}^{\ensuremath{-}}$ storage ring colliders, we usually used natural bunch length or its impedance lengthened value in beam-beam simulations instead of considering the impedance directly. In the future colliders, such as FCC-ee and CEPC, the beam-beam interaction becomes essentially three dimensional. In order to increase the luminosity, the future accelerators will collide very intense beams of high energy with low emittances and small beta functions at the collision points exploiting the crab waist collision scheme with a large Piwinski angle. For these extreme parameters several new effects become important for the collider performance such as beamstrahlung, coherent X-Z instability, 3D flip-flop so that the longitudinal beam dynamics should be also treated in a self-consistent manner. In this paper we describe the numerical code for the self-consistent 3D beam-beam simulations including beamstrahlung and the longitudinal beam coupling impedance and study interplay of different effects arising in beam-beam collisions of the future colliders.

Compact Superconducting High Gradient Quadrupole Magnets for the Interaction Regions of High Luminosity Colliders

Recent developments in the high luminosity <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sup> colliders are based on a collision scheme with a large Piwinski angle, a vertical beta function β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</sub> much smaller than the bunch length, and a crab waist transformation. This scheme is being adopted in the SuperB asymmetric collider, to be built in Italy, with a design peak luminosity of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">36</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> sec <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> . A crucial role is played by the quadrupole doublets QD0/QF1, which are placed close to the interaction point and generate gradients close to 100 T/m. The available space for the doublets is very small, causing the magnets to be operated with a high engineering current density (2000 A/mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). Starting from the helical coil concept, an advanced design of the quadrupole has been developed. The paper discusses the basic design concepts and the development of a coil model aimed at assessing the design criteria and demonstrating the feasibility of the quadrupole. The successful test of the coil model opens the way to new compact superconducting high gradient quadrupole magnets for the interaction regions of high luminosity colliders.

Design, Construction and Test of a Model Superconducting Quadrupole for the Interaction Region of Super $B$ Factory

Super is an asymmetric energy e+e- collider operating at the Y(4S) peak (√s ~ 10.58 GeV) to be built in Italy, with a design peak luminosity of 1036 Hz/cm2. In order to get the required high luminosity, a novel collision scheme, the so called “large Piwinski angle and crab waist”, has been designed. This scheme requires that two doublets of high gradient superconducting quadrupoles (denominated in the Super B naming scheme as QD0 and QF1) are placed as close as possible to the interaction point. This layout is critical because the space allowed to the doublets is very small. An advanced design of the quadrupole has been developed, based on the so-called helical coil concept. The paper discusses the design and construction concept of a model of the superconducting quadrupole based on NbTi technology.

Simulations of electron-cloud heat load for the cold arcs of the CERN Large Hadron Collider and its high-luminosity upgrade scenarios

The heat load generated by an electron cloud in the cold arcs of the Large Hadron Collider (LHC) is a concern for operation near and beyond nominal beam current. We report the results of simulation studies, with updated secondary-emission models, which examine the severity of the electron heat load over a range of possible operation parameters, both for the nominal LHC and for various luminosity-upgrade scenarios, such as the so-called ``full crab crossing'' and ``early separation'' schemes, the ``large Piwinski angle'' scheme, and a variant of the latter providing ``compatibility'' with the (upgraded) LHCb experiment. The variable parameters considered are the maximum secondary-emission yield, the number of particles per bunch, and the spacing between bunches. In addition, the dependence of the heat load on the longitudinal bunch profile is investigated.

DAΦNE STATUS AND PLANS

The DAΦNE e+e- collider in Frascati has steadily improved its performances since year 2000, reaching in 2006 a maximum luminosity of 1.6 1032 cm-2s-1. Recently the crab waist collision scheme has been proposed, which allows to keep in collision two beams at large Piwinski angle with the effect of reducing the spot size at the interaction point while suppressing synchrobetatron resonances. The DAΦNE e+e- collider has been upgraded according to this scheme and the first measurements are confirming the expectations. Meanwhile a proposal for an extension of the KLOE physics program, namely a KLOE-2 program, aiming to collect at least a factor of 10 more statistics with a partially upgraded detector, has been submitted. A first step of this program has been approved to take data during year 2009.

PRESENT STATUS OF THE DAΦNE UPGRADE AND PERSPECTIVES

The DAΦNE collider has been recently upgraded in order to implement a new collision scheme based on large Piwinski angle and cancellation of the synchro-betatron resonances by means of electromagnetic sextupoles (Crab-Waist compensation). The novel approach has proved to be effective in improving beam-beam interaction and collider luminosity. The results and the measurements taken during commissioning as well as the perspectives for the SIDDHARTA run are presented and discussed.

Compensations of beam–beam resonances using crabbing schemes at large Piwinski crossing angles

We study combined effects of the crab crossing and of the crab waist lattice options on the luminosity performance of a collider where the crossing angle collisions are used. We have found that for collisions at large Piwinski angle a proper combination of the crab crossing and of the crab waist lattice insertions results in exact cancellation of all synchro-betatron as well as of all betatron coupling beam–beam resonances of odd orders. The beam–beam limitations on the luminosity for such a collider with the crossing angle collisions will be the same like that for a collider with head-on collisions of short bunches.

SuperB project status and prospectives

An international collaboration on the design of a Super B-Factory aiming at a 1036cm-2 s-1 luminosity is in progress. The design relies on a new collision scheme with large Piwinski's angle and very small IP beam sizes, where possible harmful resonances will be cancelled by the newly proposed 'crab waist' method. A Conceptual Design Report has been published in April this year. A review of the design principles and of the project status will be 2given.

SuperB project status and prospectives

An international collaboration on the design of a Super B-Factory aiming at a 1036cm-2 s-1 luminosity is in progress. The design relies on a new collision scheme with large Piwinski's angle and very small IP beam sizes, where possible harmful resonances will be cancelled by the newly proposed ‘crab waist’ method. A Conceptual Design Report has been published in April this year. A review of the design principles and of the project status will be 2given.