Feasibility Conditions for Interference Alignment

The degrees of freedom of MIMO interference networks with constant channel coefficients are not known in general. Determining the feasibility of a linear interference alignment solution is a key step toward solving this open problem. Our approach in this paper is to view the alignment problem as a system of bilinear equations and determine its solvability by comparing the number of equations and the number of variables. To this end, we divide interference alignment problems into two classes - proper and improper. An interference alignment problem is called proper if the number of equations does not exceed the number of variables. Otherwise, it is called improper. Examples are presented to support the intuition that for generic channel matrices, proper systems are almost surely feasible and improper systems are almost surely infeasible.Comment: 6 pages. Submitted to IEEE Globecom March 31 200

FEL potential of eRHIC

Brookhaven National Laboratory plans to build a 5-to-30 GeV energy-recovery linac (ERL) for its future electron-ion collider, eRHIC. In past few months, the Laboratory turned its attention to the potential of this unique machine for free electron lasers (FELS), which we initially assessed earlier. In this paper, we present our current vision of a possible FEL farm, and of narrow-band FEL-oscillators driven by this accelerator. eRHIC, the proposed electron-ion collider at BNL, takes advantage of the existing Relativistic Heavy Ion Collider (RHIC) complex. Plans call for adding a six-pass super-conducting (SRF) ERL to this complex to collide polarized- and unpolarized- electron beams with heavy ions (with energies up to 130 GeV per nucleon) and with polarized protons (with energies up to 325 GeV). RHIC, with a circumference of 3.834 km, has three-fold symmetry and six straight sections each {approx} 250 m long. Two of these straight sections will accommodate 703-MHz SRF linacs. The maximum energy of the electron beam in eRHIC will be reached in stages, from 5 GeV to 30 GeV, by increasing the lengths of its SRF linacs. We plan to install at the start the six-pass magnetic system with small gap magnets. The structure of the eRHIC's electron beam will be identical with that of its hadron beam, viz., 166 bunches will be filled, reserving about a one-microsecond gap for the abort kicker. With modest modifications, we can assure that eRHIC's ERL will become an excellent driver for continuous wave (CW) FELs (see Fig.1). The eRHIC's beam structure will support the operation of several such FELs in parasitic mode

Unique Features in Magnet Designs for R and D Energy Recovery Linac at BNL.

In this paper we describe the unique features and analysis techniques used on the magnets for a R&D Energy Recovery Linac (ERL) [1] under construction at the Collider Accelerator Department at BNL. The R&D ERL serves as a test-bed for future BNL ERLs, such as an electron-cooler-ERL at RHIC [2] and a future 20 GeV ERL electron-hadron at eRHIC [3]. Here we present select designs of various dipole and quadruple magnets which are used in Z-bend merging systems [4] and the returning loop, 3-D simulations of the fields in aforementioned magnets, particle tracking analysis, and the magnet's influence on beam parameters. We discuss an unconventional method of setting requirements on the quality of magnetic field and transferring them into measurable parameters as well as into manufacturing tolerances. We compare selected simulation with results of magnetic measurements. A 20 MeV R&D ERL (Fig. 1) is in an advanced phase of construction at the Collider-Accelerator Department at BNL, with commissioning planned for early 2009. In the R&D ERL, an electron beam is generated in a 2 MeV superconducting RF photo-gun, next is accelerated to 20 MeV in a 5 cell SRF linac, subsequently passed through a return loop, then decelerated to 2 MeV in the SRF linac, and finally is sent to a beam dump. The lattice of the R&D ERL is designed with a large degree of flexibility to enable the covering of a vast operational parameter space: from non-achromatic lattices to achromatic with positive, zero and negative R56 parameter. It also allows for large range tunability of Rlz and lattice RS4 parameters (which are important for transverse beam-break-up instability). Further details of the R&D ERL can be found elsewhere in these proceedings [5]. The return loop magnets are of traditional design with the following exceptions: (a) The bending radius of the 60{sup o} dipole magnets is 20 cm, which is rather small. We use 15{sup o} edges on both sides of the dipoles to split very strong focusing evenly between the horizontal and vertical planes (so-called chevron-magnet). (b) The requirements on field quality of the loop's quadrupoles had been determined by the requirement to preserve a very low normalized transverse slice emittance of electron beam ({var_epsilon} {approx} 1 mm-mrad). We used direct tracking of a sample electron beam to verify a high degree of the emittance preservation. (c) Each quadrupole is equipped with a dipole trim coil, which can be also used to excite a sextupole component, if required, for emittance preservation of e-beam with a large energy spread. One of the unique features of all ERLs is the necessity for merging low and high energy electron beams. In the R&D ERL, 2 MeV from the SRF gun merges with the 20 MeV electron beam coming around the return loop into the same trajectory at a position within the SRF linac. In the linac, injected bunch is accelerated to 20 MeV, while the returned or ''used'' bunch is decelerated to 2 MeV. The challenge for a merger design is to provide conditions for emittance compensation [5] and also for achromatic conditions of a low energy, space-charge dominated-e-beam [4,6]. The scheme which satisfies these requirements (called 2-bend [4]) is used on the R&D ERL. The Z-bend is approximately 4-meter long. It bends the beam trajectory in the vertical plane. It is comprised of four dipole magnets designed to be equally focusing in both planes, with bending radius {approx} 60 cm, and bending angles of: +15{sup o}, -30{sup o}, +30{sup o} and -15{sup o}. The beam dynamics in the Z-bend results in a large-size (centimeters) near-laminar electron beam [7]. The large beam size and very low slice emittance of the e-beam dictates the tolerances on the magnetic field to be very tight. The integrated nonlinear kicks should not exceed {approx} 20 micro-radian per magnet at a typical radius {approx} 1 cm. The magnets in the Z-bend are rather short (15 cm effective length for the 15{sup o} magnet) and have a rather large aperture of 6 cm. Analysis predicts that the influence of various field components on the emittance growth are complicated by the fact that the beam trajectory bends significantly in the Einge fields. Hence, we decided to use direct tracking in the calculated fields extracted from Opera3d of test beam to evaluate and to minimize influence of magnetic field on the beam emittance. In addition, we used predictions of Opera3d and compared them with results of magnetic measurements for the return loop dipole and quadrupole. One of the features of the loop magnets is that they are fabricated with a very high geometric tolerance, allowing them to be an excellent test bed for bench-marking our predictions. Agreement with the prediction provides us with sufficient confidence that Z-bend magnets will preserve beam emittance

A Large Hadron Electron Collider at CERN

This document provides a brief overview of the recently published report on the design of the Large Hadron Electron Collider (LHeC), which comprises its physics programme, accelerator physics, technology and main detector concepts. The LHeC exploits and develops challenging, though principally existing, accelerator and detector technologies. This summary is complemented by brief illustrations of some of the highlights of the physics programme, which relies on a vastly extended kinematic range, luminosity and unprecedented precision in deep inelastic scattering. Illustrations are provided regarding high precision QCD, new physics (Higgs, SUSY) and electron-ion physics. The LHeC is designed to run synchronously with the LHC in the twenties and to achieve an integrated luminosity of O(100) fb$^{-1}$. It will become the cleanest high resolution microscope of mankind and will substantially extend as well as complement the investigation of the physics of the TeV energy scale, which has been enabled by the LHC

European Strategy for Particle Physics -- Accelerator R&D Roadmap

The 2020 update of the European Strategy for Particle Physics emphasised the importance of an intensified and well-coordinated programme of accelerator R&D, supporting the design and delivery of future particle accelerators in a timely, affordable and sustainable way. This report sets out a roadmap for European accelerator R&D for the next five to ten years, covering five topical areas identified in the Strategy update. The R&D objectives include: improvement of the performance and cost-performance of magnet and radio-frequency acceleration systems; investigations of the potential of laser / plasma acceleration and energy-recovery linac techniques; and development of new concepts for muon beams and muon colliders. The goal of the roadmap is to document the collective view of the field on the next steps for the R&D programme, and to provide the evidence base to support subsequent decisions on prioritisation, resourcing and implementation.Comment: 270 pages, 58 figures. Editor: N. Mounet. LDG chair: D. Newbold. Panel chairs: P. V\'edrine (HFM), S. Bousson (RF), R. Assmann (plasma), D. Schulte (muon), M. Klein (ERL). Panel editors: B. Baudouy (HFM), L. Bottura (HFM), S. Bousson (RF), G. Burt (RF), R. Assmann (plasma), E. Gschwendtner (plasma), R. Ischebeck (plasma), C. Rogers (muon), D. Schulte (muon), M. Klein (ERL

Gluons and the quark sea at high energies:distributions, polarization, tomography

This report is based on a ten-week program on "Gluons and the quark sea at high-energies", which took place at the Institute for Nuclear Theory in Seattle in Fall 2010. The principal aim of the program was to develop and sharpen the science case for an Electron-Ion Collider (EIC), a facility that will be able to collide electrons and positrons with polarized protons and with light to heavy nuclei at high energies, offering unprecedented possibilities for in-depth studies of quantum chromodynamics. This report is organized around four major themes: i) the spin and flavor structure of the proton, ii) three-dimensional structure of nucleons and nuclei in momentum and configuration space, iii) QCD matter in nuclei, and iv) Electroweak physics and the search for physics beyond the Standard Model. Beginning with an executive summary, the report contains tables of key measurements, chapter overviews for each of the major scientific themes, and detailed individual contributions on various aspects of the scientific opportunities presented by an EIC