A common attribute of capturing schemes used to find approximate solutions to the Euler equations is a sub-linear rate of convergence with respect to mesh resolution. Purely nonlinear jumps, such as shock waves produce a first-order convergence rate, but linearly degenerate discontinuous waves, where present, produce sub-linear convergence rates which eventually dominate the global rate of convergence. The classical explanation for this phenomenon investigates the behavior of the exact solution to the numerical method in combination with the finite error terms, often referred to as the modified equation. For a first-order method, the modified equation produces the hyperbolic evolution equation with second-order diffusive terms. In the frame of reference of the traveling wave, the solution of a discontinuous wave consists of a diffusive layer that grows with a rate of t{sup 1/2}, yielding a convergence rate of 1/2. Self-similar heuristics for higher order discretizations produce a growth rate for the layer thickness of {Delta}t{sup 1/(p+1)} which yields an estimate for the convergence rate as p/(p+1) where p is the order of the discretization. In this paper we show that this estimated convergence rate can be derived with greater rigor for both dissipative and dispersive forms of the discrete error. In …

Atom interferometry is now reaching sufficient precision to motivate laboratory tests of general relativity. We begin by explaining the non-relativistic calculation of the phase shift in an atom interferometer and deriving its range of validity. From this we develop a method for calculating the phase shift in general relativity. This formalism is then used to find the relativistic effects in an atom interferometer in a weak gravitational field for application to laboratory tests of general relativity. The potentially testable relativistic effects include the non-linear three-graviton coupling, the gravity of kinetic energy, and the falling of light. We propose experiments, one currently under construction, that could provide a test of the principle of equivalence to 1 part in 10{sup 15} (300 times better than the present limit), and general relativity at the 10% level, with many potential future improvements. We also consider applications to other metrics including the Lense-Thirring effect, the expansion of the universe, and preferred frame and location effects.

Electron microscopists are increasingly turning to Intermediate Voltage Electron Microscopes (IVEMs) operating at 300 - 400 kV for a wide range of studies. They are also increasingly taking advantage of slow-scan charge coupled device (CCD) cameras, which have become widely used on electron microscopes. Under some conditions CCDs provide an improvement in data quality over photographic film, as well as the many advantages of direct digital readout. However, CCD performance is seriously degraded on IVEMs compared to the more conventional 100 kV microscopes. In order to increase the efficiency and quality of data recording on IVEMs, we have developed a CCD camera system in which the electrons are decelerated to below 100 kV before impacting the camera, resulting in greatly improved performance in both signal quality and resolution compared to other CCDs used in electron microscopy. These improvements will allow high-quality image and diffraction data to be collected directly with the CCD, enabling improvements in data collection for applications including high-resolution electron crystallography, single-particle reconstruction of protein structures, tomographic studies of cell ultrastructure and remote microscope operation. This approach will enable us to use even larger format CCD chips that are being developed with smaller pixels.

The aim of the SPARC project, is to promote an R&D activity oriented to the development of a high brightness photoinjector to drive SASE-FEL experiments. We discuss in this paper the status of the beam dynamics simulation activities.

We design a single bunch transverse beam size monitor which will be tested to measure the 28.5 GeV electron/positron beam at the SLAC FFTB beam line. The beam size monitor uses the CCD images of the interference pattern of the optical diffraction radiation from two slit edges which are placed close to the beam path. In this method, destruction of the accelerated electron/positron beam bunches due to the beam size monitoring is negligible, which is vital to the operation of the Linear Collider project.

At Lawrence Livermore National Laboratory, we are developing a new type of accelerator, known as a Dielectric Wall Accelerator, in which compact pulse forming lines directly apply an accelerating field to the beam through an insulating vacuum boundary. The electrical strength of this insulator may define the maximum gradient achievable in these machines. To increase the system gradient, we are using 'High Gradient Insulators' composed of alternating layers of dielectric and metal for the vacuum insulator. In this paper, we present our recent results from experiment and simulation, including the first test of a High Gradient Insulator in a functioning Dielectric Wall Accelerator cell.

The strong-strong beam-beam effect is one of the most important effects limiting the luminosity of ring colliders. Little is known about it analytically, so most studies utilize numeric simulations. The two-dimensional realm is readily accessible to workstation-class computers (cf.,e.g.,[1, 2]), while three dimensions, which add effects such as phase averaging and the hourglass effect, require vastly higher amounts of CPU time. Thus, parallelization of three-dimensional simulation techniques is imperative; in the following we discuss parallelization strategies and describe the algorithms used in our simulation code, which will reach almost linear scaling of performance vs. number of CPUs for typical setups.

The usual approach to predict particle loss in storage rings in the presence of nonlinearities consists in the determination of the dynamic aperture of the machine. This method, however, will not directly predict the lifetimes of beams. We have developed a code which can, by parallelization and careful speed optimization, predict lifetimes in the presence of 100 parasitic beam-beam crossings by tracking > 10{sup 10} particles-turns. An application of this code to the anti-proton lifetime in the Tevatron at injection is discussed.

A prototype of an analog, transverse (vertical) feedback system for active damping of the two-stream (e-p) instability has been developed and successfully tested at the Los Alamos Proton Storage Ring (PSR). This system was able to improve the instability threshold by approximately 30% (as measured by the change in RF buncher voltage at instability threshold). The feedback system configuration, setup procedures, and optimization of performance are described. Results of several experimental tests of system performance are presented including observations of instability threshold improvement and grow-damp experiments, which yield estimates of instability growth and damping rates. A major effort was undertaken to identify and study several factors limiting system performance. Evidence obtained from these tests suggests that performance of the prototype was limited by higher instability growth rates arising from beam leakage into the gap at lower RF buncher voltage and the onset of instability in the horizontal plane, which had no feedback.

Recent beam physics studies on the two-stream e-p instability at the LANL proton storage ring (PSR) have focused on the role of the electron cloud generated in quadrupole magnets where primary electrons, which seed beam-induced multipacting, are expected to be largest due to grazing angle losses from the beam halo. A new diagnostic to measure electron cloud formation and trapping in a quadrupole magnet has been developed, installed, and successfully tested at PSR. Beam studies using this diagnostic show that the 'prompt' electron flux striking the wall in a quadrupole is comparable to the prompt signal in the adjacent drift space. In addition, the 'swept' electron signal, obtained using the sweeping feature of the diagnostic after the beam was extracted from the ring, was larger than expected and decayed slowly with an exponential time constant of 50 to 100 {micro}s. Other measurements include the cumulative energy spectra of prompt electrons and the variation of both prompt and swept electron signals with beam intensity. Experimental results were also obtained which suggest that a good fraction of the electrons observed in the adjacent drift space for the typical beam conditions in the 2006 run cycle were seeded by electrons ejected from the …

Recent experiments and simulations have shown that positron beams propagating in plasmas can be focused and also create wakes with large accelerating gradients. For similar parameters, the wakes driven by positron beams are somewhat smaller compared to the case of an electron beam. Simulations have shown that the wake amplitude can be increased if the positron beam is propagated in a hollow plasma channel (Ref. 1). This paper, compares experimentally, the propagation and beam dynamics of a positron beam in a meter scale homogeneous plasma, to a positron beam hollow channel plasma. The results show that positron beams in hollow channels are less prone to distortions and deflections. Hollow channels were observed to guide the positron beam onto the channel axis. Beam energy loss was also observed implying the formation of a large wake amplitude. The experiments were carried out as part of the E-162 plasma wakefield experiments at SLAC.

Fermilab is presently in Run II collider operations and is developing instrumentation to improve luminosity. Improving the orbit matching between accelerator components using a Beam Line Tuner (BLT) can improve the luminosity. Digital Down Conversion (DDC) has been proposed as a method for making more accurate beam position measurements. Fermilab has implemented a BLT system using a DDC technique to measure orbit oscillations during injections from the Main Injector to the Tevatron. The output of a fast ADC is downconverted and filtered in software. The system measures the x and y positions, the intensity, and the time of arrival for each proton or antiproton bunch, on a turn-by-turn basis, during the first 1024 turns immediately following injection. We present results showing position, intensity, and time of arrival for both injected and coasting beam. Initial results indicate a position resolution of {approx}20 to 40 microns and a phase resolution of {approx}25 ps.

We present the results of electron beam longitudinal modulation studies in the DUV-FEL accelerator. For bunch length determination we used the 'zero-phasing' method, based on a measurement of the chirped electron bunch energy spectra. The measurements revealed a spiky structure in the longitudinal phase space [1]. A model based on space charge effect is considered [2] to explain of the obtained phenomena. The analysis of the energy spectra has shown a sensitivity of the structure to the electron beam peak current, energy and longitudinal non-uniformity of the RF gun drive laser. Analytical calculations have demonstrated a qualitative agreement with experimental observations. Several experiments have been made to compare with theory; measured results are reviewed in this paper. The obtained effect is briefly discussed in relation to high brightness accelerators.

For synchrotron light sources and for damping rings of linear colliders it is important to be able to minimize the vertical emittance and to correct the spurious vertical dispersion. This allows one to maximize the brightness and/or the luminosity. A commonly used tool to measure the skew error distribution is the analysis of orbit response matrices using codes like LOCO. Using the new Matlab version of LOCO and 18 newly installed power supplies for individual skew quadrupoles at the ALS the emittance ratio could be reduced below 0.1% at 1.9 GeV yielding a vertical emittance of about 5 pm. At those very low emittances, additional effects like intra beam scattering become more important, potentially limiting the minimum emittance for machine like the damping rings of linear colliders.

The Spallation Neutron Source (SNS) accumulator ring is designed to accumulate, via H{sup -} injection, protons of 2 MW beam power at 1 GeV kinetic energy at a repetition rate of 60 Hz [1]. At such beam intensity, electron-cloud is expected to be one of the intensity-limiting mechanisms that complicate ring operations. This paper summarizes mitigation strategy adopted in the design, both in suppressing electron-cloud formation and in enhancing Landau damping, including tapered magnetic field and monitoring system for the collection of stripped electrons at injection, TiN coated beam chamber for suppression of the secondary yield, clearing electrodes dedicated for the injection region and parasitic on BPMs around the ring, solenoid windings in the collimation region, and planning of vacuum systems for beam scrubbing upon operation.

Previous lattice designs for the Next Linear Collider Main Damping Rings [1] have met the specifications for equilibrium emittance, damping rate and dynamic aperture. Concerns about the effects of the damping wiggler on the beam dynamics [2] led to the aim of reducing the total length of the wiggler to a minimum consistent with the required damping rate, so high-field dipoles were used to provide a significant energy loss in the arcs. However, recent work has shown that the wiggler effects may not be as bad as previously feared. Furthermore, other studies have suggested the need for an increased momentum compaction (by roughly a factor of four) to raise the thresholds of various collective effects. We have therefore developed a new lattice design in which we increase the momentum compaction by reducing the field strength in the arc dipoles, compensating the loss in damping rate by increasing the length of the wiggler. The new lattice again meets the specifications for emittance, damping rate and dynamic aperture, while having the benefit of significantly higher thresholds for a number of instabilities.