Bench Measurements and Simulations of Beam Coupling Impedance

After a general introduction, the basic principles of wake-field and beamcoupling- impedance computations are explained. This includes time domain, frequency domain, and methods that do not include excitations by means of a particle beam. The second part of this paper deals with radio frequency bench measurements of beam coupling impedances. The general procedure of the wire measurement is explained, and its features and limitations are discussed.Comment: presented at the Proceedings of the CAS-CERN Accelerator School on Intensity Limitation in Particle Beams, Geneva, Switzerland -2-11 November 201

Analytic Modeling, Simulation and Interpretation of Broadband Beam Coupling Impedance Bench Measurements

In the first part of the paper a generalized theoretical approach towards beam coupling impedances and stretched-wire measurements is introduced. Applied to a circular symmetric setup, this approach allows to estimate the systematic measurement error due to the presence of the wire. Further, the interaction of the beam or the TEM wave, respectively, with dispersive material such as ferrite is discussed. The dependence of the obtained impedances on the relativistic velocity $\beta$ is investigated and found as material property dependent. The conversion formulas for the TEM scattering parameters from measurements to impedances are compared with each other and the analytical impedance solution. In the second part of the paper the measurements are compared to numerical simulations of wakefields and scattering parameters. In practice, the measurements have been performed for the circularly symmetric example setup. The optimization of the measurement process is discussed. The paper concludes with a summary of systematic and statistic error sources for impedance bench measurements and their diminishment strategy

Beam Dynamics Analysis of Dielectric Laser Acceleration using a Fast 6D Tracking Scheme

A six-dimensional symplectic tracking approach exploiting the periodicity properties of Dielectric Laser Acceleration (DLA) gratings is presented. The longitudinal kick is obtained from the spatial Fourier harmonics of the laser field within the structure, and the transverse kicks are obtained using the Panofsky-Wenzel theorem. Additionally to the usual, strictly longitudinally periodic gratings, our approach is also applicable to periodicity chirped (sub-relativistic) and tilted (deflection) gratings. In the limit of small kicks and short periods we obtain the 6D Hamiltonian, which allows, for example, to obtain matched beam distributions in DLAs. The scheme is applied to beam and grating parameters similar to recently performed experiments. The paper concludes with an outlook to laser based focusing schemes, which are promising to overcome fundamental interaction length limitations, in order to build an entire microchip-sized laser driven accelerator

Non-trivial \theta-Vacuum Effects in the 2-d O(3) Model

We study \theta-vacua in the 2-d lattice O(3) model using the standard action and an optimized constraint action with very small cut-off effects, combined with the geometric topological charge. Remarkably, dislocation lattice artifacts do not spoil the non-trivial continuum limit at \theta\ non-zero, and there are different continuum theories for each value of \theta. A very precise Monte Carlo study of the step scaling function indirectly confirms the exact S-matrix of the 2-d O(3) model at \theta = \pi.Comment: 4 pages, 3 figure

Study of theta-Vacua in the 2-d O(3) Model

We investigate the continuum limit of the step scaling function in the 2-d O(3) model with different theta-vacua. Since we find a different continuum value of the step scaling function for each value of theta, we can conclude that theta indeed is a relevant parameter of the theory and does not get renormalized non-perturbatively. Furthermore, we confirm the result of the conjectured exact S-matrix theory, which predicts the continuum value at theta = pi. To obtain high precision data, we use a modified Hasenbusch improved estimator and an action with an optimized constraint, which has very small cut-off effects. The optimized constraint action combines the standard action of the 2-d O(3) model with a topological action. The topological action constrains the angle between neighboring spins and is therefore invariant against small deformations of the field.Comment: 7 pages, 4 figures, The 30 International Symposium on Lattice Field Theory - Lattice 2012, June 24-29, 2012, Cairns, Australi

Towards a perfect fixed point action for SU(3) gauge theory

We present an overview of the construction and testing of actions for SU(3) gauge theory which are approximate fixed points of renormalization group equations (at $\beta\rightarrow \infty$). Such actions are candidates for use in numerical simulations on coarse lattices.Comment: 6 pages, uuencoded compressed postscript file, contribution to LAT9

Electron Beam Dynamics in Dielectric Laser Accelerators

Dielectric Laser Acceleration (DLA) is a nascent scheme of electron acceleration, which is particularly promising due to its high acceleration gradients. Although these gradients are lower than what is obtained in plasma-based schemes, they are the highest in structure based schemes, which are limited by material breakdown. DLAs can be implemented on microchips, leveraging on the nano-technology available in the semiconductor industry. This work aims to tackle the electron beam dynamics in DLAs systematically, with the goal to turn the already experimentally demonstrated record gradients into large energy gain. In other words, the goal is to increase the length of the acceleration channels while keeping a full 6D (3 coordinates and 3 momenta) confinement of the electron beam. This is particularly challenging, since DLAs are based on optical near-fields, requiring the transversal size of the channel to be tiny, down to a tenth of the laser wavelength at subrelativistic electron energies. In order to keep the electron beam in this nanophotonic channel, enormous focusing strengths are required. Conventional techniques, usually involving solenoid- or quadrupole magnets, are too weak, since their aperture cannot be de-magnified in the same ratio as the DLA cells are de-magnified compared to conventional radiofrequency (RF) accelerator cavities. The solution to this problem is brought up in this work. It borrows from the Alternating Phase Focusing (APF) scheme as introduced for heavy ion accelerators in the 1950’. APF uses the laser fields themselves to focus the electron beam and thereby enables to omit external focusing devices entirely. While only a small amount of the large available acceleration gradient is sacrificed, full 6D confinement is obtained in length scalable strucures. Thus in principle arbitrary high energy can be obtained provided the required laser parameters are available. This work comprises two parts: A theoretical one introducing the DLA structures and a semi-analytic highly numerically efficient simulation approach named DLAtrack6D. From this approach, the Hamiltonian and the entire dynamics in DLAs is derived. This leads to the recipe to design scalable APF DLA structures, especially suitable for fabrication on Silicon-On-Insulator (SOI) wafers, which are very common in commercial nanophotonics. More conventional structures are also created on the basis of pure silicon technology. These devices are also experimentally investigated in the second part of this work, where simulations and experimental results are matched. The requirements and experimental achievements of subrelativistic DLAs in ultralow-emittance injector chambers are discussed. While low energy DLAs mostly aim at ultrafast (attosecond!) dynamics, high energy DLAs particularly exploit the available high acceleration gradient, in order to provide high energy electrons in small scale facilites. Furthermore DLA devices can also be used as a versatile bunch-shaping tool in large-scale, high-energy conventional accelerator facilities. For that purpose, the beam current limit as being imposed by wakefields due to the structure surfaces that come very close to the beam is investigated. Our semianalytic tracking code DLAtrack6D is supplemented with a wakefield module to assess collective effects and coherent beam instabilities. Moreover, the wakefields of DLAs can also be used in beneficial ways to shape the longitudinal phase space in high energy conventional accelerator facilites. Application goals for DLA are Ultrafast Electron-Microscopy and -Diffraction (UEM/ UED) at boosted energy and on a longer time scale the high acceleration gradients can be exploited for a high energy electron-positron collider for elementary particle physics. High energy ultrashort electron pulses can also be used for radiation generation, potentially in DLA-based microchip undulators. Another imaginable goal would be to accumulate electrons from a continuously running DLA injector in a storage ring. All these applications require a length scalable DLA and stable 6D-confined electron beam dynamics therein

Design Study of a Dielectric Laser Undulator

Dielectric laser acceleration (DLA) achieves remarkable gradients from the optical near fields of a grating structure. Tilting the dielectric grating with respect to the electron beam leads to deflection forces and the DLA structure can be utilized as a microchip undulator. We investigate the beam dynamics in such structures analytically and by numerical simulations. A crucial challenge is to keep the beam focused, especially in direction of the narrow channel. An alternating phase focusing scheme is optimized for this purpose and matched lattice functions are obtained. We distinguish synchronous operation with phase jumps in the grating and asynchronous operation with a strictly periodic grating and well-designed synchronicity mismatch. Especially the asynchronous DLA undulator is a promising approach, since a simple, commercially available grating suffices for the focusing lattice design. We pave the way towards experiments of radiation generation in these structures and provide estimates of the emitted radiation wavelength and power. The analytical models are validated by numerical simulations in the dedicated DLA simulation tool DLAtrack6D and Astra, where the underlying laser fields are computed by CST Studio