A Two-Parameter Accelerating FODO Cell

A beamline containing accelerating cavities sandwiched between focusing and defocusing quadrupoles is made periodic by (a) postulating the simplest effect of cavities on transverse dynamics and (b) adopting a fiction that the ratio of initial to final momenta, (p{sub i}/p{sub f})--not the difference in energies, (E{sub f}-E{sub i})--is the same for all cavities. While not realistic, the optics of such a linac can be expressed without reference to initial beam parameters, using methods devised for storage rings. We will derive results for a simple two-parameter thin lens model, the parameters being p{sub i}/p{sub f} and the ratio of quadrupole spacing to focal length

Theory and praxis pf map analsys in CHEF part 1: Linear normal form

This memo begins a series which, put together, could comprise the 'CHEF Documentation Project' if there were such a thing. The first--and perhaps only--three will telegraphically describe theory, algorithms, implementation and usage of the normal form map analysis procedures encoded in CHEF's collection of libraries. [1] This one will begin the sequence by explaining the linear manipulations that connect the Jacobian matrix of a symplectic mapping to its normal form. It is a 'Reader's Digest' version of material I wrote in Intermediate Classical Dynamics (ICD) [2] and randomly scattered across technical memos, seminar viewgraphs, and lecture notes for the past quarter century. Much of its content is old, well known, and in some places borders on the trivial.1 Nevertheless, completeness requires their inclusion. The primary objective is the 'fundamental theorem' on normalization written on page 8. I plan to describe the nonlinear procedures in a subsequent memo and devote a third to laying out algorithms and lines of code, connecting them with equations written in the first two. Originally this was to be done in one short paper, but I jettisoned that approach after its first section exceeded a dozen pages. The organization of this document is as follows. A brief description of notation is followed by a section containing a general treatment of the linear problem. After the 'fundamental theorem' is proved, two further subsections discuss the generation of equilibrium distributions and issue of 'phase'. The final major section reviews parameterizations--that is, lattice functions--in two and four dimensions with a passing glance at the six-dimensional version. Appearances to the contrary, for the most part I have tried to restrict consideration to matters needed to understand the code in CHEF's libraries

Preliminaries toward studying resonant extraction from the Debuncher

A recent proposal to detect {mu} {yields} e direct conversion at Fermilab asks for slow extraction of protons from the antiproton source, specifically from the Debuncher. [1] A third-integer resonance originally was considered for this, partly because of the Debuncher's three-fold symmetry and partly because its operational horizontal tune, {nu}{sub x} {approx} 9.765, is already within 0.1 of {nu}{sub x} = 29/3. Using a half integer resonance, {nu}{sub x} = 19/2, though not part of the original proposal, has been suggested more recently because (a) Fermilab has had a good deal of experience with half-integer extraction from the Tevatron, the Main Injector and the erstwhile Main Ring, and (b) for reasons we shall examine later, it depopulates the entire bunch without an abort at the end. This memo presents considerations preliminary to studying both possibilities. It is meant only as a starting point for investigations to be carried out in the future. The working constraints and assumptions have oscillated between two extremes: (1) making minimal changes in the antiproton source to minimize cost and (2) building another machine in the same tunnel. In this memo we adopt an attitude aligned more toward the first. The assumed parameters are listed in Table 1. A few are not (easily) subject to change, such as those related to the beam's momentum and revolution frequency and the acceptance of the debuncher. Two resonance exemplars are presented in the next section, with an explanation of the analytic and semi-analytic calculations that can be done for each. Section 3 contains preliminary numerical work that was done to validate the exemplars within the context of extraction from the Debuncher. A final section contains a summary. Following the bibliography, appendices contain (a) a qualitative, conceptual discussion of extraction for the novice, (b) a telegraphic review of the perturbative incantations used to filter the exemplars as principal resonances of quadrupole, sextupole and octupole distributions, (c) a brief discussion of linearly independent control circuits, and (d) two files describing the antiproton source's rings in MAD v.8 format, not readily available elsewhere. All figures are located at the end. We emphasize again, the work reported here barely begins the effort that will be required to design, validate and perform resonant extraction from the Debuncher. Our goal was to compile these preliminary notes in one place for easy future reference, preferably by a young, intelligent, motivated and energetic graduate student

Recent studies of dispersion matched steering for the ILC bunch compressor and main linac

The Dispersion Matched Steering (DMS) method is studied in detail in the context of a curved main linac. In the absence of cavity tilts (rotations in the YZ plane), DMS provides a unique and stable solution with negligible emittance growth. If cavity tilts are about 300 {micro}rad, the algorithm is not very robust. The emittance growth through the entire linac for positrons is about 5 nm, if the system is strictly static and statistical averaging can be used to improve beam position measurements. This growth is mostly eliminated if the dispersion and its derivative at injection can be adjusted. If anticipated ground motion, beam and klystron jitter, beam position measurement resolution are introduced (i.e. dynamical case), the emittance preservation goal is currently not achieved by DMS alone. Mitigation strategies are outlined

Bloch surface waves-controlled fluorescence emission: coupling into nanometer-sized polymeric waveguides

The lateral confinement of Bloch surface waves on a patterned multilayer is investigated by means of leakage radiation microscopy (LRM). Arrays of nanometric polymeric waveguides are fabricated on a proper silicon-nitride/silicon-oxide multilayer grown on a standard glass coverslip. By exploiting the functional properties of the polymer, fluorescent proteins are grafted onto the waveguides. A fluorescence LRM analysis of both the direct and the Fourier image plane reveals that a substantial amount of emitted radiation couples into a guided mode and then propagates into the nanometric waveguide. The observations of the mode are supported by numerical simulations

Fluorescence diffraction assisted by Bloch surface waves on a one-dimensional photonic crystal

The use of linear and circular subwavelength gratings for improving the fluorescence extraction from organic dyes spotted on the surface of a one-dimensional photonic crystal is demonstrated. The one-dimensional photonic crystal hosting the gratings allows Bloch surface waves (BSWs) to be coupled in the visible range. We provide experimental evidence for the distributed diffraction of BSW-coupled fluorescence that is locally excited using a microscope-based setup. By diffracting the BSW-coupled fluorescence, a significant improvement in the total fluorescence collection is obtained as compared to a flat one-dimensional photonic crystal

Surface nanophotonics with Bloch waves on dielectric multilayers

Planar mutilayers sustaining either TE or TM polarized Bloch Surface Waves (BSWs) offer new opportunities for management of light at the nanoscale. We will discuss how BSWs can be exploited in guiding and confining light on nanometric relieves, enhancing fluorescence emission and providing additional features for plasmonic nano-antennas