Quasiperiodic spin-orbit motion and spin tunes in storage rings

We present an in-depth analysis of the concept of spin precession frequency for integrable orbital motion in storage rings. Spin motion on the periodic closed orbit of a storage ring can be analyzed in terms of the Floquet theorem for equations of motion with periodic parameters and a spin precession frequency emerges in a Floquet exponent as an additional frequency of the system. To define a spin precession frequency on nonperiodic synchro-betatron orbits we exploit the important concept of quasiperiodicity. This allows a generalization of the Floquet theorem so that a spin precession frequency can be defined in this case too. This frequency appears in a Floquet-like exponent as an additional frequency in the system in analogy with the case of motion on the closed orbit. These circumstances lead naturally to the definition of the uniform precession rate and a definition of spin tune. A spin tune is a uniform precession rate obtained when certain conditions are fulfilled. Having defined spin tune we define spin-orbit resonance on synchro--betatron orbits and examine its consequences. We give conditions for the existence of uniform precession rates and spin tunes (e.g. where small divisors are controlled by applying a Diophantine condition) and illustrate the various aspects of our description with several examples. The formalism also suggests the use of spectral analysis to ``measure'' spin tune during computer simulations of spin motion on synchro-betatron orbits.Comment: 62 pages, 1 figure. A slight extension of the published versio

Optimal Axes of Siberian Snakes for Polarized Proton Acceleration

Accelerating polarized proton beams and storing them for many turns can lead to a loss of polarization when accelerating through energies where a spin rotation frequency is in resonance with orbit oscillation frequencies. First-order resonance effects can be avoided by installing Siberian Snakes in the ring, devices which rotate the spin by 180 degrees around the snake axis while not changing the beam's orbit significantly. For large rings, several Siberian Snakes are required. Here a criterion will be derived that allows to find an optimal choice of the snake axes. Rings with super-period four are analyzed in detail, and the HERA proton ring is used as an example for approximate four-fold symmetry. The proposed arrangement of Siberian Snakes matches their effects so that all spin-orbit coupling integrals vanish at all energies and therefore there is no first-order spin-orbit coupling at all for this choice, which I call snakes matching. It will be shown that in general at least eight Siberian Snakes are needed and that there are exactly four possibilities to arrange their axes. When the betatron phase advance between snakes is chosen suitably, four Siberian Snakes can be sufficient. To show that favorable choice of snakes have been found, polarized protons are tracked for part of HERA-p's acceleration cycle which shows that polarization is preserved best for the here proposed arrangement of Siberian Snakes.Comment: 14 pages, 16 figure

Comment on Mie Scattering from a Sonoluminescing Bubble with High Spatial and Temporal Resolution [Physical Review E 61, 5253 (2000)]

A key parameter underlying the existence of sonoluminescence (SL)is the time relative to SL at which acoustic energy is radiated from the collapsed bubble. Light scattering is one route to this quantity. We disagree with the statement of Gompf and Pecha that -highly compressed water causes the minimum in scattered light to occur 700ps before SL- and that this effect leads to an overestimate of the bubble wall velocity. We discuss potential artifacts in their experimental arrangement and correct their description of previous experiments on Mie scattering.Comment: 10 pages, 2 figure

Using intervention mapping to develop a culturally appropriate intervention to prevent childhood obesity: the HAPPY (Healthy and Active Parenting Programme for Early Years) study.

INTRODUCTION: Interventions that make extensive use of theory tend to have larger effects on behaviour. The Intervention Mapping (IM) framework incorporates theory into intervention design, implementation and evaluation, and was applied to the development of a community-based childhood obesity prevention intervention for a multi-ethnic population. METHODS: IM was applied as follows: 1) Needs assessment of the community and culture; consideration of evidence-base, policy and practice; 2) Identification of desired outcomes and change objectives following identification of barriers to behaviour change mapped alongside psychological determinants (e.g. knowledge, self-efficacy, intention); 3) Selection of theory-based methods and practical applications to address barriers to behaviour change (e.g., strategies for responsive feeding); 4) Design of the intervention by developing evidence-based interactive activities and resources (e.g., visual aids to show babies stomach size). The activities were integrated into an existing parenting programme; 5) Adoption and implementation: parenting practitioners were trained by healthcare professionals to deliver the programme within Children Centres. RESULTS: HAPPY (Healthy and Active Parenting Programme for Early Years) is aimed at overweight and obese pregnant women (BMI > 25); consists of 12 × 2.5 hr. sessions (6 ante-natal from 24 weeks; 6 postnatal up to 9 months); it addresses mother's diet and physical activity, breast or bottle feeding, infant diet and parental feeding practices, and infant physical activity. CONCLUSION: We have demonstrated that IM is a feasible and helpful method for providing an evidence based and theoretical structure to a complex health behaviour change intervention. The next stage will be to assess the impact of the intervention on behaviour change and clinical factors associated with childhood obesity. The HAPPY programme is currently being tested as part of a randomised controlled feasibility trial

Design and performance of a multicentre, randomized controlled trial of teleconsulting.

We have designed and performed a multicentre, randomized controlled trial of teleconsulting. The trial investigated the effectiveness and cost implications in rural and inner-city settings of using videoconferencing as an alternative to general practitioner referral to a hospital specialist. The participating general practitioners referred a total of 3170 patients who satisfied the entry criteria. Of these, 1040 (33%) failed to provide consent or otherwise refused to participate in the trial. Of the patients recruited to the trial, a total of 1902 (91%) completed and returned the baseline questionnaire. Although the trial was successful in recruiting sufficient patients and in obtaining high questionnaire response rates, the findings will require careful interpretation to take account of the limits which the protocol placed on the ability of general practitioners to select patients for referral

Derivation of a dynamic model of the kinetics of nitrogen uptake throughout the growth of lettuce : calibration and validation

A kinetic model of nitrogen (N) uptake throughout growth was developed for lettuce cultivated in nutrient solution under varying natural light conditions. The model couples nitrogen uptake with dry matter accumulation using a two-compartment mechanistic approach, incorporating structural and non-structural pools. Maximum nitrogen uptake rates are assumed to decline with shoot dry weight, to allow for the effects of plant age. The model was parameterized using data from the literature, and calibrated for differences in light intensity using an optimization algorithm utilizing data from three experiments in different growing seasons. The calibrated model was validated against the data from two independent experiments conducted under different light conditions. Results showed that the model made good predictions of nitrogen uptake by plants from seedlings to maturity under fluctuating light levels in a glasshouse. Plants grown at a higher light intensity showed larger maximum nitrogen uptake rates, but the effect of light intensity declined towards plant maturity

Mechanisms for Stable Sonoluminescence

A gas bubble trapped in water by an oscillating acoustic field is expected to either shrink or grow on a diffusive timescale, depending on the forcing strength and the bubble size. At high ambient gas concentration this has long been observed in experiments. However, recent sonoluminescence experiments show that in certain circumstances when the ambient gas concentration is low the bubble can be stable for days. This paper presents mechanisms leading to stability which predict parameter dependences in agreement with the sonoluminescence experiments.Comment: 4 pages, 3 figures on request (2 as .ps files

Gauge Theories with Cayley-Klein SO(2;j)SO(2;j) and SO(3;j)SO(3;j) Gauge Groups

Gauge theories with the orthogonal Cayley-Klein gauge groups $SO(2;j)$ and $SO(3;{\bf j})$ are regarded. For nilpotent values of the contraction parameters ${\bf j}$ these groups are isomorphic to the non-semisimple Euclid, Newton, Galilei groups and corresponding matter spaces are fiber spaces with degenerate metrics. It is shown that the contracted gauge field theories describe the same set of fields and particle mass as $SO(2), SO(3)$ gauge theories, if Lagrangians in the base and in the fibers all are taken into account. Such theories based on non-semisimple contracted group provide more simple field interactions as compared with the initial ones.Comment: 14 pages, 5 figure

Strength of Higher-Order Spin-Orbit Resonances

When polarized particles are accelerated in a synchrotron, the spin precession can be periodically driven by Fourier components of the electromagnetic fields through which the particles travel. This leads to resonant perturbations when the spin-precession frequency is close to a linear combination of the orbital frequencies. When such resonance conditions are crossed, partial depolarization or spin flip can occur. The amount of polarization that survives after resonance crossing is a function of the resonance strength and the crossing speed. This function is commonly called the Froissart-Stora formula. It is very useful for predicting the amount of polarization after an acceleration cycle of a synchrotron or for computing the required speed of the acceleration cycle to maintain a required amount of polarization. However, the resonance strength could in general only be computed for first-order resonances and for synchrotron sidebands. When Siberian Snakes adjust the spin tune to be 1/2, as is required for high energy accelerators, first-order resonances do not appear and higher-order resonances become dominant. Here we will introduce the strength of a higher-order spin-orbit resonance, and also present an efficient method of computing it. Several tracking examples will show that the so computed resonance strength can indeed be used in the Froissart-Stora formula. HERA-p is used for these examples which demonstrate that our results are very relevant for existing accelerators.Comment: 10 pages, 6 figure