Isodrastic Magnetic fields for suppressing transitions in guiding-centre motion

In a magnetic field, transitions between classes of guiding-centre motion can lead to cross-field diffusion and escape. We say a magnetic field is isodrastic if guiding centres make no transitions between classes of motion. Therefore, this is an important ideal for enhancing confinement. First, we present a weak formulation, based on the longitudinal adiabatic invariant, generalising omnigenity. To demonstrate that isodrasticity is strictly more general than omnigenity, we construct weakly isodrastic mirror fields that are not omnigenous. Then we present a strong formulation that is exact for guiding-centre motion. We develop a first-order treatment of the strong version via a Melnikov function and show that it recovers the weak version. The theory provides quantification of deviations from isodrasticity that can be used as objective functions in optimal design. The theory is illustrated on some simple examples.Comment: 72 pages, 31 Figure

Generalized Grad-Shafranov equation for non-axisymmetric MHD equilibria

The structure of static MHD equilibria that admit continuous families of Euclidean symmetries is well understood. Such field configurations are governed by the classical Grad-Shafranov equation, which is a single elliptic PDE in two space dimensions. By revealing a hidden symmetry, we show that in fact all smooth solutions of the equilibrium equations with non-vanishing pressure gradients away from the magnetic axis satisfy a generalization of the Grad-Shafranov equation. In contrast to solutions of the classical Grad-Shafranov equation, solutions of the generalized equation are not automatically equilibria, but instead only satisfy force balance averaged over the one-parameter hidden symmetry. We then explain how the generalized Grad-Shafranov equation can be used to reformulate the problem of finding exact three-dimensional smooth solutions of the equilibrium equations as finding an optimal volume-preserving symmetry

Some mathematics for quasi-symmetry

The concept of quasi-symmetry was introduced in (Booozer, 1983) and then distilled into a design principle for stellarators by N¨uhrenberg & Zille (1988). In its strongest sense it means integrability of first-order guiding-centre motion. An excellent survey of the subject was provided by Helander (2014), assuming magnetohydrostatic (MHS) fields, that is, magnetohydrodynamic equilibrium with isotropic pressure and no mean flow. A fundamental step was made by Burby & Qin (2013), who stated necessary and sufficient local conditions for integrability of guiding-centre motion in terms of a continuous symmetry of three differential forms derived from the magnetic field and made clear that quasi-symmetry can be separated from the issue of whether the magnetic field is MHS or not. Perturbative calculations of Garren & Boozer (1991), however, make it look very likely that the only possibility for exact quasi-symmetry for MHS fields with bounded magnetic surfaces is axisymmetry. Our paper gives first steps to deciding whether or not this is true. In this paper we prove many consequences of quasi-symmetry and thereby restrictions on possible quasi-symmetric fields. In the case of a quasi-symmetric MHS field we derive a generalisation of the axisymmetric Grad-Shafranov equation. Burby & Qin (2013) built in an assumption that a quasi-symmetry must be a circleaction. Here we relax this requirement, though prove that under some mild conditions it is actually a circle-action. We write many equations using differential forms. For those unfamiliar with differential forms, (Arnol’d, 1978, chap. 7) is a classic and there is a tutorial (MacKay, 2019) specifically for plasma physicists. Throughout the paper we will assume enough smoothness that the equations we write make sense, at least in a weak sense

Approximate symmetries of guiding-centre motion

In a strong, inhomogeneous magnetic field, charged particle dynamics may be studied in the guiding-centre approximation, which is known to be Hamiltonian. When the magnetic field is quasisymmetric, the first-order guiding-centre Hamiltonian structure admits a continuous symmetry, and therefore a conserved quantity in addition to the energy. Since the first-order guiding-centre system is only an approximation, it is also interesting to consider approximate symmetries of the guiding-centre Hamiltonian structure. We find that any approximate spatial symmetry coincides with quasisymmetry at first order. For approximate phase-space symmetries, we derive weaker conditions than quasisymmetry. The latter include "weak quasisymmetry" as a subcase, recently proposed by Rodriguez et al. Our results, however, show that weak quasisymmetry is necessarily non-spatial at first order. Finally, if the magnetic field is constrained to satisfy magnetohydrostatic force balance then an approximate symmetry must agree with quasisymmetry to first order

Compressed gas domestic aerosol valve design using high viscous product

Most of the current universal consumer aerosol products using high viscous product such as cooking oil, antiperspirants, hair removal cream are primarily used LPG (Liquefied Petroleum Gas) propellant which is unfriendly environmental. The advantages of the new innovative technology described in this paper are: i. No butane or other liquefied hydrocarbon gas is used as a propellant and it replaced with Compressed air, nitrogen or other safe gas propellant. ii. Customer acceptable spray quality and consistency during can lifetime iii. Conventional cans and filling technology There is only a feasible energy source which is inert gas (i.e. compressed air) to replace VOCs (Volatile Organic Compounds) and greenhouse gases, which must be avoided, to improve atomisation by generating gas bubbles and turbulence inside the atomiser insert and the actuator. This research concentrates on using “bubbly flow” in the valve stem, with injection of compressed gas into the passing flow, thus also generating turbulence. The new valve designed in this investigation using inert gases has advantageous over conventional valve with butane propellant using high viscous product (> 400 Cp) because, when the valving arrangement is fully open, there are negligible energy losses as fluid passes through the valve from the interior of the container to the actuator insert. The use of valving arrangement thus permits all pressure drops to be controlled, resulting in improved control of atomising efficiency and flow rate, whereas in conventional valves a significant pressure drops occurs through the valve which has a complex effect on the corresponding spray

Non-Global Logarithms in Filtered Jet Algorithms

We analytically and numerically study the effect of perturbative gluons emission on the "Filtering analysis", which is part of a subjet analysis procedure proposed two years ago to possibly identify a low-mass Higgs boson decaying into b\bar{b} at the LHC. This leads us to examine the non-global structure of the resulting perturbative series in the leading single-log large-N_c approximation, including all-orders numerical results, simple analytical approximations to them and comments on the structure of their series expansion. We then use these results to semi-analytically optimize the parameters of the Filtering analysis so as to suppress as much as possible the effect of underlying event and pile-up on the Higgs mass peak reconstruction while keeping the major part of the perturbative radiation from the b\bar{b} dipole.Comment: 47 pages, 25 figures, 1 figure and a few comments added, version accepted for publication in JHE

Non-global Structure of the O({\alpha}_s^2) Dijet Soft Function

High energy scattering processes involving jets generically involve matrix elements of light- like Wilson lines, known as soft functions. These describe the structure of soft contributions to observables and encode color and kinematic correlations between jets. We compute the dijet soft function to O({\alpha}_s^2) as a function of the two jet invariant masses, focusing on terms not determined by its renormalization group evolution that have a non-separable dependence on these masses. Our results include non-global single and double logarithms, and analytic results for the full set of non-logarithmic contributions as well. Using a recent result for the thrust constant, we present the complete O({\alpha}_s^2) soft function for dijet production in both position and momentum space.Comment: 55 pages, 8 figures. v2: extended discussion of double logs in the hard regime. v3: minor typos corrected, version published in JHEP. v4: typos in Eq. (3.33), (3.39), (3.43) corrected; this does not affect the main result, numerical results, or conclusion

Event Shape/Energy Flow Correlations

We introduce a set of correlations between energy flow and event shapes that are sensitive to the flow of color at short distances in jet events. These correlations are formulated for a general set of event shapes, which includes jet broadening and thrust as special cases. We illustrate the method for electron-positron annihilation dijet events, and calculate the correlation at leading logarithm in the energy flow and at next-to-leading-logarithm in the event shape.Comment: 43 pages, eight eps figures; minor changes, references adde

Spatial Dynamics Of Vertical And Horizontal Intergovernmental Collaboration

Although researchers have made progress in understanding motivations behind local government collaboration, there is little research that explores the spatial dynamics of such interactions. Does the idea of collaboration travel horizontally, passed from neighbor to neighbor, or is vertical leadership from state, county, or regional actors more important in influencing local governments’ decisions to share resources and functions? What factors influence local governments’ choices to collaborate with their neighbors versus a regional entity, county, or state government? In this article, we investigate the importance of vertical and horizontal influences when local governments decide to collaborate around land use planning. Using data from a survey of Michigan local government officials, we take a spatial statistical approach to answering this question. We find widespread evidence of collaboration at multiple scales, and observe patterns of both horizontal and vertical influence. We also find that contextual factors help to explain these patterns of collaboration.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/112248/1/juaf12139.pd