The Relationship between Principal Leadership Behaviors and School Climate

The No Child Left Behind Act (2001) revised the Elementary and Secondary Education Act of 1965 by making substantial modifications in the major federal programs that support schools‘ efforts to educate all children (U.S. Department of Education, Office of the Deputy Secretary, 2004). Since the inception of this law, demand for greater accountability for student achievement from politicians and legislators has increased exponentially (Carnoy, Elmore, & Siskin, 2003). Strict accountability measures, developed and implemented with limited if any consent or involvement of educators, were imposed on students, teachers, schools, and school districts (Waite, Boone, & NcGgee, 2001). The increased emphasis on accountability heightened the demands on teachers and administrators more than ever before in the history of education in the United States (Carnoy et al., 2003). As increased accountability became the norm, school leadership became more challenging and demanding in order to achieve the newly stipulated accountability (Salazar, 2008)

Optimizing stellarators for large flows

Plasma flow is damped in stellarators because they are not intrinsically ambipolar, unlike tokamaks, in which the flux-surface averaged radial electric current vanishes for any value of the radial electric field. Only quasisymmetric stellarators are intrinsically ambipolar, but exact quasisymmetry is impossible to achieve in non-axisymmetric toroidal configurations. By calculating the violation of intrinsic ambipolarity due to deviations from quasisymmetry, one can derive criteria to assess when a stellarator can be considered quasisymmetric in practice, i.e. when the flow damping is weak enough. Let us denote by $\alpha$ a small parameter that controls the size of a perturbation to an exactly quasisymmetric magnetic field. Recently, it has been shown that if the gradient of the perturbation is sufficiently small, the flux-surface averaged radial electric current scales as $\alpha^2$ for any value of the collisionality. It was also argued that when the gradient of the perturbation is large, the quadratic scaling is replaced by a more unfavorable one. In this paper, perturbations with large gradients are rigorously treated. In particular, it is proven that for low collisionality a perturbation with large gradient yields, at best, an $O(|\alpha|)$ deviation from quasisymmetry. Heuristic estimations in the literature incorrectly predicted an $O(|\alpha|^{3/2})$ deviation.Comment: 24 pages, 2 figures. To appear in Plasma Physics and Controlled Fusio

Flow damping in stellarators close to quasisymmetry

Quasisymmetric stellarators are a type of optimized stellarators for which flows are undamped to lowest order in an expansion in the normalized Larmor radius. However, perfect quasisymmetry is impossible. Since large flows may be desirable as a means to reduce turbulent transport, it is important to know when a stellarator can be considered to be sufficiently close to quasisymmetry. The answer to this question depends strongly on the size of the spatial gradients of the deviation from quasisymmetry and on the collisionality regime. Recently, formal criteria for closeness to quasisymmetry have been derived in a variety of situations. In particular, the case of deviations with large gradients was solved in the $1/\nu$ regime. Denoting by $\alpha$ a parameter that gives the size of the deviation from quasisymmetry, it was proven that particle fluxes do not scale with $\alpha^{3/2}$, as typically claimed, but with $\alpha$. It was also shown that ripple wells are not necessarily the main cause of transport. This paper reviews those works and presents a new result in another collisionality regime, in which particles trapped in ripple wells are collisional and the rest are collisionless.Comment: 14 pages, 2 figures. To appear in Plasma Physics and Controlled Fusio

When omnigeneity fails

A generic non-symmetric magnetic field does not confine magnetized charged particles for long times due to secular magnetic drifts. Stellarator magnetic fields should be omnigeneous (that is, designed such that the secular drifts vanish), but perfect omnigeneity is technically impossible. There always are small deviations from omnigeneity that necessarily have large gradients. The amplification of the energy flux caused by a deviation of size $\epsilon$ is calculated and it is shown that the scaling with $\epsilon$ of the amplification factor can be as large as linear. In opposition to common wisdom, most of the transport is not due to particles trapped in ripple wells, but to the perturbed motion of particles trapped in the omnigeneous magnetic wells around their bounce points.Comment: 6 pages, 2 figure

The effect of tangential drifts on neoclassical transport in stellarators close to omnigeneity

In general, the orbit-averaged radial magnetic drift of trapped particles in stellarators is non-zero due to the three-dimensional nature of the magnetic field. Stellarators in which the orbit-averaged radial magnetic drift vanishes are called omnigeneous, and they exhibit neoclassical transport levels comparable to those of axisymmetric tokamaks. However, the effect of deviations from omnigeneity cannot be neglected in practice. For sufficiently low collision frequencies (below the values that define the $1/\nu$ regime), the components of the drifts tangential to the flux surface become relevant. This article focuses on the study of such collisionality regimes in stellarators close to omnigeneity when the gradient of the non-omnigeneous perturbation is small. First, it is proven that closeness to omnigeneity is required to preserve radial locality in the drift-kinetic equation for collisionalities below the $1/\nu$ regime. Then, it is shown that neoclassical transport is determined by two layers in phase space. One of the layers corresponds to the $\sqrt{\nu}$ regime and the other to the superbanana-plateau regime. The importance of the superbanana-plateau layer for the calculation of the tangential electric field is emphasized, as well as the relevance of the latter for neoclassical transport in the collisionality regimes considered in this paper. In particular, the tangential electric field is essential for the emergence of a new subregime of superbanana-plateau transport when the radial electric field is small. A formula for the ion energy flux that includes the $\sqrt{\nu}$ regime and the superbanana-plateau regime is given. The energy flux scales with the square of the size of the deviation from omnigeneity. Finally, it is explained why below a certain collisionality value the formulation presented in this article ceases to be valid.Comment: 36 pages. Version to be published in Plasma Physics and Controlled Fusio

Electrostatic potential variations on stellarator magnetic surfaces in low collisionality regimes

The component of the neoclassical electrostatic potential that is non-constant on the magnetic surface, that we denote by $\tilde\varphi$, can affect radial transport of highly charged impurities, and this has motivated its inclusion in some modern neoclassical codes. The number of neoclassical simulations in which $\tilde\varphi$ is calculated is still scarce, partly because they are usually demanding in terms of computational resources, especially at low collisionality. In this paper the size, the scaling with collisionality and with aspect ratio, and the structure of $\tilde\varphi$ on the magnetic surface are analytically derived in the $1/\nu$, $\sqrt{\nu}$ and superbanana-plateau regimes of stellarators close to omnigeneity; i. e. stellarators that have been optimized for neoclassical transport. It is found that the largest $\tilde\varphi$ that the neoclassical equations admit scales linearly with the inverse aspect ratio and with the size of the deviation from omnigeneity. Using a model for a perturbed omnigeneous configuration, the analytical results are verified and illustrated with calculations by the code KNOSOS. The techniques, results and numerical tools employed in this paper can be applied to neoclassical transport problems in tokamaks with broken axisymmetry.Comment: 30 pages, 12 figures, 1 table. Published versio

Posada a punt d'un mètode d'anàlisi d'arsènic en lixiviats de minerals i sòls mitjançant fluorescència atòmica

En aquest projecte s’ha posat a punt un mètode d’anàlisi d’As mitjançant fluorescència atòmica. S’han utilitzat mostres sintètiques per a l’obtenció de tots els resultats. Abans de procedir a les etapes d’anàlisi s’ha fet una posada a punt de l’aparell, per comprovar el seu correcte funcionament. En una primera etapa s’han fet anàlisis utilitzant els patrons sintètics d’As (III), trobant rectes de calibratge, límits de detecció, precisió i exactitud i caducitats dels productes. En una segona etapa s’han fet proves utilitzant l’altre patró sintètic de As (V), obtenint una comparativa entre els resultats obtinguts amb l’As (III) i amb l’As (V). En la tercera i ultima etapa s’han realitzat proves addicionals com la contaminació d’As en el blanc de fons, experiments sobre la matriu de la mostra, utilitzant ambdós patrons d’As sintètic, i un últim experiment amb unes barreges d’As (III) amb As (V). Paral·lelament s’han enviat mostres sintètiques preparades a un laboratori extern per analitzar-les mitjançant el mètode ICP-MS i comparar els resultats del mètode de fluorescència amb aquest altre. Com a conclusió s’ha extret que és un mètode molt vàlid per a l’anàlisi d’As, amb uns nivells de precisió, exactitud i sensibilitat notables, amb una productivitat molt elevada. També s’ha extret com a conclusió que les mostres han de contenir un alt percentatge de blanc en la matriu per tal de ser analitzables, fixat a un 80 %, el que comporta una dilució prèvia de les mostres. Finalment s’ha fet un estudi de l’impacte ambiental que té el projecte i un estudi econòmic que inclou el cost d’anàlis