Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Lastly, an application of the guiding-center Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.Comment: 11 page

Second order nonlinear gyrokinetic theory : From the particle to the gyrocenter

A gyrokinetic reduction is based on a specific ordering of the different small parameters characterizing the background magnetic field and the fluctuating electromagnetic fields. In this tutorial, we consider the following ordering of the small parameters: $\epsilon\_B=\epsilon\_\delta^2$ where $\epsilon\_B$ is the small parameter associated with spatial inhomogeneities of the background magnetic field and $\epsilon\_\delta$ characterizes the small amplitude of the fluctuating fields. In particular, we do not make any assumption on the amplitude of the background magnetic field. Given this choice of ordering, we describe a self-contained and systematic derivation which is particularly well suited for the gyrokinetic reduction, following a two-step procedure. We follow the approach developed in [Sugama, Physics of Plasmas 7, 466 (2000)]:In a first step, using a translation in velocity, we embed the transformation performed on the symplectic part of the gyrocentre reduction in the guiding-centre one. In a second step, using a canonical Lie transform, we eliminate the gyroangle dependence from the Hamiltonian. As a consequence, we explicitly derive the fully electromagnetic gyrokinetic equations at the second order in $\epsilon\_\delta$

Creation of a Transport Barrier for the E x B drift in magnetized plasmas

International audienceWe modelize the chaotic dynamics of charged test-particles in a turbulent electric field, across the confining magnetic field in controlled thermonuclear fusion devices by a 1.5 degrees of freedom Hamiltonian dynamical system. The external electric field E is given by a some potential V and the magnetic field B is considered uniform. We prove that, by introducing a small additive control term to the external electric field, it is possible to create a transport barrier. The robustness of this control method is also numerically investigated

Verification of Gyrokinetic codes: theoretical background and applications

In fusion plasmas the strong magnetic field allows the fast gyro-motion to be systematically removed from the description of the dynamics, resulting in a considerable model simplification and gain of computational time. Nowadays, the gyrokinetic (GK) codes play a major role in the understanding of the development and the saturation of turbulence and in the prediction of the subsequent transport. Naturally, these codes require thorough verification and validation. Here we present a new and generic theoretical framework and specific numerical applications to test the faithfulness of the implemented models to theory and to verify the domain of applicability of existing GK codes. For a sound verification process, the underlying theoretical GK model and the numerical scheme must be considered at the same time, which has rarely been done and therefore makes this approach pioneering. At the analytical level, the main novelty consists in using advanced mathematical tools such as variational formulation of dynamics for systematization of basic GK code's equations to access the limits of their applicability. The verification of numerical scheme is proposed via the benchmark effort. In this work, specific examples of code verification are presented for two GK codes: the multi-species electromagnetic ORB5 (PIC) and the radially global version of GENE (Eulerian). The proposed methodology can be applied to any existing GK code. We establish a hierarchy of reduced GK Vlasov-Maxwell equations implemented in the ORB5 and GENE codes using the Lagrangian variational formulation. At the computational level, detailed verifications of global electromagnetic test cases developed from the CYCLONE Base Case are considered, including a parametric $\beta$-scan covering the transition from ITG to KBM and the spectral properties at the nominal $\beta$ value.Comment: 16 pages, 2 Figures, APS DPP 2016 invited pape

Abnormalities of apoptosis of the thyroid gland cells from extratumoral microfollicular tissue

Aim: The aim of this study was to evaluate the frequency of existence of thyroid extratumoral normo- and microfollicular tissue in patients with thyroid carcinoma and peculiarities of apoptosis in mentioned tissue. Materials and Methods: Using samples of normo- and microfollicular thyroid tissue it was determined the content of fragmented DNA and intensity of stimulated internucleosomal DNA fragmentation; activities of caspase-3 and cysteine lysosomal cathepsins. Results: It was found that normofollicular tissue is observed more often in patients with nodal euthyroid goiter but microfollicular tissue is more common for patients with carcinoma. Extratumoral microfollicular tissue was found in the thyroid of patients above 50 years old mostly, and more rarely in young ones. The fragmented DNA concentration in microfollicular tissue was lower by a factor of 3.5 and intensity of stimulated internucleosomal DNA fragmentation was also decreased. Activity both of cathepsin B in lisosomes and caspase-3 in lysates of such tissue was also decreased. Conclusions: The decrease of intensity of spontaneous apoptosis and the absence of its modulation/induction following proapoptotic factors in extratumoral microfollicular thyroid tissue may be considered as a respond of the thyroid gland tissue to an existence of carcinoma

Автокореляційні функції та їх застосування для оцінки якості заходу на посадку

The article describes the correlation functions between the information on the flight path and distortions in tracking operations of an operator. This is due to its psychophysiological abilities in a state of high tension.В этой статье описываются функции корреляции между информацией о траектории полета и искажениями при операции слежения оператора. Это связано с его психофизиологическими особенностями в состоянии высокой напряженности.У цій статті описуються функції кореляції між інформацією про траєкторію польоту і викривленнями при операції слідкування оператора. Це пов'язано з його психофізіологічними особливостями в стані високої напруженості

Використання поляриметрії для вимірювання рельєфу місцевості

The article discusses modern geodetic measurement methods of relief, their advantages and disadvantages. It is also offered a polarimetric measurement method of relief. This method is intended for measuring relief and can also be used to measure slope road and airport paving, railways to geometric description of the surface complex engineering objects, such as bridges, roofs of buildings, architectural elements.Статья посвящена проблеме использования поляриметрии для измерения рельефа местности. Предложен поляриметрический метод измерения. В сравнении с существующими методами измерения поляриметрический метод обеспечивает сокращение времени и при этом обеспечивает высокую точность. Он обеспечивает непрерывность и высокую точность измерения за счёт использования поляриметра, высокую скорость и низкую трудоемкость измерительного процесса за счёт автоматизации процесса измерения.Статтю присвячено проблемі використання поляриметрії для вимірювання рельєфу місцевості. Запропоновано поляриметричний метод вимірювання. У порівнянні з наявними методами вимірювання поляриметричний метод забезпечує скорочення часу вимірювання й при цьому забезпечує високу точність. Він забезпечує неперервність і високу точність вимірювання завдяки застосуванню поляриметра, високу швидкість і низькі трудозатрати вимірювального процесу за рахунок автоматизації процесу вимірювання