Weak turbulence theory of the non-linear evolution of the ion ring distribution

The nonlinear evolution of an ion ring instability in a low-beta magnetospheric plasma is considered. The evolution of the two-dimensional ring distribution is essentially quasilinear. Ignoring nonlinear processes the time-scale for the quasilinear evolution is the same as for the linear instability 1/t_ql gamma_l. However, when nonlinear processes become important, a new time scale becomes relevant to the wave saturation mechanism. Induced nonlinear scattering of the lower-hybrid waves by plasma electrons is the dominant nonlinearity relevant for plasmas in the inner magnetosphere and typically occurs on the timescale 1/t_ql w(M/m)W/nT, where W is the wave energy density, nT is the thermal energy density of the background plasma, and M/m is the ion to electron mass ratio, which has the consequence that the wave amplitude saturates at a low level, and the timescale for quasilinear relaxation is extended by orders of magnitude

Experimental Signatures of Critically Balanced Turbulence in MAST

Beam Emission Spectroscopy (BES) measurements of ion-scale density fluctuations in the MAST tokamak are used to show that the turbulence correlation time, the drift time associated with ion temperature or density gradients, the particle (ion) streaming time along the magnetic field and the magnetic drift time are consistently comparable, suggesting a "critically balanced" turbulence determined by the local equilibrium. The resulting scalings of the poloidal and radial correlation lengths are derived and tested. The nonlinear time inferred from the density fluctuations is longer than the other times; its ratio to the correlation time scales as $\nu_{*i}^{-0.8\pm0.1}$, where $\nu_{*i}=$ ion collision rate/streaming rate. This is consistent with turbulent decorrelation being controlled by a zonal component, invisible to the BES, with an amplitude exceeding the drift waves' by $\sim \nu_{*i}^{-0.8}$.Comment: 6 pages, 4 figures, submitted to PR

ALPS: The Arbitrary Linear Plasma Solver

The Arbitrary Linear Plasma Solver (ALPS) is a parallelised numerical code that solves the dispersion relation in a hot (even relativistic) magnetised plasma with an arbitrary number of particle species with arbitrary gyrotropic equilibrium distribution functions for any direction of wave propagation with respect to the background field. ALPS reads the background momentum distributions as tables of values on a $(p_{\perp},p_{\parallel})$ grid, where $p_{\perp}$ and $p_{\parallel }$ are the momentum coordinates in the directions perpendicular and parallel to the background magnetic field, respectively. We present the mathematical and numerical approach used by ALPS and introduce our algorithms for the handling of poles and the analytic continuation for the Landau contour integral. We then show test calculations of dispersion relations for a selection of stable and unstable configurations in Maxwellian, bi-Maxwellian, $\kappa$-distributed, and J\"uttner-distributed plasmas. These tests demonstrate that ALPS derives reliable plasma dispersion relations. ALPS will make it possible to determine the properties of waves and instabilities in the non-equilibrium plasmas that are frequently found in space, laboratory experiments, and numerical simulations.Comment: 26 pages, 13 figures, submitte

Suppression of turbulence and subcritical fluctuations in differentially rotating gyrokinetic plasmas

Differential rotation is known to suppress linear instabilities in fusion plasmas. However, even in the absence of growing eigenmodes, subcritical fluctuations that grow transiently can lead to sustained turbulence. Here transient growth of electrostatic fluctuations driven by the parallel velocity gradient (PVG) and the ion temperature gradient (ITG) in the presence of a perpendicular ExB velocity shear is considered. The maximally simplified case of zero magnetic shear is treated in the framework of a local shearing box. There are no linearly growing eigenmodes, so all excitations are transient. The maximal amplification factor of initial perturbations and the corresponding wavenumbers are calculated as functions of q/\epsilon (=safety factor/aspect ratio), temperature gradient and velocity shear. Analytical results are corroborated and supplemented by linear gyrokinetic numerical tests. For sufficiently low values of q/\epsilon (<7 in our model), regimes with fully suppressed ion-scale turbulence are possible. For cases when turbulence is not suppressed, an elementary heuristic theory of subcritical PVG turbulence leading to a scaling of the associated ion heat flux with q, \epsilon, velocity shear and temperature gradient is proposed; it is argued that the transport is much less stiff than in the ITG regime.Comment: 36 pages in IOP latex style; 12 figures; submitted to PPC

Оценка энергетической эффективности схем неадиабатической ректификации смеси ацетон–толуол–н-бутанол с использованием экстрактивного агента в первой колонне

Objectives. To investigate the effectiveness of various options for organizing the process of diabatic distillation in the separation of a mixture of acetone–toluene–n-butanol by extractive distillation (ED) with dimethylformamide as an entrainer in a scheme where an entrainer is used in the first column.Methods. Mathematical modeling in the Aspen Plus v. 12.1 software package was used as the primary research method. The local Non-Random Two Liquid composition equation was used as a model for describing vapor–liquid equilibrium. Parametric optimization of diabatic schemes was carried out according to the criterion of reduced energy costs.Results. Based on ED scheme for an acetone–toluene–n-butanol mixture with an entrainer in the first column, four options for organizing diabatic distillation schemes were considered, both with and without increasing the temperature of the flows due to compression.Conclusion. It is shown that the use of diabatic schemes in the ED of an acetone–toluene–n-butanol mixture with dimethylformamide can decrease energy consumption by 11–17%. While the maximum reduction in energy consumption is achieved in a scheme using a compressor, the efficiency of schemes without a compressor is slightly lower. Nevertheless, the technological design of the latter is much simpler.Цели. Исследовать эффективность применения различных вариантов организации процесса недиабатической ректификации при разделении смеси ацетон–толуол–н-бутанол экстрактивной ректификацией с диметилформамидом в схеме с использованием экстрактивного агента в первой колонне.Методы. Математическое моделирование проводилось в программном комплексе Aspen Plus v. 12.1. Для моделирования парожидкостного равновесия применяли уравнение локальных составов Non-Random Two Liquid. Параметрическая оптимизация неадеабатических схем проводилась по критерию приведенных энергетических затрат.Результаты. На основе схемы экстрактивной ректификации смеси ацетон–толуол–н-бутанол с использованием разделяющего агента в первой колонне было рассмотрено четыре варианта организации схем неадиабатической ректификации, как с применением повышения температуры потоков за счет сжатия в компрессоре, так и без него.Выводы. Показано, что применение неадиабатических схем в экстрактивной ректификации смеси ацетон–толуол–н-бутанол с диметилформамидом позволяет снизить приведенные энергетические затраты на 11–17%, при этом максимальное снижение энергозатрат достигается в схеме с использованием компрессора. Однако эффективность схем без компрессора ниже незначительно, но технологическое оформление таких решений существенно проще

Применение схем неадиабатической экстрактивной ректификации с предварительным отделением азеотропообразующих компонентов для разделения смеси ацетон-толуол-н-бутанол

Objectives. The study aims to investigate the effectiveness of the use of various options for organizing the process of diabatic distillation in the separation of a mixture of acetone-toluene-n-butanol by extractive distillation using dimethylformamide as an entrainer in a scheme with preliminary separation of azeotropic components.Methods. As the main research method, mathematical modeling in the Aspen Plus V. 12 software package was used. As a model for describing vapor-liquid equilibrium, the local composition Non-Random Two Liquid equation model was used. Parametric optimization of diabatic schemes was carried out according to the criterion of reduced energy costs.Results. Based on the scheme for extractive distillation of an acetone-toluene-n-butanol mixture with preliminary separation of azeotropic components, five options for organizing diabatic distillation schemes were considered, both with and without use of a compressor to reach a required flows temperature.Conclusion. It is shown that the use of diabatic schemes in the extractive distillation of a acetone-toluene-n-butanol mixture with dimethylformamide makes it possible to diminish the reduced energy costs by 8.9-43.5%. Meanwhile the maximum reduction in energy consumption is achieved in a scheme where upper vapor flows of two other columns are used to heat the azeotropic components separating column.Цели. Исследование энергетической эффективности применения неадиабатической экстрактивной ректификации при разделении смеси ацетон-толуол-н-бутанол с диметилформамидом в качестве разделяющего агента в схеме с предварительным отделением азеотропообразующих компонентов.Методы. В качестве основного метода исследования применялось математическое моделирование с использованием программного комплекса Aspen Plus V. 12. Моделирование парожидкостного равновесия производилось по уравнению локальных составов Non-Random Two Liquid. Параметрическая оптимизация неадиабатических схем проводилась по критерию приведенных энергетических затрат.Результаты. На основе схемы экстрактивной ректификации смеси ацетон-толуол-н-бутанол с предварительным отделением азеотропообразующих компанентов было рассмотрено пять вариантов организации схем неадиабатической ректификации, как с использованием компрессора для достижения необходимой температуры потоков, так и без него.Выводы. Показано, что применение неадиабатической экстрактивной ректификации в схеме разделения смеси ацетон-толуол-н-бутанол с диметилформамидом с предварительным отделением азеотропообразующих компонентов позволяет снизить приведенные энергетические затраты на 8.9-43.5%, при этом максимальное снижение энергозатрат достигается в схеме с использованием для обогрева колонны отделения азеотропообразующих компонентов верхних паровых потоков двух других колонн

Statistical features of edge turbulence in RFX-mod from Gas Puffing Imaging

Plasma density fluctuations in the edge plasma of the RFX-mod device are measured through the Gas Puffing Imaging Diagnostics. Statistical features of the signal are quantified in terms of the Probability Distribution Function (PDF), and computed for several kinds of discharges. The PDFs from discharges without particular control methods are found to be adequately described by a Gamma function, consistently with the recent results by Graves et al [J.P. Graves, et al, Plasma Phys. Control. Fusion 47, L1 (2005)]. On the other hand, pulses with external methods for plasma control feature modified PDFs. A first empirical analysis suggests that they may be interpolated through a linear combination of simple functions. An inspection of the literature shows that this kind of PDFs is common to other devices as well, and has been suggested to be due to the simultaneous presence of different mechanisms driving respectively coherent bursts and gaussian background turbulence. An attempt is made to relate differences in the PDFs to plasma conditions such as the local shift of the plasma column. A simple phenomenological model to interpret the nature of the PDF and assign a meaning to its parameters is also developed.Comment: 27 pages. Published in PPC

Энергосбережение в экстрактивной ректификации смеси изобутиловый спирт–изобутилацетат с бутилпропионатом

Objectives. Determination of the effectiveness of using various types of heat pumps in the extractive distillation of an isobutyl alcohol–isobutyl acetate mixture with n-butyl propionate as the entrainer.Methods. As the main research method, mathematical modeling was performed using the Aspen Plus V. 9 software package. As a model for describing the vapor–liquid equilibrium, the local composition equation-based UNIQUAC model was employed, and the Redlich–Kwong model was adopted to examine the non-ideal vapor phase. When modeling the conventional scheme of extractive distillation, parametric optimization was carried out according to the criterion of total energy costs in the reboilers of the columns. For economical evaluation, Aspen Process Economic Analyzer V10.1 tools were employed. Results. In comparison with the conventional extractive distillation scheme, three variants of schemes with vapor-recompression heat pumps were considered: with a heat pump placed on an extractive distillation column, on an extractive agent regeneration column, and with two heat pumps placed on both columns of the scheme. A scheme with an internal heat pump was also proposed, in which the heat pump compressor is located between sections of extractive columns that operate at different pressures: 506.6 kPa in the top sections and 101.3 in the bottom section. An economic analysis was conducted for all the considered schemes to calculate the total annual costs. It was shown that schemes with vapor-recompression heat pumps can significantly reduce the energy costs of extractive distillation by up to 39.6%; however, a significant reduction in the total annual costs is achieved only with sufficiently long operation periods of the plants. The reduction in the energy costs in the scheme with an internal heat pump was 44%, and the total annual costs were in the range of 20.2–30.1%, depending on the operating time of the plant. Conclusions. It was shown that using heat pumps in the extractive distillation of the mixture of isobutyl alcohol–isobutyl acetate with n-butyl propionate as the entrainer can significantly reduce energy costs. The scheme with an internal heat pump is the most economical of all the considered schemes.Цели. Определение эффективности применения тепловых насосов различного типа в экстрактивной ректификации смеси изобутиловый спирт–изобутилацетат с н-бутилпропионатом в качестве разделяющего агента. Методы. Основной метод исследования – математическое моделирование в программном комплексе Aspen Plus V. 9. В качестве модели описания парожидкостного равновесия применялась основанная на уравнении локальных составов модель UNIQUAC, для учета неидеальности паровой фазы – модель Редлиха–Квонга. При моделировании традиционной схемы экстрактивной ректификации производилась параметрическая оптимизация по критерию суммарных энергетических затрат в кипятильниках колонн. Для экономической оценки применялись инструменты Aspen Process Economic Analyzer V10.1.Результаты. В сравнении с традиционной схемой экстрактивной ректификации рассмотрено три варианта схемы с применением тепловых насосов открытого типа – с размещением теплового насоса на колонне экстрактивной ректификации, на колонне регенерации разделяющего агента и с размещением двух тепловых насосов на обоих колоннах схемы. Также предложена схема с внутренним тепловым насосом, в которой компрессор теплового насоса расположен между секциями экстрактивной колонны, которые работают при различных давлениях – 506.6 кПа в укрепляющей и экстрактивной секциях и 101.3 в отгонной. Была произведена экономическая оценка всех рассмотренных схем и вычисление полных приведенных затрат. Показано, что применение схем с тепловыми насосами открытого типа позволяет значительно, вплоть до 39.6%, снизить энергетические затраты на экстрактивную ректификацию, однако значительное снижение полных приведенных затрат достигается только при достаточно большом сроке функционирования установок. Снижение энергетических затрат в схеме с внутренним тепловым насосом составило 44%, а полных приведенных затрат – 20.2–30.1% в зависимости от времени функционирования установки.Выводы. Показано, что применение тепловых насосов в процессе экстрактивной ректификации смеси изобутиловый спирт–изобутилацетат с бутилпропионатом в качестве разделяющего агента позволяет значительно снизить энергетические затраты. Наиболее экономичной из рассмотренных является схема с применением внутреннего теплового насоса

A functorial construction of moduli of sheaves

We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical aspects of existing constructions and yields new simpler definitions of theta functions, about which more complete results can be proved.Comment: 52 pp. Dedicated to the memory of Joseph Le Potier. To appear in Inventiones Mathematicae. Slight change in the definition of the Kronecker algebra in Secs 1 (p3) and 2.2 (p6), with corresponding small alterations elsewhere, to make the constructions work for non-reduced schemes. Section 6.5 rewritten. Remark 2.6 and new references adde