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

Physical and mathematical modelling of the conditions of coal and gas outbursts

Purpose. Experimental study and theoretical modeling of conditions initiating destructive processes and development of gas generation in coals. Methods. Analysis, generalization and statistical processing of experimental data and results of analytical studies followed by the identification of patterns, and numerical solution of equations in partial derivatives. Findings. Experimental studies of changes in properties of mechanically activated samples of gas coal and fat coal in weak electric fields have been performed. The experimental results were compared with the characteristics of coals taken from the zones of different outburst hazard probability, which enabled to formulate new ideas about the causes of gas generation in coals. A mathematical model has been elaborated for gas outburst development taking into consideration the solid phase porosity changes due to the transition of coal organic mass to gas. Originality. The treated samples with the broken microstructure demonstrated a significant increase (1.5 – 3 times) in the characteristic time of methane desorption and manifestation of electret properties identified by the value of the evoked potential and electrochemical activity, while qualitative and quantitative changes in the treated coal properties were identical to the natural analogues. It is for the first time that the developed mathematical model of gas flow during the outburst reproduces the changes in porosity and permeability of the rock caused by chemical reactions of gas generation by coal organic mass. Practical implications. The improvement of the proposed outburst model can be used for predictive estimations of instantaneous outbursts taking into account the changes in thermodynamic and kinetic stability parameters of the “coal – gas” system.Цель. Экспериментальные исследования и теоретическое моделирование условий инициирования деструктивных и развития газогенерирующих процессов в каменных углях. Методика. Анализ, обобщение и статистическая обработка экспериментальных показателей и результатов аналитических исследований с последующим выделением закономерностей, численное решение уравнений в частных производных. Результаты. Выполнены экспериментальные исследования изменения свойств механоактивированных образцов угля марок Г и Ж в слабых электрических полях. Экспериментальные результаты сопоставлены с характеристиками углей, отобранных из зон с разной вероятностью выбросоопасности, на основе чего сформулированы новые представления о причинах газогенерации в углях. Разработана математическая модель развития выброса газа при изменении пористости твердой фазы вследствие перехода органической массы угля в газ. Научная новизна. Установлено, что для обработанных образцов с нарушенной микроструктурой наблюдается значительное увеличение (в 1.5 – 3 раза) характерного времени десорбции метана и проявление электретных свойств по величине вызванного потенциала и электрохимической активности, при этом, качественные и количественные изменения свойств в обработанных углях идентичны природным аналогам. Разработанная математическая модель течения газа во время выброса впервые отражает изменения пористости и проницаемости породы, обусловленные химическими реакциями генерации газа органической массой угля. Практическая значимость. Совершенствование предложенной модели выброса может быть использовано в прогнозных оценках внезапных выбросов с учетом изменения параметров термодинамической и кинетической устойчивости системы “уголь – газ”.Мета. Експериментальні дослідження та теоретичне моделювання умов ініціювання деструктивних і розвитку газогенеруючих процесів у кам’яному вугіллі. Методика. Аналіз, узагальнення та статистична обробка експериментальних показників і результатів аналітичних досліджень з подальшим виділенням закономірностей, чисельне рішення рівнянь у частинних похідних. Результати. Виконано експериментальні дослідження зміни властивостей механоактивованих зразків вугілля марок Г і Ж у слабких електричних полях. Експериментальні результати зіставлені з характеристиками вугілля, відібраних із зон з різною ймовірністю небезпеки викиду, на основі чого сформульовані нові уявлення про причини газогенерації у вугіллі. Розроблено математичну модель розвитку викиду газу при зміні пористості твердої фази внаслідок переходу органічної маси вугілля в газ. Наукова новизна. Встановлено, що для оброблених зразків з порушеною мікроструктурою спостерігається значне збільшення (у 1.5 – 3 рази) характерного часу десорбції метану і прояв електретних властивостей за величиною викликаного потенціалу та електрохімічної активності; при цьому якісні та кількісні зміни властивостей в обробленому вугіллі ідентичні природним аналогам. Розроблена математична модель течії газу під час викиду вперше відображає зміни пористості й проникності породи, які зумовлені хімічними реакціями генерації газу органічною масою вугілля. Практична значимість. Удосконалення запропонованої моделі викиду може бути використано у прогнозних оцінках раптових викидів з урахуванням зміни параметрів термодинамічної і кінетичної стійкості системи “вугілля – газ”.Данная работа выполнена при поддержке и финансировании Министерством образования и науки Украины проекта ГП-491 “Исследование наноструктуры ископаемых углей как источника метана угольных месторождений”. Авторы благодарят доктора технических наук Е.В. Ульянову за помощь в проведении физических исследований углей, обработанных слабыми электрическими полями

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

Index

The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, the basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell–Jüttner model distributions. The main properties of the competing modes (developing parallel, transverse, and oblique to the beam) are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.Original Publication: Antoine Bret, Laurent Gremillet and Mark Eric Dieckmann, Multidimensional electron beam-plasma instabilities in the relativistic regime, 2010, Physics of Plasmas, (17), 12, 120501-1-120501-36. http://dx.doi.org/10.1063/1.3514586 Copyright: American Institute of Physics http://www.aip.org/</p

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

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

Use of Ar pellet ablation rate to estimate initial runaway electron seed population in DIII-D rapid shutdown experiments

Small (2-3 mm, 0.9-2 Pa • m3) argon pellets are used in the DIII-D tokamak to cause rapid shutdown (disruption) of discharges. The Ar pellet ablation is typically found to be much larger than expected from the thermal plasma electron temperature alone; the additional ablation is interpreted as being due to non-thermal runaway electrons (REs) formed during the pellet-induced temperature collapse. Simple estimates of the RE seed current using the enhanced ablation rate give values of order 1-10 kA, roughly consistent with estimates based on avalanche theory. Analytic estimates of the RE seed current based on the Dreicer formula tend to significantly underestimate it, while estimates based on the hot tail model significantly overestimate it

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