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

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

Stark Broadening of the B III 2s-2p Lines

We present a quantum-mechanical calculation of Stark line widths from electron-ion collisions for the $2s_{1/2}-2p_{1/2,3/2}$, lambda = 2066 and 2067 A, resonance transitions in B III. The results confirm the previous quantum-mechanical R-matrix calculations but contradict recent measurements and semi-classical and some semi-empirical calculations. The differences between the calculations can be attributed to the dominance of small L partial waves in the electron-atom scattering, while the large Stark widths inferred from the measurements would be substantially reduced if allowance is made for hydrodynamic turbulence from high Reynolds number flows and the associated Doppler broadening.Comment: 21 pages, 4 figures; to be published in Phys. Rev.

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

Quasi-Two-Dimensional Dynamics of Plasmas and Fluids

In the lowest order of approximation quasi-twa-dimensional dynamics of planetary atmospheres and of plasmas in a magnetic field can be described by a common convective vortex equation, the Charney and Hasegawa-Mirna (CHM) equation. In contrast to the two-dimensional Navier-Stokes equation, the CHM equation admits "shielded vortex solutions" in a homogeneous limit and linear waves ("Rossby waves" in the planetary atmosphere and "drift waves" in plasmas) in the presence of inhomogeneity. Because of these properties, the nonlinear dynamics described by the CHM equation provide rich solutions which involve turbulent, coherent and wave behaviors. Bringing in non ideal effects such as resistivity makes the plasma equation significantly different from the atmospheric equation with such new effects as instability of the drift wave driven by the resistivity and density gradient. The model equation deviates from the CHM equation and becomes coupled with Maxwell equations. This article reviews the linear and nonlinear dynamics of the quasi-two-dimensional aspect of plasmas and planetary atmosphere starting from the introduction of the ideal model equation (CHM equation) and extending into the most recent progress in plasma turbulence.U. S. Department of Energy DE-FG05-80ET-53088Ministry of Education, Science and Culture of JapanFusion Research Cente

Understanding the effect of sheared flow on microinstabilities

The competition between the drive and stabilization of plasma microinstabilities by sheared flow is investigated, focusing on the ion temperature gradient mode. Using a twisting mode representation in sheared slab geometry, the characteristic equations have been formulated for a dissipative fluid model, developed rigorously from the gyrokinetic equation. They clearly show that perpendicular flow shear convects perturbations along the field at a speed we denote by $Mc_s$ (where $c_s$ is the sound speed), whilst parallel flow shear enters as an instability driving term analogous to the usual temperature and density gradient effects. For sufficiently strong perpendicular flow shear, $M >1$, the propagation of the system characteristics is unidirectional and no unstable eigenmodes may form. Perturbations are swept along the field, to be ultimately dissipated as they are sheared ever more strongly. Numerical studies of the equations also reveal the existence of stable regions when $M < 1$, where the driving terms conflict. However, in both cases transitory perturbations exist, which could attain substantial amplitudes before decaying. Indeed, for $M \gg 1$, they are shown to exponentiate $\sqrt{M}$ times. This may provide a subcritical route to turbulence in tokamaks.Comment: minor revisions; accepted to PPC

Edge localized mode control with an edge resonant magnetic perturbation

A low amplitude (δbr∕BT=1 part in 5000) edge resonantmagnetic field perturbation with toroidalmode number n=3 and poloidal mode numbers between 8 and 15 has been used to suppress most large type I edge localized modes(ELMs) without degrading core plasma confinement. ELMs have been suppressed for periods of up to 8.6 energy confinement times when the edge safety factor q95 is between 3.5 and 4. The large ELMs are replaced by packets of events (possibly type II ELMs) with small amplitude, narrow radial extent, and a higher level of magnetic field and density fluctuations, creating a duty cycle with long “active” intervals of high transport and short “quiet” intervals of low transport. The increased transport associated with these events is less impulsive and slows the recovery of the pedestal profiles to the values reached just before the large ELMs without the n=3 perturbation. Changing the toroidal phase of the perturbation by 60° with respect to the best ELM suppression case reduces the ELM amplitude and frequency by factors of 2–3 in the divertor, produces a more stochastic response in the H-mode pedestal profiles, and displays similar increases in small scale events, although significant numbers of large ELMs survive. In contrast to the best ELM suppression case where the type I ELMs are also suppressed on the outboard midplane, the midplane recycling increases until individual ELMs are no longer discernable. The ELM response depends on the toroidal phase of the applied perturbation because intrinsic error fields make the target plasma nonaxisymmetric, and suggests that at least some of the variation in ELM behavior in a single device or among different devices is due to differences in the intrinsic error fields in these devices. These results indicate that ELMs can be suppressed by small edge resonantmagnetic field perturbations. Extrapolation to next-step burning plasma devices will require extending the regime of operation to lower collisionality and understanding the physical mechanism responsible for the ELM suppression.This work was funded by the U.S. Department of Energy under Grant Nos. DE-FC02-04ER54698, DE-FG02- 04ER54758, DE-FG03-01ER54615, W-7405-ENG-48, DEFG03-96ER54373, DE-FG02-89ER53297, DE-AC05- 00OR22725, and DE-AC04-94AL85000

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

Solar Wind Turbulence and the Role of Ion Instabilities

International audienc