Nonlinear wave propagation through cold plasma

Electromagnetic wave propagation through cold collision free plasma is studied using the nonlinear perturbation method. It is found that the equations can be reduced to the modified Kortweg-de Vries equation

The global build-up to intrinsic ELM bursts and comparison with pellet triggered ELMs seen in JET

We focus on JET plasmas in which ELMs are triggered by pellets in the presence of ELMs which occur naturally. We perform direct time domain analysis of signals from fast radial field coils and toroidal full flux azimuthal loops. These toroidally integrating signals provide simultaneous high time resolution measurements of global plasma dynamics and its coupling to the control system. We examine the time dynamics of these signals in plasmas where pellet injection is used to trigger ELMs in the presence of naturally occurring ELMs. Pellets whose size and speed are intended to provide maximum local perturbation for ELM triggering are launched at pre-programmed times, without correlation to the occurrence times of intrinsic ELMs. Pellet rates were sufficiently low to prevent sustained changes of the underlying plasma conditions and natural ELM behaviour. We find a global signature of the build-up to natural ELMs in the temporal analytic phase of both the full flux loops and fast radial field coil signals. Before a natural ELM, the signal phases align to the same value on a ∼2–5ms timescale. This global build up to a natural ELM occurs whilst the amplitude of the full flux loop and fast radial field coil signals are at their background value: it precedes the response seen in these signals to the onset of ELMing. In contrast these signals do not clearly phase align before the ELM for ELMs which are the first to occur following pellet injection. This provides a direct test that can distinguish when an ELM is triggered by a pellet as opposed to occurring naturally. It further supports the idea [1–4] of a global build up phase that precedes natural ELMs; pellets can trigger ELMs even when the signal phase is at a value when a natural ELM is unlikely to occurEURATOM 633053ONR NICOP N62909-15-1-N14

Evaluation of abrupt energy transfer among turbulent plasma structures using singular value decomposition

A method to quantify the energy transfer among turbulent structures using singular value decomposition (SVD) is presented. We apply the method to numerical turbulence data obtained from a global plasma simulation using the Hasegawa–Wakatani fluid model, in which the Kelvin–Helmholtz instability plays a dominant role. Using the SVD method, the electrostatic potential is decomposed into a background potential deformation, a zonal flow, a coherent mode and an intermittent structure. Thus there are four key structures, as distinct from the three found in conventional theory. The kinetic energy of each structure is evaluated, and the limit cycle among them is obtained. In the limit cycle, an abrupt change of the background is found to be synchronised with the period of the zonal flow. The energy transfer function of each turbulence structure, which is defined on the basis of a vorticity equation, is evaluated. This then provides physical understanding of how the limit cycle is sustained by dynamical changes in the energy transfer among structures over the its period. In addition, it is shown that the abrupt deformation of the background is caused by the non-linear self-coupling of the intermittent structure

Testing the SOC hypothesis for the magnetosphere

As noted by Chang, the hypothesis of Self-Organised Criticality provides a theoretical framework in which the low dimensionality seen in magnetospheric indices can be combined with the scaling seen in their power spectra and the recently-observed plasma bursty bulk flows. As such, it has considerable appeal, describing the aspects of the magnetospheric fuelling:storage:release cycle which are generic to slowly-driven, interaction-dominated, thresholded systems rather than unique to the magnetosphere. In consequence, several recent numerical "sandpile" algorithms have been used with a view to comparison with magnetospheric observables. However, demonstration of SOC in the magnetosphere will require further work in the definition of a set of observable properties which are the unique "fingerprint" of SOC. This is because, for example, a scale-free power spectrum admits several possible explanations other than SOC. A more subtle problem is important for both simulations and data analysis when dealing with multiscale and hence broadband phenomena such as SOC. This is that finite length systems such as the magnetosphere or magnetotail will by definition give information over a small range of orders of magnitude, and so scaling will tend to be narrowband. Here we develop a simple framework in which previous descriptions of magnetospheric dynamics can be described and contrasted. We then review existing observations which are indicative of SOC, and ask if they are sufficient to demonstrate it unambiguously, and if not, what new observations need to be made?Comment: 29 pages, 0 figures. Based on invited talk at Spring American Geophysical Union Meeting, 1999. Journal of Atmospheric and Solar Terrestrial Physics, in pres

Recurrence plot statistics and the effect of embedding

Recurrence plots provide a graphical representation of the recurrent patterns in a timeseries, the quantification of which is a relatively new field. Here we derive analytical expressions which relate the values of key statistics, notably determinism and entropy of line length distribution, to the correlation sum as a function of embedding dimension. These expressions are obtained by deriving the transformation which generates an embedded recurrence plot from an unembedded plot. A single unembedded recurrence plot thus provides the statistics of all possible embedded recurrence plots. If the correlation sum scales exponentially with embedding dimension, we show that these statistics are determined entirely by the exponent of the exponential. This explains the results of Iwanski and Bradley (Chaos 8 [1998] 861-871) who found that certain recurrence plot statistics are apparently invariant to embedding dimension for certain low-dimensional systems. We also examine the relationship between the mutual information content of two timeseries and the common recurrent structure seen in their recurrence plots. This allows time-localized contributions to mutual information to be visualized. This technique is demonstrated using geomagnetic index data; we show that the AU and AL geomagnetic indices share half their information, and find the timescale on which mutual features appear

25 Years of Self-organized Criticality: Concepts and Controversies

Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak’s own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld’s original papers

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)

Relationship of edge localized mode burst times with divertor flux loop signal phase in JET

A phase relationship is identified between sequential edge localized modes (ELMs) occurrence times in a set of H-mode tokamak plasmas to the voltage measured in full flux azimuthal loops in the divertor region. We focus on plasmas in the Joint European Torus where a steady H-mode is sustained over several seconds, during which ELMs are observed in the Be II emission at the divertor. The ELMs analysed arise from intrinsic ELMing, in that there is no deliberate intent to control the ELMing process by external means. We use ELM timings derived from the Be II signal to perform direct time domain analysis of the full flux loop VLD2 and VLD3 signals, which provide a high cadence global measurement proportional to the voltage induced by changes in poloidal magnetic flux. Specifically, we examine how the time interval between pairs of successive ELMs is linked to the time-evolving phase of the full flux loop signals. Each ELM produces a clear early pulse in the full flux loop signals, whose peak time is used to condition our analysis. The arrival time of the following ELM, relative to this pulse, is found to fall into one of two categories: (i) prompt ELMs, which are directly paced by the initial response seen in the flux loop signals; and (ii) all other ELMs, which occur after the initial response of the full flux loop signals has decayed in amplitude. The times at which ELMs in category (ii) occur, relative to the first ELM of the pair, are clustered at times when the instantaneous phase of the full flux loop signal is close to its value at the time of the first ELM