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Register a new userStatistical Characterisation and Classification of Edge Localised Plasma Instabilities
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The statistics of edge-localised plasma instabilities (ELMs) in toroidal magnetically confined fusion plasmas are considered. From first principles, standard experimentally motivated assumptions are shown to determine a specific probability distribution for the waiting times between ELMs: the Weibull distribution. This is confirmed empirically by a statistically rigorous comparison with a large data set from the Joint European Torus (JET). The successful characterisation of ELM waiting times enables future work to progress in various ways. Here we present a quantitative classification of ELM types, complementary to phenomenological approaches. It also informs us about the nature of ELMing processes, such as whether they are random or deterministic.
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The generic question is considered: How can we determine the probability of an otherwise quasirandom event, having been triggered by an external influence? A specific problem is the quantification of the success of techniques to trigger, and hence control, edge-localised plasma instabilities (ELMs) in magnetically confined fusion (MCF) experiments. The development of such techniques is essential to ensure tolerable heat loads on components in large MCF fusion devices, and is necessary for their development into economically successful power plants. Bayesian probability theory is used to rigorously formulate the problem and to provide a formal solution. Accurate but pragmatic methods are developed to estimate triggering probabilities, and are illustrated with experimental data. These allow results from experiments to be quantitatively assessed, and rigorously quantified conclusions to be formed. Example applications include assessing whether triggering of ELMs is a statistical or deterministic process, and the establishment of thresholds to ensure that ELMs are reliably triggered.
For a two week period during the Joint European Torus (JET) 2012 experimental campaign, the same high confinement plasma was repeated 151 times. The dataset was analysed to produce a probability density function (pdf) for the waiting times between edge-localised plasma instabilities (ELMS). The result was entirely unexpected. Instead of a smooth single peaked pdf, a succession of 4-5 sharp maxima and minima uniformly separated by 7-8 millisecond intervals was found. Here we explore the causes of this newly observed phenomenon, and conclude that it is either due to a self-organised plasma phenomenon or an interaction between the plasma and a real-time control system. If the maxima are a result of resonant frequencies at which ELMs can be triggered more easily, then future ELM control techniques can, and probably will, use them. Either way, these results demand a deeper understanding of the ELMing process.
An electron or electron-positron beam streaming through a plasma is notoriously prone to micro-instabilities. For a dilute ultrarelativistic infinite beam, the dominant instability is a mixed mode between longitudinal two-stream and transverse filamentation modes, with a phase velocity oblique to the beam velocity. A spatiotemporal theory describing the linear growth of this oblique mixed instability is proposed, which predicts that spatiotemporal effects generally prevail for finite-length beams, leading to a significantly slower instability evolution than in the usually assumed purely temporal regime. These results are accurately supported by particle-in-cell (PIC) simulations. Furthermore, we show that the self-focusing dynamics caused by the plasma wakefields driven by finite-width beams can compete with the oblique instability. Analyzed through PIC simulations, the interplay of these two processes in realistic systems bears important implications for upcoming accelerator experiments on ultrarelativistic beam-plasma interactions.
Global electromagnetic gyrokinetic simulations show the existence of near threshold conditions for both a high-$n$ kinetic ballooning mode (KBM) and an intermediate-$n$ kinetic version of peeling-ballooning mode (KPBM) in the edge pedestal of two DIII-D H-mode discharges. When the magnetic shear is reduced in a narrow region of steep pressure gradient, the KPBM is significantly stabilized, while the KBM is weakly destabilized and hence becomes the most-unstable mode. Collisions decrease the KBMs critical $beta$ and increase the growth rate.
Wave properties and instabilities in a magnetized, anisotropic, collisionless, rarefied hot plasma in fluid approximation are studied, using the 16-moments set of the transport equations obtained from the Vlasov equations. These equations differ from the CGL-MHD fluid model (single fluid equations by Chew, Goldberger, and Low, 1956) by including two anisotropic heat flux evolution equations, where the fluxes invalidate the double polytropic CGL laws. We derived the general dispersion relation for linear compressible wave modes. Besides the classic incompressible fire hose modes there appear four types of compressible wave modes: two fast and slow mirror modes - strongly modified compared to the CGL model - and two thermal modes. In the presence of initial heat fluxes along the magnetic field the wave properties become different for the waves running forward and backward with respect to the magnetic field. The well known discrepancies between the results of the CGL-MHD fluid model and the kinetic theory are now removed: i) The mirror slow mode instability criterion is now the same as that in the kinetic theory. ii) Similarly, in kinetic studies there appear two kinds of fire hose instabilities - incompressible and compressible ones. These two instabilities can arise for the same plasma parameters, and the instability of the new compressible oblique fire hose modes can become dominant. The compressible fire hose instability is the result of the resonance coupling of three retrograde modes - two thermal modes and a fast mirror mode. The results can be applied to the theory of solar and stellar coronal and wind models.
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