Impurity flows and plateau-regime poloidal density variation in a tokamak pedestal

In the pedestal of a tokamak, the sharp radial gradients of density and temperature can give rise to poloidal variation in the density of impurities. At the same time, the flow of the impurity species is modified relative to the conventional neoclassical result. In this paper, these changes to the density and flow of a collisional impurity species are calculated for the case when the main ions are in the plateau regime. In this regime it is found that the impurity density can be higher at either the inboard or outboard side. This finding differs from earlier results for banana- or Pfirsch-Schl\"uter-regime main ions, in which case the impurity density is always higher at the inboard side in the absence of rotation. Finally, the modifications to the impurity flow are also given for the other regimes of main-ion collisionality.Comment: 15 pages, 5 figures, submitted to Physics of Plasma

Impurity transport and bulk ion flow in a mixed collisionality stellarator plasma

The accumulation of impurities in the core of magnetically confined plasmas, resulting from standard collisional transport mechanisms, is a known threat to their performance as fusion energy sources. Whilst the axisymmetric tokamak systems have been shown to benefit from the effect of temperature screening, that is an outward flux of impurities driven by the temperature gradient, impurity accumulation in stellarators was thought to be inevitable, driven robustly by the inward pointing electric field characteristic of hot fusion plasmas. We have shown in Helander et. al. (2017b) that such screening can in principle also appear in stellarators, in the experimentally relevant mixed collisionality regime, where a highly collisional impurity species is present in a low collisionality bulk plasma. Details of the analytic calculation are presented here, along with the effect of the impurity on the bulk ion flow, which will ultimately affect the bulk contribution to the bootstrap current

Impurity transport in a mixed-collisionality stellarator plasma

A potential threat to the performance of magnetically confined fusion plasmas is the problem of impurity accumulation, which causes the concentration of highly charged impurity ions to rise uncontrollably in the center of the plasma and spoil the energy confinement by excessive radiation. It has long been thought that the collisional transport of impurities in stellarators always leads to such accumulation (if the electric field points inwards, which is usually the case), whereas tokamaks, being axisymmetric, can benefit from "temperature screening", i.e., an outward flux of impurities driven by the temperature gradient. Here it is shown, using analytical techniques supported by results from a new numerical code, that such screening can arise in stellarator plasmas too, and indeed does so in one of the most relevant operating regimes, where the impurities are highly collisional whilst the bulk plasma is in any of the low-collisionality regimes.Comment: 11 pages, 3 figure

Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas

In this work, we examine the validity of several common simplifying assumptions used in numerical neoclassical calculations for nonaxisymmetric plasmas, both by using a new continuum drift-kinetic code and by considering analytic properties of the kinetic equation. First, neoclassical phenomena are computed for the LHD and W7-X stellarators using several versions of the drift-kinetic equation, including the commonly used incompressible-ExB-drift approximation and two other variants, corresponding to different effective particle trajectories. It is found that for electric fields below roughly one third of the resonant value, the different formulations give nearly identical results, demonstrating the incompressible ExB-drift approximation is quite accurate in this regime. However, near the electric field resonance, the models yield substantially different results. We also compare results for various collision operators, including the full linearized Fokker-Planck operator. At low collisionality, the radial transport driven by radial gradients is nearly identical for the different operators, while in other cases it is found to be important that collisions conserve momentum

Impurities in a non-axisymmetric plasma: transport and effect on bootstrap current

Impurities cause radiation losses and plasma dilution, and in stellarator plasmas the neoclassical ambipolar radial electric field is often unfavorable for avoiding strong impurity peaking. In this work we use a new continuum drift-kinetic solver, the SFINCS code (the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver) [M. Landreman et al., Phys. Plasmas 21 (2014) 042503] which employs the full linearized Fokker-Planck-Landau operator, to calculate neoclassical impurity transport coefficients for a Wendelstein 7-X (W7-X) magnetic configuration. We compare SFINCS calculations with theoretical asymptotes in the high collisionality limit. We observe and explain a 1/nu-scaling of the inter-species radial transport coefficient at low collisionality, arising due to the field term in the inter-species collision operator, and which is not found with simplified collision models even when momentum correction is applied. However, this type of scaling disappears if a radial electric field is present. We also use SFINCS to analyze how the impurity content affects the neoclassical impurity dynamics and the bootstrap current. We show that a change in plasma effective charge Zeff of order unity can affect the bootstrap current enough to cause a deviation in the divertor strike point locations.Comment: 36 pages, 13 figure

On neoclassical impurity transport in stellarator geometry

The impurity dynamics in stellarators has become an issue of moderate concern due to the inherent tendency of the impurities to accumulate in the core when the neoclassical ambipolar radial electric field points radially inwards (ion root regime). This accumulation can lead to collapse of the plasma due to radiative losses, and thus limit high performance plasma discharges in non-axisymmetric devices.\\ A quantitative description of the neoclassical impurity transport is complicated by the breakdown of the assumption of small $\mathbf{E}\times \mathbf{B}$ drift and trapping due to the electrostatic potential variation on a flux surface $\tilde{\Phi}$ compared to those due to the magnetic field gradient. The present work examines the impact of this potential variation on neoclassical impurity transport in the Large Helical Device (LHD) stellarator. It shows that the neoclassical impurity transport can be strongly affected by $\tilde{\Phi}$. The central numerical tool used is the $\delta f$ particle in cell (PIC) Monte Carlo code EUTERPE. The $\tilde{\Phi}$ used in the calculations is provided by the neoclassical code GSRAKE. The possibility of obtaining a more general $\tilde{\Phi}$ self-consistently with EUTERPE is also addressed and a preliminary calculation is presented.Comment: 11 pages, 15 figures, presented at Joint Varenna-Lausanne International Workshop on Theory of Fusion Plasmas, 2012. Accepted for publication to Plasma Phys. and Control. Fusio

The comprehensive cohort model in a pilot trial in orthopaedic trauma

Background: The primary aim of this study was to provide an estimate of effect size for the functional outcome of operative versus non-operative treatment for patients with an acute rupture of the Achilles tendon using accelerated rehabilitation for both groups of patients. The secondary aim was to assess the use of a comprehensive cohort research design (i.e. a parallel patient-preference group alongside a randomised group) in improving the accuracy of this estimate within an orthopaedic trauma setting. Methods: Pragmatic randomised controlled trial and comprehensive cohort study within a level 1 trauma centre. Twenty randomised participants (10 operative and 10 non-operative) and 29 preference participants (3 operative and 26 non-operative). The ge range was 22-72 years and 37 of the 52 patients were men. All participants had an acute rupture of their Achilles tendon and no other injuries. All of the patients in the operative group had a simple end-to-end repair of the tendon with no augmentation. Both groups then followed the same eight-week immediate weight-bearing rehabilitation programme using an off-the-shelf orthotic. The disability rating index (DRI; primary outcome), EQ-5D, Achilles Total Rupture Score and complications were assessed ed at two weeks, six weeks, three months, six months and nine months after initial injury. Results: At nine months, there was no significant difference in DRI between patients randomised to operative or non-operative management. There was no difference in DRI between the randomised group and the parallel patient preference group. The use of a comprehensive cohort of patients did not provide useful additional information as to the treatment effect size because the majority of patients chose non-operative management. Conclusions: Recruitment to clinical trials that compare operative and non-operative interventions is notoriously difficult; especially within the trauma setting. Including a parallel patient preference group to create a comprehensive cohort of patients has been suggested as a way of increasing the power of such trials. In our study, the comprehensive cohort model doubled the number of patients involved in the study. However, a strong preference for non-operative treatment meant that the increased number of patients did not significantly increase the ability of the trial to detect a difference between the two interventions

Silicon, endophytes and secondary metabolites as grass defenses against mammalian herbivores

Article Accepted Date: 30 August 2014 Acknowledgments This study was supported by the Academy of Finland (grant no. 133495 to Otso Huitu; grants no. 137909 and 110658 to Kari Saikkonen) and by the NERC (grant no. NE/F003994/1 to Xavier Lambin). We thank Dr. Stefan Reidinger and Dr. James Stockdale for help with the silicon analyses. Technician Sinikka Sorsa conducted the phenolic extractions. Stephen Ryan and Anaïs Zimmer assisted with field work.Peer reviewedPublisher PD