Linear Collisionless Landau Damping in Hilbert Space

The equivalence between the Laplace transform [Landau L., J. Phys. USSR, 10 (1946), 25] and Hermite transform [Zocco and Schekochihin, Phys. Plasmas, 18, 102309 (2011)] solutions of the linear collisionless Landau damping problem is proven

Quasilinear particle transport from gyrokinetic instabilities in general magnetic geometry

The quasilinear particle flux arising from gyrokinetic instabilities is calculated in the electrostatic and collisionless approximation, keeping the geometry of the magnetic field arbitrary. In particular, the flux of electrons and heavy impurity ions is studied in the limit where the former move quickly, and the latter slowly, along the field compared with the mode frequency. Conclusions are drawn about how the particle fluxes of these species depend on the magnetic-field geometry, mode structure and frequency of the instability. Under some conditions, such as everywhere favourable or unfavourable magnetic curvature and modest temperature gradients, it is possible to make general statements about the fluxes independently of the details of the instability. In quasi-isodynamic stellarators with favourable bounce-averaged curvature for most particles, the particle flux is always outward if the temperature gradient is not too large, suggesting that it might be difficult to fuel such devices with gas puffing from the wall. In devices with predominantly unfavourable magnetic curvature, the particle flux can be inward, resulting in spontaneous density peaking in the centre of the plasma. In the limit of highly charged impurities, ordinary diffusion (proportional to the density gradient) dominates over other transport channels and the diffusion coefficient becomes independent of mass and charge. An estimate for the level of transport caused by magnetic-field fluctuations arising from ion-temperature-gradient instabilities is also given and is shown to be small compared with the electrostatic component

A three-dimensional reduced MHD model consistent with full MHD

Within the context of a viscoresistive magnetohydrodynamic (MHD) model with anisotropic heat transport and cross-field mass diffusion, we introduce novel three-term representations for the magnetic field (background vacuum field, field line bending and field compression) and velocity ($\vec E\times\vec B$ flow, field-aligned flow and fluid compression), which are amenable to three-dimensional treatment. Once the representations are inserted into the MHD equations, appropriate projection operators are applied to Faraday's law and the Navier-Stokes equation to obtain a system of scalar equations that is closed by the continuity and energy equations. If the background vacuum field is sufficiently strong and the $\beta$ is low, MHD waves are approximately separated by the three terms in the velocity representation, with each term containing a specific wave. Thus, by setting the appropriate term to zero, we eliminate fast magnetosonic waves, obtaining a reduced MHD model. We also show that the other two velocity terms do not compress the magnetic field, which allows us to set the field compression term to zero within the same reduced model. Dropping also the field-aligned flow, a further simplified model is obtained, leading to a fully consistent hierarchy of reduced and full MHD models for 3D plasma configurations. Finally, we discuss the conservation properties and derive the conditions under which the reduction approximation is valid. We also show that by using an ordering approach, reduced MHD equations similar to what we got from the ansatz approach can be obtained by means of a physics-based asymptotic expansion.Comment: 18 pages. This article was published in Physics of Plasma

Testing of the new JOREK stellarator-capable model in the tokamak limit

In preparation for extending the JOREK nonlinear MHD code to stellarators, a hierarchy of stellarator-capable reduced and full MHD models has been derived and tested. The derivation was presented at the EFTC 2019 conference. Continuing this line of work, we have implemented the reduced MHD model (arXiv:1907.12486) as well as an alternative model which was newly derived using a different set of projection operators for obtaining the scalar momentum equations from the full MHD vector momentum equation. With the new operators, the reduced model matches the standard JOREK reduced models for tokamaks in the tokamak limit and conserves energy exactly, while momentum conservation is less accurate than in the original model whenever field-aligned flow is present.Comment: 23 pages, 1 table, 7 figures. Submitted to Journal of Plasma Physic

Augmented Command and Control Table to Support Network-Centric Operations

The success in network-centric warfare requires information superiority to obtain dominant battlespace awareness. The time required to take a decision has been reduced by orders of magnitude, while the volume of accessible data has been increased exponentially. When this volume is displayed to an operator, the risk of reaching a state of information overload is real and great care shall be taken to make sure that what is provided is actually information and not noise. In this paper we propose a novel interaction environment that leverages the augmented reality technology to provide a digitally enhanced view of a real command and control table. The operator equipped with an optical see-through head-mounted display controls the virtual context, a synthetic view of the common operational picture, remaining connected to the real world. Technical details of the system are described together with the evaluation method. The results showed effectiveness of the proposed system in terms of understanding perception, depth impression, and level of immersion. A relevant reduction of the reaction time and of the number of errors made during the execution of complex tasks, have been obtained. Defence Science Journal, Vol. 65, No. 1, January 2015, pp.39-45, DOI:http://dx.doi.org/10.14429/dsj.65.671

ECCD-induced sawtooth crashes at W7-X

The optimised superconducting stellarator W7-X generates its rotational transform by means of external coils, therefore no toroidal current is necessary for plasma confinement. Electron cyclotron current drive experiments were conducted for strikeline control and safe divertor operation. During current drive experiments periodic and repetitive crashes of the central electron temperature, similar to sawtooth crashes in tokamaks, were detected. Measurements from soft x-ray tomography and electron cyclotron emission show that the crashes are preceded by weak oscillating precursors and a displacement of the plasma core, consistent with a (m, n) = (1, 1) mode. The displacement occurs within 100μs, followed by expulsion and redistribution of the core into the external part of the plasma. Two types of crashes, with different frequencies and amplitudes are detected in the experimental program. For these non-stationary parameters a strong dependence on the toroidal current is found. A 1-D heuristic model for current diffusion is proposed as a first step to explain the characteristic crash time. Initial results show that the modelled current diffusion timescale is consistent with the initial crash frequency and that the toroidal current rise shifts the position where the instability is triggered, resulting in larger crash amplitudes.EC/H2020/633053/EU/Implementation of activities described in the Roadmap to Fusion during Horizon 2020 through a Joint programme of the members of the EUROfusion consortium/Eurato

Confinement degradation and plasma loss induced by strong sawtooth crashes at W7-X

Sawtooth-like crashes were observed during electron cyclotron current drive experiments for strikeline controls at the optimised superconducting stellarator Wendelstein 7-X (W7-X). The majority of the crashes did not have a relevant impact on plasma performance. However, a limited number of events, characterised by a large plasma volume affected by the instability, have been related to a strong deterioration performance and even to the premature termination of the plasma. The hot plasma core expelled during these sawtooth crashes can reach the plasma edge, where plasma surface interaction can occur and impurities can be released. The x-ray tomography shows a strong radiation increase starting from the edge and moving towards the inner plasma regions. This results in the cooling down and shrinking of the plasma, which eventually leads to a poor coupling of the ECRH to the electrons, that can in turn result in a plasma loss. A relation between the size and amplitude of the sawtooth crashes and the impurity increase is reported.EC/H2020/633053/EU/Implementation of activities described in the Roadmap to Fusion during Horizon 2020 through a Joint programme of the members of the EUROfusion consortium/Eurato

Ion temperature clamping in Wendelstein 7-X electron cyclotron heated plasmas

The neoclassical transport optimization of the Wendelstein 7-X stellarator has not resulted in the predicted high energy confinement of gas fueled electron-cyclotron-resonance-heated (ECRH) plasmas as modelled in (Turkin et al 2011 Phys. Plasmas 18 022505) due to high levels of turbulent heat transport observed in the experiments. The electron-turbulent-heat transport appears non-stiff and is of the electron temperature gradient (ETG)/ion temperature gradient (ITG) type (Weir et al 2021 Nucl. Fusion 61 056001). As a result, the electron temperature Te can be varied freely from 1 keV–10 keV within the range of PECRH = 1–7 MW, with electron density ne values from 0.1–1.5 × 1020 m−3. By contrast, in combination with the broad electron-to-ion energy-exchange heating profile in ECRH plasmas, ion-turbulent-heat transport leads to clamping of the central ion temperature at Ti ∼ 1.5 keV ± 0.2 keV. In a dedicated ECRH power scan at a constant density of 〈ne〉 = 7 × 1019 m−3, an apparent \u27negative ion temperature profile stiffness\u27 was found in the central plasma for (r/a < 0.5), in which the normalized gradient ∇Ti/Ti decreases with increasing ion heat flux. The experiment was conducted in helium, which has a higher radiative density limit compared to hydrogen, allowing a broader power scan. This \u27negative stiffness\u27 is due to a strong exacerbation of turbulent transport with an increasing ratio of Te/Ti in this electron-heated plasma. This finding is consistent with electrostatic microinstabilities, such as ITG-driven turbulence. Theoretical calculations made by both linear and nonlinear gyro-kinetic simulations performed by the GENE code in the W7-X three-dimensional geometry show a strong enhancement of turbulence with an increasing ratio of Te/Ti. The exacerbation of turbulence with increasing Te/Ti is also found in tokamaks and inherently enhances ion heat transport in electron-heated plasmas. This finding strongly affects the prospects of future high-performance gas-fueled ECRH scenarios in W7-X and imposes a requirement for turbulence-suppression techniques