Filamentary plasma eruptions in tokamaks

The nonlinear MHD ballooning model is exploited for two distinct studies: firstly, the interaction of multiple filamentary eruptions in magnetised plasmas in a slab geometry is investigated and secondly, this model is examined quantitatively against experimental observations of ELMs in MAST and JET-like geometries. The model consists of two differential equations which characterise the spatial and temporal evolution of the displacement: the first differential equation describes the displacement along the field line, the second differential equation is a two-dimensional nonlinear ballooning-like equation which is often second order in time, but can involve a fractional derivative in a tokamak geometry. Filaments always evolve independently in the linear regime and equally sized filaments evolve independently in the nonlinear regime. However, we find that filaments with varying heights interact with each other in the nonlinear regime: Smaller filaments are slowed down and eventually are completely suppressed by the larger filaments which grow faster due to the interaction. This mechanism is explained by the down-draft caused by the nonlinear drive of the larger filaments which pushes the smaller filaments downwards. To employ the second differential equation for a specific geometry one has to evaluate the coefficients of the equation which is non-trivial in a tokamak geometry as it involves field line averaging of slowly converging functions. The coefficients of a Type I ELMy equilibrium from MAST and a Type II ELMy JET-like equilibrium have been determined. In both cases the two coefficients of the nonlinear terms are negative which would imply imploding rather than exploding filaments. By changing the equilibrium the signs of these coefficients can be inverted. This suggests that either the nonlinear Ballooning model does not capture the behaviour of Type I and Type II ELMs, or that the calculation of the coefficients are too sensitive to a given equilibrium

How well can VMEC predict the initial saturation of external kink modes in near circular tokamaks and l=2l=2 stellarators?

The equilibrium code, VMEC, is used to study external kinks in low $\beta$ tokamaks and $l=2$ stellarators. The applicability of the code when modelling nonlinear MHD effects is explored in an attempt to understand and predict how the initial saturation of the MHD mode depends on the external rotational transform. It is shown that helicity preserving, free boundary VMEC computations do not converge to a single perturbed solution with increasing spectral resolution. Additional constraints are therefore applied to narrow down the numerical resolution parameters appropriate for physical scans. The dependence of the modelled (4, 1) kink mode on the external rotational transform and field periodicity is then studied. While saturated states can be identified which decrease in amplitude with increasing external rotational transform, bifurcated states are found that contradict this trend. It was therefore not possible to use VMEC alone to identify the physical dependency of the nonlinear mode amplitude on the magnetic geometry. The accuracy of the VMEC solutions is nevertheless demonstrated by showing that the expected toroidal mode coupling is captured in the magnetic energy spectrum for stellarator cases. Comparing with the initial value code, JOREK, the predicted redistribution of poloidal magnetic energy from the vacuum to plasma region in VMEC is shown to be physical. This work is a first step towards using VMEC to study MHD modes in stellarator geometry.Comment: Submitted to Physics of Plasmas. The submission has been modified according to reviewer comment

Constructing precisely quasi-isodynamic magnetic fields

We present a novel method for numerically finding quasi-isodynamic stellarator magnetic fields with excellent fast-particle confinement and extremely small neoclassical transport. The method works particularly well in configurations with only one field period. We examine the properties of these newfound quasi-isodynamic configurations, including their bootstrap currents, particle confinement, and available energy for trapped-electron driven turbulence, as well as the degree to which they change when a finite pressure profile is added. We finally discuss the differences between the magnetic axes of the optimized solutions and their respective initial conditions, and conclude with the prospects for future quasi-isodynamic optimization.Comment: 25 pages, 10 figure

Associations Between Aldosterone-Renin-Ratio and Bone Parameters Derived from Peripheral Quantitative Computed Tomography and Impact Microindentation in Men

Components of the renin–angiotensin–aldosterone system (RAAS) are present on bone cells. One measure of RAAS activity, the aldosterone-renin-ratio (ARR), is used to screen for primary aldosteronism. Associations between ARR and bone mineral density are conflicting. This study investigated associations between ARR and peripheral quantitative computed tomography (pQCT) and impact microindentation (IMI). Male participants (n = 431) were from the Geelong Osteoporosis Study. “Likely” primary aldosteronism was defined as ARR ≥ 70 pmol/mIU. Another group, “possible” primary aldosteronism, was defined as either ARR ≥ 70 pmol/mIU or taking a medication that affects the RAAS, but not a beta blocker, and renin  0.05). There were no associations between ARR or aldosterone and pQCT-derived bone parameters. Men with likely primary aldosteronism had lower bone area, suggesting clinically high levels of ARR may have a negative impact on bone health

Confirmation of the topology of the Wendelstein 7-X magnetic field to better than 1:100,000

Fusion energy research has in the past 40 years focused primarily on the tokamak concept, but recent advances in plasma theory and computational power have led to renewed interest in stellarators. The largest and most sophisticated stellarator in the world, Wendelstein 7-X (W7-X), has just started operation, with the aim to show that the earlier weaknesses of this concept have been addressed successfully, and that the intrinsic advantages of the concept persist, also at plasma parameters approaching those of a future fusion power plant. Here we show the first physics results, obtained before plasma operation: that the carefully tailored topology of nested magnetic surfaces needed for good confinement is realized, and that the measured deviations are smaller than one part in 100,000. This is a significant step forward in stellarator research, since it shows that the complicated and delicate magnetic topology can be created and verified with the required accuracy

Major results from the first plasma campaign of the Wendelstein 7-X stellarator

\u3cp\u3eAfter completing the main construction phase of Wendelstein 7-X (W7-X) and successfully commissioning the device, first plasma operation started at the end of 2015. Integral commissioning of plasma start-up and operation using electron cyclotron resonance heating (ECRH) and an extensive set of plasma diagnostics have been completed, allowing initial physics studies during the first operational campaign. Both in helium and hydrogen, plasma breakdown was easily achieved. Gaining experience with plasma vessel conditioning, discharge lengths could be extended gradually. Eventually, discharges lasted up to 6 s, reaching an injected energy of 4 MJ, which is twice the limit originally agreed for the limiter configuration employed during the first operational campaign. At power levels of 4 MW central electron densities reached 3 10\u3csup\u3e19\u3c/sup\u3e m\u3csup\u3e-3\u3c/sup\u3e, central electron temperatures reached values of 7 keV and ion temperatures reached just above 2 keV. Important physics studies during this first operational phase include a first assessment of power balance and energy confinement, ECRH power deposition experiments, 2nd harmonic O-mode ECRH using multi-pass absorption, and current drive experiments using electron cyclotron current drive. As in many plasma discharges the electron temperature exceeds the ion temperature significantly, these plasmas are governed by core electron root confinement showing a strong positive electric field in the plasma centre.\u3c/p\u3

Major results from the first plasma campaign of the Wendelstein 7-X stellarator

After completing the main construction phase of Wendelstein 7-X (W7-X) and successfully commissioning the device, first plasma operation started at the end of 2015. Integral commissioning of plasma start-up and operation using electron cyclotron resonance heating (ECRH) and an extensive set of plasma diagnostics have been completed, allowing initial physics studies during the first operational campaign. Both in helium and hydrogen, plasma breakdown was easily achieved. Gaining experience with plasma vessel conditioning, discharge lengths could be extended gradually. Eventually, discharges lasted up to 6 s, reaching an injected energy of 4 MJ, which is twice the limit originally agreed for the limiter configuration employed during the first operational campaign. At power levels of 4 MW central electron densities reached 3 1019 m-3, central electron temperatures reached values of 7 keV and ion temperatures reached just above 2 keV. Important physics studies during this first operational phase include a first assessment of power balance and energy confinement, ECRH power deposition experiments, 2nd harmonic O-mode ECRH using multi-pass absorption, and current drive experiments using electron cyclotron current drive. As in many plasma discharges the electron temperature exceeds the ion temperature significantly, these plasmas are governed by core electron root confinement showing a strong positive electric field in the plasma centre.Peer reviewe