Audoly-Pomeau Linear Law of the Gol'denveizer Torus

The Gol'denveizer problem of a torus was studied analytically by Audoly and Pomeau (2002), and the accuracy of the Audoly and Pomeau linear law was confirmed numerically by Sun (2021). However, the law does not include the major radius R of the torus. To find the influence of the major radius, we used finite element numerical simulation to simulate different cases, and we propose a modified Audoly and Pomeau linear law for vertical deformation, which includes R. A linear law of horizontal deformation is presented as well. Our studies show that the Audoly and Pomeau linear law has high accuracy. With modified vertical and horizontal deformation, a displacement-compatible relation between them is formulated.

Plasma diagnostic systems and methods used on the stellarator TJ-II

The TJ-II is a heliac-type stellarator device with major radius of 1.5 m and averaged minor radius ⩽0.22 m that has been operated at CIEMAT, Madrid since 1998. Its full magnetic field is created by a system of poloidal, central, toroidal and vertical field coils, thus it possesses a fully 3-dimensional plasma structure and a bean-shaped plasma cross-section. Although this results in a complicated vacuum-vessel layout, it has excellent port access for diagnostics (96 portholes). During its initial operational phase, it was equipped with a limited set of essential diagnostics. Since then, a broad variety and large number of both passive and active diagnostics have been installed. The former include Hα monitors, light spectrometers, an electron cyclotron emission radiometer, X-ray filter monitors, neutral particle analysers, magnetic diagnostics, as well as cameras, among others, while the latter include various laser, atomic and ion beam based diagnostics, microwave probe beams, Langmuir probes plus impurity injection techniques. In this paper, after describing the TJ-II stellarator, its heating and fuelling systems, the diagnostic systems employed are outlined and discussed briefly here. Finally, results obtained with selected systems are highlighted.

Prediction of divertor heat flux width for ITER Pre-Fusion Power Operation using BOUT++ transport code

Prediction of divertor heat flux width is performed for the first and the second Pre-Fusion Power Operation (PFPO) phases specified in the new ITER Research Plan using BOUT++ transport code [Li N.M. et al 2018 Comput. Phys. Commun. 228 69–82]. The initial plasma profiles inside the separatrix are taken from CORSICA scenario studies. Transport coefficients in transport code are calculated by inverting the plasma profiles inside the separatrix and are assumed to be constants in the scrape-off-layer (SOL). An anomalous thermal diffusivity scan is performed with E×B and magnetic drifts. The results in two scenarios identify two distinct regimes: a drift dominant regime when diffusivity is smaller than the respective critical diffusivity χc and a turbulence dominant regime when diffusivity is larger than it. The Goldston heuristic drift model and the ITPA multi-machine experimental scaling yield a lower limit of the width λq. From transport simulations, we obtain the critical diffusivity χc = 0.5 m2⁄ s in 5MA/1.77T PFPO-1 scenario and χc = 0.3 m2⁄ s in 7.5MA/2.65T PFPO-2 scenario. Separatrix temperature and collisionality also have a significant impact on the heat flux width in the drift dominant regime. The investigation clearly yields a scaling for critical thermal diffusivity χc ∝ A½ ⁄ ((Z(1+Z)½ Bp 2)) using ITER scenarios with fixed safety factor q95, major radius R, aspect ratio R/a, and the separatrix temperature T, as well as established the connection with CFETR and C-Mod discharges. This scaling implies that for a given tokamak device with q95, R, R/a, and T fixed, a reduction of poloidal magnetic field by a factor of 3 leads to a 9 times higher critical value of thermal diffusivity χc, possibly yielding a transition from turbulence to drift dominant regime.

Avalanche transport of energetic-ions in magnetic confinement plasmas: Nonlinear multiple wave-number simulation

Large burst activity, identified as toroidal Alfv\'{e}n eigenmode (TAE) avalanche, occurs frequently in neutral-beam heated plasmas in National Spherical Torus Experiment (NSTX). Based on the typical experimental observation of TAE avalanche on NSTX, a self-consistent nonlinear multiple wave-number ($k_{\parallel}\simeq n/R$, where $n$ toroidal mode-number and $R$ major radius) simulation associated with TAE avalanches is performed using the experimental parameters and profiles before the occurrence of TAE avalanche as the M3D-K input. The wave-wave nonlinear coupling among different modes and the resonant interaction between different modes and energetic-ions during TAE avalanches are identified in the nonlinear multiple wave-number simulations. The resonance overlap during the TAE avalanche is clearly observed in the simulation. It is found that the effective wave-wave coupling and a sufficiently strong drive are two important ingredients for the onset of TAE avalanches. TAE avalanche is considered to be a strongly nonlinear process and it is always accompanied by the simultaneous rapid frequency-chirping and large amplitude bursting of multiple modes and significant energetic-ion losses. The experimental phenomenon is observed on NSTX and is qualitatively reproduced by the simulation results in this work. These findings indicate that the onset of avalanche is triggered by nonlinearity of the system, and are also conducive to understanding the underlying mechanism of avalanche transport of energetic particles in the future burning plasmas, such as ITER.

Cost Assessment of a Tokamak Fusion Reactor with an Inventive Method for Optimum Build Determination

An inventive method was applied to determine the minimum major radius, R0, and the optimum build of a tokamak fusion reactor that simultaneously meets all physics, engineering, and neutronics constraints. With a simple cost model, tokamak systems analyses were carried out over ranges of system parameters to find an optimum build of a tokamak fusion reactor at minimum cost. The impact of a wide range of physics parameters and advanced engineering elements on costs were also addressed. When a central solenoid was used to ramp up a plasma current, design solutions with a cost of electricity (COE) between 109 and 140 mills/kWh, direct capital cost between 5000 and 6000 M/USD, and net electric power, Pe between 1000 and 1600 MW could be found with a minimum R0 between 6.0 and 7.0 m, and fusion power, Pfusion between 2000 and 2800 MW. When the plasma current was driven by a non-inductive external system, the system size and costs could be reduced further; a COE between 98 and 130 mills/kWh, direct capital cost between 4000 and 5000 M$, and Pe between 1000 and 1420 MW could be found with a minimum R0 between 5.1 and 6.7 m, and Pfusion between 2000 and 2650 MW.

Kink Oscillations of Coronal Loops

Kink oscillations of coronal loops, i.e., standing kink waves, is one of the most studied dynamic phenomena in the solar corona. The oscillations are excited by impulsive energy releases, such as low coronal eruptions. Typical periods of the oscillations are from a few to several minutes, and are found to increase linearly with the increase in the major radius of the oscillating loops. It clearly demonstrates that kink oscillations are natural modes of the loops, and can be described as standing fast magnetoacoustic waves with the wavelength determined by the length of the loop. Kink oscillations are observed in two different regimes. In the rapidly decaying regime, the apparent displacement amplitude reaches several minor radii of the loop. The damping time which is about several oscillation periods decreases with the increase in the oscillation amplitude, suggesting a nonlinear nature of the damping. In the decayless regime, the amplitudes are smaller than a minor radius, and the driver is still debated. The review summarises major findings obtained during the last decade, and covers both observational and theoretical results. Observational results include creation and analysis of comprehensive catalogues of the oscillation events, and detection of kink oscillations with imaging and spectral instruments in the EUV and microwave bands. Theoretical results include various approaches to modelling in terms of the magnetohydrodynamic wave theory. Properties of kink oscillations are found to depend on parameters of the oscillating loop, such as the magnetic twist, stratification, steady flows, temperature variations and so on, which make kink oscillations a natural probe of these parameters by the method of magnetohydrodynamic seismology.

Numerical Study on Dimensions and Orientation Effect of Semi-Elliptical Cracks in PE100 Pipelines

The through-thickness crack or surface crack in PE100 pipes subjected to internal pressure represents a serious risk to the structural integrity of HDPE pipes, which has attracted wide attention in modern industry. Although experimental research offers reliable predictions of surface crack influence on pipes, the relatively high cost hinders its application. The numerical simulation, as a cost-effective alternative, has been widely applied to assess stress displacement and strain to the entire pipe structure. This is the initial approach adopted in recent decades. This article provides simulations tests of an uncracked pipe and cracked PE100 pipe under different internal pressure values, with varying each time the dimensions of the crack with 1 mm rate for minor and major radius and 0.5mm rates for the largest contour radius, using ANSYS MECHANICAL STRUCTURAL STATIC for simulation.

Magnetic well and Mercier stability of stellarators near the magnetic axis

We have recently demonstrated that by expanding in small distance from the magnetic axis compared with the major radius, stellarator shapes with low neoclassical transport can be generated efficiently. To extend the utility of this new design approach, here we evaluate measures of magnetohydrodynamic interchange stability within the same expansion. In particular, we evaluate the magnetic well, Mercier's criterion, and resistive interchange stability near a magnetic axis of arbitrary shape. In contrast to previous work on interchange stability near the magnetic axis, which used an expansion of the flux coordinates, here we use the ‘inverse expansion’ in which the flux coordinates are the independent variables. Reduced expressions are presented for the magnetic well and stability criterion in the case of quasisymmetry. The analytic results are shown to agree with calculations from the VMEC equilibrium code. Finally, we show that near the axis, Glasser, Greene and Johnson's stability criterion for resistive modes approximately coincides with Mercier's ideal condition.

Neutronic Study on Conceptual Lithium Fluoride Salt Cooled Fusion Driven System for Actinide Transmutation

The subcritical fission system could be used to transmute actinide elements from spent fuel into thermal power. Since the subcritical system needs an external neutron source, the D-T Fusion reactor was introduced as a fast neutron source to drive the chain reaction. Fusion driven system based on Spherical tokamak with a 1.7 m major radius has been designed. The breeding blanket has been modified to accommodate space for a 4.8 m length oxide fuel rod. Oxide fuel rods were immersed inside the lithium fluoride salt blanket, which acts as a coolant and liquid tritium breeder. The fully liquid blanket design was taken to reduce structure complexity and maximize tritium breeding volume. The neutronic study has been performed to calculate the neutron multiplication factor, actinide burnup in 400 days cycle and theoretical Tritium Breeding Ratio using MCNPX code. The design goal of fusion driven system with a fully liquid blanket is to reach keff value from 0.8 to 0.9 by burning sufficient actinide while breeding Tritium in Fluoride salt coolant. Various lithium fluoride coolant and reflector options have been simulated with the designed geometry. FLiNaBe salt liquid blanket was used as a reference since it could reach a keff value of 0.942 and able to transmute the actinide element in oxide fuel.

The exterior gravitational potential of toroids

ABSTRACT We perform a bivariate Taylor expansion of the axisymmetric Green function in order to determine the exterior potential of a static thin toroidal shell having a circular section, as given by the Laplace equation. This expansion, performed at the centre of the section, consists in an infinite series in the powers of the minor-to-major radius ratio e of the shell. It is appropriate for a solid, homogeneous torus, as well as for inhomogeneous bodies (the case of a core stratification is considered). We show that the leading term is identical to the potential of a loop having the same main radius and the same mass – this ‘similarity’ is shown to hold in the ${\cal O}(e^2)$ order. The series converges very well, especially close to the surface of the toroid where the average relative precision is ∼10−3 for e = 0.1 at order zero, and as low as a few 10−6 at second order. The Laplace equation is satisfied exactly in every order, so no extra density is induced by truncation. The gravitational acceleration, important in dynamical studies, is reproduced with the same accuracy. The technique also applies to the magnetic potential and field generated by azimuthal currents as met in terrestrial and astrophysical plasmas.