Inversion Radius Research Articles

Tomographic reconstructions of the fast-ion phase space using imaging neutral particle analyser measurements

In this paper we demonstrate how the inversion, in energy and major radius (E, R) coordinates, of imaging neutral particle analyser (INPA) measurements can be used to obtain the fast-ion distribution. The INPA is most sensitive to passing ions with energies in the range (20–150) keV and pitches near 0.5 in the core and 0.7 near the plasma edge. Inversion of synthetic signals, via 0th-order Tikhonov and Elastic Net regularization, were performed to demonstrate the capability of recovering the ground truth fast-ion 2D phase-space distribution resolved in major radius and energy, even in the presence of moderate noise levels (10%). Finally, we apply our method to measure the 2D phase-space distribution in an MHD quiescent plasma at ASDEX Upgrade and find good agreement with the slowing down fast-ion distribution predicted by TRANSP.

Core electron temperature turbulence and transport during sawtooth oscillations in the DIII-D tokamak

Sawteeth are one of the concerning instabilities in ITER and future burning plasma experiments. Sawtooth dynamics and its interaction with broadband plasma turbulence has been a challenge for predictive simulations of core transport in future fusion devices. This study provides new observations of core turbulence behavior during sawtooth oscillations in DIII-D hydrogen L-mode neutral beam injection heated plasmas in an inner wall limited configuration. A strong correlation of electron temperature and density turbulence levels with the sawtooth oscillation phase has been observed at locations inside the T e inversion radius and/or safety factor q = 1 magnetic surface. The T e turbulence amplitude in the core during the sawtooth ramp exhibits a critical T e gradient behavior inside but not near the T e inversion radius/q = 1 magnetic surface. The most unstable mode calculated from the trapped gyro-landau fluid turbulence simulations reveal a change from low-k ion-type to low-k electron-type modes from pre- to post- sawtooth crash time periods.

Formation of small-scale modes via ECCD injection into KSTAR plasma core

In KSTAR experiments exhibiting sawtooth instability, the formation of multiple flux tubes (MFTs) has been frequently observed when electron cyclotron resonance heating or a current drive is applied near the inversion radius of the sawtooth. On the global scale, these MFTs evolve into a single flux tube mode or dual modes. The modes are observed as multiple Fourier harmonics in the spectrogram. A comprehensive correlation analysis of 2D imaging diagnostic data reveals a notable energy transfer within structures of varying sizes during the global mode transition. Broadband fluctuations are enhanced, and energy transfer between Fourier harmonics occurs in the presence of MFTs. Cross-power spectrum in the presence of multiple Fourier harmonics aligns with power law of inverse cascade. This suggests that energy inverse cascade process can contribute to formation of MFTs.

Tangential extreme ultraviolet and soft x-ray diagnostic system for time-resolved temperature measurement on the High Beta Tokamak-Extended Pulse.

The High Beta Tokamak-Extended Pulse has recently incorporated a tangential multi-energy extreme ultraviolet and soft x-ray diagnostic system. This system enables measurements of the electron temperature and the examination of mode dynamics within the tokamak. While other systems have been built for poloidal views over similar temperature ranges, this is the first multi-energy tangential-view system designed to work in a temperature range below 200eV in a tokamak. To facilitate these measurements, a filter wheel comprising five distinct groups of dual-filters has been developed and implemented. By employing a combination of 0.1μm aluminum and 0.2μm titanium filters, the system allows estimation of electron temperature profiles through reconstruction of the emission profile using the standard "double-foil" technique. The influence of impurities and filter oxide layers on measurement outcomes is examined. Results reveal that, while the absolute electron temperature values may exhibit some deviations, key characteristics like the electron temperature profile shape and inversion radius during sawtooth events remain consistent. This consistency confirms the system's suitability for core plasma studies. This system has proven effective in detecting and analyzing internal magnetohydrodynamic phenomena, such as sawteeth.

Nonlinear magnetohydrodynamic modeling of current-drive-induced sawtooth-like crashes in the W7-X stellarator

Sawtooth-like core electron temperature crashes have been observed in W7-X experiments with electron cyclotron current drive. We present nonlinear single-fluid magnetohydrodynamic simulations of this phenomenon using the newly developed stellarator modeling capability of the M3D-C1 code. The near-axis current drive gives rise to two ι = 1 resonances in the equilibrium rotational transform profile so that two consecutive (1, 1) internal kink modes are seen in the simulations. A small-amplitude crash at the inner resonance occurs first, which may correspond to the sawtooth precursors observed in the experiments. A bigger crash at the outer resonance then flattens the core temperature profile, which shows semi-quantitative agreements with experimental measurements on certain metrics such as the crash amplitude and the inversion radius of the temperature change. These results illustrate a likely mechanism of the current-drive-induced sawtooth-like crashes in W7-X and, to some extent, validate the stellarator modeling capability of M3D-C1.

Role of magnetohydrodynamic activity in sawtooth induced heat pulse propagation in ADITYA tokamak

Fast propagation of sawtooth induced heat pulse is observed in the magnetohydrodynamic (MHD) active plasmas of ADITYA tokamak. The sawtooth crash deposits heat beyond the inversion radius, which gets transported to the edge region of the plasma, and is reflected as inverted sawtooth modulation in the edge channels of electron cyclotron emission (ECE) and spectral line emission. The time-lag analysis on ECE signal reveals the propagation time from plasma core to edge of ∼150 µs. From this analysis, the estimated transient electron heat diffusivity is found to be ∼50–60 m2 s−1, which is ten times higher than that of power balance heat diffusivity , in the MHD active discharges of ADITYA. It has been observed that the presence of MHD (m/n = 2/1, 3/1) activity in the intermediate region between the q = 1 and the edge radii, significantly influences the heat transport from the plasma core to the edge region. Stochastic magnetic field region formation with overlapping m/n = 2/1 and 3/1 MHD islands facilitates the fast heat-pulse propagation during a sawtooth crash in ADITYA tokamak. The disparity between the measured and the power-balance estimated diffusivity is significantly reduced by considering the electron heat diffusivity due to stochastization of magnetic field in the intermediate region.

Observation of the poloidally asymmetrical density perturbation of sawtooth collapse on J-TEXT

The detailed density perturbations provided by the advanced polarimeter–interferometer system (Polaris) during sawtooth collapse on the Joint Texas Experimental Tokamak (J-TEXT) are reported in this article. During a sawtooth collapse and the crash of plasma pressure at the center, it is found that the increase in density in the region between the inversion radius and mixing radius is poloidally asymmetrical, while the increase in temperature is poloidally symmetrical. The poloidal location where the density increases is dependent on the phase of the precursory m/n = 1/1 kink mode. It is always out of phase with the hot core of the m/n = 1/1 mode. The behaviors of density perturbations during sawtooth collapse observed in J-TEXT are beyond the expectations of the standard model, and this can shed new light on the understanding of sawtooth collapse.

Experimental investigation of a partial collapse during the sawtooth instability in EAST

ABSTRACT In this article, partial and full collapses of sawtooth activity are investigated with the high-resolution two-dimensional electron cyclotron emission (ECE) Imaging diagnostic in EAST. The partial collapse in normal sawtooth behavior is detected during the precursor phase of an L-mode plasma heated by ICRF. The electron heat diffusivity is determined with the time-to-peak analysis. The experimental results revealed that heat diffusivity suppresses at the time of the partial collapse. As a result, the partial collapse process interrupts and the small amount of heat releases outward. The hot core survives and is enclosed by the cold magnetic island. The inversion radii are estimated with the help of sawtooth and the only single inversion radius is found during the entire collapse process.

Improved algorithm of aerosol particle size distribution based on remote sensing data.

The optical parameters (extinction or backscatter coefficients) of multi-wavelength beams can be used for the retrieval of the aerosol particle size distribution (APSD). An improved algorithm for APSD and aerosol microphysical parameters (AMPs) is studied and discussed by using only multi-wavelength extinction coefficients data. The regularized algorithm and prior value are combined for the retrieval of APSD and AMPs. The regularization algorithm, based on minimum discrepancy principle and averaging procedure, is used for the retrieval of fine-mode APSD and an averaging procedure that can achieve stable outputs is proposed. The 1% averaging result near the minimum of the discrepancy is selected and verified. Based on the inversion results of fine mode from the regularization algorithm, the lognormal distribution with a prior value (model radius) is applied to reconstruct the coarse mode of APSDs through fitting the data. The comprehensive application of the regularization algorithm and averaging process improves the stability of the inversion in the fine mode, and the use of the prior value broadens the inversion radius range of APSD. The complex refractive index need not be assumed for this method. The inversion error for different types of aerosols is analyzed and studied. The reliability of the algorithm is tested and verified by many typical APSDs and the measured APSDs by particle size spectrometer in different pollution days. The algorithm sensitivity analysis is also provided and discussed. The algorithm can obtain reliable inversion of APSD and AMPs with large radius range.

Shock wave Boundary Layer Interaction (SWBLI) in hypersonic flow over a Blunt body double wedge configuration

Present investigations are focused on the study of effects of dimensional and parametric changes in shock wave boundary layer interaction (SWBLI) for an axisymmetric double wedge with leading edge bluntness in hypersonic flows. This study is specifically the point of interest since it attributes most of the characteristics of the hypersonic flow around the atmosphere re-entry vehicles. Successfully implemented simulations in hypersonic flow are in a double wedge configuration, to study shock wave boundary layer interaction in hypersonic flows. Inversion radius was found at different deflection angles for change in leading edge radius (LER). It was found that for lower deflection angle Crocco’s theorem affect the flow early compared to higher deflection angles. Shock-shock Interaction-I (SSI I) and Shock-shock Interaction-II (SSI II) shifts downstream with increase in leading edge radius. (Key Words: Hypersonic flows, Shock wave boundary layer interaction, Shock–shock interaction and Leading edge radius)

Current Profile Reconstruction Using Motional Stark Effect Polarimeter Data on HL-2A Tokamak

In order to reconstruct the plasma current density, the Current Profile Fitting (CPF) code has been successfully developed on the HL-2A tokamak. A seven-channel motional Stark effect (MSE) diagnostic based on dual photoelastic modulators is installed to measure the pitch angle of the magnetic field, which can be used as an internal magnetic field constraint for the CPF code. Recently, the MSE polarimeter was upgraded with a real-time wavelength matching system to improve the signal-to-noise ratio. The magnetic field angle (γpitch) with a temporal resolution of 10 ms can be provided. In the CPF code, the plasma current density is described as a polynomial, and the Least-Squares method is used to determine the coefficients of the polynomial. The Finite Difference method and the Strongly Implicit Procedure method are used to solve the Grad-Shafranov equation. The code operation is stable. With the improved-quality MSE data, the CPF calculation result of shot 30782 suggests that the safety factor q profile is monotonic. The minimum q value is less than 1 on-axis during sawtooth oscillations in shot 30782. And, the position of the q = 1 surface is consistent with the sawtooth inversion radius measured by electron cyclotron emission and soft X-ray diagnostics.

Sawtooth oscillation behavior with varying amounts of applied stellarator rotational transform

Tokamak-like sawtooth oscillations are observed in the Compact Toroidal Hybrid (CTH), a current-carrying stellarator. CTH has the unique ability to change the amount of the applied vacuum rotational transform from external stellarator coils relative to the rotational transform generated by the internal plasma current to investigate the effects of strong three-dimensional magnetic shaping on sawtooth behavior. The observed sawteeth in CTH, for plasmas with monotonically decreasing rotational transform profiles dominated by the plasma current, have characteristics of those observed on tokamaks including (1) a central emissivity rise and then a sudden crash with a well-defined inversion radius, (2) the presence of an m = 1 emissivity fluctuation, and (3) the normalized inversion surface radius scales with the total edge rotational transform. We explore the properties of an ensemble of discharges in CTH in which the fractional rotational transform, defined as the vacuum rotational transform divided by the total rotational transform, is systematically varied from 0.04 to 0.42 to observe changes in sawtooth oscillation dynamics. Over this range of the fractional rotational transform, the measured sawtooth period decreased by a factor of two. At a high fractional rotational transform, the sawtooth amplitude is observed to consist of only low-amplitude oscillations while the measured crash time of the sawtooth oscillation does not appear to have a strong dependence on the amount of the fractional transform applied. Experimental results indicate that the low-amplitude sawteeth are accompanied by a decrease in the sawtooth period and predominantly correlated with the mean elongation (due to the increasing fractional rotational transform) of the non-axisymmetric plasmas within CTH rather than other global equilibrium parameters.

Conformal transformations and curvature

In this paper, we discuss the relationship between conformal transformations of [Formula: see text] and the curvature of curves. First, for any non-circular closed curve, there exists a length-preserving inversion such that the maximum pointwise absolute curvature can be made arbitrarily large. In contrast, we show that the total absolute curvatures of a family of curves conformally equivalent to a given simple or simple closed curve are uniformly bounded. Furthermore, we show that the total absolute curvature of an inverted regular [Formula: see text] simple closed curve as a function of inversion center and radius is removably discontinuous along the curve with exactly a [Formula: see text] drop, and continuous elsewhere.

Process window of tube-end inversion: experimentation and numerical analysis

A systematic methodology for determining the formability limits of thin-walled tubes based on strain analysis has been recently presented by the authors with the aim of evaluating formability and failure within the principal strain space, analogously to the conventional procedures used in sheet metal. This methodology for establishing the formability limits in tube-end expansions combined numerical simulations and analytical approaches. Preliminary investigations have been conducted with the aim of applying the same principles to other tube forming processes. In this context, this paper focuses on the investigation of the formability limits of tube-end external inversion and combines the experimental determination of strain paths by means of digital image correlation (DIC) with finite element (FE) modelling. Results show that the process window is limited by local buckling and by fracture as a function of the inversion radius of the forming die.

Slow crash in modified sawtooth patterns driven by localized electron cyclotron heating and current drive in KSTAR

Fast sawtooth crash of m = 1 mode (tens of µs) is a common MHD phenomenon in the core of tokamak plasma. In KSTAR plasmas with localized heating and current drive close to the sawtooth inversion radius (ρinv), very slow sawtooth crashes are observed with time scales of a few ms. Scan of heating deposition along with power modulation revealed two different mechanisms of the slow crash with the help of detailed 2D imaging diagnostics. The slow crash appears with slow heat transport of the remained m = 1 mode after the partial crash of outer multiple m/n = 1 modes, or with the growth of an island formed on ρinv when the heating deposition locates just inside ρinv or just outside ρinv. In the heating power modulation experiment, the slow crash with the island was sustained for the redistribution time scale of the driven current by a very short blip of heating.

Non-linear MHD simulations of sawteeth and their control by current and power depositions

Sawteeth in tokamak plasmas correspond to periodic relaxations of the temperature and density in the central region of the plasma, caused by the internal kink mode. They play an important role in core confinement and impurity transport in the central region of a tokamak discharge, and they can trigger secondary instabilities. Being able to control their dynamics is therefore important. In this article, we explore by means of MHD simulations the control of sawteeth, relying on current or power deposition in the vicinity of the q = 1 surface. To do so, simulations with the full-MHD code xtor-2f (Lütjens and Luciani 2010 J. Comput. Phys. 229 8130–43), which features power and current source terms mimicking the effects of ECCD and ECRH, are performed. Simulations show that a deposition of current inside the inversion radius leads to an increase of the sawtooth frequency whereas a deposition near or outside the inversion radius leads to a decrease of the sawtooth frequency, in agreement with theoretical and experimental predictions. For power depositions, the situation appears however to be more complex. The modification of the sawtooth shape in presence of additional heating or current drive is also investigated. The existence of a critical shear setting the condition of the sawtooth crash is found to apply, although the inter-crash dynamics is often too complex and MHD-dependent to be summarized as a periodic instantaneous redistribution of current and energy, as assumed in the analytical models. Finally, we briefly explore possible scenarios for the triggering of magnetic islands, and show how controlling the sawteeth can help to prevent the triggering of tearing instabilities.

Effect of sawtooth crashes on fast ion distribution in NSTX-U

During the 2016 experimental campaign of NSTX-U (Menard et al 2012 Nucl. Fusion 52 083015), long L-mode and reproducible sawtoothing plasmas have been achieved that were previously not accessible before the upgrade. This provides a good opportunity to study the effect of sawtooth crashes on fast ion confinement and redistribution in spherical tokamaks. The solid-state neutral particle analyzer (SSNPA) and fast ion D-alpha (FIDA) diagnostics on NSTX-U each have a tangentially-viewing instrument and a radially- or vertically-viewing instrument, which are mainly sensitive to passing and trapped fast ions, respectively. It has been observed on both diagnostics that passing particles are strongly expelled from the plasma core to the edge during sawtooth crashes, while trapped fast ions are weakly affected. The tangentially-viewing SSNPA observes large signal spikes at the sawtooth crashes because fast ions move to the edge and charge exchange with edge neutrals. The radially-viewing SSNPA data suggest that there is a small drop of trapped particles in the core. The tangentially-viewing FIDA (t-FIDA) system observes a depletion as large as 25% in the region inside the inversion radius, while an increase at the outer region. There is almost no change in the signals of the vertically-viewing FIDA system. The neutron emission can drop as much as 15% at the sawtooth crashes, accompanied by an increase of edge light. Simulations with the Kadomstev and Porcelli sawtooth models have been performed and compared with the measurements. The full reconnection Kadomtsev model overestimates the neutron rate drop at each sawtooth crash. When tuning the sawtooth input parameters, the partial reconnection Porcelli sawtooth model can qualitatively reproduce the neutron rate drop and t-FIDA signal drop in the core, but it fails to predict the t-FIDA signal increase at the edge.

Study of impurity transport in HL-2A ECRH L-mode plasmas with radially different ECRH power depositions

In HL-2A, an inverse sawtooth oscillation is observed with a long-lasting m/n = 1/1 mode during ECRH phase with power deposition inside sawtooth inversion radius (inner-deposited ECRH), while a normal sawtooth instead appears when the ECRH power is deposited outside sawtooth inversion radius (outer-deposited ECRH). Aluminum is then injected as a trace impurity with laser blow-off (LBO) method into the inner- and outer-deposited ECRH phases of HL-2A discharges to investigate the effect of ECRH on impurity transport. Temporal behavior of soft x-ray (SXR) array signals is analyzed with a 1D impurity transport code, and radial structures of impurity transport coefficients are obtained. The result shows that the radial transport of Al ions is strongly enhanced during the inner-deposited ECRH phase. In particular, an outward convection velocity is developed with positive values of 0 ⩽ V(ρ) ⩽ 3.8 m s−1 in ρ ⩽ 0.5, while the convection velocity is inward in ρ ⩾ 0.6. In the outer-deposited ECRH discharge, on the other hand, the convection velocity takes a big negative value in ρ ⩽ 0.4 and close to zero at ρ ~ 0.6. In ohmic discharges, an inward V(ρ) always appears in the whole plasma radii and gradually increases toward the plasma edge (−3.2 m s−1 at ρ = 1). The simulation result also indicates that centrally-peaked Al ion density profiles presented in the outer-deposited ECRH discharge can be flattened by the inner-deposited ECRH. Modification of impurity transport is discussed in the presence of long-lasting m/n = 1/1 MHD mode.

Dynamics between the fishbone instability and nonlocal transient transport in HL-2A NBI plasmas

Understanding of nonlocal electron heat transport is of key importance for current magnetic confinement fusion research. Global nonlocal response presents a fundamental challenge to the standard anomalous transport model based on local microinstabilities and turbulence. Here, we present for the first time a new nonlocal phenomenon triggered by the fishbone instability in HL-2A neutral beam injection plasmas. Rapid core heating leads to a simultaneous decrease in temperature at the plasma edge. The effect reveals fast anomalous transport of core heat pulses to the plasma edge, not compatible with diffusive time scales. More importantly, variations at different locations are restricted by the intensity of magnetic fluctuations. The and form two types of hysteresis loops at two sides of the inversion radius. The ECEIs show that the 2D mode structure of the fishbone is intensive shearing/spiraling during the nonlocal transport. Experimental results suggest that magnetic perturbation, long-range correlation, mesoscale structure and flow play crucial roles in the nonlocal response. The Hurst exponent and auto-correlation coefficient indicate that the nonlocal transport is potentially linked to the self-organized critical (SOC) dynamics. This work will be beneficial for understanding of the plasma dynamics in future fusion reactors.

Theoretical model of a metal tube under inversion over circular dies

The inversion of a metal tube over a circular die is an important energy absorption device. Taking into consideration the curvature change during inversion process, this study proposes a two-dimensional theoretical model. Using rigid-perfectly plastic (R-PP) material idealization, its steady inversion load, curling radius after the tube׳s separation from the die, and the optimization of the die radius are analytically obtained based on energy conservation.Compared with the FE simulations, the current model greatly improves the prediction accuracy of the steady inversion force, with the deviation smaller than 10%. The prediction of the tube radius after inversion agrees well with the FE simulation and experimental data. Out of our expectation, the optimized die radius is found to be different from that of free inversion radius of the same tube. In this study, a simple formula of the optimized die radius is given.