Magnetic Axis Position Research Articles

Confirmation of the Absence of Contact Between Edge Boundary Plasma and Inboard First Wall in LHD Discharges Based on Radial Profile Measurement of Hβ Line Emissions

In the Large Helical Device (LHD), a high-performance plasma has been obtained at the inwardly shifted magnetic axis position of Rax = 3.60 m in which a spatial distance between the first wall on the vacuum vessel and the outermost edge boundary of the stochastic magnetic field layer existing outside the last closed flux surface takes a minimum value of ~12 mm at the inboard side. In order to investigate contact between the edge plasma boundary and the inboard first wall, a radial profile of Hβ line emissions at 4861 Å has been measured using a Czerny-Turner visible spectrometer and a 40-channel optical fiber array. All Hβ profiles measured at different magnetic axis positions of Rax = 3.60, 3.75, and 3.90 m showed a centrally peaked profile except for a few fiber channels observing the outboard edge plasma. The Hβ emission near the inboard first wall was negligibly weak, in particular, in the case of Rax = 3.60 m, suggesting no significant contact between the edge boundary plasma and the vacuum vessel first wall. The radial Hβ profile was then analyzed in detail using the EMC3-EIRENE edge plasma simulation code. The simulation well reproduced the measured profiles, including the extremely weak Hβ emission around the inboard first wall in the Rax = 3.60 m configuration. The centrally peaked profiles are found to originate in the Hβ emissions around X-points, while hydrogen neutrals are dominantly localized near the divertor plates. These results confirm the formation of a complete open divertor configuration in the LHD discharge without significant contact with the first wall. The presence of a region with extremely short magnetic field connection lengths (Lc < 5 m) between the inboard first wall and the outermost edge boundary is a key point to eliminate the strong plasma-wall interaction because sustainment of a significant edge plasma is entirely difficult in such a low Lc region.

Particle control in long-pulse discharge using divertor pumping in LHD

Density control is crucial for maintaining stable confined plasma. Divertor pumping, where neutral particles are compressed and exhausted in the divertor region, was developed for this task for the Large Helical Device. In this study, neutral particle pressure, which is related to recycling, was systematically scanned in the magnetic configuration by changing the magnetic axis position. High neutral particle pressure and compression were obtained in the divertor for a high plasma electron density and the inner magnetic axis configuration. Density control using divertor pumping with gas puffing was applied to electron cyclotron heated plasma in the inner magnetic axis configuration, which provides high neutral particle compression and exhaust in the divertor. Stable plasma density and electron temperature were maintained with divertor pumping. A heat analysis shows that divertor pumping did not affect edge electron heat conductivity, but it led to low electron heat conductivity in the core caused by electron-internal-transport-barrier-like formation.

Plasma position measurement with collimated neutron flux monitor diagnostics on JET

In future burning plasma devices measuring the plasma position and its shape with great spatial and temporal resolution is a crucial task. Nowadays these information are obtained by means of magnetic coils installed inside the vacuum vessel that in the future devices (like ITER and DEMO), due to the harsh environment caused by the high plasma temperature, will experience degradation over the time. Furthermore, the long plasma discharges will result in large integration drift causing a lack of accuracy in the measured signal. In order to assist the magnetic diagnostics and at the same time provide a novel tool to benchmark them, here the measurement of the plasma magnetic axis position by means of a collimated neutron flux monitor is proposed. Three different methods are here described and applied on JET by means of the neutron camera: a weighted average, the asymmetry method and a neural network. The methods are calibrated on a large database of plasma discharges including NBI and ICRH heated ones, and then compared with the magnetic axis position reconstructed by EFIT. The neural network outperforms the two other methods. In particular, the asymmetry method results to be sensitive to MHD activity, NBI power variation and to neutron emissivity profiles presenting a strong asymmetry, such as in case of peripheral NBI deposition due to high density plasmas or ICRH resonance layer. A possible application to vertical displacement events and disruptions is discussed and envisaged for future applications on DEMO. Finally, the performances of the neural network and of the asymmetry methods are studied in the case of one or two missing channels in the neutron flux monitor, showing how in general the reconstruction of the radial magnetic axis in both methods is more sensitive to the lack of channels than the vertical one. The methods here proposed can be applied and benchmarked on DTT and ITER neutron cameras as part of a future real-time control system.

General, compact and easy‐to‐compute winding factor formulation

With the use of the discrete Fourier transform (DFT), the study provides a compact relation to calculate the winding factor of any winding distribution among regularly space-shifted slots. The new expression is general, meaningful and particularly easy-to-compute. The phase winding layout is represented with a distribution vector whose length equals the slot number: each component corresponds to a slot and indicates the proportion of conductor allocated to the considered phase (forward turns positively counted and backward turns negatively counted). From winding factor definition, mathematical developments allow to demonstrate that, in any case, the winding factors simply relate to the DFT of the distribution vector: each component of the DFT vector corresponds to a space harmonic order and equals the so-called complex winding factor. The module of the complex winding factor is the usual winding factor while the angle of the complex winding factor reveals the magnetic axis position for the considered space harmonic.

Model Predictive Control with Time Varying Parameters for Plasma Shape and Current in a Tokamak

Synthesis and modeling of the advanced time-varying magnetic control system for plasma shape and current on the base of the Model Predictive Control principle in a tokamak is considered. The study was done for the Globus-M2 tokamak (Ioffe Institute, St. Petersburg, RF). The system presented has a hierarchical structure with a time-varying Model Predictive Controller at the top level and robust time-invariant controllers at the low level. The approach of adaptation of the plasma magnetic axis position to the shape parameters is used to resolve the contradiction between plasma position and shape. Numerical modeling of the control system synthesized has shown the efficiency of the proposed approach and a possibility to apply it in physical experiments.

Energetic ion confinement studies using comprehensive neutron diagnostics in the Large Helical Device

Understanding energetic particle (EP) confinement is one of the critical issues in realizing fusion reactors. In stellarator/helical devices, the research on EP confinement is one of the key topics to obtain better confinement by utilizing the flexibility of a 3D magnetic field. A study of EP transport in the Large Helical Device (LHD) has been performed by means of escaping EP diagnostics in hydrogen plasma operation. By starting deuterium operation of the LHD, the confinement study of EPs has progressed remarkably using newly developed comprehensive neutron diagnostics providing information for EPs confined in the core region. The total neutron emission rate (Sn) increases due to the relatively low deviation of the beam ion orbit from the flux surface with the inward shift of the magnetic axis. The Sn has a peak around the electron density of 2 × 1019 m−3 to 3 × 1019 m−3, as predicted. It is found that the fraction of beam–beam components in Sn is evaluated to be approximately 20% by the Fokker–Planck models TASK/FP in the plasma with both co- and counter-neutral beam injections. The equivalent fusion gain in DT plasma achieved 0.11 in a negative-ion-based neutral beam heated plasma. Time evolution of Sn following the short pulse neutral beam injection into the electron–cyclotron-heated low-beta plasma is reproduced by drift kinetic simulation, indicating that transport of a beam ion injected by a short pulse neutral beam can be described with neoclassical models in magnetohydrodynamic quiescent low-beta plasmas. The vertical neutron camera works successfully, demonstrating that in the co-neutral beam-injected plasma, the neutron emission profile shifts according to the magnetic axis position. The shift of the neutron emission profile is reproduced by orbit-following models. The triton burnup study is performed for the first time in a stellarator/heliotron to understand the alpha particle confinement. It is found that the triton burnup ratio, which largely increases at inward-shifted configurations due to the better triton orbit and better plasma performance in the inward-shifted configuration, is similar to that measured in a tokamak having a similar minor radius to the LHD. We study the confinement capability of EPs toward a helical reactor in the magnetohydrodynamic quiescent region and expansion of the energetic ion physics study in toroidal fusion plasmas.

Plasma magnetic cascade multiloop control system design methodology in a tokamak

The paper treats the methodology of the design and analysis of a tokamak plasma magnetic cascade multiloop control system with the example of the Globus-M spherical tokamak (Ioffe Institute, S-Petersburg, Russia) including a set of new features. The methodology covers: plasma equilibrium reconstruction based on the experimental data, derivation of linear plasma models relative to the reconstructed plasma equilibrium taking into account plasma diagnostics methods and equipment, development of a new original model of a thyristor current inverter as an actuator included in the system feedback, original multivariable cascade multiloop structure analysis by Relative Gain Array/μ-procedures, and design of an H∞, multivariable plasma shape control system with adaptation of the magnetic axis position.

Study of first orbit losses of 1 MeV tritons using the Lorentz orbit code in the LHD

Shot-integrated measurement of the triton burnup ratio has been performed in the Large Helical Device. It was reported that the triton burnup ratio, defined as total DT neutron yield divided by total DD neutron yield, increases significantly in inward shifted configurations. To understand the magnetic configuration dependence of the triton burnup ratio, the first orbit loss fraction of 1 MeV tritons is evaluated by means of the Lorentz orbit code for various magnetic configurations. The first orbit loss of 1 MeV tritons is seen at t of less than 10−5 s and loss points of the triton are concentrated on the side of the helical coil case where the magnetic field is relatively weak. The significant decrease of the first orbit loss fraction by 15% is obtained with the inward shift of the magnetic axis position from 3.90 to 3.55 m. It is found that the decrease of first orbit loss is due to the reduction of the first orbit loss of transition and helically trapped tritons.

Time dependent neutron emission rate analysis for neutral-beam-heated deuterium plasmas in a helical system and tokamaks

A neutron emission rate analysis code called FBURN, based on the classical energetic ion confinement assumption with radial diffusion, is developed for the time-dependent analysis of the total neutron emission rate (Sn) in neutral beam (NB) heated deuterium plasmas. The time trend of Sn evaluated by FBURN shows good agreement with the Sn measured by the neutron flux monitor on the deuterium operation of the Large Helical Device. The dependence of Sn on line-averaged electron density (ne_avg) has a peak at ne_avg of around 2.5 × 1019 m−3 in both experiment and calculation. Here, the absolute value of Sn evaluated by calculation agrees with that obtained in experiments within a factor of two. A time trend analysis of Sn in an electron cyclotron heated plasma with a short pulse NB injection is performed. The analysis shows that the diffusion coefficient of co-going transit beam ions is 0.2 to 0.3 m2 s−1. In addition, the diffusion coefficient of helically trapped beam ions decreases from 5 to 3 m2 s−1 with the inward shift of the magnetic axis position. Time-resolved analysis of the triton burnup experiment shows that the diffusion coefficient of tritons is around 0.15 m2 s−1. It is found that the diffusion coefficients of the beam and tritons are of a similar value as obtained in JT-60U. The trend of the triton burnup ratio on the ne_avg calculated by the FBURN agrees with the experiments. The results suggest that the decrease of the triton burnup ratio with the increase of ne_avg is due to the shorter slowing down time of tritons by the decrease of the electron temperature, and the increase of the triton burnup ratio with the increase of ne_avg is due to the diffusion of tritons. Time trend analysis of Sn in the Korea Superconducting Tokamak Advanced Research and the Experimental Advanced Superconducting Tokamak plasmas with a short pulse NB injection is performed. The time trend of Sn is successfully reproduced by FBURN.

On-field monitoring of the magnetic axis misalignment in multi-coils solenoids

A method for monitoring the coils alignment in multi-coil magnets, directly during their operation in particle accelerators, is proposed. Few measures of the magnetic field by Hall transducers and a local field model allows one to monitor the magnetic axis position of each coil. Thus, the particle beam can be kept strongly focused over its operation time by means of feedback. Furthermore, the uncertainty in measuring the magnetic axis was studied with the aim of finding the optimal placing of the transducers, where the minimum uncertainty is achieved. The method was validated on a challenging case study on the European project “ELI Nuclear Physics” (ELI-NP). In particular, simulations results, based on both analytical and finite-element models of the ELI-NP multi-coil solenoid, point to an uncertainty below 100 μm, for misalignment of the magnetic axes in rotation up to π/1000 and in translation of 1/1000 times the length of a single coil. This uncertainty is limited by the Hall transducers technology, but has potential for large improvement margins, because the measurement model error is below 100 μm.

Three-dimensional simulations of edge impurity flow obtained by the vacuum ultraviolet emission diagnostics in the Large Helical Device with EMC3-EIRENE

Edge carbon impurity flow in the stochastic layer of the Large Helical Device (LHD) has been investigated with the three-dimensional (3D) edge transport code EMC3-EIRENE. The simulated synthetic C3+ impurity flow profile from EMC3-EIRENE shows a reasonable agreement with the vacuum ultraviolet (VUV) measurements according to the CIV (1548.20 × 2 Å) Doppler- shift spectrum. The same horizontally outward C3+ impurity flows at the top and bottom edges of the stochastic layer are determined by the 3D magnetic field structure and the parallel C3+ impurity flow velocity. The observed up-down asymmetric structure of the C3+ impurity flow at the top and bottom edges is caused by the vertical displacement of the VUV spectrometer from the midplane. The horizontally outward shift of the magnetic axis position from 3.6 to 3.9 m leads to a change of the C3+ impurity flow direction at the top and bottom edges. For a high upstream plasma density, the transport of the C3+ impurity flow is mainly determined by the background parallel plasma flow, while a reversed C3+ impurity flow is obtained for a low upstream plasma density, due to the expansion of the thermal force dominant regions. The enhanced thermal force leads to a suppression of the impurity screening effect.

Observations of core ion cyclotron emission on ASDEX Upgrade tokamak.

The B-dot probe diagnostic suite on the ASDEX Upgrade tokamak has recently been upgraded with a new 125 MHz, 14 bit resolution digitizer to study ion cyclotron emission (ICE). While classic edge emission from the low field side plasma is often observed, we also measure waves originating from the core with fast fusion protons or beam injected deuterons being a possible emission driver. Comparing the measured frequency values with ion cyclotron harmonics present in the plasma places the origin of this emission on the magnetic axis, with the fundamental hydrogen/second deuterium cyclotron harmonic matching the observed values. The actual values range from ∼27 MHz at the on-axis toroidal field BT = -1.79 T to ∼40 MHz at BT = -2.62 T. When the magnetic axis position evolves during this emission, the measured frequency values track the changes in the estimated on-axis cyclotron frequency values. Core ICE is usually a transient event lasting ∼100 ms during the neutral beam startup phase. However, in some cases, core emission occurs in steady-state plasmas and lasts for longer than 1 s. These observations suggest an attractive possibility of using a non-perturbing ICE-based diagnostic to passively monitor fusion alpha particles at the location of their birth in the plasma core, in deuterium-tritium burning devices such as ITER and DEMO.

Correcting for background fields and multipole field errors in the localization of the magnetic axis in quadrupole magnets

The fiducial marker localization with respect to the magnetic axis of the magnet elements is a crucial step in the qualification of the magnets for particle accelerators. Background fields, such as the Earth’s magnetic field and fringe fields from electrical sources may degrade the accuracy of this axis localization. In this paper, we discuss stretched-wire measurements, in static and vibrating operation modes, for the correction of stray fields in the quadrupole axis localization to an accuracy of 0.3 μm. Moreover, we present an analytical model to correct the magnetic axis position error due to higher-order multipole field errors in the magnet. This correction is particularly important for the static stretched-wire measurement because the wire movement must be large enough to obtain a sufficient signal-to-noise ratio.

In situ calibration of neutron activation system on the large helical device.

In situ calibration of the neutron activation system on the Large Helical Device (LHD) was performed by using an intense 252Cf neutron source. To simulate a ring-shaped neutron source, we installed a railway inside the LHD vacuum vessel and made a train loaded with the 252Cf source run along a typical magnetic axis position. Three activation capsules loaded with thirty pieces of indium foils stacked with total mass of approximately 18 g were prepared. Each capsule was irradiated over 15 h while the train was circulating. The activation response coefficient (9.4 ± 1.2) × 10-8 of 115In(n, n')115mIn reaction obtained from the experiment is in good agreement with results from three-dimensional neutron transport calculations using the Monte Carlo neutron transport simulation code 6. The activation response coefficients of 2.45 MeV birth neutron and secondary 14.1 MeV neutron from deuterium plasma were evaluated from the activation response coefficient obtained in this calibration experiment with results from three-dimensional neutron calculations using the Monte Carlo neutron transport simulation code 6.

Superconducting Focusing Lenses for the SSR1 Cryomodule of PXIE Test Stand at Fermilab

Five solenoid-based focusing lenses designed for use inside the SSR1 cryomodule of the PXIE test stand at Fermilab have been fabricated and tested. In addition to a focusing solenoid, each lens is equipped with a set of windings that generate magnetic field in the transverse plane and can be used in the steering dipole mode or as a skew quadrupole corrector. The lenses will be installed between superconducting cavities in the cryomodule, so getting sufficiently low fringe magnetic field was one of the main design requirements. Beam dynamics simulations indicated a need for high accuracy positioning of the lenses in the cryomodule, which triggered a study towards understanding uncertainties of the magnetic axis position relative to the geometric features of the lens. This report summarizes the efforts towards certification of the lenses, including results of performance tests, fringe field data, and uncertainty of the magnetic axis position.

Effects of varying stochastic layer on edge plasma and impurity transport in 3D EMC3-EIRENE simulations of LHD

The transport properties of edge plasma and carbon impurity in the stochastic layer of the Large Helical Device (LHD) have been studied with the three-dimensional edge transport code EMC3-EIRENE. The recent development of computational meshes, which store the magnetic configurations, has been used to carry out the studies of the impact of the magnetic field structure on the edge plasma and impurity transport in the stochastic layer. The horizontal variation of the magnetic axis position (Rax) from 3.60m to 3.90m leads to more open flux channels connecting to the divertor and thus a stronger particle exhaust on the target, which results in a higher erosion of divertor target. Furthermore, the outboard divertor target plates suffer from the stronger erosion compared to the inboard divertor target plates for Rax=3.90m, which is in contrast to the case of Rax=3.60m. It is also found that the stronger CIV line emission is obtained at the outboard X-point region when the magnetic axis location moves outwards horizontally.

Experimental observation of response to resonant magnetic perturbation and its hysteresis in LHD

The magnetic island in the large helical device (LHD) shows the dynamic behaviour of the healing/growth transition with the hysteretic behaviour. The thresholds of plasma beta and poloidal flow for island healing are larger than that for growth. The threshold of resonant magnetic perturbation (RMP) for healing is smaller than that for growth. Furthermore, thresholds of the amplitude of RMP depend on the magnetic axis position Rax in the LHD. The RMP threshold increases as the magnetic axis position Rax increases. The poloidal viscosity may be considered as a candidate to explain the experimental observation from the viewpoint of the relationship between the electromagnetic torque and the viscous torque.

Solenoid-Based Focusing Lens for the Low-Beta Section of a Superconducting Proton Linac

A superconducting solenoid-based focusing lens was designed and built for use in the SSR1 cryomodule of PXIE test facility at FNAL. As the cryomodule contains superconducting spoke-type cavities, one of main goals during design stage was minimization of magnetic field on walls of the cavities. The design also attempted minimization of the uncertainty of the magnetic axis position in the lens. This report describes main features of the design and summarizes results of performance tests and magnetic axis position measurements.

Roles of effective helical ripple rates in nonlinear stability of externally induced magnetic islands

Magnetic islands are externally produced by resonant magnetic perturbations (RMPs) in toroidal plasmas. Spontaneous annihilation of RMP-induced magnetic islands called self-healing has been observed in helical systems. A possible mechanism of the self-healing is shielding of RMP penetration by helical ripple-induced neoclassical flows, which give rise to neoclassical viscous torques. In this study, effective helical ripple rates in multi-helicity helical systems are revisited, and a multi-helicity effect on the self-healing is investigated, based on a theoretical model of rotating magnetic islands. It is confirmed that effective helical ripple rates are sensitive to magnetic axis positions. It is newly found that self-healing thresholds also strongly depend on magnetic axis positions, which is due to dependence of neoclassical viscous torques on effective helical ripple rates.

Internal Magnetic Configuration Measured by ECE Imaging on EAST Tokamak

ECE imaging (electron cyclotron emission imaging) is an important diagnostic which can give 2D imaging of temperature fluctuation in the core of tokamak. A method based on ECE imaging is introduced which can give the information of the position of magnetic axis and the structure of internal magnetic surface for EAST tokamak. The EFIT equilibrium reconstruction is not reliable due to the absence of important core diagnostic at the initial phase for EAST, so the information given by ECE imaging could help to improve the accuracy of EFIT equilibrium reconstruction.