On-axis Field Research Articles

Inferring the scrape-off layer heat flux width in a divertor with a low degree of axisymmetry

Plasma facing components (PFCs) in the next generation of tokamak devices will operate in challenging environments, with heat loads predicted to exceed 10 MW/m2. The magnitude of these heat loads is set by the width of the channel, the ‘scrape-off layer’ (SOL), into which heat is exhausted, and can be characterised by an e-folding length scale for the decay of heat flux across the channel. It is expected this channel will narrow as tokamaks move towards reactor relevant conditions. Understanding the processes involved in setting the SOL heat flux width is imperative to be able to predict the heat loads PFCs must handle in future devices. Measurements of the SOL width are performed on the high-field spherical tokamak, ST40, using a newly commissioned infrared thermography system. With its high on-axis toroidal magnetic field (≥1.5 T) ST40 is uniquely positioned to investigate the influence of toroidal field on the heat flux width in spherical tokamaks, whilst also extending measurements of the SOL width in spherical tokamaks to increased poloidal field (≥0.3 T). Due to the divertor on ST40 having a low degree of axisymmetry, it is necessary for a set of radial measurements of the heat flux to be taken across the divertor, made possible using an automated toolchain that fully incorporates its 3D geometry. These radial profiles are combined with the magnetic geometry of the plasma to infer the width of the SOL, with both Eich and double exponential profiles of heat flux observed. A reduction in the heat flux is observed toroidally across part of the divertor, along with increased heat loads observed locally around the edges of the tiles. Future work in characterising the impact of tile misalignment and uncertainties in the reconstructed divertor magnetic geometry is required in order to further understand the observed heat flux patterns, as are additional investigations into the role potentially being played by an inhomogeneous sheath electric field.

Observation of high frequency Alfvén eigenmodes excited by RF-accelerated minority hydrogen ions in the EAST tokamak

Abstract The paper presents the original observation of high frequency Alfvén eigenmode excited by fast minority hydrogen ions accelerated by ion cyclotron range of frequency waves in EAST. The frequency of high frequency Alfvén eigenmodes is around 0.75~8*Ω H, where Ω H is the cyclotron frequency of hydrogen ions evaluated at the low-field side plasma edge. It tracks the on-axis magnetic field B t and the edge plasma electron density n e via the Alfvenic relation ω~ B t *n e -1/2. The high frequency Alfvén eigenmodes are always accompanied by sub-cyclotron modes in several experiments at EAST, consistent with the high frequency Alfvén eigenmode detected on other conventional tokamaks, namely ASDEX Upgrade and DIII-D. Based on the previous study, these sub-cyclotron modes are consistent with the spectrum splitting produced by toroidal mode numbers[Nuclear Fusion 43, 228 (2003)]. We also found that the location of eigenmode excitation of high frequency Alfvén eigenmode driven by RF-accelerated minority hydrogen ions remains unchanged even though the cyclotron resonance location of hydrogen ions varies with B t.

Helical undulators of magnetized ring sectors

A periodic helical array of magnetized ring rare-earth sectors (quasi-helices) creates a helical field on its axis, close in structure and magnitude to the field of a solid helix. In some cases, such permanent undulators, made of a relatively small number of readily available magnets, are easier to manufacture and assemble than a system containing magnetized helices made of one piece. The field magnitude of the quasi-helices depends only weakly on the number of sectors per undulator period. According to calculations and measurements, the prototype Halbach-type helical undulator assembled from longitudinally and “radially” magnetized quasi-helices consisting of NdFeB ring sectors with a period of 2 cm and a relatively large inner diameter of 8 mm, provides an on-axis field of about 0.6T. By reducing the inner diameter to 5 mm, one can achieve twice as strong a field. When assembling such an undulator, to weaken the mutual effect of strongly interacting magnetized elements, it turned out to be structurally more convenient, while maintaining the position of all ring sectors, to use the division of the undulator not into quasi-helices, but into cylindrical sectors shifted along the axis and rotated relative to each other. Permanent undulators made from ring sectors can provide high oscillation velocity of electrons and seem promising for increasing the efficiency of Free Electron Lasers in various frequency ranges.

Magnetic enhancement of the electrical asymmetry effect in capacitively coupled plasmas

The development of real-time control strategies for key discharge parameters, such as densities, fluxes, and energy distributions, is of fundamental interest to many plasma sources. Over the last decade, multi-harmonic ‘tailored’ voltage waveforms have been successfully employed to achieve enhanced control of key parameters in a wide range of radio-frequency (RF) plasma sources through application of the electrical asymmetry effect (EAE). More recently, the analogous magnetic asymmetry effect (MAE) has been numerically and experimentally demonstrated to achieve a notable degree of control in parallel plate RF plasma sources. The MAE is achieved via selectively magnetising the charged species adjacent to one electrode, altering the charge flux to the surface and enforcing a DC self-bias to maintain quasineutrality. This study addresses the degree of control achieved by the MAE in a non-planar geometry via 2D fluid/kinetic simulations of a magnetised RF capacitively coupled plasma source employing two different magnetic topologies. The simultaneous application of the EAE and MAE is then presented for the same geometry, demonstrating a degree of non-linear behaviour dependant upon the applied magnetic topology. Control of the DC self-bias voltage ηdc is demonstrated for a single 600 Vpp , 13.56 MHz discharge in both ‘convergent’ (maximum on-axis field strength) and ‘divergent’ (minimum on-axis field strength) magnetic topolgies. MAE induced modulations of ηdc = 0.13 Vpp and ηdc = 0.03 Vpp are achieved for each magnetic topology, respectively, for magnetic field strengths between 50 and 1000 G. Simultaneous application of an EAE and MAE is achieved through a multi-harmonic ‘peak’-type tailored voltage waveform employing varying harmonic phase offsets between 0∘ ⩽ θ ⩽ 360∘ . The degree to which the DC self-bias voltage is modulated by the applied EAE is mediated by the orientation and magnitude of the applied magnetic field. The EAE induced DC self-bias modulations exhibit non-linear behaviour in response to a superimposed MAE, such that the resulting DC self-bias differs from an additive combination of the two effects alone Simultaneous application of the electrical and MAEs offers the possibility of further decoupling ion and electron dynamics in RF plasma sources, and represents an improvement over each approach in isolation.

Novel correction procedure for compensating thermal contraction errors in the measurement of the magnetic field of superconducting undulator coils in a liquid helium cryostat.

Superconducting undulators (SCUs) can offer a much higher on-axis undulator field than state-of-the-art cryogenic permanent-magnet undulators with the same period and vacuum gap. The development of shorter-period and high-field SCUs would allow the free-electron laser and synchrotron radiation source community to reduce both the length of undulators and the dimensions of the accelerator. Magnetic measurements are essential for characterizing the magnetic field quality of undulators for operation in a modern light source. Hall probe scanning is so far the most mature technique for local field characterization of undulators. This article focuses on the systematic error caused by thermal contraction that influences Hall probe measurements carried out in a liquid helium cryostat. A novel procedure, based on the redundant measurement of the magnetic field using multiple Hall probes at known relative distance, is introduced for the correction of such systematic error.

First measurements of an imaging heavy ion beam probe at the ASDEX Upgrade tokamak.

The imaging heavy ion beam probe (i-HIBP) diagnostic has been successfully commissioned at ASDEX Upgrade. The i-HIBP injects a primary neutral beam into the plasma, where it is ionized, leading to a fan of secondary (charged) beams. These are deflected by the magnetic field of the tokamak and collected by a scintillator detector, generating a strike-line light pattern that encodes information on the density, electrostatic potential, and magnetic field of the plasma edge. The first measurements have been made, demonstrating the proof-of-principle of this diagnostic technique. A primary beam of 85/87Rb has been used with energies ranging between 60 and 72keV and extracted currents up to 1.5 mA. The first signals have been obtained in experiments covering a wide range of parameter spaces, with plasma currents (Ip) between 0.2 and 0.8 MA and on-axis toroidal magnetic field (Bt) between 1.9 and 2.7T. Low densities appear to be critical for the performance of the diagnostic, as signals are typically observed only when the line integrated density is below 2.0-3.0 × 1019m-2 in the central interferometer chord, depending on the plasma shape. The strike line moves as expected when Ip is ramped, indicating that current measurements are possible. Additionally, clear dynamics in the intensity of the strike line are often observed, which might be linked to changes in the edge profile structure. However, the signal-to-background ratio of the signals is hampered by stray light, and the image guide degradation is due to neutron irradiation. Finally, simulations have been carried out to investigate the sensitivity of the expected signals to plasma density and temperature. The results are in qualitative agreement with the experimental observations, suggesting that the diagnostic is almost insensitive to fluctuations in the temperature profile, while the signal level is highly determined by the density profile due to the beam attenuation.

Two-Dimensional Distribution of Plasma Electric Potential in the T-10 Tokamak

Heavy ion beam probe (HIBP) is a unique plasma diagnostics that makes it possible to measure the electric potential φ of high-temperature plasma and its fluctuations y, as well as the density ne and poloidal magnetic field Bpol fluctuations. Position of the point of performing measurements in the plasma vertical cross-section depends on the beam energy and angle of its entrance into the plasma. The variation of these two parameters makes it possible to construct a two-dimensional (2D) detector grid, which covers the domain of possible measurements. The measurement results obtained in the detector grid points provide for constructing 2D distributions of plasma parameters. For the OH and ECRH stages of the T-10 tokamak shots, 2D distributions of the plasma electric potential are presented for the regime with the on-axis magnetic field of Bt = 2.2 T, plasma current of Ipl = 230 kA, line-average density of ne ≈ 1.1 × 1019 m–3 and off-axis ECRH power of PECRH = 1.7 MW.

Optimization of on-axis magnetic field of uniformly magnetized cones

The magnetic field B induced along the axis of symmetry of axially magnetized cones was studied analytically and experimentally for various cone angles α. An explicit algebraic equation was derived for sharp-pointed and truncated cones. A sharp cone is characterized by singularities of B and ∇B at its apex point. For a truncated cone, the maximum values of these quantities are achieved for αmax∼54.7° and α∇∼39.2°, respectively. Two truncated cones with αuni∼63.4° positioned in a mirrored co-apex configuration produce a uniform axial field in the free-space gap. For smaller angles, the minimum field is located in the center of the airgap, while for larger, it is at the cones’ surfaces with extremum at αmin∼71.6°. These predictions were investigated using a tunable apparatus in which Co–Fe cones are magnetized by cylindrical NdFeB magnets. Strong ∼4 T B-field was achieved. Experimental results are discussed in detail, including incomplete magnetization and other secondary effects.

An analytical method and practical verification for evaluating the undulator performance

The mechanical performance of an undulator has a significant effect on the on-axis magnetic field and thus a directly affect the performance of photon flux and stable operation in a storage ring. During the phase of mechanical design and construction, it becomes important to develop a method to evaluate the effects of magnetic fields caused by mechanical properties. This paper reveals a method to predict the distribution of a magnetic field utilizing the practice that mechanical performance combined with an ideal magnet assembly enables identification whether the magnet array structure is satisfactory. Moreover, the systematic errors expected from the mechanical inspection can be confirmed in the magnetic field measurement data. This scheme could be used to predict the systematic effects and then to apply effective remedies before the entire machine is completed.

Real-time wavefront correction using diffractive optical networks.

Real-time wavefront correction is a challenging problem to present for conventional adaptive optics systems. Here, we present an all-optical system to realize real-time wavefront correction. Using deep learning, the system, which contains only multiple transmissive diffractive layers, is trained to realize high-quality imaging for unknown, random, distorted wavefronts. Once physically fabricated, this passive optical system is physically positioned between the imaging lens and the image plane to all-optically correct unknown, new wavefronts whose wavefront errors are within the training range. Simulated experiments showed that the system designed for the on-axis field of view increases the average imaging Strehl Ratio from 0.32 to 0.94, and the other system intended for multiple fields of view increases the resolvable probability of binary stars from 30.5% to 69.5%. Results suggested that DAOS performed well when performing wavefront correction at the speed of light. The solution of real-time wavefront correction can be applied to other wavelengths and has great application potential in astronomical observation, laser communication, and other fields.

Derivation of the Field Due to a Magnetic Dipole Without Use of the Vector Potential

The mathematical form of the magnetic field due to a current loop, and the fact that it is identical to the electric field due to an electric dipole in the far field, are fundamental to our understanding of electromagnetism. While undergraduate level electromagnetism textbooks usually derive the electric field from an electric dipole, few derive the magnetic field from a current loop. Most simply state it without proof, or perform the derivation for simpler cases such as the on-axis field. Those that perform the derivation use the magnetic vector potential, a relatively advanced concept that most undergraduate students would not encounter until their final year of study, if at all. Here, a simple derivation to obtain the magnetic field due to a current loop in the far-field approximation is presented. The derivation begins from the Biot–Savart law and does not require the vector potential. The problem is set up so that only a single integration is necessary (from angle α = 0 to α = 2π around the current loop), and the result is compared with that for the electric field surrounding an electric dipole.

Construction of Cryogen-Free 4.3T Superconducting Wiggler for NSLS-II Ring

With the 3 GeV electron beam energy for the National Synchro-tron Light Source II (NSLS-II) ring, only superconducting wig-glers (SCW) producing greater than 4T peak field can cover the photon energy range of 20keV and 200keV with sufficient num-ber of photons. The High energy Engineering X-ray (HEX) Dif-fraction beamline, which is primarily funded by the New York State Energy Research and Development Authority (NYSERDA) and NSLS-II, will be equipped with a 1.2m-long SCW with 70mm period length and 4.3T on-axis field. This SCW is free from the use of liquid Helium and is cooled only with cryo-coolers. The Electron Beam Chamber (EBC) with vertical aper-ture of 8mm is made from 316LN stainless steel and copper plat-ing is applied both entire upper surface and +- 12.5mm wide from the center in the inner surface. The expected heat load from the electron beam of the NSLS-II ring is estimated to be 10W/m. This paper describes the design principles and engineering chal-lenges for the device.

MAGNETIC SYSTEM FOR CLEANING THE GAMMA BEAM AT THE LUE-40 ELECTRON LINAC OUTPUT

The bremsstrahlung of accelerated electrons passing through a converter is used to study multiparticle photonuclear reactions. The results of calculations, numerical modeling, design, and testing of a special magnetic cleaning system to obtain a “pure” beam of bremsstrahlung quanta when studying the cross-sections of such reactions at the LUE-40 linac are presented. The system is based on commercially available permanent magnets of rectangular cross-sections. The maximum on-axis field is 0.9 T, which provides sufficient separation of the electron beam and gamma rays at a distance of more than 90 mm from the magnet.

Evaluation of MU2net as an online secondary dose check for MR guided radiation therapy with the Elekta unity MR linac.

During the adaptive workflow associated with MRgRT, a secondary dose calculation is required and MU2net (DOSIsoft, France) is one commercial option. The suitability of MU2net to be used in conjunction with the online Monaco treatment planning system of the Elekta Unity (Elekta AB, Stockholm, Sweden), is evaluated in this work. Monaco and MU2net point doses are compared for various fields on and off axis and at different SSDs. To investigate the comparative effects of attenuation due to the cryostat, couch and posterior coil, measured, MU2net and Monaco dose outputs at the isocentre, as a function of gantry angle, were compared. Point doses for the beams of nine step and shoot IMRT (SSIMRT) test plans (courtesy Elekta) were calculated with Monaco v5.4 and compared to corresponding doses computed with MU2net. In addition, Monaco v5.4 and MU2net point doses were compared for 1552 beams treated on the Unity at our facility. For the on-axis fields investigated the agreement between MU2net and measured data is acceptable. MU2net and Monaco point doses for the Elekta SSIMRT test plans were within ± 5.0% and ± 6.4% for beams delivered from gantry zero and at planned beam angles, respectively. For the 1552 beams delivered approximately 80.0% of MU2net and Monaco point doses agree within ± 5.0%, therefore it is recommended to correlate MU2net Dose Reference Points (DRPs) with pre and post treatment dosimetry verification. Computational accuracy of MU2net could be enhanced with improved modelling of attenuation due to the couch, cryostat and posterior MR imaging coil.

Numerical Design of RF Antennas for Ion Cyclotron Resonance Heating in ECRIS Environment

In this paper we present the numerical design and simulation of RF antennas to be employed in Ion Cyclotron Resonance Heating (ICRH) systems working in ECRIS environment. A 3D full-wave numerical model, based on the coupling between COMSOL FEM solution of Maxwell equations and the MATLAB-computed non-homogeneous plasma dielectric tensor, has been employed in order to study the performances of several ICRH antennas. Results in terms of S-parameters, on-axis electric field and RF absorbed power inside the plasma chamber have been obtained and compared between the chosen antenna geometries. The presented study will permit to better understand the fundamental aspects of ion dynamics in ECRISs as well as allowing the design of a proper matching network between the RF amplifier and the antenna, necessary to cope with the plasma properties’ fast variations. Further ion kinetic simulations are ongoing.

Physics design point of high-field stellarator reactors

The ongoing development of electromagnets based on high temperature superconductors has led to the conceptual exploration of high-magnetic-field fusion reactors of the tokamak type, operating at on-axis fields above 10 T. In this work we explore the consequences of the potential future availability of high-field three-dimensional electromagnets on the physics design point of a stellarator reactor. We find that, when an increase in the magnetic field strength B is used to maximally reduce the device linear size R ∼ B −4/3 (with otherwise fixed magnetic geometry), the physics design point is largely independent of the chosen field strength/device size. A similar degree of optimization is to be imposed on the magnetohydrodynamic, transport and fast ion confinement properties of the magnetic configuration of that family of reactor design points. Additionally, we show that the family shares an invariant operation map of fusion power output as a function of the auxiliary power and relative density variation. The effects of magnetic field over-engineering and the R(B) scaling of design points with constant neutron wall loading are also inspected. In this study we use geometric parameters characteristic of the helical axis advanced stellarator reactor, but most results apply to other stellarator configurations.

The DEMO magnet system – Status and future challenges

We present the pre-concept design of the European DEMO Magnet System, which has successfully passed the DEMO plant-level gate review in 2020. The main design input parameters originate from the so-called DEMO 2018 baseline, which was produced using the PROCESS systems code. It defines a major and minor radius of 9.1 m and 2.9 m, respectively, an on-axis magnetic field of 5.3 T resulting in a peak field on the toroidal field (TF) conductor of 12.0 T.Four variants, all based on low-temperature superconductors (LTS), have been designed for the 16 TF coils. Two of these concepts were selected to be further pursued during the Concept Design Phase (CDP): the first having many similarities to the ITER TF coil concept and the second being the most innovative one, based on react-and-wind (RW) Nb3Sn technology and winding the coils in layers. Two variants for the five Central Solenoid (CS) modules have been investigated: an LTS-only concept resembling to the ITER CS and a hybrid configuration, in which the innermost layers are made of high-temperature superconductors (HTS), which allows either to increase the magnetic flux or to reduce the outer radius of the CS coil. Issues related to fatigue lifetime which emerged in mechanical analyses will be addressed further in the CDP. Both variants proposed for the six poloidal field coils present a lower level of risk for future development. All magnet and conductor design studies included thermal-hydraulic and mechanical analyses, and were accompanied by experimental tests on both LTS and HTS prototype samples (i.e. DC and AC measurements, stability tests, quench evolution etc.). In addition, magnet structures and auxiliary systems, e.g. cryogenics and feeders, were designed at pre-concept level. Important lessons learnt during this first phase of the project were fed into the planning of the CDP. Key aspects to be addressed concern the demonstration and validation of critical technologies (e.g. industrial manufacturing of RW Nb3Sn and HTS long conductors, insulation of penetrations and joints), as well as the detailed design of the overall Magnet System and mechanical structures.

Electron acceleration using twisted laser wavefronts

Using plasma mirror injection we demonstrate, both analytically and numerically, that a circularly polarized helical laser pulse can accelerate highly collimated dense bunches of electrons to several hundred MeV using currently available laser systems. The circular-polarized helical (Laguerre–Gaussian) beam has a unique field structure where the transverse fields have helix-like wave-fronts which tend to zero on-axis where, at focus, there are large on-axis longitudinal magnetic and electric fields. The acceleration of electrons by this type of laser pulse is analyzed as a function of radial mode number and it is shown that the radial mode number has a profound effect on electron acceleration close to the laser axis. Using three-dimensional particle-in-cell simulations a circular-polarized helical laser beam with power of 0.6 PW is shown to produce several dense attosecond bunches. The bunch nearest the peak of the laser envelope has an energy of 0.47 GeV with spread as narrow as 10%, a charge of 26 pC with duration of as, and a very low divergence of 20 mrad. The confinement by longitudinal magnetic fields in the near-axis region allows the longitudinal electric fields to accelerate the electrons over a long period after the initial reflection. Both the longitudinal E and B fields are shown to be essential for electron acceleration in this scheme. This opens up new paths toward attosecond electron beams, or attosecond radiation, at many laser facilities around the world.

Wide-Field Telescope Alignment Using the Model-Based Method Combined with the Stochastic Parallel Gradient Descent Algorithm

To acquire images with higher accuracy of wide-field telescopes, deformable mirrors with more than 100 actuators are used, making the telescope alignment more complex and time-consuming. Furthermore, the position of the obscuration caused by the secondary mirror in the experiment system is changed with the difference of fields of view, making the response matrix of the deformable mirror different in various fields of view. To solve this problem, transfer functions corresponding to different fields of view are calculated according to the wavefront edge check and boundary conditions. In this paper, a model-based method combined with the stochastic parallel gradient descent (SPGD) algorithm is used. The experiment results show that our method can correct the aberrations with a high accuracy in both on-axis and off-axis fields, indicating that the effective actuators are well chosen corresponding to different fields of view.

Single and double null equilibria in the SMART Tokamak

The SMall Aspect Ratio Tokamak (SMART) device is a novel, compact (R geo = 0.42 m, a = 0.22 m, A ≥ 1.70) spherical tokamak, currently under development at the University of Seville. The SMART device is being developed over 3 phases, with target on-axis toroidal magnetic fields between 0.1 ≤ B ϕ ≤ 1.0 T, and target plasma currents of between 35 ≤ I p ≤ 400 kA; with phases 2 and 3 enabling access to a wide range of elongations (κ ≤ 2.30) and triangularities ( − 0.50 ≤ δ ≤ 0.50). SMART employs four internal divertor coils with two internal and two external poloidal field coils, enabling operation in lower-single, upper-single and double-null configurations. This work examines phase 3 of the SMART device, presenting a prospective L-mode discharge scenario without external heating, before examining five highly-shaped equilibria, including: two double null triangular configurations, two single null triangular configurations and a baseline double null configuration. All equilibria are obtained via an axisymmetric Grad-Shafranov force balance solver (Fiesta), in combination with a circuit equation rigid current displacement model (RZIp) to obtain time-resolved vessel and plasma currents.