Toroidal Magnetic Field Strength Research Articles

Three-dimensional magnetic field imaging of protoplanetary disks using Zeeman broadening and linear polarization observations

Context. Magnetic fields are predicted to have a crucial impact on the structure, evolution, and chemistry of protoplanetary disks. However, a direct detection of the magnetic field toward these objects has yet to be achieved. Aims. In order to characterize the magnetic fields of protoplanetary disks, we investigate the impact of the Zeeman effect on the (polarized) radiative transfer of emission from paramagnetic molecules excited in protoplanetary disks. Methods. While the effects of the Zeeman effect are commonly studied in the circular polarization of spectral lines, we also performed a comprehensive modeling of the Zeeman-induced broadening of spectral lines and their linear polarization. We developed simplified radiative transfer models adapted to protoplanetary disks, which we compare to full three-dimensional polarized radiative transfer simulations. Results. We find that the radiative transfer of circular polarization is heavily affected by the expected polarity change of the magnetic field between opposite sides of the disk. In contrast, Zeeman broadening and linear polarization are relatively unaffected by this sign change due to their quadratic dependence on the magnetic field. We can match our simplified radiative transfer models to full polarization modeling with high fidelity, which in turn allows us to prescribe straightforward methods to extract magnetic field information from Zeeman broadening and linear polarization observations. Conclusions. We find that Zeeman broadening and linear polarization observations are highly advantageous methods to characterize protoplanetary disk magnetic fields as they are both sensitive probes of the magnetic field and are marginally affected by any sign change of the disk magnetic field. Applying our results to existing circular polarization observations of protoplanetary disk specral lines suggests that the current upper limits on the toroidal magnetic field strengths have to be raised.

Feasibility study of neutral beam injection in Thailand Tokamak-1

Thailand Institute of Nuclear Technology (TINT) is developing Thailand Tokamak-1 (TT-1) from a former device HT-6 M of China. The first hydrogen plasma will be initiated in 2023. To investigate high-β plasma and physics related to fast ions, TT-1 will be equipped with auxiliary heating systems. In this work, a feasibility study for installing a neutral beam injection (NBI) heating system in TT-1 is carried out. This work is motivated to characterize beam ion's orbits in different injection angles and to explore a condition suitable in terms of higher heating efficiency. In this work, we assume that a hydrogen beam will be launched into the TT-1 plasma with an acceleration voltage of 20 kV. The orbit simulations using the gyromotion following code LORBIT are performed in various magnetic field equilibria, i.e., different plasma current (Ip), toroidal magnetic field strength (Bt), and the magnetic axis (Rax). Furthermore, beam ions are injected in different directions, i.e., tangential co-injection and tangential counter-injection. In the case of co-injection, beam ion loss is not significant, by about 6%, whereas beam ion loss fraction is evaluated to be 26–34% in the case of counter-injection. Also, it is found that the number of lost beam ions is significantly affected by changing Ip and Rax. The results obtained in this work will directly support the experiment plan for the high-performance plasmas, design of the fast-ion diagnostic system, and systematic understanding of beam ion's confinement property and beam-ion-driven magnetohydrodynamic (MHD) instabilities in TT-1.

Design of an arrangement of cubic magnets for a quasi-axisymmetric stellarator experiment

The usage of permanent magnets to shape the confining magnetic field of a stellarator has the potential to reduce or eliminate the need for non-planar coils. As a proof-of-concept for this idea, we have developed a procedure for designing an array of cubic permanent magnets that works in tandem with a set of toroidal-field (TF) coils to confine a stellarator plasma. All of the magnets in the design are constrained to have identical geometry and one of three polarization types in order to simplify fabrication while still producing sufficient field accuracy. We present some of the key steps leading to the design, including the geometric arrangement of the magnets around the device, the procedure for optimizing the polarizations according to the three allowable magnet types, and the choice of magnet types to be used. We apply these methods to design an array of rare-Earth permanent magnets that can be paired with a set of planar TF coils to confine a quasi-axisymmetric plasma with a toroidal magnetic field strength of about 0.5 T on axis.

Design study of an edge current density diagnostic using new high-performance single-channel beam emission spectrometers at DIII-D.

A novel Motional Stark Effect spectroscopy system has been designed for application at the DIII-D tokamak. The system is optimized for studies of the poloidal and toroidal magnetic field in the plasma pedestal region with frame rates of up to 10kHz. Light from an existing high-photon-throughput collection lens is analyzed using four single-channel f/2.8 Czerny-Turner spectrometers that use custom-made lens systems instead of mirrors. Each spectrometer has two separate outgoing legs and is operated in a positive grating order, which allows for simultaneous observations of D-alpha and D-beta spectra. Forward modeling using the code FIDASIM shows a radial resolution of the system close to 0.6cm and sufficiently good spectral resolution when masking the high throughput light collection lens in the horizontal direction to avoid overly strong Doppler broadening of beam emission lines. Moreover, a detailed sensitivity study considering realistic levels of readout and photon noise shows that the poloidal and toroidal magnetic field strengths can be inferred with an uncertainty of less than 1%, which will allow the inference of changes of the plasma current during transient events.

Mode structure measurements of ion cyclotron emission and sub-cyclotron modes on DIII-D

We report mode structure measurements of coherent ion cyclotron emission (ICE) and sub-cyclotron modes on DIII-D. Through a dedicated experiment, we aimed to characterize a variety of modes via the upgraded ICE diagnostic in both L- and H-mode plasmas. In the L-mode plasmas, autopower spectrum peaks at harmonics of the ion cyclotron frequency f ci were observed and are localized in the core of the plasma. Sub-cyclotron modes (f ∼ 0.5f ci) were also observed in L-mode plasmas when the toroidal magnetic field strength was lowered from B T = 2.17 T. In H-mode plasmas, many ICE harmonics localized to the plasma edge were observed, with some exceeding the nominal ICE diagnostic bandwidth of f ∈ [0, 100] MHz. Polarization estimates made using an orthogonal pair of vertical and horizontal magnetic pickup loops on the outer wall of the machine indicate that ICE and sub-cyclotron modes have compressional polarization at the plasma edge, the latter being consistent with simulation efforts for comparable DIII-D plasmas. For all modes, the same harmonics are observed on both the centerpost and outer wall loops, indicating that ICE is poloidally extended. Finally, toroidal mode numbers were calculated using three outer wall loops for both core ICE and sub-cyclotron modes in L-mode plasmas. The sub-cyclotron case served as a benchmark for our calculation method, with measured numbers of n ∈ [−24, −18] roughly agreeing with heuristic estimates of n ∈ [−20, −13]. Core ICE mode numbers were measured to be n ∈ [−10, 5], which is comparable to measurements made on other machines.

Ideal MHD Limited Electron Temperature in Spherical Tokamaks.

It is well documented that the central electron temperature in the national spherical torus experiment (NSTX) remains largely unchanged as the external heating power, and hence the normalized volume averaged plasma pressure β increases [Stutman, Phys. Rev. Lett. 102, 115002 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.115002]. Here we present a hypothesis that low n, pressure driven ideal magnetohydrodynamic (MHD) instabilities that are nondisruptive, can break magnetic surfaces in the central region and thereby flatten the electron temperature profiles. We demonstrate this mechanism in a 3D resistive MHD simulation of a NSTX discharge. By varying the toroidal magnetic field strength, and/or the heating power, we show that there is a critical value of β, above which the central temperature profile no longer peaks on axis.

ALMA CN Zeeman Observations of AS 209: Limits on Magnetic Field Strength and Magnetically Driven Accretion Rate

Abstract While magnetic fields likely play an important role in driving the evolution of protoplanetary disks through angular momentum transport, observational evidence of magnetic fields has only been found in a small number of disks. Although dust continuum linear polarization has been detected in an increasing number of disks, its pattern is more consistent with that from dust scattering than from magnetically aligned grains in the vast majority of cases. Continuum linear polarization from dust grains aligned to a magnetic field can reveal information about the magnetic field’s direction, but not its strength. On the other hand, observations of circular polarization in molecular lines produced by Zeeman splitting offer a direct measure of the line-of-sight magnetic field strength in disks. We present upper limits on the net toroidal and vertical magnetic field strengths in the protoplanetary disk AS 209 derived from Zeeman splitting observations of the CN 2–1 line. The 3σ upper limit on the net line-of-sight magnetic field strength in AS 209 is 5.0 mG on the redshifted side of the disk and 4.2 mG on the blueshifted side of the disk. Given the disk’s inclination angle, we set a 3σ upper limit on the net toroidal magnetic field strength of 8.7 and 7.3 mG for the red and blue sides of the disk, respectively, and 6.2 and 5.2 mG on the net vertical magnetic field on the red and blue sides of the disk. If magnetic disk winds are a significant mechanism of angular momentum transport in the disk, magnetic fields of a strength close to the upper limits would be sufficient to drive accretion at the rate previously inferred for regions near the protostar.

Comparison of measurements with different types of divertor Langmuir probe in EAST tokamak

Divertor Langmuir probes (Div-LPs), embedded in the divertor target plates, are the important diagnostic tools to measure the plasma parameters in EAST divertor region. A series of measurement methods, i.e., single-probe, double-probe and triple-probe schemes, are applied and compared for the Div-LPs on EAST, to get the electron temperature Te and the electron density ne at the same poloidal position, respectively. It is found that the electron temperature Te and the electron density ne measured by the single-probe and the double-probe schemes are basically the same during the plasma discharge phase. Further analysis of the electron energy distribution function (EEDF) represented by the first derivative curve method shows that the electrons conform to a Maxwell distribution, which indicate that the three methods can be applied in the EAST divertor region. Besides, the domed and flush-mounted probe tips for measuring the plasma parameters are also compared, and the results show a good match. The sheath potential coefficient Λ is also calculated from the I-V characteristic curves by two ways, i.e. Λp=(Vplasma-Vf)/Te and ΛI= ln (|Ies/Iis|), and compared with the traditional value Λ=2.8, the results indicate that the ∼1.5ΛI and Λ=2.8 are available to replace the Λp under the different strength of toroidal magnetic field in EAST tokamak.

Effects of drifts on divertor plasma transport in LHD

An asymmetric plasma particle load on divertor tiles located at positions of symmetric magnetic field lines structure has been investigated in the Large Helical Device (LHD). The asymmetry reverses with reversing the toroidal magnetic field direction. This suggests that drifts affect the asymmetry. It is found that the degree of the asymmetry depends on the electron temperature in the edge plasma and on the toroidal magnetic field strength. The degree of the asymmetry becomes large and then saturates with an increase of electron temperature. In the lower magnetic field discharge, the degree of the asymmetry is larger. The mass dependence of the asymmetry is not clear among hydrogen, deuterium and helium. Results presented suggests that E × B drift plays a role in formation of the asymmetry.

Thermal and magnetic properties of electron gas in toroidal quantum dot

One-electron states in a toroidal quantum dot in the presence of an external magnetic field have been considered. The magnetic field operator and the Schrodinger equation have been written in toroidal coordinates. The dependence of one-electron energy spectrum and wave function on the geometrical parameters of a toroidal quantum dot and magnetic field strength have been studied. The energy levels are employed to calculate the canonical partition function, which in its turn is used to obtain mean energy, heat capacity, entropy, magnetization, and susceptibility of noninteracting electron gas. The possibility to control the thermodynamic and magnetic properties of the noninteracting electron gas via changing the geometric parameters of the QD, magnetic field, and temperature, was demonstrated.

Characterization of SOL plasma flows and potentials in ICRF-heated plasmas in Alcator C-mod

Gas-puff imaging techniques are employed to determine the far SOL region radial electric field and the plasma potential in ICRF heated discharges in the Alcator C-Mod tokamak. The two-dimensional velocity fields of the turbulent structures, which are advected by RF-induced flows, are obtained via the time-delay estimation (TDE) techniques. Both the magnitude and radial extension of the radial electric field Er are observed to increase with the toroidal magnetic field strength Bφ and the ICRF power. In particular, the RF-induced Er extends from the vicinity of the ICRF antenna to the separatrix when and . In addition, low-Z impurity seeding near the antenna is found to substantially reduce the sheath potential associated with ICRF power. The TDE techniques have also been used to revisit and estimate ICRF-induced potentials in different antenna configurations: (1) conventional toroidally aligned (TA) antenna versus field-aligned (FA) antenna; (2) FA monopole versus FA dipole. It shows that FA and TA antennas produce similar magnitude of plasma potentials, and the FA monopole induced greater potential than the FA dipole phasing. The TDE estimations of RF-induced plasma potentials are consistent with previous results based on the poloidal phase velocity.

Spatiotemporal Evolution of Runaway Electron Momentum Distributions in Tokamaks.

Novel spatial, temporal, and energetically resolved measurements of bremsstrahlung hard-x-ray (HXR) emission from runaway electron (RE) populations in tokamaks reveal nonmonotonic RE distribution functions whose properties depend on the interplay of electric field acceleration with collisional and synchrotron damping. Measurements are consistent with theoretical predictions of momentum-space attractors that accumulate runaway electrons. RE distribution functions are measured to shift to a higher energy when the synchrotron force is reduced by decreasing the toroidal magnetic field strength. Increasing the collisional damping by increasing the electron density (at a fixed magnetic and electric field) reduces the energy of the nonmonotonic feature and reduces the HXR growth rate at all energies. Higher-energy HXR growth rates extrapolate to zero at the expected threshold electric field for RE sustainment, while low-energy REs are anomalously lost. The compilation of HXR emission from different sight lines into the plasma yields energy and pitch-angle-resolved RE distributions and demonstrates increasing pitch-angle and radial gradients with energy.

Non-kinematic Flux-transport Dynamos Including the Effects of Diffusivity Quenching

Abstract Turbulent magnetic diffusivity is quenched when strong magnetic fields suppress turbulent motion in a phenomenon known as diffusivity quenching. Diffusivity quenching can provide a mechanism for amplifying magnetic field and influencing global velocity fields through Lorentz force feedback. To investigate this effect, we conducted mean field flux-transport dynamo simulations that included the effects of diffusivity quenching in a non-kinematic regime. We found that toroidal magnetic field strength is amplified by up to approximately 1.5 times in the convection zone as a result of diffusivity quenching. This amplification is much weaker than that in kinematic cases as a result of Lorentz force feedback on the system’s differential rotation. While amplified toroidal fields lead to the suppression of equatorward meridional flow locally near the base of the convection zone, large-scale equatorward transport of magnetic flux via meridional flow, which is the essential process of the flux-transport dynamo, is sustainable in our calculations.

Dual behavior of the toroidal magnetic field versus the Rossby wave instability

The Rossby wave instability (RWI) theory has been considered as one of the top topics in astrophysics due to the fact that it deals with some ambiguous questions, such as the angular momentum transport in the poorly ionized regions of the protoplanetary discs. Based on the theoretical and simulation works, two important factors in the study of the RWI are the viscosity and magnetic field, which are directly connected to each other because the large-scale toroidal magnetic fields are produced by the magnetohydrodynamic (MHD) turbulence. Therefore, it is essential to consider more details about the toroidal magnetic field both in the steady state and perturbation state. In this paper, the role of the strength and gradient of the toroidal magnetic field is investigated on the RWI at the dead zone in the regions of bump. The obtained results show that the gradient of the toroidal magnetic field or its strength have a major role in the RWI occurrence, which have received relatively less attention in previous works. Also, the role of the gradient of the toroidal magnetic field in the RWI is important even in the weak magnetic fields. Hence, the obtained results are very different from what we previously expected, and it seems crucial to research and develop this issue in the theoretical and simulation works. This paper can be helpful on the study of the angular momentum transport in the cold accretion discs, such as accretion discs in quiescent dwarf novae or around the white-dwarf primary.

The I-mode confinement regime at ASDEX Upgrade: global properties and characterization of strongly intermittent density fluctuations

Properties of the I-mode confinement regime on the ASDEX Upgrade tokamak are summarized. A weak dependence of the power threshold for the L-I transition on the toroidal magnetic field strength is found. During improved confinement, the edge radial electric field well deepens. Stability calculations show that the I-mode pedestal is peeling-ballooning stable. Turbulence investigations reveal strongly intermittent density fluctuations linked to the weakly coherent mode in the confined plasma, which become stronger as the confinement quality increases. Across all investigated structure sizes (–12 cm−1, with the perpendicular wavenumber of turbulent density fluctuations), the intermittent turbulence bursts are observed. Comparison with bolometry data shows that they move poloidally toward the X-point and finally end up in the divertor. This might be indicative that they play a role in inhibiting the density profile growth, such that no pedestal is formed in the edge density profile.

Large-scale magnetic field in the accretion discs of young stars: the influence of magnetic diffusion, buoyancy and Hall effect

We investigate the fossil magnetic field in the accretion and protoplanetary discs using the Shakura and Sunyaev approach. The distinguishing feature of this study is the accurate solution of the ionization balance equations and the induction equation with Ohmic diffusion, magnetic ambipolar diffusion, buoyancy and the Hall effect. We consider the ionization by cosmic rays, X-rays and radionuclides, radiative recombinations, recombinations onto dust grains, and also thermal ionization. The buoyancy appears as the additional mechanism of magnetic flux escape in the steady-state solution of the induction equation. Calculations show that Ohmic diffusion and magnetic ambipolar diffusion constraint the generation of the magnetic field inside the `dead' zones. The magnetic field in these regions is quasi-vertical. The buoyancy constraints the toroidal magnetic field strength close to the disc inner edge. As a result, the toroidal and vertical magnetic fields become comparable. The Hall effect is important in the regions close to the borders of the `dead' zones because electrons are magnetized there. The magnetic field in these regions is quasi-radial. We calculate the magnetic field strength and geometry for the discs with accretion rates $(10^{-8}-10^{-6})\,\rm{M}_{\odot}\,\rm{yr}^{-1}$. The fossil magnetic field geometry does not change significantly during the disc evolution while the accretion rate decreases. We construct the synthetic maps of dust emission polarized due to the dust grain alignment by the magnetic field. In the polarization maps, the `dead' zones appear as the regions with the reduced values of polarization degree in comparison to those in the adjacent regions.

Constraining the ellipticity of strongly magnetized neutron stars powering superluminous supernovae

Abstract Superluminous supernovae (SLSNe) have been suggested to be powered by strongly magnetized, rapidly rotating neutron stars which are often called magnetars. In this process, rotational energy of the magnetar is radiated via magnetic dipole radiation and heats the supernova ejecta. However, if magnetars are highly distorted in their geometric shape, rotational energy is mainly lost as gravitational wave radiation and thus such magnetars cannot power SLSNe. By simply comparing electromagnetic and gravitational wave emission time-scales, we constrain upper limits to the ellipticity of magnetars by assuming that they power the observed SLSNe. We find that their ellipticity typically needs to be less than about a few 10−3. This indicates that the toroidal magnetic field strengths in these magnetars are typically less than a few 1016 G so that their distortions remain small. Because light-curve modelling of SLSNe shows that their dipole magnetic field strengths are of the order of 1014 G, the ratio of poloidal to toroidal magnetic field strengths is found to be larger than ∼0.01 in magnetars powering SLSNe.

Accretion disc dynamo activity in local simulations spanning weak-to-strong net vertical magnetic flux regimes

Strongly magnetized accretion discs around black holes have attractive features that may explain enigmatic aspects of X-ray binary behaviour. The structure and evolution of these discs are governed by a dynamo-like mechanism, which channels part of the accretion power liberated by the magnetorotational instability (MRI) into an ordered toroidal magnetic field. To study dynamo activity, we performed three-dimensional, stratified, isothermal, ideal magnetohydrodynamic shearing box simulations. The strength of the self-sustained toroidal magnetic field depends on the net vertical magnetic flux, which we vary across almost the entire range over which the MRI is linearly unstable. We quantify disc structure and dynamo properties as a function of the initial ratio of mid-plane gas pressure to vertical magnetic field pressure, $\beta_0^{\rm mid} = p_{\rm gas} / p_B$. For $10^5 \geq \beta_0^{\rm mid} \geq 10$ the effective $\alpha$-viscosity parameter scales as a power-law. Dynamo activity persists up to and including $\beta_0^{\rm mid} = 10^2$, at which point the entire vertical column of the disc is magnetic pressure-dominated. Still stronger fields result in a highly inhomogeneous disc structure, with large density fluctuations. We show that the turbulent steady state $\beta^{\rm mid}$ in our simulations is well-matched by the analytic model of Begelman et al. (2015) describing the creation and buoyant escape of toroidal field, while the vertical structure of the disc can be broadly reproduced using this model. Finally, we discuss the implications of our results for observed properties of X-ray binaries.

Concept Design of CFETR Tokamak Machine

China Fusion Engineering Test Reactor (CFETR) is a tokamak reactor; one design option under the consideration of the China National Integration Design Group employs superconducting magnets. The fusion power is at the range of 50-200 MW and the duty cycle (or burning time) was envisioned as 30%-50%. The plasma current will be 10 MA and the major and minor radii are 5.7 and 1.6 m, respectively. The concept engineering design including the magnet system, vacuum vessel (VV) system, and maintenance method has been carried out in the past years. The toroidal magnetic field strength at R0 is 5 T and the maximum flux swing provided by central solenoid winding will be 160 VS. The main design work, including the electromagnetic analysis of the magnet system, has already been carried out. This paper mainly probes into the VV design and optimization based on three types of maintenance ports. Furthermore, the maintenance method, counted as one of the most important design studies, is presented specifically in this paper. It includes the design of the maintenance ports and the remote handling system design, and so on. The next design stage will mainly include mechanical design, conductor stability, different types of divertor system design, and so on.

HIGH-RESOLUTION OBSERVATIONS AND THE PHYSICS OF HIGH-VELOCITY CLOUD A0

The neutral hydrogen structure of high-velocity cloud A0 (at about -180 km/s) has been mapped with a 9.1 arcmin resolution. Gaussian decomposition of the profiles is used to separately map families of components defined by similarities in center velocities and line widths. About 70% of the HI gas is in the form of a narrow, twisted filament whose typical line widths are of order 24 km/s. Many bright features with narrow line widths of order 6 km/s, clouds, are located in and near the filament. A third category with properties between those of the filament and clouds appears in the data. The clouds are not always co-located with the broader line width filament emission as seen projected on the sky. Under the assumption that magnetic fields underlie the presence of the filament, a theorem is developed for its stability in terms of a toroidal magnetic field generated by the flow of gas along field lines. It is suggested that the axial magnetic field strength may be derived from the excess line width of the HI emission over and above that due to kinetic temperature by invoking the role of Alfven waves that create what is in essence a form of magnetic turbulence. At a distance of 200 pc the axial and the derived toroidal magnetic field strengths in the filament are then about 6 microGauss while for the clouds they are about 4 microGauss. The dependence of the derived field strength on distance is discussed.