Poloidal Mode Research Articles

Overview of the ITER Correction Coils Design

The Correction Coils (CC) of the ITER Tokamak are developed to reduce the range of magnetic error fields created by imperfections in the location and geometry of the other coils used to confine, heat, and shape the plasma. The proposed system consists of three sets of 6 coils each, located at the top (TCC), side (SCC) and bottom (BCC) of the Tokamak device and using a NbTi cable-in-conduit superconducting conductor (CICC). Within each set, the coils are connected in pairs to produce a toroidal field to reduce the most troublesome, lower order, poloidal mode number fields (m = 1,2,3) in order to operate below the locked mode threshold. The conductor is designed to operate up to 6 T. The winding uses pancakes of one-in-hand conductor (quadpancakes for SCC, octopancakes for TCC and BCC), thus avoiding internal joints. The winding-pack is enclosed inside a 20 mm thick stainless steel casing. The coils are supported by rigid connections to the Toroidal Field (TF) coils. The structural design of the CC is mainly driven by the allowable fatigue stress levels in the conductor jacket, in the case material and in the glass-polyimide electrical insulation system. The boundary conditions on the CC are imposed by the TF coils deformation and the electromagnetic interactions with the PF coils system. The thermo-hydraulic and electrical performance of the CICC is also addressed.

Neoclassical tearing mode (NTM) magnetic spectrum and magnetic coupling in JET tokamak

An experimental study on the poloidal mode number (m) spectrum produced by a single toroidal mode number (n) neoclassical tearing mode (NTM) in the JET tokamak is presented. Clear evidence of the existence of more than one significant m component is given. The analysis is performed comparing several methods and diagnostics; among the latter we mention high frequency magnetic pick-up coils and an electron cyclotron emission radiometer, which measures detailed electron temperature radial profiles at high time resolution. The two diagnostics are also used together in a cross coherence calculation technique. The issue of the interaction of this multiple m structure with the plasma is addressed as well, with particular attention paid to plasma toroidal rotation and rotation shear, obtained from charge exchange spectroscopy data. This effect has been studied under two different operational plasma scenarios on JET in order to investigate both dependences on plasma parameters and consequences on the scenario itself.

Electromagnetic effects on geodesic acoustic and beta-induced Alfvén eigenmodes

The local kinetic theory of geodesic acoustic modes and beta-induced Alfvén eigenmodes is developed. The local dispersion relations are derived in two opposite limits: and , where k0 = (m − nq)/qR, m and n are poloidal and toroidal mode numbers, and is the electron thermal velocity. It is shown that the nature of the (m ± 1, n) sideband oscillations depends on the radial modes width. The localized modes are mostly electrostatic, while the meso-scale modes of the radial width larger than c/(ωpiq) have a strong electromagnetic component. It is shown that the dispersion relations are remarkably similar provided the radial mode width of the principal (m, n) harmonic is sufficiently small.

Functional Performance Analysis and Optimization for the High-Frequency Magnetic Diagnostic System in ITER — I: Overview of the Results

The measurement performance of the baseline system design for the ITER high-frequency magnetic diagnostic has been analyzed using an algorithm based on the sparse representation of signals. This algorithm, derived from the SparSpec code [S. Bourguignon et al., Astron. Astrophys., 462, 379 (2007)] has previously been extensively benchmarked on real and simulated JET data. To optimize the system design of the ITER high-frequency magnetic diagnostic, we attempt to reduce false detection of the modes and to minimize the sensitivity of the measurement with respect to noise in the data, loss of faulty sensors, and the displacement of the sensors. Using this approach, the original layout design for the ITER high-frequency magnetic diagnostic system, which uses 168 sensors, is found to be inadequate to meet the ITER measurement requirements.Based on this analysis, and taking into account the guidelines for the risk mitigation strategies that are given in the ITER management plan, various attempts at optimization of this diagnostic system have been performed. A revised proposal for its implementation has been developed, which now meets the ITER requirements for measurement performance and risk management. For toroidal mode number detection, this implementation includes two arrays of 50 to 55 sensors and two arrays of 25 to 35 unevenly spaced sensors each on the low-field side and two arrays of 25 to 35 unevenly spaced sensors each on the high-field side. For poloidal mode number detection, we propose six arrays of 25 to 40 sensors each located in nonequidistant machine sectors, not covering the divertor region and, possibly, poloidal angles in the range 75 < |θ|(deg) < 105, as this region is the most sensitive to the details of the magnetic equilibrium. In this paper we present the general summary results of this work, for which more details and an overview of our test calculations are reported in the companion paper.

Alfvén node-free vibrations of white dwarf in the model of solid star with toroidal magnetic field

In the context of the white dwarf asteroseismology, we investigate vibrational properties of a non-convective solid star with an axisymmetric purely toroidal intrinsic magnetic field of two different shapes. Focus is laid on regime of node-free global Lorentz-force-driven vibrations about symmetry axis at which material displacements have one and the same form as those for nodeless spheroidal and torsional vibrations restored by Hooke's force of elastic shear stresses. Particular attention is given to the even-parity poloidal Alfven modes whose frequency spectra are computed in analytic form showing how the purely toroidal magnetic fields completely buried beneath the star surface can manifest itself in seismic vibrations of non-magnetic white dwarfs. The obtained spectral formulae are discussed in juxtaposition with those for Alfven modes in the solid star model with the poloidal, homogeneous internal and dipolar external, magnetic field whose inferences are relevant to Alfven vibrations in magnetic white dwarfs.

Cluster observations of simultaneous resonant interactions of ULF waves with energetic electrons and thermal ion species in the inner magnetosphere

In this study, we report in situ observations on the simultaneous periodic modulations in the drifting energetic electrons (∼100 keV) and in the bouncing thermal ion species (O+ at ∼4.5 keV and H+ at ∼280 eV) with the same frequency of 3.3 mHz during the storm recovery phase on 21 October 2001. The Cluster fleet was traveling outbound in the inner magnetosphere from the Southern to Northern Hemisphere on the morning sector (0900 MLT). The ultra‐low‐frequency (ULF) waves from the magnetic field and electric field measurements show a mixture of several dominant wave components in the transverse modes. The poloidal mode at the modulation frequency of 3.3 mHz appears to be a standing wave with an odd harmonic, although other wave components reveal propagating features. The radial extent of this standing wave is around 0.58 RE. The oscillation periods of the energetic electron fluxes (∼100 keV) and the thermal O+ (∼4.5 keV) and H+ (∼280 eV) fluxes are observed the same as the period of the poloidal standing wave, indicating that the energetic electrons and the thermal ion species are modulating by the same wave. Further, we suggest the simultaneous drift resonances of the energetic electrons around 94 keV and the bounce resonances of the thermal O+ around 4.5 keV and H+ around 280 eV with the same poloidal standing wave. In addition, the electron energy spectra variations reveal the accelerations of the electrons in the energy range of 50∼110 keV, which are most likely due to the drift resonances. This is the first study to show both energetic particles (radiation belt population, ∼ a few hundred keV) and thermal ions (background plasma population, ∼ a few keV) can be affected by the same ULF wave simultaneously. Furthermore, this study implies that the superdense ionospheric origin O+ ions in the inner magnetosphere during storm times can modify the local field line eigenfrequency and result in the energetic electron accelerations by the ULF waves in the deep region of the radiation belt.

Noble magnetic barriers in the ASDEX UG tokamak

The second-order perturbation method of creating invariant tori inside chaos in Hamiltonian systems (Ali, H.; Punjabi, A. Plasma Phys. Contr. F. 2007, 49, 1565–1582) is applied to the axially symmetric divertor experiment upgrade (ASDEX UG) tokamak to build noble irrational magnetic barriers inside chaos created by resonant magnetic perturbations (m, n)=(3, 2)+(4, 3), with m and n the poloidal and toroidal mode numbers of the Fourier expansion of the magnetic perturbation. The radial dependence of the Fourier modes is ignored. The modes are considered to be locked and have the same amplitude δ. A symplectic mathematical mapping in magnetic coordinates is used to integrate magnetic field line trajectories in the ASDEX UG. Tori with noble irrational rotational transform are the last ones to be destroyed by perturbation in Hamiltonian systems. For this reason, noble irrational magnetic barriers are built inside chaos, and the strongest noble irrational barrier is identified. Three candidate locations for the strongest noble barrier in ASDEX UG are selected. All three candidate locations are chosen to be roughly midway between the resonant rational surfaces ψ32 and ψ43. ψ is the magnetic coordinate of the flux surface. The three candidate surfaces are the noble irrational surfaces close to the surface with q value that is a mediant of q=3/2 and 4/3, q value of the physical midpoint of the two resonant surfaces, and the q value of the surface where the islands of the two perturbing modes just overlap. These q values of the candidate surfaces are denoted by q MED, q MID, and q OVERLAP. The strongest noble barrier close to q MED has the continued fraction representation (CFR) [1;2,2,1∞] and exists for δ≤2.6599×10−4; the strongest noble barrier close to q MID has CFR [1;2,2,2,1∞] and exists for δ≤4.6311×10−4; and the strongest noble barrier close to q OVERLAP has CFR [1;2,2,6,2,1∞] and exists for δ≤1.367770×10−4. From these results, the strongest noble barrier is found to be close to the surface that is located physically exactly in the middle of the two resonant surfaces.

Alfvén continuum deformation by kinetic geodesic effect in rotating tokamak plasmas

Using a quasitoroidal set of coordinates with coaxial circular magnetic surfaces, Vlasov equation is solved for collisionless plasmas in drift approach and a perpendicular dielectric tensor is found for large aspect ratio tokamaks in a low frequency band. Taking into account plasma rotation and charge separation parallel electric field, it is found that an ion geodesic effect deform Alfvén wave continuum producing continuum minimum at the rational magnetic surfaces, which depends on the plasma rotation and poloidal mode numbers. In kinetic approach, the ion thermal motion defines the geodesic effect but the mode frequency also depends on electron temperature. A geodesic ion Alfvén mode predicted below the continuum minimum has a small Landau damping in plasmas with Maxwell distribution but the plasma rotation may drive instability.

Magnetic Components of Geodesic Acoustic Modes in Plasmas with Anisotropic Ion Distribution

The existence of magnetic components in geodesic acoustic modes is investigated for a weakly anisotropic tokamak plasma with dual-temperature Maxwellian distributions for ions. An m = 1 perpendicular magnetic perturbation is discovered to be proportional to the relative difference between the two temperatures in addition to an m = 2 perpendicular magnetic perturbation which always exists due to the m = 2 parallel return current, with m the poloidal mode number. The dispersion relation and the mode frequency are also modified by the anisotropic distribution.

Effect of Magnetic Island Associated with Neoclassical Tearing Modes on Plasma Rotation in JT-60U

This paper describes the dependence of the rotation frequency of an m/n = 2/1 neoclassical tearing mode (NTM) on its magnetic island width in JT-60U (m and n are the poloidal and toroidal mode numbers, respectively). Throughout the experiments, the island width is actively controlled by changing the location of the electron cyclotron current drive (ECCD), based on the fact that aligned ECCD and misaligned ECCD make the NTM islands shrink and grow, respectively. The NTM frequency was found to gradually decrease with the increasing island width. While the frequency is 5.5 kHz for zero island width, it is 3 kHz for the full island width of about 15% of the plasma minor radius. Also, the mode frequency suddenly decreases (typically by 80%) shortly after the misaligned ECCD, during which the increment in the island width is only less than 10%. A sudden increase in the mode frequency is observed shortly after the ECCD turnoff, which is nearly the reverse process of the sudden decrease, but with a hysteresis in the island width at which downward and upward frequency changes occur. The downward frequency change occurs when the frequency decreases to about half of that without the NTM.

Gyrokinetic Vlasov Code Including Full Three-dimensional Geometry of Experiments

A new gyrokinetic Vlasov simulation code, GKV-X, is developed for investigating the turbulent transport in magnetic confinement devices with non-axisymmetric configurations. Effects of the magnetic surface shapes in three-dimensional equilibrium obtained from the VMEC code are accurately incorporated. Linear simulations of ion temperature gradient (ITG) instabilities and zonal flows in the Large Helical Device (LHD) [O. Motojima, N. Oyabu, A. Komori et al., Nucl. Fusion 43, 1674 (2003)] configuration are carried out by the GKV-X code as benchmark tests against the GKV code [T.-H. Watanabe and H. Sugama, Nucl. Fusion 46, 24 (2006)]. For high poloidal wavenumbers, the frequency, growth rate, and mode structure of the ITG instability are influenced by the VMEC geometrical data such as the metric tensor components of the Boozer coordinates, while the difference between the zonal flow responses obtained by the GKV and GKV-X codes is found to be small in the core LHD region.

Nonlinear Mode Couplings in a Cylindrical Magnetized Plasma

Nonlinear mode couplings in plasma turbulence generate mesoscale global structures, such as zonal flows and streamers. A streamer is a poloidally localized structure that is radially elongated. In the Large Mirror Device-Upgrade, a streamer structure was observed in the ion saturation-current fluctuation measured with a 64channel poloidal Langmuir probe array. The bunching of waves was poloidally localized and rotated slowly in the ion diamagnetic direction. The frequency and poloidal mode number of its envelope corresponded to one particular mode, which was strongly coupled with many other modes. By calculating the radial biphase profile of three pronounced modes, including the particular mode, the streamer structure was confirmed to be radially elongated.

Relativistic Quasilinear Description of Three-Dimensional Diffusion

Quasilinear theory is developed by using canonical variables for a relativistic plasma. It is self-consistent, including momentum, pitch angle, and spatial diffusions. By assuming the wave field as a superposition of known toroidal and poloidal Fourier modes, the quasilinear diffusion coefficients are written in a form which can be directly evaluated using the output of a spectral full-wave solver of Maxwell equations in toroidal plasmas. The formalism is special for tokamas and, therefore, simple and suitable for simulations of cyclotron heating, current drive, and radio-frequency wave-induced radial transport in ITER.

Electric and magnetic field observations of Pc4 and Pc5 pulsations in the inner magnetosphere: A statistical study

Ultralow frequency (ULF) waves in the Pc4 and Pc5 bands are ubiquitous in the inner magnetosphere and have significant influence on energetic particle transport. Investigating the source and characteristics of ULF waves also helps us better understand the interaction processes between the solar wind and the magnetosphere. However, owing to the limitation in instrumentation and spatial coverage, the distribution of ULF waves in local time and L shell in the inner magnetosphere has not been completely studied. The recent Time History of Events and Macroscale Interactions During Substorms (THEMIS) mission provides unique opportunities to investigate the spatial distribution of ULF pulsations across different L shells with full local time coverage in the inner magnetosphere during solar minimum, with both electric and magnetic field measurements. Pc4 and Pc5 pulsations in the electric field observations are identified throughout 13 months of measurements, covering 24 h in local time. The pulsations are characterized as either toroidal or poloidal (including compressional) mode, depending on the polarization of the electric field. Subsequently, the pulsations' occurrence rate and wave power distributions in radial distance and local time are recorded. While the distributions of both Pc4 and Pc5 events vary greatly with radial distance and local time, Pc4 events are more frequently observed in the inner region around 5–6 RE and Pc5 events are more frequently observed in the outer region around 7–9 RE, which suggests that the field line resonance is an important source of the ULF waves. In the flank regions, the wave power is dominated by the toroidal mode, likely associated with the Kelvin‐Helmholtz (KH) instability. In the noon sector, the Pc5 ULF wave power is dominated by the poloidal mode, likely associated with the solar wind dynamic pressure disturbance. The KH instability plays an important role, suggested by our observations, during the solar minimum when the solar wind dynamic pressure is relatively weak. We also find that the contributions to the Pc5 ULF wave power from the external sources are larger than the contributions from the internal sources. These statistical results are important in characterizing Pc4 and Pc5 waves and also important for any efforts to model the transport of energetic particles in the magnetosphere.

On the electromagnetic fields produced by marine frequency domain controlled sources

SUMMARY In recent years, marine controlled source electromagnetics (CSEM) has found increasing use in hydrocarbon exploration due to its ability to detect thin resistive zones beneath the seafloor. Although it must be recognized that the quantitative interpretation of marine CSEM data over petroleum-bearing formations will typically require 2-D surveys and 2-D or 3-D modelling, the use of the 1-D approximation is useful under some circumstances and provides considerable insight into the physics of marine CSEM. It is the purpose of this paper to thoroughly explore the 1-D solutions for all four fundamental source types—vertical and horizontal, electric and magnetic dipole (VED, HED, VMD and HMD)—using a set of canonical reservoir models that encompass brine to weak to strong hydrocarbon types. The paper introduces the formalism to solve the Maxwell equations for a 1-D structure in terms of independent and unique toroidal and poloidal magnetic modes that circumscribe the salient diffusion physics. Green’s functions for the two modes from which solutions for arbitrary source current distributions can be constructed are derived and used to obtain the electromagnetic (EM) fields produced by finite VED, HED, VMD and HMD sources overlying an arbitrary 1-D electrical structure. Field behaviour is analysed using the Poynting vector that represents the time-averaged flow of energy through the structure and a polarization ellipse decomposition of the triaxial seafloor EM field that is a complete field description. The behaviour of the two EM modes using unimodal VED and VMD sources is presented. The paper closes by extending these results to the bimodal HED and HMD sources.

Density fluctuation of geodesic acoustic mode on the HL-2A tokamak

The density fluctuations of the geodesic acoustic mode (GAM) have been observed in Ohmic deuterium plasma discharges with a combination of rake-like and three-step Langmuir probe arrays on the HL-2A tokamak. The probe arrays with poloidal and toroidal separations of 36 and 1330 mm are applied to measure the spectral property and intermittency of the GAM density fluctuations. The poloidal and toroidal mode numbers of the fluctuations are simultaneously measured for the first time. The measured fluctuation amplitude is consistent with the theoretical prediction. High coherence and near zero phase shift of the GAM density fluctuations separated toroidally by 37.5° at the same magnetic flux surface was first observed, indicating the symmetric structure of the GAM in the toroidal direction. The peak time delays of the cross-correlation function of the fluctuations above and below the midplane suggest the expected sin θ dependence. The nonlinear three wave coupling between the GAM and the ambient turbulence is shown to be a plausible mechanism for the generation of the GAM density fluctuations. The significant coherence and the corresponding fixed phase shift (∼π) between the original data and the envelope of the high frequency ambient turbulence provide the experimental evidence for the envelope modulation. The GAM amplitude is out of phase with the particle flux. Most of the intermittent frequencies for particle flux are close to the GAM frequency.

Low-frequency magnetohydrodynamics and geodesic acoustic modes in toroidally rotating tokamak plasmas

This paper analyses low-frequency magnetohydrodynamic (MHD) modes, especially the geodesic acoustic modes (GAMs), in toroidal plasmas with large aspect ratio and circular cross section, including the effects of toroidal plasma rotation. A system of equations describing MHD modes with frequency of the order of the sound frequency in such plasmas is derived from the Frieman–Rotenberg equation, using a technique where the plasma perturbation \U0001d6cf and the perturbed magnetic field Q are expanded separately in the inverse aspect ratio ε = r/R, where r and R denote the minor and major radii of the plasma torus, respectively. The large-scale, ideal MHD properties of the GAM induced by toroidal rotation (Wahlberg 2008 Phys. Rev. Lett. 101 115003) are thereafter analysed in more detail employing this system of equations. It is shown that both the axisymmetric GAMs existing in rotating plasmas are localized on a specific magnetic surface only to leading order in ε, and that a ‘halo’ consisting of finite components of both \U0001d6cf and Q with dominant poloidal mode numbers m = ±2 appears outside this magnetic surface to higher orders in ε.

Generic Mechanism of Microturbulence Suppression by Vortex Flows

The interaction between two-dimensional vortex flows and microturbulence is studied numerically using gyrofluid simulations. It is shown that, qualitatively different from usual mean flows, vortex flows can dramatically suppress microturbulence even with weak flow shear. A generic suppression mechanism is identified as the multiplied effect of both radial and poloidal mode couplings, which induce the formation of a new global mode. Furthermore, an oscillatory zonal flow is found to form through interaction between the vortex flows and microturbulence.

Observations of abrupt changes in the fluctuation spectrum on LMD-U

A transition of the fluctuation spectrum of ion saturation current is observed in linear magnetized plasmas. A power spectrum with regular peaks and a broadband spectrum appear alternately during a discharge. The temporal order of changes in the modes is investigated at the transition. The low poloidal mode number components change before the higher modes begin to change. The delay times of change between modes are determined.

Stochastic layer scaling in the two-wire model for divertor tokamaks

AbstractThe question of magnetic field structure in the vicinity of the separatrix in divertor tokamaks is studied. The authors have investigated this problem earlier in a series of papers, using various mathematical techniques. In the present paper, the two-wire model (TWM) [Reiman, A. 1996 Phys. Plasmas3, 906] is considered. It is noted that, in the TWM, it is useful to consider an extra equation expressing magnetic flux conservation. This equation does not add any more information to the TWM, since the equation is derived from the TWM. This equation is useful for controlling the step size in the numerical integration of the TWM equations. The TWM with the extra equation is called the flux-preserving TWM. Nevertheless, the technique is apparently still plagued by numerical inaccuracies when the perturbation level is low, resulting in an incorrect scaling of the stochastic layer width. The stochastic broadening of the separatrix in the flux-preserving TWM is compared with that in the low mn (poloidal mode number m and toroidal mode number n) map (LMN) [Ali, H., Punjabi, A., Boozer, A. and Evans, T. 2004 Phys. Plasmas11, 1908]. The flux-preserving TWM and LMN both give Boozer–Rechester 0.5 power scaling of the stochastic layer width with the amplitude of magnetic perturbation when the perturbation is sufficiently large [Boozer, A. and Rechester, A. 1978, Phys. Fluids21, 682]. The flux-preserving TWM gives a larger stochastic layer width when the perturbation is low, while the LMN gives correct scaling in the low perturbation region. Area-preserving maps such as the LMN respect the Hamiltonian structure of field line trajectories, and have the added advantage of computational efficiency. Also, for a $1\frac12$ degree of freedom Hamiltonian system such as field lines, maps do not give Arnold diffusion.