Poloidal Mode Research Articles

Determination of MHD mode structures using soft x-ray diagnostics in TCV

A forward modeling technique is developed for determining the characteristic features of observed MHD modes from the line-of-sight data of the soft x-ray (SXR) diagnostics with 64 vertical lines-of-sight in theTokamak à Configuration Variable tokamak. Using diagnostics with excellent spatial resolution, this technique is shown to evaluate the poloidal mode numbers m, radial location and ballooning character of the MHD modes. In the first stage, the poloidal mode structures are modeled by the radially localized Gaussian-shaped emission regions rotating along the magnetic flux surfaces. In the second stage, the space structures of observed 95–100 kHz toroidal Alfvén eigenmodes (TAEs) are investigated numerically using HELENA, CSCAS and MISHKA codes. The calculated TAE eigenfunctions are then used in our forward modeling similarly to the approach of contrast imaging diagnostics (Edlund et al 2009 Phys. Rev. Lett. 102 165003) and SXR diagnostics (Piovesan et al 2008 Nucl. Fusion 48 065001). A ballooning structure of the observed n= 1 TAE mode can be analyzed more easily due to the low poloidal mode number m in contrast to the high-m modes analyzed by a similar SXR technique in the W7-X stellarator (Dreval et al 2021 Plasma Phys. Control. Fusion 63 065006).

Observations of mode frequency increase and the appearance of ITB during the m/n = 1/1 kink mode in EAST high electron temperature long pulse operation

A new long-pulse high electron temperature () regime has been achieved on experimental advanced superconducting tokamak by pure radio frequency heating. In this new scenario, there are mainly two confinement states involving two magneto-hydrodynamic (MHD) modes, one of which is identified as m/n = 1/1 kink mode (where m and n are the poloidal and toroidal mode numbers, respectively). The frequency evolution of the kink mode is investigated through the three-dimensional, toroidal, and nonlinear Hall-MHD code CLT. We firstly find that the frequency of the m/n = 1/1 kink mode significantly increases during each sawtooth crash and then confirmed it through the experimental data. The simulation results indicate that the increase of the mode frequency is mainly due to the significant increase of the electron diamagnetic frequency nearby the reconnection region. We have also observed the internal transport barrier (ITB) during the m/n = 1/1 kink mode. To further investigate this m/n = 1/1 kink mode in this new regime, the multi-scale interactions between the m/n = 1/1 kink mode and turbulence are discussed.

Electron gases in toroidal shells: Mode coupling and state functions

Eigenvalues and wave functions describing free electron gases in toroidal shells are determined using a basis set expansion natural to the system geometry. Couplings between azimuthal and poloidal modes are found to be appreciable at lower values of ${m_\phi}$, modifying single particle density distributions within the shells. Thermodynamic state functions are calculated and contrasted with those of a solid toroidal volume.

Mechanism of low-temperature helical streamer discharge driven by pulsed electromagnetic field

Under the condition of specific pulsed discharge parameters, the discharge mode conversion of the low-temperature plasma jet discharge channel that originally propagates along a straight line will occur, forming a three-dimensional helical plasma channel. Unlike the traditional helical wave discharge, there are no factors such as an external constant magnetic field that destroys the poloidal symmetry of the dielectric tube, and the chiral direction of the helical streamer will change with the discharge parameters. In order to understand in depth the electromagnetic mechanism of the helical structure in the plasma jet, and the source and influencing factors of the poloidal electric field that leads to the helical shape and determines the chirality in this new type of discharge, we analyze the complex characteristics and electromagnetic mechanism of the helical streamer, such as the chiral direction, pitch, branching, by establishing a self-consistent plasma theoretical model. It is found that the phase of the poloidal wave mode has an effect on the chiral selection of the helical streamer, that the electron density has an influence on the pitch of the streamer, and that the repetition frequency has an effect on the bifurcation point. The above discharge characteristics and their influencing factors are of scientific significance in exploring the interaction mechanism of electromagnetic wave and plasma, and also in providing experimental and theoretical support for the chiral application of low-temperature plasma.

Trapped particle resonance effects on the NTM driven losses of energetic particles

The m = 2, n = 1 (where m and n are the poloidal and toroidal mode numbers, respectively) neoclassical tearing mode (NTM) has been proposed as a candidate to explain the larger than expected losses of high energy ions produced by neutral beam injection observed in several experiments. Although the numerical simulations performed so far to study the effect of NTMs on energetic ions have reproduced several features observed in experiments, the agreement is not completely satisfactory. In particular, it has been difficult to reproduce the total amount of losses, which are affected by the details of the perturbation in the edge region. In this work, we study the effect of NTMs on the confinement of energetic ions produced by NBI injection using FOCUS, a full orbit code that runs in graphical processing units. This allows us to follow the evolution of a large number of ions with modest resources. A reconstruction technique that includes the experimental information available is employed to calculate the perturbed magnetic field. The main result of this study is that when the frequency of the NTM matches the toroidal precession frequency ω tp of the trapped ions (, where E is the energy of the ion), the losses increase significantly.

Simulation of electric field response of horizontal circular electric half wave dipole antenna for seabed logging

Seabed logging (SBL) is a direct and remote application of controlled source electromagnetic (CSEM) method to detect hydrocarbon resources beneath the seafloor in offshore conditions. In this method, electromagnetic waves are used to detect the resistivity contrast between various sediment layers. The current source of electromagnetic waves is a horizontal electric dipole (HED) antenna. The antenna design represents a challenge in shallow waters (less than500 m seawater depth) due to the presence of airwaves that lead to a low signal-to-noise ratio, hence hindering the detection of a hydrocarbon reservoir. A horizontal circular electric half-wave dipole will be used in this work as the source of electromagnetic waves. The numerical solution for the electric field response will be developed based on solving the Maxwell equations in two modes: the poloidal and toroidal modes. Simulation results have shown that the new antenna is able to detect the presence of deep hydrocarbon reservoirs (up to 5000 m) in shallow-water environment. Comparison of the average percentage difference in delineation between the circular and the HED was carried out. The new antenna results in 61 % delineation compared to 15 % for the HED at 5000 m hydrocarbon depth and 200 m seawater depth, indicating the ability of the antenna to disperse the airwaves. The results also show that the airwaves are significantly reduced from nearly 15000 m (for the HED) to 10000 m offset for the proposed antenna, hence increasing the signal-to-noise ratio. These results seem to indicate the potential for the new antenna to be used as an EM source for SBL in shallow-water environment.

Neutron-yield reduction in sawtooth crashes from n = 2 resonant magnetic perturbations in EAST

A significant reduction in neutron yield in the plasma core has been observed in EAST neutral beam injection into plasmas with a low-edge safe factor of q95=3.5 and a n = 2 resonant magnetic perturbation (RMP) during a sawtooth crash. Harmonics of the m/n = 1/1 mode (m and n being the poloidal and toroidal mode numbers) develop simultaneously. A sawtooth crash is triggered when the current of the RMP exceeds a critical value; saturated fishbone phase occurs with small RMP currents. Soft x-ray (SXR) tomographic patterns obtained during sawtooth crashes have annular hot-ring shapes outside the q = 1 surface that are similar to those of double tearing modes triggered by off-axis sawtooth crashes in TFTR reversed magnetic shear plasma. M3D nonlinear simulations confirmed the initial penetration of the n = 2 RMP in the plasma core and further demonstrated a complete sawtooth crash with the appearance of a right annular hot ring near the q = 1 surface. Reconstruction of the trajectory of SXR signals before the crash shows chaotic behavior. Moreover, a high-frequency mode was seen to appear just before the sawtooth crash, accompanied by an edge geodesic acoustic mode. This edge mode is free in the saturated fishbone phase. The role of high-frequency mode in the sawtooth crash remains unclear.

Destabilization of low-frequency modes (LFMs) driven by a thermal pressure gradient in EAST plasmas with q min ⩽ 2

Mode structures and excitation conditions for the low-frequency modes (LFMs) have been investigated in experimental advanced superconducting tokamak (EAST) plasmas with q min ⩽ 2. Two different stages/categories of the LFM instabilities are observed during the oscillation of annular/central collapse events: (I) the upward sweeping frequency of LFMs; (II) the upward frequency jumpsof LFMs. The annular/central events are triggered by the m/n = 2/1 double tearing modes with different q-profiles, while the LFMs are characterized by higher mode numbers m/n = 4/2, 6/3, …, where m and n are the poloidal and toroidal mode numbers, respectively. The maximum radial coverage of the LFMs is located in the annular region of 1.97 2.07 m with the normalized minor radius 0.2 0.4, while the higher-frequency (or upward sweeping frequency) branch is more localized to the radial position of 2 2.02 m (q min). The frequency characteristics of upward sweeps or upward jumps of the LFMs are mainly attributed to the change in the q-profile, e.g. the upward sweeping frequency in stage I is caused by q min decreasing. Accordingly, the linear wave properties of LFMs in EAST with weak/reversed magnetic shear are studied numerically and analytically based on a general fishbone-like dispersion relation. Without considering the contribution of energetic ions, it is shown that the LFM with Alfvénic polarization is an MHD-unstable kinetic ballooning mode with frequency of the order of the ion diamagnetic drift frequency. Several important factors for the excitation of LFM instability are analyzed: (1) the role of energetic ions is unimportant, and the LFMs can be excited under the two conditions of with/without energetic ions; (2) the higher τ = T e/T i with larger η i = L ni /L Ti are required, namely the normalized pressure gradient α ∝ (1 + τ)(1 + η i) should be large enough to overcome the stability effect of finite field line bending; (3) the weak/reversed shear q-profile with q min ⩽ 2 and suitable S ≡ (r/q)(q″)1/2 are required.

Distribution of ULF Wave Power in Magnetic Latitude and Local Time Using THEMIS and Arase Measurements

AbstractUltra‐low‐frequency (ULF) waves are known to radially diffuse hundreds‐keV to few‐MeV electrons in the magnetosphere, as the range of drift frequencies of such electrons overlaps with the frequencies of the waves, leading to resonant interactions. The theoretical framework for this process is described by analytic expressions of the resonant interactions between electrons and toroidal and poloidal ULF wave modes in a background magnetic field. However, most expressions estimate the radial diffusion rates based on estimates of the power of ULF waves that are obtained either from spacecraft close to the equatorial plane or from the ground. In this study, using multiyear measurements from the THEMIS and Arase missions, we present a statistical analysis of the distribution of ULF wave power in magnetic latitude and local time and show that the wave power of the radial and azimuthal components of the magnetic field increases away from the magnetic equator. Our result could have significant implications for the radial diffusion rates as currently estimated.

Observation and Simulation of n = 1 Reversed Shear Alfvén Eigenmode on the HL-2A Tokamak

A branch of high-frequency Alfvénic modes is observed on the HL-2A tokamak. The electromagnetic mode can be driven unstably in the plasma with an off-axis neutral beam heating. Its mode frequency keeps almost unchanged or presents a slow-sweeping behavior, depending on the detail current evolution. The poloidal and toroidal mode numbers are m/n = 1/1. The mode has a quite short duration (≤20 ms) and usually appears 5–10 ms after the neutral beam being injected into the plasma. Hybrid simulations based on M3D-K have also been carried out. The result suggests that co-passing energetic particles are responsible for the mode excitation. The simulated mode structures are localized nearby location of minimum safety factor (q min) and agree with the structures obtained through tomography of soft x-ray arrays. Further, the modes are localized in the continuum gap and their frequencies increase with variation of q min in a wide range. Last but not least, the characteristic of unchanged frequency on experiment is also reproduced by the nonlinear simulation with a fixed safety factor. All those evidences indicate that the n = 1 high-frequency mode may belong to a reversed shear Alfvén eigenmode.

Development of a soft x-ray (SXR) array diagnostic system on versatile experiment spherical torus (VEST).

A new soft x-ray (SXR) array diagnostic system has been developed on versatile experiment spherical torus (VEST) for measurements of 2D SXR emissivity profile and identification of poloidal mode structure. Through tomographic inversion techniques, 2D SXR emissivity profile can be acquired from the line-integrated SXR data, which enables the visualization of mode structure of plasma instability, such as the magnetohydrodynamics mode. The SXR array diagnostic system consists of two 20-channel arrays positioned at the middle and the top on the same poloidal plane for horizontal and vertical lines of sight, respectively. Each array of the diagnostic system uses absolute extreme ultraviolet photodiode array as the detector. To apply appropriate filters (up to four) for different energy regimes without breaking the vacuum, a filter wheel and its rotatable vacuum feed-through are installed behind the pinhole. SXR data are acquired with a digitizer at the sampling rate of up to 125MHz. Finally, we discuss initial measurement data obtained from Ohmic plasma in VEST.

Simulations of energetic particle driven instabilities in CFQS

A nonlinear simulation of the energetic particle driven instabilities in the Chinese First Quasi-axisymmetric Stellarator (CFQS) has been conducted for the first time. MEGA, a hybrid simulation code for energetic particles interacting with a magneto-hydrodynamic fluid, was used in the present work. Both the m/n = 3/1 energetic-particle-mode (EPM) like mode and the m/n = 5/2 toroidal Alfvén eigenmode (TAE) were found, where m is the poloidal mode number and n is the toroidal mode number. Four important results were obtained as follows. First, the instability in the CFQS in three-dimensional form was shown for the first time. Second, strong toroidal mode coupling was found for the spatial profiles, and it is consistent with the theoretical prediction. Third, the resonant condition caused by the absence of axial symmetry in CFQS was demonstrated for the first time. The general resonant condition is f mode = Nf ϕ − Lf θ , where f mode, f ϕ , and f θ are mode frequency, particle toroidal transit frequency, and particle poloidal transit frequency, respectively; N and L are arbitrary integers, represent toroidal and poloidal resonance numbers. For EPM-like mode, the dominant and subdominant resonant conditions are f mode = 3f ϕ − 7f θ and f mode = f ϕ − f θ , respectively. For TAE, the dominant and subdominant resonant conditions are f mode = 4f ϕ − 9f θ and f mode = 2f ϕ − 3f θ , respectively. On the one hand, the toroidal resonance numbers are different from the toroidal mode numbers by 2. This indicates that the two-fold rotational symmetry affects the resonance condition. On the other hand, the subdominant resonances satisfy N = n, which is expected for the axisymmetric plasmas and most of the toroidal plasmas including stellarators. Fourth, the nonlinear frequency chirpings in CFQS were demonstrated for the first time. Hole and clump structures were formed in the pitch angle and energy phase space, and the particles comprising the hole and clump were kept resonant with the modes during the mode frequencies chirping.

Gyrokinetic investigations of the electromagnetic geodesic acoustic mode

The linear characteristics of the electromagnetic geodesic acoustic mode (GAM) are investigated numerically with the gyrokinetic code GEM. The results indicate that the electromagnetic effect has little influence on the frequency and damping rate of the GAM. The results also show that both and poloidal magnetic components of the GAM exist, and the magnetic component has comparable sine and cosine components, while the magnetic component is dominated by the sine component, where is the poloidal mode number. In addition, the amplitudes of various magnetic components increase with respect to the ratio of plasma pressure to magnetic pressure and safety factor . Most importantly, the amplitude of the magnetic component is comparable to, or even slightly larger than, that of the magnetic component. It is also found that the trapped electron effect may be important for the magnetic components. Furthermore, the various magnetic components are compared with the previous analytical results and some discussions are given.

Observation of neoclassical tearing-mode excitation in EAST low-β p H-mode plasmas using a gas electron multiplier-based camera

The excitation of an initially stable neoclassical tearing mode (NTM) is investigated in Experimental Advanced Superconducting Tokamak (EAST) low-β p H-mode plasmas (β p is defined as the ratio of the thermal pressure to the poloidal magnetic pressure). Using similar plasma parameters, n = 1 resonant magnetic perturbation (RMP) cannot always successfully excite the m/n = 2/1 NTM with the same RMP coil current setup (n and m are the toroidal and poloidal mode numbers, respectively). Data from a gas electron multiplier camera shows that NTM destabilization is related to RMP-induced crashes at the q = 1 resonant surface during the RMP ramp-up phase. The second RMP-induced crash amplitude decays exponentially as β p increases. There is a critical value above which the crash amplitude (or seed island width) is too small (below the critical island width) to trigger an NTM. Observation and analysis indicate that the m/n = 2/1 NTM is not forcibly driven by the n = 1 RMP (such as the m/n = 2/1 component), but is probably due to electron heat transport between the q = 1 and the q = 2 resonant surfaces. This paper describes experimental observations of NTM excitation which also have implications for further investigations of NTM locking and disruptions.

Causal impact of tearing mode on zonal flows and local turbulence in the edge of HL-2A plasmas

Direct causality analysis of the multi-scale interactions among macro-scale tearing mode (TM), meso-scale geodesic acoustic mode (GAM) and small-scale turbulence in the edge plasma of the HL-2A tokamak utilizing transfer entropy (TE) method is reported. Experimental results have demonstrated that the (m/n) = (2/1) (with m and n being the poloidal and toroidal mode numbers, respectively) TM modulates the turbulence with the frequency range of f = 50–150 kHz and the GAM mainly modulates that with higher frequencies. The TM has both amplitude and phase modulation on turbulence energy while the GAM has only amplitude regulation effect. TE analyses have shown that both TM and GAM will modulate the turbulence energy during which the impact of the former is of about an order magnitude larger than the latter, whereas the causal effect of TM on particle transport is about twice that of the GAM, which is due to the different causal effects on density and electric field fluctuations caused by TM and GAM, respectively. It is suggested that the magnetic fluctuation strongly modulates the Reynolds stress which serves as a mediator, leading to a cooperative interaction between TM and GAM in the edge of tokamak plasmas.

Effects of plasma boundary shape on the βN threshold in the suppression of tearing mode in toroidal tokamak plasmas with reversed magnetic shear

The toroidal magnetohydrodynamic code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) is adopted to investigate the plasma boundary shape effect on the threshold ( is the normalized plasma pressure) reported in (Liu et al 2017 Plasma Phys. Control. Fusion 59 065009) in reversed magnetic shear toroidal tokamak plasmas under different separations between the two rational surfaces of the same helicity. The boundary shape effect is modeled via elongation and triangularity . Here, the study focuses on cases ( is the toroidal mode number). In the small regime, the critical value increases as increases (without triangularity), and barely changes with triangularity (at small elongation). On the other hand, at large elongation (e.g. ), the critical value of decreases with increasing . The change in the may be due to a change in the coupling strength between different poloidal harmonics, due to the fact that, besides toroidal coupling ( is the poloidal mode number), a large elongation (or triangularity ) can result in the () equilibrium component and thus enhances the coupling between the and (). In the large regime, with increasing (without triangularity), first slightly increases followed by a quick reduction. Moreover, as increases, the critical value decreases at small elongation, and first increases followed by a decrease at large elongation (e.g. ). Besides the change in the coupling strength between different poloidal harmonics, the change in the in the large regime is also related to the mode transition. The corresponding physics mechanisms underlying the shift of due to the plasma boundary shape are all discussed in detail.

Behavior of multiple modes before and during minor disruption with the external resonant magnetic perturbations on J-TEXT tokamak

The behavior of multiple modes before and during minor disruption with the external resonant magnetic perturbations (RMPs) has been studied on a J-TEXT tokamak. The main component of RMPs is m/n = 2/1, where m and n are the numbers of the poloidal and toroidal modes, respectively. During the mode-locking caused by RMPs, it is found that before a minor or a major disruption (if there is no minor disruption), strong oscillations in both electron temperature and density occur if the edge safety factor q a > 3. The analysis shows that the oscillations are caused by the m/n = 3/1 mode. In addition, using the ECE, Mirnov coils and 2D electron cyclotron emission imaging diagnostic systems, it is found that a thermal collapse occurs on the inner side of the 2/1 magnetic island during the minor disruption, and before the collapse, a 3/2 island increases, after the collapse, the 3/2 island may disappear. Moreover, the study also shows that these 3/1, 2/1 and 3/2 modes play roles in the thermal collapse of disruptions.

Coupling among neoclassical tearing modes, edge localized modes and Alfvén eigenmodes in HL-2A high β H-mode plasmas

In this work, the coupling among several MHD modes across different spatial regions, including the neoclassical tearing mode (NTM) and two branches of Alfvén eigenmode (AE) in the core and the edge localized mode (ELM), has been investigated in the HL-2A high beta H-mode plasmas. The NTMs induce a saturated m/n = 1/1 helical core (m and n are the poloidal and toroidal mode numbers, respectively) through the ‘magnetic-flux pumping’ effect. The ELM crash results in a rapid (<1 ms) decrease of the NTM island width followed by a much slower recovery. The degree of the island-width drop is proportional to the normalized beta as well as the ELM size, and can be up to 60%. In addition, two branches of AEs, in the toroidal Alfvén eigenmode (TAE) and beta-induced Alfvén eigenmode (BAE) bands, become evident after the 2/1 NTM onset and their magnitudes are modulated by the 2/1 NTM rotation. Besides, the changes of the TAE and BAE amplitudes are closely related to the temporal evolution of the ELM crash event, implying the strong interaction between AEs and the ELM. It is found that the coupling among these MHD modes in the core region during the NTM phase regulates the edge transport, i.e., relaxation of the pressure profile, mitigation of the peeling-ballooning instability, reduction of the radial electric field shear and enhancement of the turbulent transport in the pedestal region.

Analytical study on magnetic component of geodesic acoustic mode

To understand the role of geodesic acoustic modes (GAMs) in regulating the transport by interacting with background electromagnetic turbulence, a thorough theoretical understanding of the magnetic components of the mode is required. In this study, the magnetic components of GAM are analytically investigated under the gyrokinetic framework with both the and harmonics are considered, where is the poloidal mode number. With the quasi-neutrality condition and Ampère’s law, the amplitudes of various poloidal magnetic components are derived. It is shown that both and magnetic components exist and are dominated by the cosine and sine components, respectively. In addition, it is found that the amplitudes of all magnetic components increase with respect to the ratio of plasma pressure to magnetic pressure and safety factor Most importantly, the amplitude of magnetic component is significantly enhanced due to the coupling of magnetic drift frequency with the first and second harmonics of the distribution functions, thus it can be comparable to that of magnetic component under certain conditions. The various magnetic components derived in this study may provide some guidance for experimental measurements.

The synergetic effects of three-dimensional magnetic perturbations and finite beta on collisionless trapped electron mode in tokamak plasmas

The effects of three-dimensional (3D) magnetic perturbations (MPs) and finite beta (β, i.e., the ratio of plasma kinetic pressure to magnetic pressure) on the instability of collisionless trapped electron mode (CTEM) have been studied. Based on the local 3D equilibrium model, we have derived general expressions for longitudinal invariant and the corresponding precession drift frequency of trapped electrons, which include the synergetic effects of MPs and finite β. It is found that 3D effects can either stabilize or destabilize CTEM instability by analytically solving the linear dispersion relation of CTEM. These effects depend on the poloidal and toroidal mode numbers as well as the phase of 3D MPs. Specially, for the destabilizing phase of MPs, the stabilizing effect of finite β on CTEM can be even reversed when the displacement of magnetic flux surface exceeds a critical value. Moreover, the synergetic effects of 3D MPs with stabilizing phase and finite β can further reduce the required absolute value of negative magnetic shear to completely stabilize CTEM instability. This indicates that 3D MPs might be used as an actuator for lowing the level of anomalous electron heat transport, and thus facilitate the formation of electron internal transport barrier (eITB).