Poloidal Mode Research Articles

Experimental study of the tearing mode instability during the current ramp up stage in Sino-United Spherical Tokamak

The fierce magnetohydrodynamic (MHD) activity observed during the current ramp up stage of a tokamak discharge, which significantly limits the performance of the plasma, has been experimentally studied in Sino-United Spherical Tokamak (SUNIST). The mode structure extracted by magnetic measurements appears to be typically decreasing from to , where m and n are the poloidal and toroidal mode numbers. A phase reversal layer in the spatial distribution of the magnetic perturbation extracts the approximate position of the magnetic island chain, which gives insight on the evolution of the internal structure of the MHD activity. A matrix equation method that includes corrections for the shadowing effect of the probe array has been developed so as to derive a more accurate estimation of the current density profile. The resulting current profile evolution qualitatively explains the decrease in poloidal mode number and the spontaneous suppression of the MHD activity. Statistical results of the MHD response suggest that the deterioration of the plasma confinement is closely related to the phase inversion position of the poloidal magnetic perturbation.

Linear and nonlinear simulations of the visco-resistive internal kink mode using the M3D code

Numerical simulations of visco-resistive internal kink modes with dominant poloidal and toroidal mode numbers m/n = 1 in tokamak plasma configurations have been carried out using the M3D code. The numerical scaling of the growth rate of linear visco-resistive internal kink is found to agree reasonably well with the analytical theory. The impact of toroidal effects is assessed. Nonlinear simulations show that when viscosity increases, the nonlinear evolution of resistive internal kinks transits from cyclic, Kadomtsev-like sawtooth oscillations at relatively low values of the viscosity parameter, to pulsating m/n = 1 magnetic islands at intermediate viscosity, to steady state islands at high viscosity. For the pulsating and steady state scenarios, the safety factor profile is nearly flat and almost equals to unity in the core region. Regimes with pulsating or steady state islands may be relevant to the interpretation of partial sawteeth and of the so-called snake phenomenon sometimes observed in tokamak experiments.

Electron fishbones destabilized nonresonantly by lower hybrid current drive

Fishbone-type oscillations with poloidal and toroidal mode numbers m = 1, n = 1 have been observed during lower hybrid current drive (LHCD) in the Alcator C-Mod tokamak. At relatively high plasma density and collisionality, the driving mechanism appears to be the nonresonant destabilization of an m/n = 1/1 MHD resistive internal kink mode by the pressure of the suprathermal electrons produced by the LHCD rather than a wave-particle resonance between the mode and the fast electrons. Direct measurements of the fast electrons are consistent with nonresonant destabilization and saturation. The effects of the 1/1 mode kink displacement on the LHCD deposition and fast electron concentration lead to nonresonant saturation mechanisms that may also contribute to the saturation of resonant lower hybrid fishbones.

Studies of various physics effects on an on-axis LHCD experiment using numerical tools

The lower hybrid current drive (LHCD) plays an important role in the long pulse and high performance experiments on the EAST Tokamak, using LHW systems with frequencies of 2.45 GHz and 4.6 GHz. With the initial parallel refractive index mostly peaking at n∥∼1.8−2.1, it is difficult to have on-axis LHCD due to the accessibility conditions which prevents the LHW from propagating into the plasma core. However, according to the investigation of HXR diagnostics, LHW did provide an on-axis current drive in an EAST experiment. To interpret this on-axis LHCD phenomenon, various physics effects that give rise to variations in parallel wave numbers, thus influencing the propagation and the absorption of the LHW, have been taken into account, such as toroidal effects, full wave effects with focusing and diffraction, and scattering effects due to density fluctuations. Numerical tools including ray-tracing and full wave codes that contain one or two of the above physics effects have been used to model the heating and current drive of the LHW on EAST. Linear Landau damping and quasi-linear Landau damping have been compared by using the coupling between ray-tracing and the Fokker-Planck codes. Convergence studies have been performed for the full wave modeling, the maximum poloidal modes in the full wave have been scanned, and the results are compared with each other. The factors that characterize the amplitude, the radial thickness, and the location of the density fluctuations have been studied and scanned. The measurement of HXR diagnostics has been compared with synthetic diagnostics by reconstructing the HXR data from both the standard GENRAY/CQL3D LHCD modelling and the modeling taking the scattering effects into account.

The phase-space dependence of fast-ion interaction with tearing modesaaIAEA Technical Meeting paper for submission to Nuclear Fusion

Modulation of various neutral beam sources probes the interaction of fast ions with tearing modes (TM) in the DIII-D tokamak. As measured by electron cyclotron emission, the tearing modes have an island width of ∼8 cm and change phase at the q = 2 surface. (Here, m is the poloidal mode number and n is the toroidal mode number.) Deuterium neutral beam injection by six sources with differing injection geometries produces the fast ions. To study the interaction in different parts of phase space, on successive discharges, one of the six sources is modulated at 20 Hz to populate different fast-ion orbits. The modulation only changes the island width by a few millimeters, implying that any fast-ion effect on mode stability is below detection limits. When compared to the expected signals in the absence of TM-induced transport, both the average and modulated neutron signals deviate, implying that fast-ion transport occurs in much of phase space. Fast-ion Dα (FIDA) measurements detect reductions in signal at wavelengths that are sensitive to counter-passing ions. Neutral particle analyzer data imply poor confinement of trapped fast ions. Calculations of the expected fast-ion transport that use measured TM properties successfully reproduce the data.

Modal analysis of the full poloidal structure of the plasma response to n = 2 magnetic perturbations

Previous DIII-D research has identified the presence of a multimodal plasma response to perturbations with toroidal periodicity equal to 2, with kink-like phenomenology of the plasma response in the low field side mid-plane and a resonant-like behavior in the high field side midplane. In this paper, we extend that initial midplane observation with the first detailed analysis of the poloidal structure of the plasma response as a function of the poloidal spectrum of the applied n = 2 perturbation and compare it to predictions made with the linear magnetohydrodynamics code MARS-F, confirming an overall good agreement. Singular value decomposition analysis of both the experimental data and the modeling identifies two distinct poloidal mode structures, one peaking at the low field side midplane and one peaking at θ ± 50°, each with a well-defined dependence on the poloidal spectrum of the applied perturbation. A study of the effect that βN has on the two modes confirms the kink-like phenomenology of the plasma response that dominates the low field side mid-plane, shows that the behavior previously associated with the high field side is observable at all poloidal angles, and highlights that the mode dominant at low βN becomes the secondary one at high βN. Detailed analysis of the high field side response is presented as well, suggesting the presence of a third mode linked to the presence of non-linear effects corresponding to particular poloidal spectra of the applied perturbation.

A Comparative Study of ULF Waves' Role in the Dynamics of Charged Particles in the Plasmasphere: Van Allen Probes Observation

AbstractBy analyzing observations from Van Allen Probes in its inbound and outbound orbits, we present evidence of coherent enhancement of cold plasmaspheric electrons and ions due to drift‐bounce resonance with ultralow frequency (ULF) waves. From 18:00 UT on 28 May 2017 to 10:00 UT on 29 May 2017, newly formed poloidal mode standing ULF waves with significant electric field oscillations were observed in two consecutive orbits when Probe B was traveling inbound. In contrast to observations during outbound orbits, the cold (<150 eV) electrons measured by the HOPE instrument were characterized by flux enhancements several times larger and bidirectional pitch angle distributions during inbound orbits. The electron number density inferred from upper hybrid waves is twice as larger as during inbound orbits, which were also confirmed by an increase of spacecraft potential. The observed ULF waves are identified as second harmonic modes that satisfy the drift‐bounce resonant condition of N = 1 with cold electrons. An enhancement of the plasmaspheric ion number density to restore charge neutrality of plasmas in inbound orbits is observed, which is associated with an increase of ULF wave periods. The observations suggest that the dynamics of plasmaspheric electrons is modified by ULF waves through drift‐bounce resonance and that plasmaspheric ions are indirectly impacted.

Poloidal Mode Wave‐Particle Interactions Inferred From Van Allen Probes and CARISMA Ground‐Based Observations

AbstractUltralow‐frequency wave and test particle models are used to investigate the pitch angle and energy dependence of ion differential fluxes measured by the Van Allen Probes spacecraft on 6 October 2012. Analysis of the satellite data reveals modulations in differential flux resulting from drift resonance between H+ ions and fundamental mode poloidal Alfvén waves detected near the magnetic equator at L ∼ 5.7. Results obtained from simulations reproduce important features of the observations, including a substantial enhancement of the differential flux between ∼20 and 40° pitch angle for ion energies between ∼90 and 220 keV and an absence of flux modulations at 90°. The numerical results confirm predictions of drift‐bounce resonance theory and show good quantitative agreement with observations of modulations in differential flux produced by ultralow‐frequency waves.

A new perspective on MHD mode identification of IR-T1 tokamak plasma by frequency filtering and fitting method

Superposition of Magnetohydrodynamic (MHD) modes in Tokamak leads to complications in finding these modes. In order to obtain plasma modes, energy levels and noise filtering powerful methods such as singular value decomposition (SVD) exist. The SVD method is very effective in separating spatial and temporal dependencies in a set of temporal series which may exist in different spaces. In this paper a new analysis method for finding poloidal modes (m) on Tokamak mirnov oscillations IR-T1 is presented. This approach is based on the frequency filtering and fitting of spatial structure of SVD analysis with the aid of simulation. In the following, momentary analysis of time series main components with the aid of wavelet transform method and also the effect of external electric and magnetic fields on MHD modes are studied.

Effect of toroidal rotation on resistive magnetohydrodynamic instability with a nonmonotonic q profile in cylindrical geometry

The effect of plasma rotation on the linear stability of the resistive magnetohydrodynamic (MHD) instabilities with a nonmonotonic q profile is investigated numerically in the cylindrical geometry. The results have shown that the plasma rotation has a stabilization effect on the double tearing modes (DTMs) depending on the magnitude of the velocity, while the velocity shear has a relatively weak effect. The effect of rotation on DTMs is determined by the velocity at each rational surface. A toroidal velocity imposed on the innermost rational surface has a weak effect on m > 1 DTMs. When the velocity is imposed on the outboard resonant surface, the growth rates of the DTMs are reduced for m > 1 modes; however, it has an obvious destabilizing effect on both m = 1 (with m the poloidal mode number) DTM and single tearing mode branches if the distance between the two rational surfaces is sufficiently small. It is shown that the effect of plasma rotation on the growth rates of the MHD instabilities is in phase with the integrated value of the coupling between potential fluctuation and magnetic flux perturbation.

Magnetic evaluation of hydrogen pressures changes on MHD fluctuations in IR-T1 tokamak plasma

Identification of tokamak plasma parameters and investigation on the effects of each parameter on the plasma characteristics is important for the better understanding of magnetohydrodynamic (MHD) activities in the tokamak plasma. The effect of different hydrogen pressures of 1.9, 2.5 and 2.9 Torr on MHD fluctuations of the IR-T1 tokamak plasma was investigated by using of 12 Mirnov coils, singular value decomposition and wavelet analysis. The parameters such as plasma current, loop voltage, power spectrum density, energy percent of poloidal modes, dominant spatial structures and temporal structures of poloidal modes at different plasma pressures are plotted. The results indicate that the MHD activities at the pressure of 2.5 Torr are less than them at other pressures. It also has been shown that in the stable area of plasma and at the pressure of 2.5 Torr, the magnetic force and the force of plasma pressure are in balance with each other and the MHD activities are at their lowest level.

Observation and Numerical Simulation of Cavity Mode Oscillations Excited by an Interplanetary Shock

AbstractCavity mode oscillations (CMOs) are basic magnetohydrodynamic eigenmodes in the magnetosphere predicted by theory and are expected to occur following the arrival of an interplanetary shock. However, observational studies of shock‐induced CMOs have been sparse. We present a case study of a dayside ultralow‐frequency wave event that exhibited CMO properties. The event occurred immediately following the arrival of an interplanetary shock at 0829 UT on 15 August 2015. The shock was observed in the solar wind by the Time History of Events and Macroscale Interactions during Substorms‐B and ‐C spacecraft, and magnetospheric ultralow‐frequency waves were observed by multiple spacecraft including the Van Allen Probe‐A and Van Allen Probe‐B spacecraft, which were located in the dayside plasmasphere at L ∼1.4 and L ∼ 2.4, respectively. Both Van Allen Probes spacecraft detected compressional poloidal mode oscillations at ∼13 mHz (fundamental) and ∼26 mHz (second harmonic). At both frequencies, the azimuthal component of the electric field (Eϕ) lagged behind the compressional component of the magnetic field (Bμ) by ∼90°. The frequencies and the Eϕ‐Bμ relative phase are in good agreement with the CMOs generated in a dipole magnetohydrodynamic simulation that incorporates a realistic plasma mass density distribution and ionospheric boundary condition. The oscillations were also detected on the ground by the European quasi‐Meridional Magnetometer Array, which was located near the magnetic field footprints of the Van Allen Probes spacecraft.

Toroidal Alfvén eigenmode triggered by trapped anisotropic energetic particles in a toroidal resistive plasma with free boundary

The toroidal Alfvén eigenmode (TAE), excited by trapped energetic particles (EPs), is numerically investigated in a tokamak plasma, using the non-perturbative magnetohydrodynamic-kinetic hybrid formulation based MARS-K code (Liu et al 2008 Phys. Plasmas 15 112503). Compared with the fixed boundary condition at the plasma edge, a free boundary enhances the critical value of the EPs kinetic contribution for driving the TAE. Free boundary also induces finite perturbations at the plasma edge as expected. An anisotropic distribution of EPs, in the particle pitch angle space, strongly enhances the instability and results in a more global mode structure, compared with the isotropic case. The plasma resistivity is also found to play a role in the EPs-destabilized TAE. In particular, the mode stability domain is mapped out, in the 2D parameter space of the plasma resistivity and a quantity defining the width of the particle distribution in pitch angle (for anisotropic distribution). A resonance layer in the poloidal mode structure, with the layer width increasing with the plasma resistivity, appears at the large width of the particle distribution in pitch angle space. A mode conversion, from the modified ideal kink by the EPs kinetic effect to the TAE, is also observed while increasing the birth energy of EPs. Computational results suggest that the TAE mode structure can be modified by certain key plasma parameters, such as the EPs kinetic contribution, the equilibrium pressure, the plasma resistivity, the distribution of EPs, as well as the birth energy of EPs. Such modification of the eigenmode structure can only be obtained following the non-perturbative hybrid approach (Wang et al 2013 Phys. Rev. Lett. 111 145003, Wang et al 2015 Phys. Plasmas 22 022509), as adopted in this study. More importantly, numerical results show that near the marginal stability point, the dominant poloidal harmonics of the TAE overlap with each other, and are localized at the tip positions of the Alfvén continua. This kind of TAE structure in high beta plasma with unstable ideal kink is substantially different from that of the conventional TAE.

Experimental study of the effect of 2/1 classical tearing mode on (intermediate, small)-scale microturbulence in the core of an EAST L mode plasma

In this paper, we report an experimental study of the effect of a m/n = −2/−1 (m, n being poloidal and toroidal mode number, separately) classical tearing mode on (intermediate, small)-scale microturbulence (see the definition in section ) in the core of an EAST L mode plasma discharge. The microturbulence at different scales k⊥ = 10, 18 and 26 cm−1 (i.e., , 3.6 and 5.2, respectively. Here, is the ion gyroradius and k⊥ is the perpendicular wavenumber) were measured simultaneously by the EAST multi-channel tangential CO2 laser collective scattering diagnostics. Experimental results confirm that the decrease of microturbulent Doppler shift (), inversely correlated to the increase of microturbulent mean frequency (defined in equation ()), is due to the 2/1 tearing mode. Temporal evolution of frequency-integrated spectral power Stot of microturbulence, found to be correlated with the width of 2/1 magnetic island, suggests the modulation effect on microturbulence by the tearing mode beyond Doppler shift effect. Modulation effects on microturbulence by the tearing mode are further demonstrated by the correlation between microturbulent envelope and magnetic fluctuations.

Response of a core coherent density oscillation on electron cyclotron resonance heating in Heliotron J plasma

We report properties of a coherent density oscillation observed in the core region and its response to electron cyclotron resonance heating (ECH) in Heliotron J plasma. The measurement was performed using a multi-channel beam emission spectroscopy system. The density oscillation is observed in a radial region between the core and the half radius. The poloidal mode number is found to be 1 (or 2). By modulating the ECH power with 100 Hz, repetition of formation and deformation of a strong electron temperature gradient, which is likely ascribed to be an electron internal transport barrier, is realized. Amplitude and rotation frequency of the coherent density oscillation sitting at the strong electron temperature gradient location are modulated by the ECH, while the poloidal mode structure remains almost unchanged. The change in the rotation velocity in the laboratory frame is derived. Assuming that the change of the rotation velocity is given by the background E × B velocity, a possible time evolution of the radial electric field was deduced.

Toroidal Alfvén eigenmode driven by energetic electrons during high-power auxiliary heating on HL-2A

Toroidal Alfvén eigenmodes (TAEs) driven by energetic electrons have been observed first during high-power electron cyclotron resonant heating and neutral beam injection on HL-2A. The mode frequencies are in a wide range of 170–370 kHz and are proportional to the Alfvén velocity. The toroidal mode number is confirmed as n = 4. According to the calculated results from the Alfvén mode code, there exists a core localized TAE mode with poloidal mode numbers m = 4 and m = 5 at ρ∼0.35, and the calculated frequency is close to the experimental observation. Besides, the radial mode structures are obtained. Therefore, the modes are identified as TAEs. The TAEs propagate in the electron diamagnetic drift direction poloidally. The energy distribution of energetic electrons is obtained by the relativistic shift-down of the 3-rd harmonic frequency effect of the rough non-thermal spectrum from electron cyclotron emission. Therefore, TAEs should be driven by the energetic electrons with energy in the range of 150–230 keV.

Пространственно-временнaя структура альфвеновских волн в токамаке ТУМАН-3М

AbstractSpatial and temporal structure of Alfvén waves was studied with array of magnetic probes in compact tokamak TUMAN-3M. Poloidal mode numbers have been determined for Alfven instabilities bursts of the two types: short and long ones. Absence of poloidal rotation of magnetic field perturbations was found for both types of bursts. Also, in both cases, no pronounced asymmetry of magnetic field perturbation in the direction of the major radius was detected.

Loss and redistribution of energetic passing ions with resonant magnetic perturbations

The effects of resonant magnetic perturbations (RMPs) and the magnetic drift on the loss and redistribution of passing ions are investigated numerically by the upgrade version of the orbit following code GYCAVA. The drift island structures of passing ion orbits induced by RMPs and the magnetic drift are consistent with the given toroidal and poloidal mode numbers of RMPs in the orbit simulations. The redistribution and loss of energetic and thermal passing ions with and without RMPs are numerically studied and compared with each other. The redistribution near the edge is due to the loss induced by RMPs and the magnetic drift. The extra loss of passing ions induced by RMPs is related to the drift island structure induced by RMPs and the magnetic drift and the stochasticity induced by overlap of magnetic islands. The loss of passing ions with n = 1 RMPs is larger than that with n = 4 RMPs for the same perturbation amplitude parameter, which is due to the fact that the magnetic islands produced by n = 1 RMPs are larger than those produced by n = 4 RMPs. The loss fraction of passing ions with n = 1 RMPs increases with the amplitude of RMPs and the radial profile parameter of the ion density. The pitch and energy scan for the loss of energetic passing ions with n = 1 RMPs is simulated. For counter-passing ions, the loss fraction of low-pitch ions is larger than that of high-pitch ions. The dependence of the loss of energetic ions with RMPs on energy is related to the pitch angle.

Geodesic acoustic mode (GAM) like oscillations and RMP effect in the STOR-M tokamak

A new kind of quasi-coherent mode was observed in ohmic plasma in the STOR-M tokamak. It is featured with a clear solitary peak around 30–35 kHz in the power spectra of the ion saturation current of Langmuir probe as well as poloidal and toroidal mode numbers (m = 1,n = 0) as per the prediction of conventional geodesic acoustic mode (GAM) theory. The dispersion relation of the mode is also similar to GAM and it also shows collisional damping. In contrast to conventional GAM, the floating potential ϕ of the observed GAM-like mode does not show similar symmetric poloidal and toroidal mode numbers (m = 0,n = 0), but has (m = 1,n = 1). The GAM-like mode has also a pronounced magnetic component with mixed poloidal modes (), as observed by Mirnov coils. This mode is suppressed by the application of resonance magnetic perturbations.

Axisymmetric global Alfvén eigenmodes within the ellipticity-induced frequency gap in the Joint European Torus

Alfvén eigenmodes (AEs) with toroidal mode number n = 0 (i.e., axisymmetric) have been observed in the ellipticity-induced frequency range in the Joint European Torus. The axisymmetric modes are of interest because they can be used to diagnose fast particle energy distributions at the mode location. The modes were identified as global Alfvén eigenmodes (GAEs), with the ellipticity of the plasma cross-section preventing strong continuum damping of the modes. The MHD codes CSCAS, MISHKA, and AEGIS were used to compute the n = 0 Alfvén continuum, eigenmode structure, and continuum damping. For zero ellipticity, a single mode exists at a frequency below the Alfvén continuum branch. This mode has two dominant poloidal harmonics with poloidal mode numbers m = ±1 that have the same polarity; therefore, it is an even mode. For finite ellipticity, the continuum branch splits into two branches and the single GAE splits into two modes. An even mode exists below the minimum of the top continuum branch, and the frequency of this mode coincides with the experimentally observed AE frequency. The other mode is found below the lower continuum branch with opposite signs between the two poloidal harmonics (an odd mode structure). This mode was not excited in our experiment. Analytical theory for the n = 0 GAE in an elliptical cylinder shows the n = 0 Alfvén continuum agrees with the numerical modelling.