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Potential fluctuation associated with the energetic-particle-induced geodesic acoustic mode in the Large Helical Device
Abstract
Geodesic acoustic modes (GAM) driven by energetic particles are observed in the Large Helical Device (LHD) by a heavy ion beam probe. The GAM localizes near the magnetic axis. It is confirmed that the energetic-particle-induced GAM is accompanied by an electrostatic potential fluctuation and radial electric field fluctuation. The amplitude of the potential fluctuation is several hundred volts, and it is much larger than the potential fluctuation associated with turbulence-induced GAMs observed in the edge region in tokamak plasmas. The energetic-particle-induced GAM modulates the amplitude of the density fluctuation in a high-frequency range. The observed GAM frequency is constant at the predicted GAM frequency in plasmas with reversed magnetic shear. On the other hand, it shifts upwards from the predicted GAM frequency in plasmas with monotonic magnetic shear.
... A series of numerical studies of EGAMs were performed with a hybrid MHD-kinetic code mega [262,263,264,265] where the energetic particle distribution was calculated with the δf method and current-coupling was used for the energetic particles. The slowing-down distribution function was used for EPs with balanced beam, as in LHD experiments [266]. These simulations confirm the basic structure of the EGAM as a global mode with m = 0 poloidal velocity, m = 1 plasma density, and m = 2 magnetic field perturbations, as shown in figure 44. ...
... However, the experiment clearly displayed mode frequencies significantly lower than the expected standard GAM frequency by a factor of approximately 2 [44]. The frequency discrepancy was explained when taking the EPs into account, and was thus termed an energetic-particle-induced GAM (EGAM) [45] as described in section 3. Subsequently EGAMs were widely observed in NBI plasmas in LHD [409,266,410], JT-60U [370], HL-2A [231], AUG [313], and EAST [433]. Table 14 summarizes the main features of the energetic particle driven GAMs reported from various devices. ...
... Although the frequency chirping is a predominant feature, there are also cases where the frequency does not chirp. Such cases have been observed in reversed or weak magnetic shear configurations in LHD [409,266] and in ohmic plasmas in HL-2A [231]. In both cases other MHD modes or Alfvén Eigenmodes existed simultaneously, and thus additional mode coupling may affect the behaviour of the EGAM. ...
Geodesic acoustic modes (GAMs) are ubiquitous oscillatory flow phenomena observed in toroidal magnetic confinement fusion plasmas, such as tokamaks and stellarators. They are recognized as the non-stationary branch of the turbulence driven zonal flows which play a critical regulatory role in cross-field turbulent transport. GAMs are supported by the plasma compressibility due to magnetic geodesic curvature—an intrinsic feature of any toroidal confinement device. GAMs impact the plasma confinement via velocity shearing of turbulent eddies, modulation of transport, and by providing additional routes for energy dissipation. GAMs can also be driven by energetic particles (so-called EGAMs) or even pumped by a variety of other mechanisms, both internal and external to the plasma, opening-up possibilities for plasma diagnosis and turbulence control. In recent years there have been major advances in all areas of GAM research: measurements, theory, and numerical simulations. This review assesses the status of these developments and the progress made towards a unified understanding of the GAM behaviour and its role in plasma confinement. The review begins with tutorial-like reviews of the basic concepts and theory, followed by a series of topic orientated sections covering different aspects of the GAM. The approach adopted here is to present and contrast experimental observations alongside the predictions from theory and numerical simulations. The review concludes with a comprehensive summary of the field, highlighting outstanding issues and prospects for future developments.
... The plasma configuration is made similar to a LHD experiment with observation of GAM. 26,27) The time evolution of the radial electric field and particle flux in the simulations are shown in Figs. 1 and 2, where three cases (δ = 0.00 (without noise), 0.01, and 0.03) are plotted. In Fig. 1, the given noise portions in δ =0.01 and 0.03 cases are also plotted. ...
... Though we do not show the power spectrum of Γ D i , it has almost the same profile as that of E r . The radial position where clear peak of GAM oscillation is r/a = 0.05 ∼ 0.20, which seems consistent with the observation of GAM using Heavy-Ion-Beam-Probe (HIBP) in a LHD experiment, 27) of which profile is similar to the one in the simulation. We have also confirmed that the GAM frequency and the peak radial position of GAM in simulation are almost unaffected by varying the white-noise amplitude from δ=0.01 to 0.03. ...
... Recent analysis of LHD experiment has found that the spacial profile of GAM power shows the sim- ilar tendency as Fig. 4(b). 27) This is simply explained using a model of forced vibration of an oscillator of which natural frequency is ω 0 , ...
FORTEC-3D code, which solves the drift-kinetic equation for torus plasmas and radial electric field using the δf Monte Carlo method, has developed to study the variety of issues relating to neoclassical transport phenomena in magnetic confinement plasmas. Here the numerical techniques used in FORTEC-3D are briefly reviewed, and recent progress in the simulation method to simulate GAM oscillation is also explained. A band-limited white noise term is introduced in the equation of time evolution of radial electric field to excite GAM oscillation, which enables us to analyze GAM frequency with fine resolution even in the case the collisionless GAM damping is fast.
... Observation using the HIBP of a specific type of electric field pulsation were reported from CHS stellarator [4]. On LHD stallarator, the HIBP was used successfully for the investigation of the geodesic acoustic mode (GAM) induced by the energetic particles [5,6]. A detailed study of interplay between the GAM and the turbulence was performed on JFT-2M tokamak [7]. ...
... It is interesting to note that it was observed earlier that ohmic L-H transition initiated by the gas puffing pulse in the TUMAN-3M also features a buildup of negative plasma potential up to -150 V [5], that is that is very close to potential perturbation measured in the experiments described here. On the other hand, in the L-H transition initiated by the counter-NBI heating, the plasma potential changed much stronger, up to 300-400 V below the ohmic L-mode level [11]. ...
Heavy Ion Beam Probing (HIBP) diagnostic is a powerful tool for electric field studies in hot dense plasma of modern day toroidal magnetic confinement devices. On the TUMAN-3M to-kamak, the HIBP have been used in regimes with improved plasma confinement to clear up the role of radial electric field in the transition to good confinement regimes. Recently, a moderni-zation of the TUMAN-3M HIBP diagnostics was performed aiming to reconfigure it for a work with a reversed plasma current direction and improvement of overall stability of the diagnostic. The results of first measurements of plasma potential in co-NBI scenario are reported and dis-cussed.
... GAMs can be driven by EPs known as the energetic particle-induced geodesic acoustic modes (EGAMs), which were first theoretically predicted by Fu in 2008 [13] and discovered experimentally almost simultaneously [14]. EGAMs have been observed in nearly all main tokamaks [15][16][17][18][19][20][21] and are generally accepted as providing a new pathway for energy and momentum transfer between EPs and the bulk plasma [22][23][24]. In particular, direct evidence of the EGAMs impact on turbulent transport was reported in 2013 by Zarzoso et al using a flux-driven 5D gyro-kinetic simulation [25]. ...
Plasma elongation effects on energetic particle-induced geodesic acoustic modes (EGAMs) are theoretically investigated by using gyro-kinetic equations and the Miller local equilibrium model. Including an arbitrary elongation κ and a finite radial derivative s κ =r∂ r κ/κ, a general EGAM dispersion relation is obtained for an arbitrary energetic particle (EP) distribution. In particular, we obtain analytical EGAM dispersion relations for both the double-shifted Maxwellian distribution and the standard slowing-down distribution of EPs. In both cases, the frequency of the unstable EGAM branch decreases slowly with increasing elongation, while its growth rate decreases rapidly with κ when the ratio of the EP to the bulk ion density, n h /n i ≥ 0.1. These trends agree well with previous GENE and ORB5 simulations [A. Di Siena et al 2018 Nucl. Fusion 58 106014], but differ significantly from the elongation effects on geodesic acoustic modes (GAMs) [Zhe Gao et al 2009 Nucl. Fusion 49 045014]. The portion of the EGAM dispersion relation accounting for the first-order finite-orbit-width shows greater sensitivity to frequency compared to that of GAM, which explains the smaller variations in the frequency of EGAM as κ changes. When the EP number is small (typically, n h /n i ≈ 5%) in the double-shifted Maxwellian case, the growth rate of EGAMs first increases with the increasing elongation and then decreases, while it monotonically increases with κ in the slowing-down case. Furthermore, the effects of s κ on EGAMs are similar to the elongation κ effects but weaker.
... Observations using the HIBP of a specific type of electric field pulsation were reported from CHS stellarator [5]. On LHD stellarator, the HIBP was used successfully for the investigation of the geodesic acoustic mode (GAM) induced by the energetic particles [6,7]. A detailed study of interplay between the GAM and the turbulence was performed on JFT-2M tokamak [8]. ...
Heavy Ion Beam Probing (HIBP) diagnostic is a powerful tool for electric field studies in the hot dense plasma of modern-day toroidal magnetic confinement devices. On the TUMAN-3M tokamak, the HIBP have been used in regimes with improved plasma confinement to clear up the role of the radial electric field in the transition to good confinement regimes. Recently, a modernization of the TUMAN-3M HIBP diagnostics was performed, aiming to reconfigure it for a work with a reversed plasma current direction and improvement of the overall stability of the diagnostic. The results of the first measurements of the plasma potential in the co-NBI scenario are reported and discussed.
... In LHD hydrogen plasma experiments, a study was performed mainly using an E B neutral particle analyzer [37,38] and FILD [39,40]. Experimental studies on energetic ion transport due to toroidal Alfvén eigenmodes (TAEs) [41][42][43][44][45], EPMs [46,47], and energetic-particle-driven geodesic acoustic modes (EGAMs) [48,49] have been performed. Numerical simulation using orbit-following models [50] and the particle-in-cell-MHD hybrid simulation MEGA code showed qualitative agreement with the experimentally observed velocity distribution of transported and escaping energetic particles [51][52][53] due to TAE and EGAM channeling [54]. ...
Studies of energetic particle transport due to energetic-particle-driven Alfvénic instability have progressed using neutron and energetic particle diagnostics in Large Helical Device deuterium plasmas. Alfvénic instability excited by injecting an intensive neutral beam was observed by a magnetic probe and a far-infrared laser interferometer. The interferometer showed Alfvénic instability composed of three modes that existed from the core to the edge of the plasma. A comparison between the observed frequency and shear Alfvén spectra suggested that the mode activity was most likely classified as an Alfvénic avalanche. A neutron fluctuation detector and a fast ion loss detector indicated that Alfvénic instability induced transport and loss of co-going transit energetic ions. The dependence of the drop rate of the neutron signal on the Alfvénic instability amplitude showed that significant transport occurred. Significant transport might be induced by the large amplitude and radially extended multiple modes, as well as a large deviation of the energetic ion orbit from the flux surface.
... Theoretical analysis and numerical simulation have proven that energetic particles can excite a new branch GAM instability [7][8][9][10][11][12][13][14][15][16][17], called EGAM, which is determined by characteristic frequencies of energetic particles (such as the transit frequency of energetic particles) that are located inside the standard GAM continuum. The EGAM instabilities that are excited by energetic ions have been intensively studied on different devices: JET [18,19], DIII-D [20,21], LHD [22][23][24][25][26] and AUG [27]. Moreover, another type of EGAMs that are excited by energetic electrons in low density ohmic plasmas have also been observed in HL-2A [28,29]. ...
Energetic ions induced electromagnetic geodesic acoustic modes (EGAMs) instabilities during the modulated injection of neutral beams of NBI1L and NBI1R have been observed in EAST. The EGAMs coexist with the lower frequency modes (LFMs) instabilities: the frequencies are constant in the radial direction for EGAMs in the range of , while LFMs are located in the range . The density perturbation for EGAM is nearly up-down anti-symmetric, while the magnetic perturbation for EGAM that is standing wave with a principal m = 2 lobe, and an m = 4 side-lobe is commonly observed for . EGAMs have strong correlations with the injections of energetic ions, and the toroidal rotation velocity is partially suppressed by the mode excitations, while the magnetic islands of LFM instabilities can form the configuration of 'hollow' structure for . The most pronounced feature of the EGAMs is that the magnetic fluctuations are not antisymmetric in the poloidal angle θ, and they can be expressed as , and the is a function of the pitch angle and energy of energetic ion. The new structure of asymmetry for EGAM has been observed when , where the radial structure extends outward in bottom section, and also exhibits non-uniformity in the toroidal direction, and one possible explanation for the asymmetry is that EGAM are modulated by LSW instabilities with frequency 0 < f x < 4 kHz.
... [6][7][8] Experimental observations show that GAMs induced by fast ions (EGAMs) have much larger amplitude compared to those driven by turbulence. [9][10][11][12] Thus, the impacts of EGAMs on bulk plasmas are expected to be significant. Numerical simulation reveals the nonlinear dynamics of EGAMs, such as the coupling of EGAMs with turbulence, 13 nonlinear saturation of EGAM, 14 frequency chirping 15 and subcritical excitation of GAMs due to selfnonlinear coupling. ...
Eigenmode analysis of geodesic acoustic modes (GAMs) driven by fast ions is performed, based on a set of gyrokinetic equations. Resonance to the magnetic drift of the fast ions can destabilize GAMs. A new branch is found in the family of GAMs, whose frequency is close to the magnetic drift frequency of the fast ions. The poloidal eigenfunction of this branch has bump structures in the poloidal direction where the resonance of the magnetic drift with the mode is strong. The ion heating rate by the GAMs is evaluated in the framework of quasi-linear theory. The heating is localized poloidally around the resonance locations. Owing to the bumps in the eigenfunction, the magnitude of the heating is much larger than that estimated without the magnetic drift resonance.
To meet the demand for information on electron temperature fluctuations in low magnetic field experiments in the Large Helical Device (LHD), a new ECE radiometer covering the Q and V bands has been installed. Combination mirrors are installed in the vacuum vessel to focus the beam and efficiently propagate the radiated electron cyclotron waves. Notch filters are used to eliminate stray light from the gyrotron, and a 32-channel heterodyne radiometer is constructed using a filter bank system. As a result, oscillations of electron temperature and both electromagnetic and electrostatic fluctuations were successfully observed.
An integrated set of neutron diagnostics developed for the deuterium operation of the Large Helical Device (LHD) has been revealing behavior of energetic ions in three-dimensional plasmas, together with energetic-particle diagnostics. In order to obtain deeper understanding of physics related to energetic ions in the LHD, development of plasma diagnostics that can provide energy distribution of energetic ions is now being accelerated. Recent advances in development of the D-D neutron energy spectrometer, a neutral particle analyzer based on a single-crystal chemical vapor deposition diamond, and a tangential fast-ion D α diagnostic for deuterium discharges of the LHD are described.
Various properties of the energetic particle-induced geodesic acoustic mode (EGAM) are explored in this large database analysis of DIII-D experimental data. EGAMs are n=0 modes with m=0 electrostatic potential fluctuations (where n/m = toroidal/poloidal mode number), m=1 density fluctuations and m=2 magnetic fluctuations. The fundamental frequency ($\sim$20-40 kHz) of the mode is typically below that of the traditional geodesic acoustic mode (GAM) frequency. EGAMs are most easily destabilized by beams in the counter plasma current (counter-$I_p$) direction as compared to co-$I_p$ and off-axis beams. During counter beam injection, the mode frequency is found to have the strongest linear dependence (correlation coefficient $r$=$-0.712$) with the safety factor ($q$). The stability of the mode in the space of $q$ and poloidal beta ($\beta_p$) shows a clear boundary for the mode stability. The stability of the mode depends more strongly on damping rate than on fast-ion drive for a given injection geometry.
Understanding energetic particle transport due to magnetohydrodynamic instabilities excited by energetic particles is essential to apprehend alpha particle confinement in a fusion burning plasma. In the large helical device (LHD), beam ion and deuterium–deuterium fusion-born triton transport due to resistive interchange mode destabilized by helically-trapped energetic ions (EIC) are studied employing comprehensive neutron diagnostics, such as the neutron flux monitor and a newly developed scintillating fiber detector characterized by high detection efficiency. Beam ion transport due to EIC is studied in deuterium plasmas with full deuterium or hydrogen/deuterium beam injections. The total neutron emission rate ( S n ) measurement indicates that EIC induces about a 6% loss of passing transit beam ions and a 60% loss of helically-trapped ions. The loss rate of helically-trapped ions, which drive EIC, is larger than the loss rate of passing transit beam ions. Furthermore, the drop of S n increasing linearly with the EIC amplitude shows that barely confined beam ions existing near the confinement-loss boundary are lost due to EIC. In full deuterium conditions, a study of deuterium–deuterium fusion-born triton transport due to EIC is performed by time-resolved measurement of total secondary deuterium–tritium neutron emission rate ( S n_DT ). Drop of S n_DT increases substantially with EIC amplitude to the third power and reaches up to 30%. The relation shows that not only tritons confined in confined-loss boundary, but also tritons confined in the inner region of a plasma, are substantially transported.
The energetic-particle-induced geodesic acoustic mode (EGAM) is studied using gyrokinetic particle simulations in tokamak plasmas. In our simulations, exponentially growing EGAMs are excited by energetic particles with a slowing-down distribution. The frequencies of EGAMs are always below the frequencies of GAMs, which is due to the non-perturbative contribution of energetic particles (EPs). The mode structures of EGAMs are similar to the corresponding mode structures of GAMs. Our gyrokinetic simulations show that a high EP density can enhance the EGAM growth rate, due to high EP free energy, and that EPs' temperature and the pitch angle of the distribution modify the EGAM frequency/growth rate by means of the resonance condition. Kinetic effects of the thermal electrons barely change the EGAM frequency, and have a weak damping effect on the EGAM. Benchmarks between the gyrokinetic particle simulations and a local EGAM dispersion relation exhibit good agreement in terms of EGAM frequency and growth rate.
We analyze the effects of the passing energetic particles on the resistive ballooning modes (RBM) and the energetic particle driven modes in JT-60SA plasma, which leads to the prediction of the stability in N-NBI heated plasma. The analysis is performed using the code FAR3d that solves the reduced MHD equations describing the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particle (EP) species assuming an averaged Maxwellian EP distribution fitted to the slowing down distribution, including the effect of the acoustic modes. The simulations show the possible destabilization of a 3 / 2 − 4 / 2 TAE with a frequency ( f ) of 115 kHz, a 6 / 4 − 7 / 4 TAE with f = 98 kHz and a 6/4 or 7/4 BAE with f = 57 kHz in the ITER-like inductive scenario. If the energetic particle β increases, beta induced Alfven Eigenmodes (BAE), toroidal AEs (TAE) and elliptical AEs (EAE) are destabilized between the inner-middle plasma region, leading to the overlapping of AE of different toroidal families. If these instabilities coexist in the non-linear saturation phase the EP transport could be enhanced leading to a lower heating efficiency. For a hypothetical configuration based on the ITER-like inductive scenario but an center peaked EP profile, the EP β threshold increases and several BAEs are destabilized in the inner plasma region, indicating an improved AE stability with respect to the off-axis peaked EP profile. In addition, the analysis of a hypothetical JT-60SA scenario with a resonant q = 1 in the inner plasma region shows the destabilization of fishbones-like instabilities by the off-axis peaked EP profile. Also, the EPs have a stabilizing effect on the RBM, stronger as the population of EP with low energies (below 250 keV) increases at the plasma pedestal.
A possibility of electron density measurements with heavy ion beam probes (HIBPs) has been demonstrated, along with their capability to measure the potential and magnetic field. A method has been proposed to reconstruct the electron density profile [A. Fujisawa et al., Rev. Sci. Instrum. 74, 3335 (2003)]. In the method, the profile of secondary beam currents is converted into a local density profile by taking into account local brightness and so-called path integral effects which mean the effect of beam attenuation along the beam orbit. Here the article presents the HIBP measurement of the electron density profile after the proposed method was first applied on the real experimental data of compact helical system plasmas. In the real application, the hollow density and the peaked profiles are successfully obtained with sufficiently high temporal resolution (a few ms), in accordance with the electron density profile measured with Thomson scattering for electron cyclotron resonance heating and neutral beam injection plasmas.
Energetic-particle-driven geodesic acoustic modes (EGAMs) observed in a Large Helical Device experiment are investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid. The frequency chirping of the primary mode and the sudden excitation of the half-frequency secondary mode are reproduced for the first time with the hybrid simulation using the realistic physical condition and the three-dimensional equilibrium. Both EGAMs have global spatial profiles which are consistent with the experimental measurements. For the secondary mode, the bulk pressure perturbation and the energetic particle pressure perturbation cancel each other out, and thus the frequency is lower than the primary mode. It is found that the excitation of the secondary mode does not depend on the nonlinear MHD coupling. The secondary mode is excited by energetic particles that satisfy the linear and nonlinear resonance conditions, respectively, for the primary and secondary modes.
An unstable branch of the energetic geodesic acoustic mode (EGAM) is found using fluid theory with fast ions characterized by their narrow width in energy distribution and collective transit along field lines. This mode, with a frequency much lower than the thermal GAM frequency ωGAM, is now confirmed as a new type of unstable EGAM: a reactive instability similar to the two-stream instability. The mode can have a very small fast ion density threshold when the fast ion transit frequency is smaller than ωGAM, consistent with the onset of the mode right after the turn-on of the beam in DIII-D experiments. The transition of this reactive EGAM to the velocity gradient driven EGAM is also discussed.
Abrupt and strong excitation of a mode has been observed when the frequency of a chirping energetic-particle driven geodesic acoustic mode (EGAM) reaches twice the geodesic acoustic mode (GAM) frequency. The frequency of the secondary mode is the GAM frequency, which is a half-frequency of the primary EGAM. Based on the analysis of spatial structures, the secondary mode is identified as a GAM. The phase relation between the secondary mode and the primary EGAM is locked, and the evolution of the growth rate of the secondary mode indicates nonlinear excitation. The results suggest that the primary mode (EGAM) contributes to nonlinear destabilization of a subcritical mode.
High-frequency energetic particle driven geodesic acoustic modes (EGAM) observed in the large helical device
plasmas are investigated using a hybrid simulation code for energetic particles and magnetohydrodynamics
(MHD). Energetic particle inertia is incorporated in the MHD momentum equation for the simulation where the beam ion density is comparable to the bulk plasma density. Bump-on-tail type beam ion velocity distribution created by slowing down and charge exchange is considered. It is demonstrated that EGAMs have frequencies higher than the geodesic acoustic modes and the dependence on bulk plasma temperature is weak if (1) energetic particle density is comparable to the bulk plasma density and (2) charge exchange time (τcx
) is sufficiently shorter than the slowing down time (τs
) to create a bump-on-tail type distribution. The frequency of high-frequency EGAM rises as the energetic particle pressure increases under the condition of high energetic particle pressure. The frequency also increases as the energetic particle pitch angle distribution shifts to higher transit frequency. It is found that there are two kinds of particles resonant with EGAM: (1) trapped particles and (2) passing particles with transit frequency close to the mode frequency. The EGAMs investigated in this work are destabilized primarily by the passing particles whose transit frequencies are close to the EGAM frequency.
n = 0 modes with frequency chirping have been observed by a heavy ion beam probe and Mirnov coils in the large helical device plasmas, where n is the toroidal mode number. The spatial structures of the electrostatic potential fluctuation and the density fluctuation correspond to those of the geodesic acoustic mode (GAM). The modes are observed only during the tangential neutral beam injection with the energy of 175 keV. The energy spectra of fast ions measured by a neutral particle analyzer implies that the modes are excited by the fast ions through the inverse Landau damping. The absolute values and the temperature dependence of the frequency of the mode can be interpreted by the dispersion relation taking into account the measured energy spectra of the fast ions. Therefore, the observed n = 0 modes are identified as the energetic-particle driven GAM.
Spatio-temporal measurements of the impurity ion temperature, density, and rotation profiles around the plasma edge region have been made in the JT-60U tokamak, allowing the determination of radial electric field, Er, with the key dimensionless parameter (poloidal Mach number, Upm) at the L-H transition in a number of operational regimes. We found that there is variation in the L-H transition in terms of its time-scale; not only “hard” type transition with a faster time-scale than that seen in the plasma transport (as represented by an energy confinement time, τE) as seen in the many conventional tokamaks, but also “soft” one with a slow time-scale (≈τE) is possible solution, including a complex multi-stage Er transition in the later H-phase. The most important point is that the critical condition for the L-H transition predicted by ion-orbit loss model could be applicable only for “hard” transition (occurred at Upm ≥ 1), and not necessary for “slow” one (occurred even at Upm < 1). Characteristics of the turbulent density fluctuation with the frequency range of 100 kHz at the plasma edge region, in addition to a uniform toroidal MHD oscillation (i.e., n = 0), during ELM-free H-phase are also reported. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Energetic-particle-induced kinetic electromagnetic geodesic acoustic modes (EKEGAMs) are numerically studied in low β (=plasma pressure/magnetic pressure) tokamak plasmas. The parallel component of the perturbed vector potential is considered along with the electrostatic potential perturbation. The effects of finite Larmor radius and finite orbit width of the bulk and energetic ions as well as electron parallel dynamics are all taken into account in the dispersion relation. Systematic harmonic and ordering analysis are performed for frequency and growth rate spectra of the EKEGAMs, assuming ( k ρ i ) ∼ q − 3 ∼ β ≪ 1 , where q, k, and ρi are the safety factor, radial component of the EKEGAMs wave vector, and the Larmor radius of the ions, respectively. It is found that there exist critical βh /βi values, which depend, in particular, on pitch angle of energetic ions and safety factor, for the mode to be driven unstable. The EKEGAMs may also be unstable for pitch angle λ 0 B < 0.4 in certain parameter regions. Finite β effect of the bulk ions is shown to have damping effect on the EKEGAMs. Modes with higher radial wave vectors have higher growth rates. The damping from electron dynamics is found decreasing with decrease of the temperature ratio Te /Ti . The modes are easily to be driven unstable in low safety factor q region and high temperature ratio Th /Ti region. The harmonic features of the EKEGAMs are discussed as well.
The area of energetic particle (EP) physics in fusion research has been actively and extensively researched in recent decades. The progress achieved in advancing and understanding EP physics has been substantial since the last comprehensive review on this topic by Heidbrink and Sadler (1994 Nucl. Fusion 34 535). That review coincided with the start of deuterium–tritium (DT) experiments on the Tokamak Fusion Test Reactor (TFTR) and full scale fusion alphas physics studies.
Fusion research in recent years has been influenced by EP physics in many ways including the limitations imposed by the 'sea' of Alfvén eigenmodes (AEs), in particular by the toroidicity-induced AE (TAE) modes and reversed shear AEs (RSAEs). In the present paper we attempt a broad review of the progress that has been made in EP physics in tokamaks and spherical tori since the first DT experiments on TFTR and JET (Joint European Torus), including stellarator/helical devices. Introductory discussions on the basic ingredients of EP physics, i.e., particle orbits in STs, fundamental diagnostic techniques of EPs and instabilities, wave particle resonances and others, are given to help understanding of the advanced topics of EP physics. At the end we cover important and interesting physics issues related to the burning plasma experiments such as ITER (International Thermonuclear Experimental Reactor).
This conference report summarizes the contributions to and discussions at the 3rd Asia–Pacific Transport Working Group (APTWG) meeting held in Jeju-island, Korea, on 21–24 May 2013. The main objective of the meeting is to develop a predictive understanding of transport mechanisms in magnetically confined fusion plasmas. In an effort to accomplish this objective, four technical working groups were organized under the headings: (1) transport barrier formation and confinement enhancement, (2) 3D effects and Magnetohydrodynamic–turbulence interaction, (3) momentum transport and non-locality and (4) particle/impurity transport and energetic particles.
Nonlinear frequency chirping of the energetic-particle-driven geodesic
acoustic mode (EGAM) is investigated using a hybrid simulation code for
energetic particles interacting with a magnetohydrodynamic fluid. It is
demonstrated in the simulation result that both frequency chirping up
and chirping down take place in the nonlinear evolution of the EGAM. It
is found that two hole-clump pairs are formed in the energetic particle
distribution function in two-dimensional velocity space of pitch angle
variable and energy. One pair is formed in the phase space region that
destabilizes the instability, while the other is formed in the
stabilizing region. The transit frequency of the hole (clump) in the
destabilizing region chirps up (down), while in the stabilizing region
the hole (clump) chirps down (up). The transit frequencies of particles
in the holes and clumps are in good agreement with the chirping EGAM
frequency indicating that the particles are kept resonant with the EGAM
during the nonlinear frequency chirping. Continuous energy transfer
takes place from the destabilizing phase space region to the stabilizing
region during the spontaneous frequency chirping of the wave.
The first detailed measurements of ion-impurity dynamics for NBI-heated ELMy H-modes at the edge of the JT-60U tokamak are reported. We investigated the ability of external momentum/power input to modify and control the radial electric field, Er, and pedestal structures. The relationship between Er and pedestal structures of ion-impurity density, ni, and temperature, Ti, during the ELMing H-mode phase for various momentum input directions (i.e. co-, balanced- and counter-NBI) and input powers from perpendicular NBI are compared with the ELM-free phase. The observed trend is that the edge Er-well width increases in the co-NBI discharge, while the Er value at the base of the Er-well becomes more negative in the counter-NBI discharge. The scale length for both ni and Ti in the pedestal is ~2?cm and
values are ~1 for both ELM-free and ELMing phases with different magnitudes of Er (and/or Er shear). Characteristics of the turbulent density fluctuation, in addition to a uniform toroidal MHD oscillation (i.e. n?=?0), during both ELM-free and ELMing phases are also reported.
Linear properties of energetic particle driven geodesic acoustic mode (EGAM) in the large helical device plasmas are investigated using a hybrid simulation code for a magnetohydrodynamics fluid interacting with energetic particles. It is found that the EGAM is a global mode with the spatially uniform oscillation frequency despite the spatial variation of the local geodesic acoustic mode frequency. The poloidal mode numbers of poloidal velocity fluctuation, plasma density fluctuation, and magnetic fluctuation are m = 0, 1, and 2, respectively. Oscillation frequency, linear growth rate, and spatial width of EGAM are compared for different physics conditions. The EGAM frequency is proportional to the square root of the plasma temperature. The frequency is lower for higher energetic particle β value. The mode spatial width is larger for larger spatial width of the energetic particle distribution and for the reversed shear safety-factor profile than the normal shear profile. It is also found that the EGAM propagates radially outward in the linearly growing phase, and the propagation speed is slower for the spatially broadened modes.
Heavy ion beam probes have been installed on a variety of toroidal devices, but the first and only application on a reversed field pinch is the diagnostic on the Madison Symmetric Torus. Simultaneous measurements of spatially localized equilibrium potential and fluctuations of density and potential, previously inaccessible in the core of the reversed field pinch (RFP), are now attainable. These measurements reflect the unique strength of the heavy ion beam probe (HIBP) diagnostic. They will help determine the characteristics and evolution of electrostatic fluctuations and their role in transport, and determine the relation of the interior electric field and flows. Many aspects of the RFP present original challenges to HIBP operation and inference of plasma quantities. The magnetic field contributes to a number of the issues: the comparable magnitudes of the toroidal and poloidal fields and edge reversal result in highly three-dimensional beam trajectories; partial generation of the magnetic field by plasma current cause it and hence the beam trajectories to vary with time; and temporal topology and amplitude changes are common. Associated complications include strong ultraviolet radiation and elevated particle losses that can alter functionality of the electrostatic systems and generate noise on the detectors. These complexities have necessitated the development of new operation and data analysis techniques: the implementation of primary and secondary beamlines, adoption of alternative beam steering methods, development of higher precision electrostatic system models, refinement of trajectory calculations and sample volume modeling, establishment of stray particle and noise reduction methods, and formulation of alternative data analysis techniques. These innovative methods and the knowledge gained with this system are likely to translate to future HIBP operation on large scale stellarators and tokamaks.
This summary is based on 155 papers presented at FEC 2010 in Daejeon. It deals with a wide range of aspects of magnetic confinement experiments covering inter alia: stability, wave–plasma interactions, current drive, heating, energetic particles, plasma–material interactions, divertors, limiters and SOL aspects. Whenever possible, findings and new understanding have been organized and regrouped by issues. Particular attention has been given to issues in the critical path of ITER construction. The fusion scientific community has focused on these issues in a sticking manner.
The physical understanding of net-current-free helical plasmas has progressed in the Large Helical Device (LHD) since the last Fusion Energy Conference in Geneva, 2008. The experimental results from LHD have promoted detailed physical documentation of features specific to net-current-free 3D helical plasmas as well as complementary to the tokamak approach. The primary heating source is neutral beam injection (NBI) with a heating power of 23 MW, and electron cyclotron heating with 3.7 MW plays an important role in local heating and power modulation in transport studies. The maximum central density has reached 1.2 × 1021 m−3 due to the formation of an internal diffusion barrier (IDB) at a magnetic field of 2.5 T. The IDB is maintained for 3 s by refuelling with repetitive pellet injection. In a different operational regime with moderate density less than 2 × 1019 m−3, a plasma with a central ion temperature reaching 5.6 keV exhibits the formation of an internal transport barrier (ITB). The ion thermal diffusivity decreases to the level predicted by neoclassical transport. In addition to the rotation driven by the momentum input due to tangential NBI, the existence of intrinsic torque to drive toroidal rotation is identified in the plasma with an ITB. This ITB is accompanied by an impurity hole which generates an impurity-free core. The impurity hole is due to a large outward convection of impurities in spite of the negative radial electric field. The magnitude of the impurity hole is enhanced in the magnetic configuration with a large helical ripple and for heavier atoms. Another mechanism for suppressing impurity contamination is identified at the plasma edge with a stochastic magnetic field. A helical system shares common physics issues with tokamaks such as 3D equilibria, transport in a stochastic magnetic field, plasma response to a resonant magnetic perturbation, divertor physics and the role of radial electric field and meso-scale structure.
Geodesic Acoustic Modes (GAM) are shown to constitute a continuous spectrum due to radial inho-mogeneities. The existence of a singular layer causes GAM to mode convert to short-wavelength kinetic GAM (KGAM) via finite ion Larmor radii; analogous to kinetic Alfvén waves (KAW). KGAM are shown to propagate radially outward; consistent with experimental observations and numerical simulation results. The degeneracy of GAM/KGAM with Beta induced Alfvén Eigenmodes (BAE) is demonstrated and discussed. We show that energetic particle driven oscillations can be excited from the GAM continuum, similarly to the Energetic Particle Mode (EPM) case. Furthermore, it is shown that KGAM can be nonlinearly excited by drift-wave (DW) turbu-lence via 3-wave parametric interactions, and the resultant driven-dissipative nonlinear system exhibits typical prey-predator self-regulatory dynamics. KGAM are preferentially excited with respect to GAM because of the radial wave-number dependence of the parametric excitation process. Plasma non-uniformity effects on nonlinear KGAM excitations are discussed. In this work, we show that Geodesic Acoustic Modes (GAM) [1] constitute a continuous spec-trum due to radial inhomogeneities. The existence of a singular layer, thus, suggests GAM collisionless damping due to absorption at the GAM continuum resonance [2] and linear mode conversion to short-wavelength kinetic GAM (KGAM) via finite ion Larmor radii (FLR) and finite magnetic drift orbit widths (FOW) [3]. This result is demonstrated by derivations of the GAM/KGAM mode structure and dispersion relation in the singular layer, indicating that, typically, KGAM propagate radially outward [3]. The formal identity of the GAM/KGAM wave equation to that describing shear Alfvén wave (SAW) mode conversion to kinetic Alfvén Wave (KAW) near the SAW resonance [4], suggests a complete analogy of GAM/KGAM ⇔ SAW/KAW. Our analyses also confirm that GAM and Beta induced Alfvén Eigenmodes (BAE) [5, 6] are degenerate in the long wavelength limit, where diamagnetic effects are ig-nored, even when FLR and FOW corrections are accounted for. Besides the importance of its physics implications, the usefulness of this result on the BAE/GAM degeneracy is that we may straightforwardly derive the governing equations for GAM using the kinetic theory results on BAE developed earlier [7, 8, 9].
The present status of experiments on zonal flows in magnetic confinement experiments is examined. The innovative use of traditional and modern diagnostics has revealed unambiguously the existence of zonal flows, their spatio-temporal characteristics, their relationship to turbulence and their effects on confinement. In particular, a number of observations have been accumulated on the oscillatory branch of zonal flows, named geodesic acoustic modes, suggesting the necessity for theories to give their proper description. In addition to these basic properties of zonal flows, several new methods have elucidated the processes of zonal flow generation from turbulence. Further investigation of the relationship between zonal flows and confinement is strongly encouraged as cross-device activity including low temperature, toroidal and linear devices.
Zonal flows (ZFs) and associated geodesic oscillations are turbulence-generated time-varying Er × BT rigid poloidal plasma flows with finite radial extent. They are of major interest for tokamak confinement since they are thought to moderate drift-wave turbulence and hence edge transport. However, detection of ZFs (believed to be driven by Reynolds stress) and Geodesic acoustic modes (GAMs) (linked with poloidal pressure asymmetries) is challenging since they appear predominantly as low frequency (few kilohertz) potential or radial electric field Er fluctuations. Presented here are measurements of GAM/ZF properties in ohmic, L-mode and H-mode ASDEX Upgrade tokamak discharges using a new Doppler reflectometry technique to measure Er fluctuations directly.
Experimental results on the connection between meanE×B flows and coherent
oscillations at the frequency of the geodesic acoustic mode (GAM) in the H-1
heliac are presented. An increase in the mean local radial electric field, Er ,
is correlated with the development of several coherent modes. As mean Er
increases, spectral energy, which is mostly contained in coherent modes, grows.
This is followed by the onset of the m = 0, n = 0 finite frequency GAMlike
mode. Analysis of the heliac magnetic structure shows that geodesic
curvature is considerably stronger in H-1 than in tokamaks. A possible role
of geodesic oscillations in the transfer of spectral energy from mean zonal
flows into coherent modes leading to the generation of the GAM-like mode is
discussed. In the proposed scenario of the L–H transition in H-1 the inverse
energy cascade leads to the accumulation of turbulence energy in the mean
zonal-flowlike structure, until geodesic effects lead to the generation of coherent
modes and GAM. The coherent modes’ parallel phase velocities are very close
to the ion thermal velocity suggesting the possibility of their strong Landau
damping. It is suggested that the shear decorrelation mechanism eventually
forbids the energy transfer from Er to these modes which reinforces spectral
condensation and leads to L–H transition.
In the Large Helical Device (LHD), a reversed magnetic shear (RS) configuration having non-monotonic rotational transform profile was formed by intense counter neutral beam (NB) current drive. In the RS configuration helical plasma, the reversed shear Alfvén eigenmode (RSAE) with n=1 toroidal mode number was identified together with energetic-ion-driven geodesic acoustic mode (GAM) with n=0. Temporal sweeping of the RSAE frequency was well-explained by ideal MHD theory without introducing non-perturbative energetic ion effects. The minimum value of RSAE frequency in the sweeping phase agrees well with GAM frequency. Nonlinear interaction between the RSAE and GAM generates a lot of driven modes. In thus produced low density RS configuration, bulk ion temperature in the plasma center T io starts to increase linearly in time for more than 10 times of global energy confinement time just after the local minimum of the rotational transform has passed through the particular rational value ι/2π=1/3. When energetic ion driven AEs and GAM are re-excited appreciably, T io decreases with slower time scale than that of the rise. During the rising phase of T io , plasma potential measured by heavy ion beam probe becomes deeper in the plasma core region. Then, it becomes shallow in the decay phase of T io .
Persistent rapid up and down frequency chirping modes with a toroidal mode number of zero (n = 0) are observed in the JET tokamak when energetic ions, in the range of several hundred keV, are created by high field side ion cyclotron resonance frequency heating. Fokker–Planck calculations demonstrate that the heating method enables the formation of an energetically inverted ion distribution which supplies the free energy for the ions to excite a mode related to the geodesic acoustic mode. The large frequency shifts of this mode are attributed to the formation of phase space structures whose frequencies, which are locked to an ion orbit bounce resonance frequency, are forced to continually shift so that energetic particle energy can be released to counterbalance the energy dissipation present in the background plasma.
Reversed-shear Alfvén eigenmodes were observed for the first time in a helical plasma having negative q₀'' (the curvature of the safety factor q at the zero shear layer). The frequency is swept downward and upward sequentially via the time variation in the maximum of q. The eigenmodes calculated by ideal MHD theory are consistent with the experimental data. The frequency sweeping is mainly determined by the effects of energetic ions and the bulk pressure gradient. Coupling of reversed-shear Alfvén eigenmodes with energetic ion driven geodesic acoustic modes generates a multitude of frequency-sweeping modes.
Zonal flows, by which we mean azimuthally symmetric band‐like shear flows, are ubiquitous phenomena in nature and the laboratory. It is now widely recognized that zonal flows are a key constituent in virtually all cases and regimes of drift wave
turbulence, indeed, so much so that this classic problem is now frequently referred to as “drift wave‐zonal flow
turbulence.” In this lecture note, we present new viewpoints and unifying concepts which facilitate understanding of zonal flow physics, via theory, computation and their confrontation with the results of laboratory experiment. Special emphasis is placed on identifying avenues for further progress. We briefly survey issues such as (i) mechanism of zonal flows excitation, (ii) back interaction on turbulence, (iii) saturation mechanism of zonal flows, (iv) energy partition between fluctuations and flows, (v) turbulent
transport coefficient dressed by zonal flows, and (vi) experimental efforts to verify these fundamental processes.
AN OVERVIEW OF THE LARGE HELICAL DEVICE PROJECT. The Large Helical Device (LHD) has successfully started running plasma confinement experiments after a long construction period of eight years. During the construction and machine commissioning phases, a variety of milestones have been attained in fusion engineering, which successflly led to the first operation, and the first plasma was ignited on March 31, 1998. Two experimental campaigns are planned in 1998. In the first campaign, the magnetic flux mapping clearly demonstrated a nested structure of magnetic surfaces. The first plasma experiments were conducted with second harmonic 84-GHz and 82.6-GHz ECH at a heating power input of 0.35 MW. The magnetic field was set at 1.5 T in the first year so as to accumulate operational experience of the superconducting coils. In the second campaign, auxiliary heating with NBI at 3 MW has been carried out. The averaged electron densities up to 6x 10^19 m^-3 , central temperatures ranging 1.4 to 1.5 keV and stored energies up to 220 kJ have been attained despite the fact that impurity level is not yet minimized. The obtained scaling of energy confinement time has been found to be consistent with the ISS95 scaling law with some enhancement.
A comprehensive review of zonal flow phenomena in plasmas is presented. While the emphasis is on zonal flows in laboratory plasmas, zonal flows in nature are discussed as well. The review presents the status of theory, numerical simulation and experiments relevant to zonal flows. The emphasis is on developing an integrated understanding of the dynamics of drift wave - zonal flow turbulence by combining detailed studies of the generation of zonal flows by drift waves, the back-interaction of zonal flows on the drift waves, and the various feedback loops by which the system regulates and organizes itself. The implications of zonal flow phenomena for confinement in, and the phenomena of fusion devices are discussed. Special attention is given to the comparison of experiment with theory and to identifying directions for progress in future research.
This is a report on fluctuation measurements using twin heavy ion beam probes in CHS. The observation shows that a dozen of coherent modes with intermittent nature coexist in an electron cyclotron heated plasma. The modes are found to have long-distance correlation in toroidal direction. The radial structure of the modes are evaluated in potential fluctuation. The characteristics are not in contradictory with geodesic acoustic modes.
Intense axisymmetric oscillations driven by suprathermal ions injected in the direction counter to the toroidal plasma current are observed in the DIII-D tokamak. The modes appear at nearly half the ideal geodesic acoustic mode frequency, in plasmas with comparable electron and ion temperatures and elevated magnetic safety factor (q_{min}>or=2). Strong bursting and frequency chirping are observed, concomitant with large (10%-15%) drops in the neutron emission. Large electron density fluctuations (n[over ]_{e}/n_{e} approximately 1.5%) are observed with no detectable electron temperature fluctuations, confirming a dominant compressional contribution to the pressure perturbation as predicted by kinetic theory. The observed mode frequency is consistent with a recent theoretical prediction for the energetic-particle-driven geodesic acoustic mode.
The toroidal symmetry of the geodesic acoustic mode (GAM) zonal flows is identified with toroidally distributed three step Langmuir probes at the edge of the HuanLiuqi-2A (commonly referred to as HL-2A) tokamak plasmas for the first time. High coherence of both the GAM and the ambient turbulence for the toroidally displaced measurements along a magnetic field line is observed, in contrast with the high coherence of the GAM but low coherence of the ambient turbulence when the toroidally displaced measurements are not along the same field line. The radial and poloidal features of the flows are also simultaneously determined. The nonlinear three wave coupling between the high frequency turbulent fluctuations and the flows is demonstrated to be a plausible formation mechanism of the flows.
The geodesic acoustic mode (GAM) is a high frequency branch of zonal flows, which is observed in toroidal plasmas. Because of toroidal curvature effects, density fluctuations are excited, which are investigated with the O-mode correlation reflectometer at TEXTOR. This Letter reports on the poloidal distribution of GAM induced density fluctuation and compares them with theoretical predictions. The influence of the GAM flows on the ambient turbulence is studied, too.
A heavy-ion beam probe (HIBP) using a 3-MV tandem accelerator was installed in Large Helical Device (LHD). It is designed to measure the electrostatic potential in the core region directly. The electrostatic potential profiles can be measured successfully using the HIBP, and the radial electric field predicted by the neoclassical theory is consistent with that measured using the HIBP as long as the ambipolarity condition of the neoclassical particle flux has a single solution. Although the turbulent fluctuation is not detected because of low signal-to-noise ratio, several coherent fluctuations, which are inferred to be reversed-shear-induced Alfvén eigenmode and the geodesic acoustic mode, are observed directly in core plasmas, and the spatial distribution is revealed.
Visible bremsstrahlung emission profiles have been studied over a wide
range of electron densities in H2 gas puff and
solid-H2-pellet-fueled discharges of large helical device
(LHD). Peaked profiles are observed in high-density discharges
(ne≥ 1014 cm-3) with pellet
injection, whereas hollow profiles appeared in the normal discharges
(ne≤ 1014 cm-3) with gas puffing.
The total bremsstrahlung radiation is analyzed from the visible
bremsstrahlung profile by integrating the energy and plasma volume. It
is found that the total bremsstrahlung radiation rapidly increases with
the density in the pellet discharges, of which the increment is scaled
by the square of density, while it is roughly constant against the
density in the gas puff discharges. The total bremsstrahlung radiation
becomes equal to the total radiation loss in the pellet discharges. The
ratio of the total bremsstrahlung radiation to the total input power has
only a range of 3-10% in the gas puff discharges. In contrast, the ratio
increases with the density and reaches 30-40% in the pellet discharges.
Flat Zeff profiles are observed not only in the gas puff
discharges but also in the pellet discharges. This indicates that no
impurity accumulation occurs in the high-density operation with
H2 pellet injection.
In toroidal systems with geodesic curvature an electrostatic acoustic mode occurs with plasma motion in the magnetic surfaces, perpendicular to the field. In typical stellarators this mode should dominate ordinary sound waves associated with motion along the field.
A comprehensive review of zonal flow phenomena in plasmas is presented. While the emphasis is on zonal flows in laboratory plasmas, planetary zonal flows are discussed as well. The review presents the status of theory, numerical simulation and experiments relevant to zonal flows. The emphasis is on developing an integrated understanding of the dynamics of drift wave-zonal flow turbulence by combining detailed studies of the generation of zonal flows by drift waves, the back-interaction of zonal flows on the drift waves, and the various feedback loops by which the system regulates and organizes itself. The implications of zonal flow phenomena for confinement in, and the phenomena of fusion devices are discussed. Special attention is given to the comparison of experiment with theory and to identifying directions for progress in future research.
A numerical simulation of a kinetic instability near threshold shows how a hole and clump spontaneously appear in the particle distribution function. The hole and clump support a pair of Bernstein, Greene, Kruskal (BGK) nonlinear waves that last much longer than the inverse linear damping rate while they are upshifting and downshifting in frequency. The frequency shifting allows a balance between the power nonlinearly extracted from the resonant particles and the power dissipated into the background plasma. These waves eventually decay due to phase space gradient smoothing caused by collisionality.
Collisionless time evolution of zonal flows in helical systems is investigated. An analytical expression describing the collisionless response of the zonal-flow potential to the initial potential and a given turbulence source is derived from the gyrokinetic equations combined with the quasineutrality condition. The dispersion relation for the geodesic acoustic mode (GAM) in helical systems is derived from the short-time response kernel for the zonal-flow potential. It is found that helical ripples in the magnetic-field strength as well as finite orbit widths of passing ions enhance the GAM damping. The radial drift motions of particles trapped in helical ripples cause the residual zonal-flow level in the collisionless long-time limit to be lower for longer radial wavelengths and deeper helical ripples. On the other hand, a high-level zonal-flow response, which is not affected by helical-ripple-trapped particles, can be maintained for a longer time by reducing their radial drift velocity. This implies a possibility that helical configurations optimized for reducing neoclassical ripple transport can simultaneously enhance zonal flows which lower anomalous transport. The validity of our analytical results is verified by gyrokinetic Vlasov simulation.
Zonal flows are of keen interest in efforts to understand transport in magnetically confined plasma. Of the well-developed diagnostics, the heavy ion beam probe, HIBP, is most suited to measure the radial electric field, Er, associated with the flows in present medium to large devices. This paper discusses why the HIBP is capable of measuring Er and how to design a HIBP to optimize zonal flow measurements. The TEXT HIBP is used as an example of a typical system. The NSTX spherical torus is used in a design study for future work with emphasis on zonal flow measurements. The key diagnostic considerations are (1) sample volume size, (2) sample volume orientation, and (3) the ability to rapidly scan the sample volume in the radial direction. The measurement of principal interest here is Er but there is additional information in a nonlinear analysis of the fluctuations. © 2003 American Institute of Physics.
The three-dimensional wavenumber and frequency spectrum for the geodesic acoustic mode (GAM) has been measured in the HuanLiuqi-2A tokamak for the first time. The spectrum provides definite evidence for the GAM, which is characterized by kθ = kϕ = 0 and krρi ≈ 0.04−0.09 with the full width at half-maximum Δkrρi ≈ 0.03−0.07. The localized GAM packet is observed to propagate outward in the radial direction with nearly the same phase and group velocity. The envelopes of the radial electric field and density fluctuations are observed to be modulated by the GAM. By comparing the experimental result with that of the envelope analysis using model signals, the mechanism of the envelope modulation has been identified. The results strongly suggest that the envelope modulation of the r fluctuations is dominantly caused by the direct regulation of the GAM during the GAM generation in the energy-conserving triad interaction, and the envelope modulation of the density fluctuations is induced by the GAM shearing effect, which transfers the fluctuation energy from low to high frequencies. In addition, the cross- and auto-bicoherences for interactions between the GAM and turbulent fluctuations show a similar peaked feature that may reflect the resonant property in the nonlinear coupling between the GAM and turbulent fluctuations.
Superthermal energetic particles (EP) often drive shear Alfvén waves unstable in magnetically confined plasmas. These instabilities constitute a fascinating nonlinear system where fluid and kinetic nonlinearities can appear on an equal footing. In addition to basic science, Alfvén instabilities are of practical importance, as the expulsion of energetic particles can damage the walls of a confinement device. Because of rapid dispersion, shear Alfvén waves that are part of the continuous spectrum are rarely destabilized. However, because the index of refraction is periodic in toroidally confined plasmas, gaps appear in the continuous spectrum. At spatial locations where the radial group velocity vanishes, weakly damped discrete modes appear in these gaps. These eigenmodes are of two types. One type is associated with frequency crossings of counterpropagating waves; the toroidal Alfvén eigenmode is a prominent example. The second type is associated with an extremum of the continuous spectrum; the reversed shear Alfvén eigenmode is an example of this type. In addition to these normal modes of the background plasma, when the energetic particle pressure is very large, energetic particle modes that adopt the frequency of the energetic particle population occur. Alfvén instabilities of all three types occur in every toroidal magnetic confinement device with an intense energetic particle population. The energetic particles are most conveniently described by their constants of motion. Resonances occur between the orbital frequencies of the energetic particles and the wave phase velocity. If the wave resonance with the energetic particle population occurs where the gradient with respect to a constant of motion is inverted, the particles transfer energy to the wave, promoting instability. In a tokamak, the spatial gradient drive associated with inversion of the toroidal canonical angular momentum Pζ is most important. Once a mode is driven unstable, a wide variety of nonlinear dynamics is observed, ranging from steady modes that gradually saturate, to bursting behavior reminiscent of relaxation oscillations, to rapid frequency chirping. An analogy to the classic one-dimensional problem of electrostatic plasma waves explains much of this phenomenology. EP transport can be convective, as when the wave scatters the particle across a topological boundary into a loss cone, or diffusive, which occurs when islands overlap in the orbital phase space. Despite a solid qualitative understanding of possible transport mechanisms, quantitative calculations using measured mode amplitudes currently underestimate the observed fast-ion transport. Experimentally, detailed identification of nonlinear mechanisms is in its infancy. Beyond validation of theoretical models, the future of the field lies in the development of control tools. These may exploit EP instabilities for beneficial purposes, such as favorably modifying the current profile, or use modest amounts of power to govern the nonlinear dynamics in order to avoid catastrophic bursts.
Neoclassical transport simulation code (FORTEC-3D) applicable to both axisymmetric and non-axisymmetric configurations is developed to investigate non-local effects on neoclassical transport phenomena. The time evolution of the radial electric field is simulated in the full volume of the confinement region of tokamak and helical model plasmas. It is found that the damping rate of the geodesic-acoustic-mode (GAM) oscillation becomes faster than that predicted from a single-surface transport analysis. The time evolution of the radial electric field towards the ambipolar state shows a non-local behaviour, which indicates a coupling of GAM oscillation between the neighbouring two flux surfaces because of the finite-orbit-width effect.
Geodesic acoustic modes (GAMs) were investigated on the T-10 tokamak using heavy ion beam probe, correlation reflectometry and multipin Langmuir probe diagnostics. Regimes with Ohmic heating and with on- and off-axis ECRH were studied. It was shown that GAMs are mainly the potential oscillations. Typically, the power spectrum of the oscillations has the form of a solitary quasi-monochromatic peak with the contrast range 3–5. They are the manifestation of the torsional plasma oscillations with poloidal wavenumber m = 0, called zonal flows. The frequency of GAMs changes in the region of observation and decreases towards the plasma edge. After ECRH switch-on, the frequency increases, correlating with growth in the electron temperature Te. The frequency of the GAMs depends on the local Te as , which is consistent with a theoretical scaling for GAM, where cs is the sound speed within a factor of unity. The GAMs on T-10 are found to have density limit, some magnetic components and an intermittent character. They tend to be more excited near low-q magnetic surfaces.
Large potential oscillations were detected in JIPPT-IIU tokamak plasmas in a wide range of plasma cross-sections in measurements using a multi-sample-volume heavy ion beam probe. These oscillations have large amplitudes reaching a few hundreds of volts and their frequencies are in the range of the geodesic acoustic mode (GAM). They are found over a wide range of plasma cross-sections and commonly have m = 0 structures. As they were Fourier analysed, it was found that the central frequency is higher in the core of the plasma and lower in the edge of the plasma. These observations agree with the properties of theoretically predicted GAM oscillations. It was also found that the frequency spectrum is peaked in the core and broad in the edge, which may have something to do with damping mechanisms of the GAM. The phase relation between the density and the electric field fluctuations was studied extensively in terms of the cross-correlation function. The level of the density fluctuation was low as it should be, and the expected 90° phase difference was found in a limited radial domain.
Recent results on investigations of Alfvén eigenmodes, fast ion confinement and fast ion diagnostics in JT-60U are presented. It was found that toroidicity induced Alfvén eigenmodes (TAEs) were stable in negative shear discharges with a large density gradient at the internal transport barrier (ITB). If the density gradient was small at the ITB, multiple TAEs appeared around the q = 2 surface (pitch minimum) and showed a large frequency chirping (Δf ≈ 80 kHz). In low-q positive shear discharges, the location of the TAEs changed from outside to inside the q = 1 surface, owing to a temporal change of the q profile. A significant depression of the megaelectronvolt ion population was observed only with high-n (n up to 14) multiple TAEs inside the q = 1 surface. Non-circular triangularity induced Alfvén eigenmodes were observed for the first time. Considerable depression of the triton burnup was observed in negative shear discharges. Orbit following Monte Carlo simulations indicated that ripple loss was responsible for the enhanced triton losses. The fast ion stored energies in ICRF heated negative shear discharges were comparable to those of positive shear plasmas. Tail ion temperatures in high (second to fourth) harmonic ICRF heating experiments were first analysed with an MeV neutral particle analyser. The behaviour of MeV ions produced by ICRF heating was studied with gamma ray diagnostics. A scintillating fibre detector system for detecting the 14MeV neutron emission was developed for the triton burnup studies. Ion cyclotron emission measurements discriminating between parallel and perpendicular components of the electric field were carried out for the first time.
A method for zonal flow study by using direct density fluctuation measurements is proposed. When ambient drift-wave turbulence is modulated by zonal flows (i.e. in the drift-wave-zonal flow systems), an envelope of the ambient density fluctuations has spectral peaks around zonal flow frequencies. A spectral peak at the geodesic acoustic mode (GAM) frequency is observed in the envelope of the ambient density fluctuations measured in edge plasma of the JFT-2M tokamak. The significant cross-bicoherence is also found between the ambient density fluctuations and its envelope in the GAM frequency. This result demonstrates that we can measure the GAM only by using density fluctuation data. This method provides a possibility of zonal flow research in burning core plasma by density fluctuation diagnostics such as microwave reflectometry.
A heavy ion beam probe was installed on the Large Helical Device (LHD) to investigate the roles of radial electric fields (Er) in magnetically confined high-temperature plasmas. Two new observations are presented. One is the observation of electrostatic potential profiles during the formation of extremely hollow density profiles of impurities, called the impurity hole (Ida K et al 2009 Phys. Plasmas 16 056111), in the LHD plasmas. The measured Er is negative, and the Er determined by the ambipolarity condition of neoclassical particle fluxes is consistent with this observation. However, the transport analysis indicates that the formation of the extremely hollow profile is not attributable to the impurity fluxes driven by Er and the density and temperature gradients of the impurity. The other new observation is on the geodesic acoustic mode (GAM). The electrostatic potential fluctuation associated with the GAM, which is probably induced by energetic particles, in plasmas with the reversed or weak magnetic shear is identified. The GAM is localized in the core region of the plasma.
The characteristics of geodesic–acoustic-mode (GAM) are investigated through direct and simultaneous measurement of electrostatic and density fluctuations with a heavy ion beam probe.
The amplitude of the GAM changes in relation to the radial position; it is small near the separatrix, reaches a local maximum at 3 cm inside the separatrix and then decreases again to 5 cm inside the separatrix. The frequency is constant in the range, though the predicted GAM frequency varies according to the temperature gradient. The correlation length is about 6 cm and comparable to the structure of the amplitude of the GAM. The results indicate the GAM has a radial structure which reflects the local condition at about 3 m inside the separatrix.
The phase relation between the GAM oscillation indicates that the GAM is a radial propagating wave.
The interaction between the GAM and the ambient density fluctuation is shown by the high coherence between the GAM oscillation and the temporal behaviour of the ambient density fluctuation. Moreover, the phase relation between the electric field fluctuation of the GAM ( [\tilde{E}_{r,{\rm GAM}} ]) and the amplitude of the density fluctuation indicates that the modulation of the ambient density fluctuation delays the [\tilde{E}_{r,{\rm GAM}} ]. The causality between the GAM and the modulation of the density fluctuation is revealed.
Collisionless time evolution of zonal flows in helical systems is investigated. An analytical expression describing the collisionless response of the zonal-flow potential to the initial potential and a given turbulence source is derived from the gyrokinetic equations combined with the quasineutrality condition. The dispersion relation for the geodesic acoustic mode (GAM) in helical systems is derived from the short-time response kernel for the zonal-flow potential. It is found that helical ripples in the magnetic field strength as well as finite orbit widths of passing ions enhance the GAM damping. The radial drift motions of particles trapped in helical ripples cause the residual zonal-flow level in the collisionless long-time limit to be lower for longer radial wave lengths and deeper helical ripples. On the other hand, a high-level zonal-flow response, which is not affected by helical-ripple-trapped particles, can be maintained for a longer time by reducing their radial drift velocity. This implies a possibility that helical configurations optimized for reducing neoclassical ripple transport can simultaneously enhance zonal flows which lower anomalous transport. The validity of our analytical results is verified by gyrokinetic Vlasov simulation.
The instability of the geodesic acoustic mode (GAM) in tokamak turbulence is analyzed. It can be induced by dynamic shearing of the ambient turbulence by GAMs combined with the poloidal inhomogeneity of the turbulent flux. The dispersion relation is derived. The competition of the drive mechanism and the damping by turbulence viscosity is discussed. The GAMs are more unstable for high safety factors.
The application of time-delay-estimation techniques to two-dimensional measurements of density fluctuations, obtained with beam emission spectroscopy in DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] plasmas, has provided temporally and spatially resolved measurements of the turbulence flow-field. Features that are characteristic of self-generated zonal flows are observed in the radial region 0.85less than or equal tor/aless than or equal to1.0. These features include a coherent oscillation (approximately 15 kHz) in the poloidal flow of density fluctuations that has a long poloidal wavelength, possibly m=0, narrow radial extent (k(r)rho(I)<0.2), and whose frequency varies monotonically with the local temperature. The approximate effective shearing rate, dv(theta)/dr, of the flow is of the same order of magnitude as the measured nonlinear decorrelation rate of the turbulence, and the density fluctuation amplitude is modulated at the frequency of the observed flow oscillation. Some phase coherence is observed between the higher wavenumber density fluctuations and low frequency poloidal flow fluctuations, suggesting a Reynolds stress contribution. These characteristics are consistent with predicted features of zonal flows, specifically identified as geodesic acoustic modes, observed in 3-D Braginskii simulations of core/edge turbulence. (C) 2003 American Institute of Physics.
Alfvén spectra in a reversed-shear tokamak plasma with a population of energetic ions exhibit a quasiperiodic pattern of primarily upward frequency sweeping (Alfvén cascade). Presented here is an explanation for such asymmetric sweeping behavior which involves finding a new energetic particle mode localized around the point of zero magnetic shear.
Experiments designed for generating internal transport barriers in the plasmas of the Joint European Torus [JET, P. H. Rebut et al., Proceedings of the 10th International Conference, Plasma Physics and Controlled Nuclear Fusion, London (International Atomic Energy Agency, Vienna, 1985), Vol. I, p. 11] reveal cascades of Alfvén perturbations with predominantly upward frequency sweeping. These experiments are characterized by a hollow plasma current profile, created by lower hybrid heating and current drive before the main heating power phase. The cascades are driven by ions accelerated with ion cyclotron resonance heating (ICRH). Each cascade consists of many modes with different toroidal mode numbers and different frequencies. The toroidal mode numbers vary from n = 1 to n = 6. The frequency starts from 20 to 90 kHz and increases up to the frequency range of toroidal Alfvén eigenmodes. In the framework of ideal magnetohydrodynamics (MHD) model, a close correlation is found between the time evolution of the Alfvén cascades and the evolution of the Alfvén continuum frequency at the point of zero magnetic shear. This correlation facilitates the study of the time evolution of both the Alfvén continuum and the safety factor, q(r), at the point of zero magnetic shear and makes it possible to use Alfvén spectroscopy for studying q(r). Modeling shows that the Alfvén cascade occurs when the Alfvén continuum frequency has a maximum at the zero shear point. Interpretation of the Alfvén cascades is given in terms of a novel-type of energetic particle mode localized at the point where q(r) has a minimum. This interpretation explains the key experimental observations: simultaneous generation of many modes, preferred direction of frequency sweeping, and the absence of strong continuum damping.
Heavy ion beam probe (HIBP) on large helical device is currently equipped with three channel detectors, which can observe three spatial points simultaneously inside the plasma with resolution of approximately 10 mm. The beam trajectories and observation point location are calculated numerically and optimized allowing for the identification of the mode structure in multichannel (up to 9) HIBP measurements. The calculations show that the radial and poloidal wavenumbers can be identified by proper changing and choosing of the beam energy and trajectory.
Heavy ion beam probe (HIBP) for large helical device (LHD) has been improved to measure the potential fluctuation in high-temperature plasmas. The spatial resolution is improved to about 10 mm by controlling the focus of a probe beam. The HIBP is applied to measure the potential fluctuation in plasmas where the rotational transform is controlled by electron cyclotron current drive. The fluctuations whose frequencies change with the time constant of a few hundreds of milliseconds and that with a constant frequency are observed. The characteristics of the latter fluctuation are similar to those of the geodesic acoustic mode oscillation. The spatial profiles of the fluctuations are also obtained.
A new energetic particle-induced geodesic acoustic mode (EGAM) is shown to exist. The mode frequency and mode structure are determined nonperturbatively by energetic particle kinetic effects. In particular the EGAM frequency is found to be substantially lower than the standard GAM frequency. The radial mode width is determined by the energetic particle drift orbit width and can be fairly large for high energetic particle pressure and large safety factor. These results are consistent with the recent experimental observation of the beam-driven n=0 mode in DIII-D.
Kinetic theory of Geodesic Acoustic Modes: radial structures and nonlinear excitationsObservation of Reversed Shear Alfven Eigenmode Excited by Energetic Ions in a Helical Plasma
- F Zonca
ZONCA, F. et al., "Kinetic theory of Geodesic Acoustic Modes: radial structures and nonlinear excitations", Proc. 22nd Int. Fusion Energy Conf. 2008 (Geneva, Switzerland, 2008) (2008). [6] TOI, K. et al., "Observation of Reversed Shear Alfven Eigenmode Excited by Energetic Ions in a Helical Plasma", Phys. Rev. Lett. (2010).
Kinetic Global Analysis of Alfven Eigenmodes in Toroidal Plasmas
- A Fukuyama
FUKUYAMA, A. et al., "Kinetic Global Analysis of Alfven Eigenmodes in Toroidal Plasmas", in 19th IAEA Fusion Energy Conference, Lyon, France, TH_P3–14, 2002.
Observation of Reversed Shear Alfven Eigenmode Excited by Energetic Ions in a Helical PlasmaGeodesic Acoustic Waves in Hydromagnetic SystemsReview of zonal flowsPhysics of zonal flows
- Exw Toi
EXW/4-3Rb TOI, K. et al., “Observation of Reversed Shear Alfven Eigenmode Excited by Energetic Ions in a Helical Plasma”, Phys. Rev. Lett. (2010). WINSOR, N. et al., “Geodesic Acoustic Waves in Hydromagnetic Systems”, Phys. Fluids 11 (1968) 2448. DIAMOND, P. H. et al., “Review of zonal flows”, Plasma Phys. Control. Fusion 47 (2005) R35. ITOH, K. et al., “Physics of zonal flows”, Phys. Plasmas 13 (2006) 055502.