Inversion Radius Research Articles

Enhancement of the FIDA diagnostic at ASDEX Upgrade for velocity space tomography

Recent upgrades to the FIDA (fast-ion D-alpha) diagnostic at ASDEX Upgrade are discussed. The diagnostic has been extended from three to five line of sight arrays with different angles to the magnetic field, and a spectrometer redesign allows the simultaneous measurement of red- and blue-shifted parts of the Doppler spectrum. These improvements make it possible to reconstruct the 2D fast-ion velocity distribution from the FIDA measurements by tomographic inversion under a wide range of plasma parameters. Two applications of the tomography are presented: a comparison between the distributions resulting from 60 keV and 93 keV neutral beam injection and a velocity-space resolved study of fast-ion redistribution induced by a sawtooth crash inside and outside the sawtooth inversion radius.

Non-axisymmetric equilibrium reconstruction of a current-carrying stellarator using external magnetic and soft x-ray inversion radius measurements

Non-axisymmetric free-boundary equilibrium reconstructions of stellarator plasmas are performed for discharges in which the magnetic configuration is strongly modified by ohmically driven plasma current. These studies were performed on the compact toroidal hybrid device using the V3FIT reconstruction code with a set of 50 magnetic diagnostics external to the plasma. With the assumption of closed magnetic flux surfaces, the reconstructions using external magnetic measurements allow accurate estimates of the net toroidal flux within the last closed flux surface, the edge safety factor, and the plasma shape of these highly non-axisymmetric plasmas. The inversion radius of standard sawteeth is used to infer the current profile near the magnetic axis; with external magnetic diagnostics alone, the current density profile is imprecisely reconstructed.

Microwave Imaging Reflectometry for the study of Edge Harmonic Oscillations on DIII-D

Quiescent H-mode (QH-mode) is an ELM free mode of operation in which edge-localized harmonic oscillations (EHOs) are believed to enhance particle transport, thereby stabilizing ELMs and preventing damage to the divertor and plasma facing components. Microwave Imaging Reflectometer (MIR) enabling direct comparison between the measured and simulated 2D images of density fluctuations near the edge can determine the 2D structure of density oscillation, which can help to explain the physics behind EHO modes. MIR data sometimes indicate a counter-propagation between dominant (n=1) and higher harmonic modes of coherent EHOs in the steep gradient regions of the pedestal. To preclude diagnostic artifacts, we have performed forward modeling that includes possible optical mis-alignments to show that offsets between transmitting and receiving antennas do not account for this feature. We have also simulated the non-linear structure of the EHO modes, which induces multiple harmonics that are properly charaterized in the synthetic diagnostic. By excluding mis-alignments of optics as well as patially eliminating non-linearity of EHO mode structure as possible explanation for the data, counter-propagation observed in MIR data, which is not corroborated by external Mirnov coil array measurements, may be due to subtleties of the eigenmode structure, such as an inversion radius consistent with a magnetic island. Similar effects are observed in analysis of internal ECE-Imaging and BES data. The identification of a non-ideal structure motivates further exploration of nonlinear models of this instability.A shorter version of this contribution is due to be published in PoS at: 1st EPS conference on Plasma Diagnostics

Electron Cyclotron Emission Imaging Observations of m/n = 1/1 and Higher Harmonic Modes during Sawtooth Oscillation in ICRF Heating Plasma on EAST**Supported by the National Magnetic Confinement Fusion Energy Program of China under Grant Nos 2013GB106002 and 2014GB109002, and the National Natural Science Foundation of China under Grant Nos 10990210 and 11275200.

The m/n = 1/1 and its higher harmonic modes are observed in sawtooth oscillations by using the novel high-resolution 2D ECE imaging system on the experimental advanced superconducting Tokamak (EAST). Higher harmonic modes are appearing for a short time during the crash phase of sawtooth oscillation in lower βp plasma, which is not the preferable position in the poloidal cross section. These modes generate sharp pressure points on the inversion radius during the crash phase of sawtooth oscillation. Furthermore, reconnection events proceed in two distinctive phases. In the first phase, a small amount of heat is expelled through the weak reconnection while in the second phase the remaining large quantity of heat and particles emerged rapidly from the hot core to the peripheral region of the inversion radius. In addition, these harmonic modes are only found before and after the ICRF pulse, while in the ICRF pulse only the (1,1) mode exists in the sawtooth oscillation.

Dynamics of multiple flux tubes in sawtoothing KSTAR plasmas heated by electron cyclotron waves: II. Theoretical and numerical analysis

The dynamics of multiple closed flux tubes in the core of a sawtoothing tokamak plasma are studied using nonlinear simulations. This is motivated by recent observations of long-lived hot spots in the electron cyclotron emission (ECE) images of KSTAR plasmas with electron cyclotron heating (ECH) (Yun et al 2012 Phys. Rev. Lett. 109 145003). Using an empirical source term in a reduced set of MHD equations, it is shown that flux tubes with helicity h = 1 are easily produced and survive for the observed time intervals only if the safety factor is close to unity (|q − 1| ≪ 0.5%) and the magnetic shear is small (|s| ≪ 1). This suggests that sawteeth in KSTAR leave behind wide regions where q ≈ 1. On the basis of the relevant time scales, we discuss how this magnetic geometry and the spatial localization of the EC resonance may allow ECH to actively induce the formation of flux tubes. Using simulations with q profiles that possess a wide q = 1 region inside the sawtooth inversion radius, we examine how the flux tubes merge and annihilate, and how their dynamics depend on the strength of the drive. The phenomena seen in the simulations and experiments lead us to conclude that, during the sawtooth ramp phase, there is a dynamic competition between sources and sinks of thermal and magnetic energy, where the flux tubes may play an important role; both as carriers of and channels for energy. The development of self-consistent simulation models is motivated and directions for future experiments are given.

Sawtooth control in JET with ITER relevant low field side resonance ion cyclotron resonance heating and ITER-like wall

New experiments at JET with the ITER-like wall show for the first time that ITER-relevant low field side resonance first harmonic ion cyclotron resonance heating (ICRH) can be used to control sawteeth that have been initially lengthened by fast particles. In contrast to previous (Graves et al 2012 Nat. Commun. 3 624) high field side resonance sawtooth control experiments undertaken at JET, it is found that the sawteeth of L-mode plasmas can be controlled with less accurate alignment between the resonance layer and the sawtooth inversion radius. This advantage, as well as the discovery that sawteeth can be shortened with various antenna phasings, including dipole, indicates that ICRH is a particularly effective and versatile tool that can be used in future fusion machines for controlling sawteeth. Without sawtooth control, neoclassical tearing modes (NTMs) and locked modes were triggered at very low normalised beta. High power H-mode experiments show the extent to which ICRH can be tuned to control sawteeth and NTMs while simultaneously providing effective electron heating with improved flushing of high Z core impurities. Dedicated ICRH simulations using SELFO, SCENIC and EVE, including wide drift orbit effects, explain why sawtooth control is effective with various antenna phasings and show that the sawtooth control mechanism cannot be explained by enhancement of the magnetic shear. Hybrid kinetic-magnetohydrodynamic stability calculations using MISHKA and HAGIS unravel the optimal sawtooth control regimes in these ITER relevant plasma conditions.

Effect of leading edge bluntness on the interaction of ramp induced shock wave with laminar boundary layer at hypersonic speed

Present investigations deal with ramp induced shock wave and boundary layer interaction (R-SWBLI) in the presence of leading edge bluntness. A second order accurate finite-volume compressible flow solver is employed to assess the effectiveness of leading edge bluntness in reducing the separation bubble size. Boundary layer edge Mach number and temperature, sonic height, boundary layer thicknesses, skin friction coefficient and pressure difference are considered for this assessment. Present studies reveal the existence of two critical radii of leading edge bluntness associated with R-SWBLI. Increase in separation bubble size has been observed with increase in leading edge radius until the first critical radius called as ‘inversion radius’ which corresponds to maximum extent of separation. Swallowing of the entropy layer by the boundary layer is seen to increase the separation zone size while the separation bubble length decreases when the boundary layer is immersed within the entropy layer. The inversion radius is shown to be associated with equal thicknesses of the entropy and boundary layers. Increase in leading edge radius beyond the second critical radius, called as ‘equivalent radius’, is found to decrease the size of separation zone in comparison with that of the sharp leading edge case. This reduction is attributed mainly to the existence of a wide over pressure region. Physics-driven predictive strategies, to determine the critical radii for given geometry and freestream conditions, are derived successfully from the present numerical simulations. Current studies on a 50mm long plate with 15° compression ramp for Mach number 6 and wall temperature of 300K show that the inversion radius lies between 0.3 and 0. 6mm while the equivalent radius lies between 1 and 1.2mm.

Microwave imaging reflectometry for density fluctuation measurement on KSTAR

A dual-frequency microwave imaging reflectometry system was commissioned to measure both coherent and turbulent electron density fluctuations in KSTAR plasmas. Imaging of the density fluctuations is achieved with an array of 16 vertically aligned detectors and two X-mode probe beam frequencies (tunable over 78–92 GHz between plasma discharges). The system provides the capability of fluctuation measurements with poloidal wavenumbers (kθ) up to ∼3 cm−1 at the maximum sampling rate of 2 MHz. Following extensive laboratory tests, the system was further tested with known coherent density fluctuations during the precursor oscillation of the m/n = 1/1 internal kink mode. The phase information of the reflected beam was compared with the precursor oscillation of the electron temperature measured by an electron cyclotron emission (ECE) radiometer. Density fluctuation levels (δne/ne) at two radial positions separated by the inversion radius (inside and outside) were comparable to temperature fluctuation levels (δTe/Te) from ECE signals. Subsequently, two correlation analysis methods were applied to turbulent fluctuation measurements in a neutral beam heated L-mode plasma to determine the mean poloidal rotation velocities of density fluctuations at two radial positions. The measured mean poloidal velocities were ∼8.4 km s−1 at r/a ∼ 0.6 and ∼5 km s−1 at r/a ∼ 0.7 in the clockwise direction, which differed by 1–2 km s−1 with the projected poloidal velocities from the toroidal rotation velocity measured by charge exchange recombination spectroscopy.

Non-local heat transport, rotation reversals and up/down impurity density asymmetries in Alcator C-Mod ohmic L-mode plasmas

Several seemingly unrelated effects in Alcator C-Mod ohmic L-mode plasmas are shown to be closely connected: non-local heat transport, core toroidal rotation reversals, energy confinement saturation and up/down impurity density asymmetries. These phenomena all abruptly transform at a critical value of the collisionality. At low densities in the linear ohmic confinement regime, with collisionality ν* ⩽ 0.35 (evaluated inside of the q = 3/2 surface), heat transport exhibits non-local behaviour, core toroidal rotation is directed co-current, edge impurity density profiles are up/down symmetric and a turbulent feature in core density fluctuations with kθ up to 15 cm−1 (kθρs ∼ 1) is present. At high density/collisionality with saturated ohmic confinement, electron thermal transport is diffusive, core rotation is in the counter-current direction, edge impurity density profiles are up/down asymmetric and the high kθ turbulent feature is absent. The rotation reversal stagnation point (just inside of the q = 3/2 surface) coincides with the non-local electron temperature profile inversion radius. All of these observations suggest a possible unification in a model with trapped electron mode prevalence at low collisionality and ion temperature gradient mode domination at high collisionality.

Geometric Phase and Sidebands

Geometric phase of mixed state is expanded for a two-level atom interacting with a quantized field mode, where master equation is a modified Bloch equation with constant terms that are used to explain emergence of sidebands in the spectrum of the fluorescent light. The results show that geometric phase transition is observed for medium initial angle when the Rabi frequency associated with the driving field becomes comparable to the spectral width of the atom. We find that the geometric phase transition depends on population inversion and Bloch radius, which is helpful to understand mechanism of sideband.

Resonant field amplification with feedback-stabilized regime in current driven resistive wall mode

The stability and resonant field response of current driven resistive wall modes are numerically studied for DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] low pressure plasmas. The resonant field response of the feedback-stabilized resistive wall mode is investigated both analytically and numerically, and compared with the response from intrinsically stable or marginally stable modes. The modeling qualitatively reproduces the experimental results. Furthermore, based on some recent results and on the indirect numerical evidence in this work, it is suggested that the mode stability behavior observed in DIII-D experiments is due to the kink-peeling mode stabilization by the separatrix geometry. The phase inversion radius of the computed plasma displacement does not generally coincide with the radial locations of rational surfaces, also supporting experimental observations.

Observations of counter-current toroidal rotation in Alcator C-Mod LHCD plasmas

Following the application of lower hybrid current drive (LHCD) power, the core toroidal rotation in Alcator C-Mod L- and H-mode plasmas is found to increment in the counter-current direction, in conjunction with a decrease in the plasma internal inductance, li. Along with the drops in li and the core rotation velocity, there is peaking of the electron and impurity density profiles, as well as of the ion and electron temperature profiles. The mechanism generating the counter-current rotation is unknown, but it is consistent in sign with an inward shift of energetic electron orbits, giving rise to a negative core radial electric field. The peaking in the density, toroidal rotation (in the counter-current direction) and temperature profiles occurs over a time scale similar to the current relaxation time but slow compared with the energy and momentum confinement times. Most of these discharges exhibit sawtooth oscillations throughout, with the inversion radius shifting inward during the LHCD and profile evolution. The magnitudes of the changes in the internal inductance and the central rotation velocity are strongly correlated and found to increase with increasing LHCD power and decreasing electron density. The maximum effect is obtained with a waveguide phasing of 60° (a launched parallel index of refraction n‖ ∼ 1.5), with a significantly smaller magnitude at 120° (n‖ ∼ 3.1), and with no effect for negative or heating (180°) phasing. Regardless of the plasma parameters and launched n‖ of the waves, there is a strong correlation between the rotation velocity and li changes, possibly providing a clue for the underlying mechanism.

Closed Loop Sawtooth Period Control Using Variable ECCD Injection Angles on Tore Supra

Closed loop control of the period of fast ion stabilized sawtooth has been demonstrated for the first time on Tore Supra by varying the electron cyclotron current drive (ECCD) injection angles in real time. Fast ions generated by up to 4 MW of central ion cyclotron resonance heating (ICRH) increased the sawtooth period from the ohmic value of 25 ms to 60 to 100 ms. This sawtooth period was reduced to 30 ms by the addition of only 300 kW of ECCD. In ICRH heated shots where the normalized minor radius of the ECCD absorption location was swept from 0.4 to 0.05 in 4 s, the sawtooth period showed an abrupt change from 70 to 30 ms when the ECCD deposition normalized minor radius reached ~0.2. This short period was then maintained until the absorption location moved well inside the sawtooth inversion radius at which point it abruptly returned to 70 ms. A closed loop controller was implemented that allowed the sawtooth period to be switched in real time between short and long sawteeth with a response time of the order of 1 s.

QCD-Instantons and conformal space-time inversion symmetry

In this paper, we explore the appealing possibility that the strong suppression of large-size QCD instantons - as evident from lattice data - is due to a surviving conformal space-time inversion symmetry. This symmetry is both suggested from the striking invariance of high-quality lattice data for the instanton size distribution under inversion of the instanton size rho --> ^2 / rho and from the known validity of space-time inversion symmetry in the classical instanton sector. We project the instanton calculus onto the four-dimensional surface of a five-dimensional sphere via conformal stereographic mapping, before investigating conformal inversion. This projection to a compact, curved geometry is both to avoid the occurence of divergences and to introduce the average instanton size from the lattice data as a new length scale. The average instanton size is identified with the radius b of this 5d-sphere and acts as the conformal inversion radius. For b = , our corresponding results are almost perfectly symmetric under space-time inversion and in good qualitative agreement with the lattice data. For rho / b --> 0, we recover the familiar results of instanton perturbation theory in flat 4d-space. Moreover, we illustrate that a (weakly broken) conformal inversion symmetry would have significant consequences for QCD beyond instantons. As a further successful test for inversion symmetry, we present striking implications for another instanton dominated lattice observable, the chirality-flip ratio in the QCD vacuum.

Stabilization of neoclassical tearing modes by electron cyclotron current drive in JT-60U

Results of active control of neoclassical tearing modes (NTMs) by electron cyclotron current drive (ECCD) in JT-60U are described. Growth of an NTM with poloidal mode number m = 3 and toroidal mode number n = 2 has been suppressed by ECCD inside the sawtooth inversion radius in the co-direction, showing the possibility of the coexistence of sawtooth oscillations and a small-amplitude m/n = 3/2 NTM without large confinement degradation. Stabilization of an m/n = 2/1 NTM by ECCD at the mode rational surface has been demonstrated with a small ratio of the current density driven by the electron cyclotron (EC) wave to the local bootstrap current density (∼ 0.5). In addition, dependence of the stabilization effect on ECCD location has been investigated in detail. It has been found that an m/n = 2/1 NTM can be completely stabilized with the misalignment of the ECCD location less than about half of the full island width, and that the m/n = 2/1 NTM is destabilized with the misalignment comparable to the full island width. Time-dependent, self-consistent simulation of magnetic island evolution using the TOPICS code has shown that the stabilization and destabilization of an m/n = 2/1 NTM are well reproduced with the same set of coefficients of the modified Rutherford equation. The TOPICS simulation has also clarified that EC wave power required for complete stabilization can be significantly reduced by narrowing the ECCD deposition width.

New Insights to the Sawtooth Oscillation (“m/n = 1/1 mode”) in Hot Plasmas based on High Resolution 2-D Images of Te Fluctuations

Two dimensional (2-D) images of electron temperature fluctuations with high temporal and spatial resolution have been employed to study the sawtooth oscillation (m/n=1/1 mode) in Toroidal EXperiment for Technology Oriented Research (TEXTOR) tokamak plasmas. 2-D imaging data revealed new physics which were not available in previous studies based on the 1-D electron temperature measurement and X-ray tomography. Review of the physics of the sawtooth oscillation is given by comparative studies with prominent theoretical models suggest that a new physics paradigm is needed to describe the reconnection physics of the sawtooth oscillation. The new insights are: A pressure driven instability (not a ballooning mode) leads to the X-point reconnection process. The reconnection process is identified as a random 3-D local reconnection process with a helical structure. The reconnection time scale is similar for different types of sawtooth oscillation (kink and tearing type) and is significantly faster than the resistive time scale. Heat flow from the core to the outside of the inversion radius during the reconnection process is highly collective rather than stochastic.

Self-organized Te redistribution during driven reconnection processes in high-temperature plasmas

Two-dimensional (2D) images of electron temperature fluctuations with high temporal and spatial resolution were employed to study the sawtooth oscillation in Toroidal EXperiment for Technology Oriented Research [S. S. Abdallaev et al., Nucl. Fusion 43, 299 (2003)] tokamak plasmas. The new findings are: (1) 2D images revealed that the reconnection is localized and permitted the determination of the physical dimensions of the reconnection zone in the poloidal and toroidal planes. (2) The combination of a pressure bulge due to finite pressure effects or a kink instability accompanied with a sharp pressure point leads to an “X-point” reconnection process. (3) Reconnection can take place anywhere along the q∼1 rational magnetic surface (both high- and low-field sides). (4) Heat flow from the core to the outside of the inversion radius during the reconnection time is through the finite opening on the poloidal and toroidal planes and the flow is highly collective. These new findings are compared with the characteristics of various theoretical models and experimental results for the study of the sawtooth oscillation in tokamak plasmas.

Toroidal plasma rotation in the TCV tokamak

The first toroidal rotation measurements in TCV ohmic L-mode plasmas with no external momentum injection are presented. The toroidal velocity profile of the fully stripped carbon species is measured by active Charge eXchange Recombination Spectroscopy with a temporal resolution of typically 90 ms and a spatial resolution of 2.5 cm, about 1/10 of the plasma radius. The observed carbon velocity is of the order of the deuterium diamagnetic drift velocity and up to 1/5 of the deuterium thermal velocity. It is directed opposite to plasma current in the electron diamagnetic toroidal drift direction. The profile reverses when reversing the plasma current. The angular velocity profile is flat, or hollow, inside the sawtooth inversion radius and decreases quasi linearly towards the plasma edge. By vertically shifting the plasma magnetic axis within the TCV vessel the plasma edge velocity profile was measured with high resolution. Such experiments confirm that, close to the limiter, the stationary rotation velocity is close to zero or somewhat positive (co-current directed). This suggests that the angular momentum is not driven from the plasma edge. The maximum carbon velocity scales as vϕ,Max [km s−1] = −12.5Ti/Ip [eV/kA] for a significant range of densities and values of the edge safety factor. Comparison with neoclassical predictions show that the TCV plasma rotation is mainly driven by radial electric fields, with a negligible contribution from the toroidal electric fields. The neoclassical theory of small toroidal rotation quantitatively and qualitatively disagrees with the experimental observation. An alternative empirical equation for the angular momentum flux, able to reproduce the measured stationary profile outside the inversion radius, is proposed.

Modelling of minority ion cyclotron current drive during the activated phase of ITER

Neoclassical tearing modes, triggered by the long-period sawteeth expected in tokamaks with large non-thermal α-particle populations, may impose a severe β limit on experiments with large fusion yields and on reactors. Sawtooth destabilization by localized current drive could relax the β limit and improve plasma performance. 3He minority ion cyclotron current drive around the sawtooth inversion radius has been planned for ITER. Several ion species, including beam injected D ions and fusion born α particles, are however also resonant in the plasma and may represent a parasitic absorption of RF power.Modelling of minority ion cyclotron current drive in an ITER-FEAT-like plasma is presented, including the effects of ion trapping, finite ion drift orbit widths, wave-induced radial transport and the coupled evolution of wave fields and resonant ion distributions. The parasitic absorption of RF power by the other resonant species is concluded to be relatively small, but the 3He minority current drive is nevertheless negligible due to the strong collisionality of the 3He ions and the drag current by toroidally counter-rotating background ions and co-rotating electrons. H minority current drive is found to be a significantly more effective alternative.

Experimental observation of m/n = 1/1 mode behaviour during sawtooth activity and its manifestations in tokamak plasmas**This is an extended version of the paper presented at the 31st EPS Conf. on Plasma Physics (London, 28 June–2 July 2004).

To shed some light on the development of the fast m/n = 1/1 precursor to the sawtooth crash and its influence on plasma transport properties in the vicinity of the q = 1 surface, series of dedicated experiments have been conducted on the Tore Supra and TEXTOR tokamaks. It has been concluded that, before a crash, the hot core gets displaced with respect to the magnetic axis, drifts outwards by as much as 8–10 cm and may change its shape. Observation of the magnetic reconnection process has been made by means of electron cyclotron emission diagnostics. The heat pulse is seen far outside the inversion radius. The colder plasma develops a magnetic island on the former magnetic axis, after the hot core expulsion. Different kinds of behaviour of the m = 1 precursor before the crash, with respect to the displacement of the hot core and the duration of the oscillating phase, have been observed. An ideal kink model alone cannot be used for explanation; therefore, resistive effects play an important role in the mode development. Possible mechanisms that lead an m = 1 mode to such behaviour, and their links to the change in the central q-profile, are discussed. Results have been discussed in the light of various theoretical models of the sawtooth.