Highlights of 2016

This paper summarizes the status of the COMPASS tokamak, its comprehensive diagnostic equipment and plasma scenarios as a baseline for the future studies. The former COMPASS-D tokamak was in operation at UKAEA Culham, UK in 1992–2002. Later, the device was transferred to the Institute of Plasma Physics of the Academy of Sciences of the Czech Republic (IPP AS CR), where it was installed during 2006–2011. Since 2012 the device has been in a full operation with Type-I and Type-III ELMy H-modes as a base scenario. This enables together with the ITER-like plasma shape and flexible NBI heating system (two injectors enabling co- or balanced injection) to perform ITER relevant studies in different parameter range to the other tokamaks (ASDEX-Upgrade, DIII-D, JET) and to contribute to the ITER scallings. In addition to the description of the device, current status and the main diagnostic equipment, the paper focuses on the characterization of the Ohmic as well as NBI-assisted H-modes. Moreover, Edge Localized Modes (ELMs) are categorized based on their frequency dependence on power density flowing across separatrix. The filamentary structure of ELMs is studied and the parallel heat flux in individual filaments is measured by probes on the outer mid-plane and in the divertor. The measurements are supported by observation of ELM and inter-ELM filaments by an ultra-fast camera.

Magnetic reconnection is the topological reconfiguration of the magnetic field in a plasma, accompanied by the violent release of energy and particle acceleration. Reconnection is as ubiquitous as plasmas themselves, with solar flares perhaps the most popular example. Other fascinating processes where reconnection plays a key role include the magnetic dynamo, geomagnetic storms and the sawtooth crash in tokamaks.

Over the last few years, the theoretical understanding of magnetic reconnection in large-scale fluid systems has undergone a major paradigm shift. The steady-state model of reconnection described by the famous Sweet–Parker (SP) theory, which dominated the field for  ∼50 years, has been replaced with an essentially time-dependent, bursty picture of the reconnection layer, dominated by the continuous formation and ejection of multiple secondary islands (plasmoids). Whereas in the SP model reconnection was predicted to be slow, a major implication of this new paradigm is that reconnection in fluid systems is fast (i.e. independent of the Lundquist number), provided that the system is large enough. This conceptual shift hinges on the realization that SP-like current layers are violently unstable to the plasmoid (tearing) instability—implying, therefore, that such current sheets are super-critically unstable and thus can never form in the first place. This suggests that the formation of a current sheet and the subsequent reconnection process cannot be decoupled, as is commonly assumed.

This paper provides an introductory-level overview of the recent developments in reconnection theory and simulations that led to this essentially new framework. We briefly discuss the role played by the plasmoid instability in selected applications, and describe some of the outstanding challenges that remain at the frontier of this subject. Amongst these are the analytical and numerical extension of the plasmoid instability to (i) 3D and (ii) non-magnetohydrodynamics (MHD) regimes. New results are reported in both cases.

Pulsed beams of energetic x-rays and neutrons from intense laser interactions with solid foils are promising for applications where bright, small emission area sources, capable of multi-modal delivery are ideal. Possible end users of laser-driven multi-modal sources are those requiring advanced non-destructive inspection techniques in industry sectors of high value commerce such as aerospace, nuclear and advanced manufacturing. We report on experimental work that demonstrates multi-modal operation of high power laser-solid interactions for neutron and x-ray beam generation. Measurements and Monte Carlo radiation transport simulations show that neutron yield is increased by a factor ~2 when a 1 mm copper foil is placed behind a 2 mm lithium foil, compared to using a 2 cm block of lithium only. We explore x-ray generation with a 10 picosecond drive pulse in order to tailor the spectral content for radiography with medium density alloy metals. The impact of using  >1 ps pulse duration on laser-accelerated electron beam generation and transport is discussed alongside the optimisation of subsequent bremsstrahlung emission in thin, high atomic number target foils. X-ray spectra are deconvolved from spectrometer measurements and simulation data generated using the GEANT4 Monte Carlo code. We also demonstrate the unique capability of laser-driven x-rays in being able to deliver single pulse high spatial resolution projection imaging of thick metallic objects. Active detector radiographic imaging of industrially relevant sample objects with a 10 ps drive pulse is presented for the first time, demonstrating that features of 200 μm size are resolved when projected at high magnification.

It was noted earlier [1] that high performance regimes of many tokamaks were achieved in the condition of plasma heating power P_H limited from above. The exceeding of this limit usually ended as a plasma collapse. The analysis of the high performance regimes of well known tokamaks which operated during the last 50 years has shown that the values of such 'permissible' P_H grow approximately linearly with the area S of the first wall surface facing to the plasma. The paper attempts to explain the existence the P_H/S limit for high performance tokamak regimes as a consequence of the vacuum breakdown of the plasma sheath in the area of a plasma contact with the vessel wall and unipolar arcs which followed it.

An electron beam has gained a maximum energy of 9 GeV per particle in a 1.3 m-long electron beam-driven plasma wakefield accelerator. The amount of charge accelerated in the spectral peak was 28.3 pC, and the root-mean-square energy spread was 5.0%. The mean accelerated charge and energy gain per particle of the 215 shot data set was 115 pC and 5.3 GeV, respectively, corresponding to an acceleration gradient of 4.0 GeV m⁻¹at the spectral peak. The mean energy spread of the data set was 5.1%. These results are consistent with the extrapolation of the previously reported energy gain results using a shorter, 36 cm-long plasma source to within 10%, evincing a non-evolving wake structure that can propagate distances of over a meter in length. Wake-loading effects were evident in the data through strong dependencies observed between various spectral properties and the amount of accelerated charge.

The laser–plasma accelerator (LPA) presently provides electron beams with a typical current of a few kA, a bunch length of a few fs, energy in the few hundred MeV to several GeV range, a divergence of typically 1 mrad, an energy spread of the order of 1%, and a normalized emittance of the order of π.mm.mrad. One of the first applications could be to use these beams for the production of radiation: undulator emission has been observed but the rather large energy spread (1%) and divergence (1 mrad) prevent straightforward free-electron laser (FEL) amplification. An adequate beam manipulation through the transport to the undulator is then required. The key concept proposed here relies on an innovative electron beam longitudinal and transverse manipulation in the transport towards an undulator: a 'demixing' chicane sorts the electrons according to their energy and reduces the spread from 1% to one slice of a few ‰ and the effective transverse size is maintained constant along the undulator (supermatching) by a proper synchronization of the electron beam focusing with the progress of the optical wave. A test experiment for the demonstration of FEL amplification with an LPA is under preparation. Electron beam transport follows different steps with strong focusing with permanent magnet quadrupoles of variable strength, a demixing chicane with conventional dipoles, and a second set of quadrupoles for further focusing in the undulator. The FEL simulations and the progress of the preparation of the experiment are presented.

We report on the development of foam-based double-layer targets (DLTs) for laser-driven ion acceleration. Foam layers with a density of a few mg cm⁻³ and controlled thickness in the 8–36 μm range were grown on μm-thick Al foils by pulsed laser deposition (PLD). The DLTs were experimentally investigated by varying the pulse intensity, laser polarisation and target properties. Comparing DLTs with simple Al foils, we observed a systematic enhancement of the maximum and average energies and number of accelerated ions. Maximum energies up to 30 MeV for protons and 130 MeV for C⁶⁺ ions were detected. Dedicated three-dimensional particle-in-cell (3D-PIC) simulations were performed considering both uniform and cluster-assembled foams to interpret the effect of the foam nanostructure on the acceleration process.

Results from recent experiment and numerical simulation point towards a picture of the L-H transition in which edge shear flows interacting with edge turbulence create the conditions needed to produce a non-zero turbulent Reynolds stress at and just inside the LCFS during L-mode discharges. This stress acts to reinforce the shear flow at this location and the flow drive gets stronger as heating is increased. The L-H transition ensues when the rate of work done by this stress is strong enough to drive the shear flow to large values, which then grows at the expense of the turbulence intensity. The drop in turbulence intensity momentarily reduces the heat flux across the magnetic flux surface, which then allows the edge plasma pressure gradient to build. A sufficiently strong ion pressure gradient then locks in the H-mode state. These results are in general agreement with previously published reduced 0D and 1D predator prey models. An extended predator–prey model including separate ion and electron heat channels yields a non-monotonic power threshold dependence on plasma density provided that the fraction of heat deposited on the ions increases with plasma density. Possible mechanisms to explain other macroscopic transition threshold criteria are identified. A number of open questions and unexplained observations are identified, and must be addressed and resolved in order to build a physics-based model that can yield predictions of the macroscopic conditions needed for accessing H-mode.

The runaway electron mechanism is of great importance for the understanding of the generation of x- and gamma rays in atmospheric discharges. In 1991, terrestrial gamma-ray flashes (TGFs) were discovered by the Compton Gamma-Ray Observatory. Those emissions are bremsstrahlung from high energy electrons that run away in electric fields associated with thunderstorms. In this paper, we discuss the runaway threshold definition with a particular interest in the influence of the angular scattering for electron energy close to the threshold. In order to understand the mechanism of runaway, we compare the outcome of different Fokker–Planck and Monte Carlo models with increasing complexity in the description of the scattering. The results show that the inclusion of the stochastic nature of collisions smooths the probability to run away around the threshold. Furthermore, we observe that a significant number of electrons diffuse out of the runaway regime when we take into account the diffusion in angle due to the scattering. Those results suggest using a runaway threshold energy based on the Fokker–Planck model assuming the angular equilibrium that is 1.6 to 1.8 times higher than the one proposed by [1, 2], depending on the magnitude of the ambient electric field. The threshold also is found to be 5 to 26 times higher than the one assuming forward scattering. We give a fitted formula for the threshold field valid over a large range of electric fields. Furthermore, we have shown that the assumption of forward scattering is not valid below 1 MeV where the runaway threshold usually is defined. These results are important for the thermal runaway and the runaway electron avalanche discharge mechanisms suggested to participate in the TGF generation.

We report on a study on controlled trapping of electrons, by field ionization of nitrogen ions, in laser wakefield accelerators in variable length gas cells. In addition to ionization-induced trapping in the density plateau inside the cells, which results in wide, but stable, electron energy spectra, a regime of ionization-induced trapping localized in the density down-ramp at the exit of the gas cells, is found. The resulting electron energy spectra are peaked, with 10% shot-to-shot fluctuations in peak energy. Ionization-induced trapping of electrons in the density down-ramp is a way to trap and accelerate a large number of electrons, thus improving the efficiency of the laser-driven wakefield acceleration.

Single photon counting techniques were used with an x-ray CCD camera to measure features of synchrotron-like x-ray spectra generated by betatron oscillations of electrons in a laser wakefield accelerator (LWFA) with different injection techniques. Measurements were made using the Hercules laser system at the University of Michigan. With a single stage gas cell, we demonstrate that pure helium gas in our wakefield accelerator will produce spectra with higher critical energies than when helium mixed with nitrogen is used. This result was not evident when a two stage gas cell was used.

In HL-2A, the characteristics of the edge plasma instabilities and their effects on the dynamical evolution of the pedestal in H-mode plasmas have been investigated. In the edge pedestal region with steep pressure gradient, a quasi-coherent mode (QCM) has been observed in density fluctuations with a frequency range of 50–100 kHz. It appears during the edge localized mode (ELM)-free period after the L–H transition and prior to the first ELM. A threshold in the pedestal density gradient has been identified for the excitation of this mode. The QCM can also be observed during inter-ELM periods. It is excited early in the inter-ELM period, and disappears when the ELM onset starts. The radial wave-number of the mode is estimated with two radially separated reflectometers. It shows that the mode is radially propagating inward. The poloidal wave number estimated with the Langmuir probes is k_θ ~ 0.43 cm⁻¹. The mode propagates poloidally in the electron diamagnetic direction in the plasma frame. The toroidal mode number, deduced from Mirnov signals, is n ~ 7. The corresponding poloidal mode number is m ~ 21 according to the local safety factor value. The analysis for the dynamical evolution of the pedestal during the ELM cycle clearly shows that the mode is excited before the ELM onset. During and after the ELM crash, the mode disappears. It suggests that the QCM is driven by the pedestal density gradient, and the mode in return regulates the pedestal density evolution.

In order to understand the mechanisms that determine the structure of the high confinement mode (H-mode) pedestal, the evolution of the plasma edge electron density and temperature profiles between edge localised modes (ELMs) is investigated. The onset of radial magnetic fluctuations with frequencies above 200 kHz is found to correlate with the stagnation of the electron temperature pedestal gradient. During the presence of these magnetic fluctuations the gradients of the edge electron density and temperature are clamped and stable against the ELM onset. The detected magnetic fluctuation frequency is analysed for a variety of plasma discharges with different electron pressure pedestals. It is shown that the magnetic fluctuation frequency scales with the neoclassically estimated $\text{E}\,\times \text{B}$ velocity at the plasma edge. This points to a location of the underlying instability in the gradient region. Furthermore, the magnetic signature of these fluctuations indicates a global mode structure with toroidal mode numbers of approximately 10. The fluctuations are also observed on the high field side with significant amplitude, indicating a mode structure that is symmetric on the low field side and high field side. The associated fluctuations in the current on the high field side might be attributed to either a strong peeling part or the presence of non-adiabatic electron response.

As in many of today's tokamaks, plasma start-up in ITER will be performed in limiter configuration on either the inner or outer midplane first wall (FW). The massive, beryllium armored ITER FW panels are toroidally shaped to protect panel-to-panel misalignments, increasing the deposited power flux density compared with a purely cylindrical surface. The chosen shaping should thus be optimized for a given radial profile of parallel heat flux, ${{q}_{||}}$ in the scrape-off layer (SOL) to ensure optimal power spreading. For plasmas limited on the outer wall in tokamaks, this profile is commonly observed to decay exponentially as ${{q}_{||}}={{q}_{0}}\text{exp} ~\left(-r/\lambda _{q}^{\text{omp}}\right)$, or, for inner wall limiter plasmas with the double exponential decay comprising a sharp near-SOL feature and a broader main SOL width, $\lambda _{q}^{\text{omp}}$. The initial choice of $\lambda _{q}^{\text{omp}}$, which is critical in ensuring that current ramp-up or down will be possible as planned in the ITER scenario design, was made on the basis of an extremely restricted L-mode divertor dataset, using infra-red thermography measurements on the outer divertor target to extrapolate to a heat flux width at the main plasma midplane. This unsatisfactory situation has now been significantly improved by a dedicated multi-machine ohmic and L-mode limiter plasma study, conducted under the auspices of the International Tokamak Physics Activity, involving 11 tokamaks covering a wide parameter range with $R=\text{0}\text{.4--2}\text{.8}\,\text{m},\,{{B}_{0}}=\text{1}\text{.2--7}\text{.5}\,\text{T},\,{{I}_{\text{p}}}=\text{9--2500}\,\text{kA}.$ Measurements of $\lambda _{q}^{\text{omp}}$ in the database are made exclusively on all devices using a variety of fast reciprocating Langmuir probes entering the plasma at a variety of poloidal locations, but with the majority being on the low field side. Statistical analysis of the database reveals nine reasonable engineering and dimensionless scalings. All yield, however, similar predicted values of $\lambda _{q}^{\text{omp}}$ mapped to the outside midplane. The engineering scaling with the highest statistical significance, $\lambda _{q}^{\text{omp}}=10{{\left({{P}_{\text{tot}}}/V\,\left(\text{W}\,{{\text{m}}^{-3}}\right)\right)}^{-0.38}}{{\left(a/R/\kappa \right)}^{1.3}}$, dependent on input power density, aspect ratio and elongation, yields $\lambda _{q}^{\text{omp}}$  =  [7, 4, 5] cm for ${{I}_{\text{p}}}$  =  [2.5, 5.0, 7.5] MA, the three reference limiter plasma currents specified in the ITER heat and nuclear load specifications. Mapped to the inboard midplane, the worst case (7.5 MA) corresponds to $\lambda _{q}^{\text{imp}}\sim 57\pm 14$ mm, thus consolidating the 50 mm width used to optimize the FW panel toroidal shape.

As a starting point for a more in-depth discussion of a research strategy leading from Wendelstein 7-X to a HELIAS power plant, the respective steps in physics and engineering are considered from different vantage points. The first approach discusses the direct extrapolation of selected physics and engineering parameters. This is followed by an examination of advancing the understanding of stellarator optimisation. Finally, combining a dimensionless parameter approach with an empirical energy confinement time scaling, the necessary development steps are highlighted. From this analysis it is concluded that an intermediate-step burning-plasma stellarator is the most prudent approach to bridge the gap between W7-X and a HELIAS power plant. Using a systems code approach in combination with transport simulations, a range of possible conceptual designs is analysed. This range is exemplified by two bounding cases, a fast-track, cost-efficient device with low magnetic field and without a blanket and a device similar to a demonstration power plant with blanket and net electricity power production.

The toroidal torque due to the non-resonant interaction with external magnetic perturbations (TF ripple and perturbations from ELM mitigation coils) in ASDEX Upgrade is modelled with help of the NEO-2 and SFINCS codes and compared to semi-analytical models. It is shown that almost all non-axisymmetric transport regimes contributing to neoclassical toroidal viscosity (NTV) are realized within a single discharge at different radial positions. The NTV torque is obtained to be roughly a quarter of the NBI torque. This indicates the presence of other important momentum sources. The role of these momentum sources and possible integral torque balance measurements are briefly discussed.

Experimental observations of driven and intrinsic rotation in tokamak plasmas are reviewed. For momentum sources, there is direct drive from neutral beam injection, lower hybrid and ion cyclotron range of frequencies waves (including mode conversion flow drive), as well as indirect $\mathbf{j}\times \mathbf{B}$ forces from fast ion and electron orbit shifts, and toroidal magnetic field ripple loss. Counteracting rotation drive are sinks, such as from neutral drag and toroidal viscosity. Many of these observations are in agreement with the predictions of neo-classical theory while others are not, and some cases of intrinsic rotation remain puzzling. In contrast to particle and heat fluxes which depend on the relevant diffusivity and convection, there is an additional term in the momentum flux, the residual stress, which can act as the momentum source for intrinsic rotation. This term is independent of the velocity or its gradient, and its divergence constitutes an intrinsic torque. The residual stress, which ultimately responds to the underlying turbulence, depends on the confinement regime and is a complicated function of collisionality, plasma shape, and profiles of density, temperature, pressure and current density. This leads to the rich intrinsic rotation phenomenology. Future areas of study include integration of these many effects, advancement of quantitative explanations for intrinsic rotation and development of strategies for velocity profile control.

Azimuthal convective flow and density-depleted magnetic field-aligned current co-located in the helium plasma produced in the large plasma device (LAPD-U) at UCLA (Gekelman et al 2016 Rev. Sci. Instrum. 87 025105) support an Alfvénic perturbation that is static in the laboratory frame. Electrostatic probes measure the flow and static density perturbations in the 72 cm-diameter, 12 m-long, afterglow plasma, wherein a radially segmented electrode creates the convective flow and an off-cylindrical-axis planar-mesh electrode draws current in a channel parallel to the background magnetic field. This stationary 'wave' is measured as a fixed (in the laboratory frame) ion density structure.

A theoretical study is presented of the electrostatic electron cyclotron instability involving Bernstein modes in a magnetized plasma. The presence of a tenuous thermal ring distribution in a Maxwellian plasma decreases the frequency of the upper hybrid branch of the electron Bernstein mode until it merges with the nearest lower branch with a resulting instability. The instability occurs when the upper hybrid frequency is somewhat above the third, fourth, and higher electron cyclotron harmonics, and gives rise to a narrow spectrum of waves around the electron cyclotron harmonic nearest to the upper hybrid frequency. For a tenuous cold ring distribution together with a Maxwellian distribution an instability can take place also near the second electron cyclotron harmonic. Noise-free Vlasov simulations are used to assess the theoretical linear growth-rates and frequency spectra, and to study the nonlinear evolution of the instability. The relevance of the results to laboratory and ionospheric heating experiments is discussed.

In magnetic controlled fusion devices, plasma heating with radio-frequency (RF) waves in the ion cyclotron (IC) range of frequency relies on the electric field of the fast wave to heat the plasma. However, the slow wave can be generated parasitically. The electric field of the slow wave can induce large biased plasma potential (DC potential) through sheath rectification. The rapid variation of the rectified potential across the equilibrium magnetic field can cause significant convective transport (E  ×  B drifts) in the scrape-off layer (SOL). In order to understand this phenomenon and reproduce the experiments, 3D realistic simulations are carried out with the 3D edge plasma fluid and kinetic neutral code EMC3-Eirene in ASDEX Upgrade. For this, we have added the prescribed drift terms to the EMC3 equations and verified the 3D code results against the analytical ones in cylindrical geometry. The edge plasma potential derived from the experiments is used to calculate the drift velocities, which are then treated as input fields in the code to obtain the final density distributions. Our simulation results are in good agreement with the experiments.

Laser-wakefield accelerators (LWFAs) were proposed more than three decades ago, and while they promise to deliver compact, high energy particle accelerators, they will also provide the scientific community with novel light sources. In a LWFA, where an intense laser pulse focused onto a plasma forms an electromagnetic wave in its wake, electrons can be trapped and are now routinely accelerated to GeV energies. From terahertz radiation to gamma-rays, this article reviews light sources from relativistic electrons produced by LWFAs, and discusses their potential applications. Betatron motion, Compton scattering and undulators respectively produce x-rays or gamma-rays by oscillating relativistic electrons in the wakefield behind the laser pulse, a counter-propagating laser field, or a magnetic undulator. Other LWFA-based light sources include bremsstrahlung and terahertz radiation. We first evaluate the performance of each of these light sources, and compare them with more conventional approaches, including radio frequency accelerators or other laser-driven sources. We have then identified applications, which we discuss in details, in a broad range of fields: medical and biological applications, military, defense and industrial applications, and condensed matter and high energy density science.

The U.S. National Academies established in 2011 a steering committee to develop a comprehensive strategy for solar and space physics research. This updated and extended the first (2003) solar and space physics decadal survey. The latest decadal study implemented a 2008 Congressional directive to NASA for the fields of solar and space physics, but also addressed research in other federal agencies. The new survey broadly canvassed the fields of research to determine the current state of the discipline, identified the most important open scientific questions, and proposed the measurements and means to obtain them so as to advance the state of knowledge during the years 2013–2022. Research in this field has sought to understand:

dynamical behaviour of the Sun and its heliosphere;

properties of the space environments of the Earth and other solar system bodies;

multiscale interaction between solar system plasmas and the interstellar medium; and

energy transport throughout the solar system and its impact on the Earth and other solar system bodies.

Research in solar and space plasma processes using observation, theory, laboratory studies, and numerical models has offered the prospect of understanding this interconnected system well enough to develop a predictive capability for operational support of civil and military space systems. We here describe the recommendations and strategic plans laid out in the 2013–2022 decadal survey as they relate to measurement capabilities and plasma physical research. We assess progress to date. We also identify further steps to achieve the Survey goals with an emphasis on plasma physical aspects of the program.

The time-dependent bounce-averaged CQL3D flux-conservative finite-difference Fokker–Planck equation (FPE) solver has been upgraded to include finite-orbit-width (FOW) capabilities which are necessary for an accurate description of neoclassical transport, losses to the walls, and transfer of particles, momentum, and heat to the scrape-off layer. The FOW modifications are implemented in the formulation of the neutral beam source, collision operator, RF quasilinear diffusion operator, and in synthetic particle diagnostics. The collisional neoclassical radial transport appears naturally in the FOW version due to the orbit-averaging of local collision coefficients coupled with transformation coefficients from local (R, Z) coordinates along each guiding-center orbit to the corresponding midplane computational coordinates, where the FPE is solved. In a similar way, the local quasilinear RF diffusion terms give rise to additional radial transport of orbits. We note that the neoclassical results are obtained for 'full' orbits, not dependent on a common small orbit-width approximation. Results of validation tests for the FOW version are also presented.

This review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian chaos, and then deals with order or quasi order, for instance adiabatic and soliton theories. It ends with a shorter account of dissipative and high dimensional Hamiltonian dynamics, and of quantum chaos. Most of these contributions are a spin-off of the research on thermonuclear fusion by magnetic confinement, which started in the fifties. Their presentation is both exhaustive and compact.

In conditions of ideal axisymmetry, for a magnetized plasma in a generic bounded domain, necessarily toroidal, the uniform absorption of external energy (e.g. rf or isotropic alpha heating) clearly cannot give rise to net forces or torques. A rather common experimental observation on contemporary tokamaks is that the near central absorption of auxiliary heating power (often ICH, ECH, and LHCD) and current drive in presence of non axisymmetric magnetic perturbations, including tearing modes, drives a bulk plasma rotation in the co  −  I_p direction. Also growing tearing modes provide a nonlinear magnetic braking that tends to flatten the rotation profile and clamp it at the q-rational surfaces. The physical origin of the torque associated with P_aux absorption could be due the effects of asymmetry in deposition or in the equilibrium configuration, but here we consider also the effect of the response of the so called neoclassical offset velocity to the power dependent heat flow increment. The neoclassical toroidal viscosity (NTV), due to error fields, internal magnetic kink or tearing modes tends to relax the plasma rotation to this asymptotic speed, which in absence of auxiliary heating is of the order of the ion diamagnetic velocity. It can be shown by a kinetic calculation, this offset velocity is a function of the absorbed heat and therefore of the injected auxiliary power, thereby forcing the plasma rotation in a direction opposite to the initial, to large values. The problem is discussed in the frame of the theoretical models of neoclassical toroidal viscosity.

The operation region and the parameter region of magnetohydrodynamic (MHD) modes are analyzed for J-TEXT Ohmic discharges. The operation region is described by the Hugill diagram, which combines low-q and high density limits. It is found that the operation region has expanded over the years on J-TEXT. In detail, the high density limit has increased from less than 0.5n_G to 0.7n_G and the low-q limit has lowered from 2.8 to 2.2; this is due to the reduced impurity content that results from coating graphite on the wall. Furthermore, the operation region has further expanded to 0.85n_G and q_a ~ 2.0, respectively—a result of suppressing the disruptive precursor MHD by using externally-applied resonant magnetic perturbations (RMPs). Here, n_G and q_a are the Greenwald density limit and edge safety factor, respectively. Corresponding to the results of the operation region, the parameter regions of MHD modes are presented. It is found that a m/n  =  2/1 tearing mode (TM) appears for a wide parameters region with 2.4  <  q_a  <  4 and n_e  <  3  ×  10¹⁹ m⁻³—here m and n are the poloidal and toroidal mode numbers. Furthermore, other MHD modes such as m/n  =  5/2, 3/1, 4/1 and 7/2, appear only when their rational surfaces are close to the plasma edge or m/n ~ q_a, and these MHD modes may transit to a 2/1 TM when changing the plasma parameters. In addition, correlation analysis between the amplitude and frequency of the dominant 2/1 TM for different plasma conditions reveals that there is a threshold between normal discharges and density-limit discharges, which would be a reference to predict density-limit disruptions.