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The drift wave in the presence of impurity ions was investigated numerically in reversed-field pinch plasmas, using the gyrokinetic integral eigenmode equation. By comparing the results of regular and hollow plasma density profiles, it was found that the ion temperature gradient mode for the hollow density profile case is much harder to excite. For the impurity effects, when the impurity density gradient is opposite to the electrons, namely when L_{ez} (L_{ez}=L_{ne}/L_{nz} with 1/L_{n} being the density gradient scale length, and the subscript "e" and "z" indicates electrons and impurity ions, respectively) is negative, the impurities can enhance the instability. On the contrary, when L_{ez} is positive, the instability is stabilized. Regarding the trapped electron mode (TEM), the growth rate for plasmas with a hollow density profile remains smaller than that of the standard density gradient. There exists a threshold in L_{ez}. When L_{ez} is less than this value, the impurities destabilize the TEMs, while when L_{ez} is greater than this value, the impurities stabilize the TEMs. In addition, the influence of the collisionality on the TEMs was also studied.

Ground-state structures of a two-dimensional (2D) system composed of superparamagnetic charged particles are investigated by means of molecular dynamics simulation. The charged particles trapped in a quadratic potential interact with each other via the repulsive, attractive, and magnetic dipole-dipole forces. Simulations are performed within two regimes: a one-component system and a two-component system where the charged particles have the identical charge-to-mass ratio. The effects of magnetic dipole-dipole interaction, mixing ratio of the two species and confinement frequency on the ground-state structures are discussed. It is found that as the strength of the magnetic dipole increases, the charged particles tend to self-organize into chainlike structures. The two species particles exhibit different structural features, depending on the competition of electrostatic repulsive interaction, magnetic dipole-dipole interaction and confinement force. The potential lanes are observed through analyzing the global potential of the magnetic particles, which guide the unmagnetic particles aligning themselves in the direction of the potential lanes.

Trapped electron modes (TEMs) in tokamak plasmas with anisotropies of electron temperature and its gradient are studied by solving the gyrokinetic integral eigenmode equation. Detailed numerical analyses indicate that, in comparison with that in plasmas of isotropic electron temperature, TEMs are enhanced (weakened) by the anisotropy with temperature in the direction perpendicular to magnetic field higher (lower) than that in the direction parallel to the magnetic field when the latter is kept constant. However, the enhancement is limited such that TEMs are weakened rapidly and even stabilized when the anisotropy is higher than a critical value owing to an effective reduction of bounce movement of the trapped electrons. In addition, it is found that the gradients of perpendicular and parallel temperatures of electrons have driving and suppressing effects on the TEMs, respectively. The overall effects of the temperature gradients of electrons and ions, magnetic shear, safety factor, and density gradient on TEMs in the presence of the anisotropies are presented in detail.

Gyrokinetic simulations of electrostatic micro-turbulence have been carried out for transport barriers (TBs) in tokamak plasmas. It is found that the ion temperature gradient (ITG) mode is dominant in the pedestal with medium density gradient and steep temperature gradient. The mode width shrinks with increase of the ratio of the density and temperature gradients, which is in good agreement with the analytic theory. Unstable mode with herringbone-like structure is excited in the simulation annulus. The simulation results also indicate that multiple ITG modes are induced by a high temperature gradient. Radial electric field shear decreases the mode growth rate while increases the real frequency. Finally, the generation of the GAM and its interaction with the turbulence are also observed in the nonlinear simulation.

The gyrokinetic integral eigenmode equation is applied to study ion-temperature-gradient (ITG) mode in toroidal plasmas with magnetic shear, where the ion temperature and its gradient are anisotropic. The numerical studies demonstrate that instability of ITG mode is reduced by an ion temperature anisotropy of higher perpendicular temperature T i⊥ or high enough parallel temperature T i∥, in which Landau damping plays an important role. The temperature gradient in the perpendicular (parallel) direction is stronger to drive ITG mode for large T i⊥ (T i∥). These effects are directly related to the temperature gradient threshold for excitation of ITG mode. In addition, the synergy effect of magnetic shear and anisotropy of ion temperature and its gradient is studied in detail, where the combination of magnetic shear and large parallel temperature has the most obvious inhibitory effect on ITG mode.

Using a driven-dissipative Langevin dynamics simulation, the dynamics of two-dimensional binary dusty plasma in the liquid-like state has been investigated. The system consists of charge-asymmetric microparticles with an identical charge-mass ratio. To include the effect of particle size on the dynamics of the system, a modified Yukawa potential with consideration of the particle radius is employed to account for the electrostatic interaction between the charged particles. It is found that the mean squared displacement (MSD) of the system changes little when the ratio of particle radius to interparticle spacing is up to the order of magnitude of one tenth. By analyzing MSD at different time scales, coexistence of the distinct self-diffusion regimes for the two species is observed. The compositions of the two species together with the effective coupling strength of the system are responsible for the motion separation of the two species.

The ion temperature gradient (ITG) mode in the presence of impurity ions is numerically investigated in tokamak plasmas with hollow density profiles, using the gyrokinetic integral eigenmode equation. It is found that in the inverted density plasma, the increase of ion temperature gradient enhances the ITG growth rate and frequency, and the density gradient plays an important role in the ITG modes. For weak density gradient situations, the trapped electron effects enhance the ITG instability, while the impurity has an obviously stabilizing effect. For the strong density gradient cases, both the impurities and trapped electrons enhance the ITG instabilities. In addition, it is shown that the growth rate of ITG decreases with positive magnetic shear s while the real frequency decreases with s. The growth rate of ITG increases with the negative magnetic shear s while the real frequency decreases with s. The calculated mode structure length in the positive and negative magnetic shear interval is also presented. The results might provide hints on studies of particle and anomalous transports and plasma confinement.

Diffusion of two-dimensional (2D) superparamagnetic dust grains interacting via both Yukawa and magnetic dipole-dipole interactions is investigated based on the Langevin dynamics simulation. The magnetic dipole moment, induced by the external magnetic field, is tilted at angle α relative to the 2D layer. It is demonstrated that the system in the liquidlike state behaves in anisotropic diffusion when α is larger than the agglomeration threshold, and the anisotropic diffusions are identified as the normal type. The anisotropy degree depends on the strength of magnetic dipole-dipole interaction and tilt angle of the magnetic dipole moment. An empirical law describing the anisotropy degree as a function of α is given.

The induction and stabilization characteristics of neoclassical tearing modes (NTMs) on Hl-2A tokamak are presented. NTMs are induced by sawtooth oscillations of the m/n = 1/1 mode via toroidal coupling and by gas puffing fuelling in the experiments of HL-2A tokamak. The evolutions of NTMs are modeled with a two dimensional non-linear cylindrical tearing mode code and compared with the experimental observations. The stabilization of NTMs with electron cyclotron current drive (ECCD) is numerically studied. It is found that a driven current as low as 0.015 of total plasma current can stabilize or even fully suppress NTMs. On the other hand, a small radial misalignment decreases the stabilizing effect considerably. In addition, a phase misalignment blocks the NTM stabilization and results in island width saturation at a moderate value. The effects of island rotation frequency on NTM stabilization are explored. Furthermore, it is found that the stabilizing effect can be improved efficiently by applying ECCD when the island width is less than a threshold value.

By comparing with the Bohm-like diffusion 1/B of magnetized complex plasma, it is found that the neutral collisions, i.e., collisions between neutral gas and charged dust particles, nonlinearly damp the motion of the system at a rate much slower than 1/ν, where B is the external magnetic field and ν is the neutral collision frequency. The effects of neutral collisions on longitudinal and transverse waves are discussed based on the current-current correlation function. The non-damping feature of strong neutral collisions to shorter-wavelength modes is observed. The phonon energy of the system tends to be distributed into a broader k–ω space in the strong damping regime.By comparing with the Bohm-like diffusion 1/B of magnetized complex plasma, it is found that the neutral collisions, i.e., collisions between neutral gas and charged dust particles, nonlinearly damp the motion of the system at a rate much slower than 1/ν, where B is the external magnetic field and ν is the neutral collision frequency. The effects of neutral collisions on longitudinal and transverse waves are discussed based on the current-current correlation function. The non-damping feature of strong neutral collisions to shorter-wavelength modes is observed. The phonon energy of the system tends to be distributed into a broader k–ω space in the strong damping regime.

Using molecular dynamics simulation, we calculate the mean square displacement, the pair correlation function, the velocity autocorrelation function and the spectrum function of a two-dimensional (2D) charged dust system. Results show that the critical coupling constant Gamma* for the phase transition from a liquid-like state to a solid-like state decreases with increasing charge and mass of particles in the one-component system. A scaling relation between Gamma* and mu(Gamma* alpha mu(-1.72 +/- 0.07)) is given, where mu represents the quantities of charge and mass. In the system with two species of particles, the coagulation process is found to be delayed by the presence of one species, and Gamma* is closer to that of the 'smaller' particles species, which has the smaller charge and mass.

The structure of a two-dimensional dusty plasma in an external magnetic field has been investigated in detail by molecular dynamics simulation. The pair correlation function, mean square displacement, the static structure factor and the bond angle correlation function have been calculated to characterize the structural properties of the dusty plasma for different values of coupling constant and magnetic field strength. The results show that the dusty plasma system with a fixed coupling constant can have a phase transition from gas to fluid, and from fluid to a solid state, when the external magnetic field strength is increased to a critical value. The critical magnetic field strength generally decreases with increasing coupling constant in the system.

This paper reports the main recent results of the RFX-mod fusion science activity. The RFX-mod device is characterized by a unique flexibility in terms of accessible magnetic configurations. Axisymmetric and helically shaped reversed-field pinch equilibria have been studied, along with tokamak plasmas in a wide range of q(a) regimes (spanning from 4 down to 1.2 values). The full range of magnetic configurations in between the two, the so-called ultra-low q ones, has been explored, with the aim of studying specific physical issues common to all equilibria, such as, for example, the density limit phenomenon. The powerful RFX-mod feedback control system has been exploited for MHD control, which allowed us to extend the range of experimental parameters, as well as to induce specific magnetic perturbations for the study of 3D effects. In particular, transport, edge and isotope effects in 3D equilibria have been investigated, along with runaway mitigations through induced magnetic perturbations. The first transitions to an improved confinement scenario in circular and D-shaped tokamak plasmas have been obtained thanks to an active modification of the edge electric field through a polarized electrode. The experiments are supported by intense modeling with 3D MHD, gyrokinetic, guiding center and transport codes. Proposed modifications to the RFX-mod device, which will enable further contributions to the solution of key issues in the roadmap to ITER and DEMO, are also briefly presented. © 2017 IAEA, Vienna.

Dynamics of 2D magnetized complex plasmas is investigated based on the driven-dissipative dynamics simulation. Besides the usual Yukawa potential, a modified Yukawa potential which includes the effects of external magnetic field B on the shielding distance of the charged dust particles is used to account for the electrostatic interaction of the charged dust particles. It is found that shielding distance of the charged dust particles is greatly increased due to the magnetization of background ions, and the resulting equilibrium diffusion of the system differs from that of usual Yukawa system. Collective oscillation of the system is discussed in terms of Fourier analysis of velocity-auto-correlation function.

A Langevin dynamics simulation method is used to study the two-dimensional (2D) equilibrium structure of complex plasmas while considering an external magnetic field. The traditional Yukawa potential and a modified Yukawa potential according to Shukla et al. [Phys. Lett. A 291, 413 (2001); Shukla and Mendonca, Phys. Scr. T113 82 (2004)] and Salimullah et al. [Phys. Plasmas 10, 3047 (2003)] respectively, are employed to account for the interaction of the charged dust particles. It is found that the collisions between neutral gas and charged dust particles have minor effects on the 2D equilibrium structure of the system. Based on the modified Yukawa potential, studies on the 2D equilibrium structure show that the traditional Yukawa potential is still suitable for describing the magnetized complex plasmas, even if the shielding distance of charged dust particles is affected by the strong external magnetic field.

This paper summarizes the main achievements of the RFX fusion science program in the period between the 2008 and 2010 IAEA Fusion Energy Conferences. RFX-mod is the largest reversed field pinch in the world, equipped with a system of 192 coils for active control of MHD stability. The discovery and understanding of helical states with electron internal transport barriers and core electron temperature >1.5 keV significantly advances the perspectives of the configuration. Optimized experiments with plasma current up to 1.8 MA have been realized, confirming positive scaling. The first evidence of edge transport barriers is presented. Progress has been made also in the control of first-wall properties and of density profiles, with initial first-wall lithization experiments. Micro-turbulence mechanisms such as ion temperature gradient and micro-tearing are discussed in the framework of understanding gradient-driven transport in low magnetic chaos helical regimes. Both tearing mode and resistive wall mode active control have been optimized and experimental data have been used to benchmark numerical codes. The RFX programme also provides important results for the fusion community and in particular for tokamaks and stellarators on feedback control of MHD stability and on three-dimensional physics. On the latter topic, the result of the application of stellarator codes to describe three-dimensional reversed field pinch physics will be presented. © 2011 IAEA, Vienna.

Ion temperature gradient (ITG) driven modes in the presence of impurity ions are studied in reversed-field pinch plasmas by solving the gyrokinetic integral eigenmode equation. Detailed numerical studies for single and multiple impurity ion species indicate that the ITG modes are enhanced by impurity effects and the stability threshold values become higher than that in pure hydrogen plasmas when density gradients of the impurity ions are opposite to that of electrons and main ions. In addition, a mode is driven unstable by impurity ions no matter how low the main ion temperature gradient is when the destabilizing effect of the impurity ions is strong enough. These results resemble the effects of impurities in tokamak plasmas. Analysis of the typical RFX-mod experiments is performed and the results show that the ITG and impurity driven modes may be linearly unstable in the edge region of the plasmas when the observed radial profiles of the impurity ions are considered.

Diffusive and structural properties in the binary mixture of charged particles are investigated based on the molecular dynamical simulation. It is shown that the particles with higher charge enhance or weaken the diffusion of the whole system depending on the coupling strength, and regimes of subdiffusion as well as normal diffusion are identified. The nonmonotonous diffusion, i.e., the diffusion at first is increased and then is decreased with increasing the higher charged particles, is strongest close to the phase from liquidlike state to solidlike state. Stronger coupling and lower concentration of higher charged particles are in favor of the formation of ordered shells centered at the higher charged particles.

The drift instabilities in the toroidal reversed field pinch (RFP) plasmas are numerically studied with gyrokinetic integral eigenmode equations, by taking into account the trapped electrons (TEs) and full ion kinetic effects. Both the collisionless and collisional plasmas are investigated. Two topics are addressed: the TE effects on the ion temperature gradient driven mode, and the instability of the trapped electron mode (TEM). A comparison with a circular tokamak configuration has been made. Although the TEs generally play a similar role in RFPs as they do in tokamaks, their effects become significant in RFPs only when very steep density/temperature profiles exist. Indeed, the instability of the TEM in RFP plasmas requires a much steeper density/temperature gradient and has a much narrower kθρs spectrum than in tokamak plasmas.

This paper reports the highlights of the RFX-mod fusion science programme since the last 2010 IAEA Fusion Energy Conference. The RFX-mod fusion science programme focused on two main goals: exploring the fusion potential of the reversed field pinch (RFP) magnetic configuration and contributing to the solution of key science and technology problems in the roadmap to ITER. Active control of several plasma parameters has been a key tool in this endeavour. New upgrades on the system for active control of magnetohydrodynamic (MHD) stability are underway and will be presented in this paper. Unique among the existing fusion devices, RFX-mod has been operated both as an RFP and as a tokamak. The latter operation has allowed the exploration of edge safety factor q edge < 2 with active control of MHD stability and studies concerning basic energy and flow transport mechanisms. Strong interaction has continued with the stellarator community in particular on the physics of helical states and on three-dimensional codes. © 2013 IAEA, Vienna.

The impurity mode in toroidal reversed-field pinch (RFP) plasma is studied, using the gyrokinetic integral equation. A second species of ions with density gradient opposite to the primary ion and electron density gradients is considered. The effects of impurity charge concentration, ratio of electron density gradient scale length to impurity density gradient scale length, finite Larmor radius, safety factor, magnetic shear, ion as well as electron density gradient scale lengths on the impurity mode are investigated in detail. It is demonstrated that the impurity mode in RFP plasmas is relatively more difficult to be excited than that in tokamak plasmas under similar geometry when the density profile is flat, whereas it turns out to be easier when the density profile is rather peaked.

The ion temperature gradient (ITG) driven electrostatic modes in reversed-field pinch (RFP) plasma are studied with the gyrokinetic integral equation. A systematic threshold study is carried out and the results are compared with that in tokamaks with similar geometry and reveal that the ITG modes in RFP configurations are more stable than in tokamaks. The physics mechanism for such difference is that shorter connection length in RFPs leads to stronger landau damping, which is dominant and ultimately determinant for the stability threshold. The results confirm and extend the previous conclusion obtained with the differential equation [S. C. Guo, Phys. Plasmas 13, 122510 (2008)]. In addition, the effects of magnetic gradient and curvature drifts, which induce important interaction driving the modes, are carefully investigated. The effects of safety factor, ratio of electron temperature to ion temperature, magnetic shear as well as finite Larmor radius are also studied.

A set of simplified integral eigenmode equations with neglecting of the magnetic gradient drift effects are derived and employed to investigate the ion temperature gradient modes in plasmas of sheared slab geometry. Perturbations of both perpendicular and parallel components of magnetic vector potential are considered, as well as the perturbation of the electrostatic potential. The characteristics of the ion temperature gradient instability are studied with the equations and the corresponding computer code, and compared with those with the drift effects included. The results show that the magnetic gradient drift has a block effect on ion temperature gradient mode stabilization, and the perpendicular component of the perturbed magnetic vector potential has strong stabilizing effects on ion temperature gradient modes. Nevertheless, the results from the simplified equations are qualitatively in agreement with those from the complete equations and the differences between them are not significant quantitatively. The simplified equations have the advantages of saving computer time and being well suited to analytic methods.

25th Fusion Energy Conference (FEC), Govt Russian Federat, St ă Petersburg, RUSSIA, OCT 13-18, 2014; International audience; The RFX-mod device is operated both as a reversed field pinch (RFP), ă where advanced regimes featuring helical shape develop, and as a ă tokamak. Due to its flexibility, RFX-mod is contributing to the solution ă of key issues in the roadmap to ITER and DEMO, including MHD instability ă control, internal transport barriers, edge transport and turbulence, ă isotopic effect, high density limit and three-dimensional (3D) ă non-linear MHD modelling. This paper reports recent advancements in the ă understanding of the self-organized helical states, featuring a strong ă electron transport barrier, in the RFP configuration; the physical ă mechanism driving the residual transport at the barrier has been ă investigated. Following the first experiments with deuterium as the ă filling gas, new results concerning the isotope effect in the RFP are ă discussed. Studies on the high density limit show that in the RFP it is ă related to a toroidal particle accumulation due to the onset of a ă convective cell. In the tokamak configuration, q(a) regimes down to q(a) ă = 1.2 have been pioneered, with (2,1) tearing mode (TM) mitigated and ă (2,1) resistive wall mode (RWM) stabilized: the control of such modes ă can be obtained both by poloidal and radial sensors. Progress has been ă made in the avoidance of disruptions due to the (2,1) TM by applying ă q(a) control, and on the general issue of error field control. The ă effect of externally applied 3D fields on plasma flow and edge ă turbulence, sawtooth control and runaway electron decorrelation has been ă analysed. The experimental program is supported by substantial ă theoretical activity: 3D non-linear visco-resistive MHD and non-local ă transport modelling have been advanced; RWMs have been studied by a ă toroidal MHD kinetic hybrid stability code.