Ion Temperature Gradient Instability Research Articles

Zonal flows and ion temperature gradient instabilities in multiple-helicity magnetic fields

The effects of multiple-helicity magnetic fields on the ion temperature gradient (ITG) instability and on the zonal flow (ZF) evolution are studied with the linear gyrokinetic Vlasov code GKV [T.-H. Watanabe and H. Sugama, Nucl. Fusion 46, 24 (2006)]. The model helical fields corresponding to the standard and inward-shifted axis configurations of the Large Helical Device [O. Motojima, N. Ohyabu, A. Komori et al., Nucl. Fusion 43, 1674 (2003)] are used to investigate how ITG mode properties and ZF evolution response to a given source are influenced by the field geometry. It is shown that, in the inward-shifted configuration, the ITG mode growth rate increases slightly while the ZF is sustained for a longer time. In addition, velocity-space structures of the ion perturbed distribution function are numerically obtained which illustrate the validity of the analytical prediction that the plasma inward shift retards the radial drift of the helically trapped particles leading to the enhancement of the ZF response. This supports the conjecture that anomalous transport can be reduced by the ZF generated in the configurations optimized to decrease the neoclassical transport.

Global gyrokinetic particle simulations with kinetic electrons

A toroidal, nonlinear, electrostatic fluid-kinetic hybrid electron model is formulated for global gyrokinetic particle simulations of driftwave turbulence in fusion plasmas. Numerical properties are improved by an expansion of the electron response using a smallness parameter of the ratio of driftwave frequency to electron transit frequency. Linear simulations accurately recover the real frequency and growth rate of toroidal ion temperature gradient (ITG) instability. Trapped electrons increase the ITG growth rate by mostly not responding to the ITG modes. Nonlinear simulations of ITG turbulence find that the electron thermal and particle transport are much smaller than the ion thermal transport and that small scale zonal flows are generated through nonlinear interactions of the trapped electrons with the turbulence.

Gyrokinetic modeling: A multi-water-bag approach

Predicting turbulent transport in nearly collisionless fusion plasmas requires one to solve kinetic (or, more precisely, gyrokinetic) equations. In spite of considerable progress, several pending issues remain; although more accurate, the kinetic calculation of turbulent transport is much more demanding in computer resources than fluid simulations. An alternative approach is based on a water-bag representation of the distribution function that is not an approximation but rather a special class of initial conditions, allowing one to reduce the full kinetic Vlasov equation into a set of hydrodynamic equations while keeping its kinetic character. The main result for the water-bag model is a lower cost in the parallel velocity direction since no differential operator associated with some approximate numerical scheme has to be carried out on this variable v∥. Indeed, a small bag number is sufficient to correctly describe the ion temperature gradient instability.

Nonlocal properties of gyrokinetic turbulence and the role of E×B flow shear

The nonlocal physics associated with turbulent transport is investigated using global gyrokinetic simulations with realistic parameters in shaped tokamak plasmas. This study focuses on the turbulence spreading through a transport barrier characterized by an equilibrium E×B shear layer. It is found that an E×B shear layer with an experimentally relevant level of the shearing rate can significantly reduce, and sometimes even block, turbulence spreading by reducing the spreading extent and speed. This feature represents a new aspect of transport barrier dynamics. The key quantity in this process is identified as the local maximum shearing rate ∣ωEmax∣, rather than the amplitude of the radial electric field. These simulation studies also extend to radially local physics with respect to the saturation of the ion temperature gradient (ITG) instability, and show that the nonlinear toroidal couplings are the dominant k-space activity in the ITG dynamics, which cause energy transfer to longer wavelength damped modes, forming a downshifted toroidal spectrum in the fully developed turbulence regime.

A New Paradigm for Radial Ion Plasma Transport in Axisymmetric Magnetic Field

A series of basic transport physics experiments on the anomalous ion thermal conduction due to ion temperature gradient instabilities are performed in Columbia Linear Machine. The CLM results like most tokamak experimental data results indicate dependence of the ion thermal conductivity on the isotopic mass close to Χ[perpendicular] ˜ Ai-0.5, i.e., inverse gyro-Bohm, where Ai is the mass number of the isotope of hydrogen. This is in stark contradiction to most present theoretical models predicting Bohm (Ai0) or gyro-Bohm (Ai0.5) scaling.We now report another series of experiments designed to explore the physics basis of this scaling which appears to lead to a new model for this scaling based on 3-wave coupling of two ion temperature gradient radial harmonics and an ion acoustic wave. The resulting isotopic scaling of transport is ˜ Ai-0.5 dictated primarily by the ion acoustic damping. This basic physics is deemed to be extrapolatable to other experiments resolving the paradox and is tantamount to new paradigm for plasma turbulent transport.

Electrostatic ion-temperature-gradient drift-waves and anomalous energy transport in a collisional dusty magnetoplasma

Electrostatic ion-temperature-gradient (ITG) driven drift waves are investigated by using Brangskii's model for the ions and Boltzmann distribution for the electrons in a dust-contaminated plasma with equilibrium density, temperature, and magnetic field gradients. Within the local approximation, we are able to recover the coupled ion-acoustic drift-waves in an inhomogeneous magnetic field and the Rudakov–Sagdeev (R–S) ITG instability in the presence of dust-charge fluctuations. It has been shown that the dust charging is always dissipative and the growth rate of various modes are damped. Furthermore, we also derive an expression for the anomalous ion-energy flux and transport coefficient in the presence of nonthermal fluctuations. The present investigation should be helpful in identifying the features of low-frequency turbulence and associated cross-field ion-energy transport in magnetically confined dust-contaminated tokamak plasmas.

Critical gradients for short wavelength ion temperature gradient instability in toroidal plasmas

Marginal stability curves in ion/electron temperature gradient space are numerically obtained for the short wavelength ion temperature gradient instability. as well as the scaling of the critical gradient with respect to temperature ratio. toroidicity. magnetic shear and safety factor. Algebraic formulae for the critical gradient are presented.

Computation of turbulence in magnetically confined plasmas

Plasmas are magnetically confined if the orbits of the charged particles around the magnetic field lines are small compared to the system size. Nevertheless, particles and energy are lost via transport resulting from the fluid-like drifts of these orbits across the magnetic field. Computation of this type of low frequency electromagnetic turbulence is introduced with emphasis on nonlinear character and energetics. The physical situation is low frequency dynamics with perpendicular forces in quasistatic balance and fast gyrofrequency leading to treating the orbit gyrocentres rather than the particles themselves. The broadband turbulence necessarily involves the ion gyroradius scale in any tokamak application. Hence the use of ‘gyrofluid’ and ‘gyrokinetic’ computational models. Computations must also treat the interplay between electromagnetic wave dynamics along the magnetic field and fluid-like turbulence across it, with a method independently checked against both of these sub-processes. Tokamak core and edge turbulence differ according to the ratios of the parallel (electron) and perpendicular (E-cross-B) transit frequencies. The turbulence is also in energetic contact with flows and currents associated with the equilibrium, so computations must be well behaved over very long run times and at least the perturbed equilibrium carried self-consistently. These considerations are illustrated by treating the case of ion temperature gradient instabilities giving rise to turbulence which is then suppressed by self generated E-cross-B flows. The methods of diagnosis of the physical processes are detailed. The situation of edge turbulence and interaction with the equilibrium is briefly addressed.

A new paradigm for plasma transport and zonal flows

Most tokamak experimental results indicate dependence of the ion thermal conductivity on the isotopic mass close to χ⊥∼mi−0.5, i.e., inverse gyro-Bohm. This is in stark contradiction to most present theoretical models predicting Bohm (mi0) or gyro-Bohm (mi0.5) scaling. A basic physics isotopic scaling experiment [V. Sokolov and A. K. Sen, Phys. Rev. Lett. 89, 095001 (2002)] on the anomalous ion thermal conduction due to ion temperature gradient (ITG) instabilities in two different gases (hydrogen and deuterium) closely confirms the tokamak results. Another series of experiments designed to explore the physics basis of this scaling appears to lead to a new model for this scaling based on 3-wave coupling of two ITG radial harmonics and an IA wave. The resulting isotopic scaling of transport is ∼mi−0.5 dictated primarily by the IA damping. This basic physics may be extrapolated to tokamaks resolving the paradox [V. Sokolov and A. K. Sen, Phys. Rev. Lett. 92, 165002 (2004)]. Last, the much discussed theoretical role of zonal flows in transport regulation is critically examined by another set of experiments. A novel diagnostic has been developed on the basis of the observation that the effect of zonal flow can be seen in the FM modulation (at zonal flow frequency) of the carrier frequency of the large equilibrium Doppler shift frequency of ITG modes both in tokamaks and in the Columbia Linear Machine [V. Sokolov, X. Wei, and A. K.Sen, APS DPP meeting, Savannah (2004)]. The present results indicate zonal flow levels close to the theoretical prediction, but its shear is much lower than that predicted by theory for transport regulation.

A new paradigm for plasma turbulent transport

Most tokamak experimental results (Bessenrodt-Weberpals M. et al 1993 Nucl. Fusion 33 1205) indicate dependence of the ion thermal conductivity on the isotopic mass close to , i.e. inverse gyro-Bohm in mass scaling. This is in stark contradiction to most present theoretical models predicting Bohm or gyro-Bohm scaling. A basic physics experiment (Sokolov V. and Sen A.K. 2002 Phys. Rev. Lett. 89 095001) on the anomalous ion thermal conduction due to ion temperature gradient instabilities in two different gases (hydrogen and deuterium) closely confirms the tokamak results.We now report another series of experiments designed to explore the physical basis of this scaling, which appears to lead to a new model for this scaling based on three-wave coupling of two ion temperature gradient radial harmonics and an ion acoustic (IA) wave. The resulting isotopic scaling of transport is , dictated primarily by the IA damping. This basic physics is deemed to be extrapolatable to tokamaks resolving the paradox and is tantamount to a new paradigm for plasma turbulent transport.

Gyrokinetic global electrostatic ion-temperature-gradient modes in finite β equilibria of Wendelstein 7-X

The standard scenario for the Wendelstein 7-X (W7-X) stellarator supposes equilibria with average β up to 4.3%. Here, the gyrokinetic description for full-radius ion-temperature-gradient (ITG) driven instabilities in three-dimensional configurations is used to investigate the linear stability and global structure of electrostatic ITG modes for the finite-β W7-X configurations. A massively-parallel initial-value particle-in-cell code has been modified to include the influence of a finite β on ITG modes due to equilibrium effects. We considered a sequence of W7-X equilibria with different plasma β, and found drastic changes in the structure and drive of the ITG instability but a minor influence on the value of the growth rate. The results presented are physically explained; differences between β-effects on ITG modes in a conventional tokamak and in W7-X are discussed, as well as the different structures and physical mechanisms of ITG modes for β = 0 and finite-β W7-X configurations.

Effect of self-generated zonal flows on turbulent heat transport in a tokamak plasma

A major goal in fusion research is understanding the anomalous thermal transport of energy and particles in a tokamak. In particular, a crucial issue is the origin of its empirical dependence on the various dimensionless parameters controlling the energy confinement. This paper addresses the impact of ion-ion collisions and of self-generated zonal flows (largescale E × B sheared poloidal flows) on turbulent ion thermal transport, in the core of a tokamak plasma. A three-dimensional fluid model is used, which describes flux-driven electrostatic plasma turbulence, generated by Ion Temperature Gradient (ITG) instabilities. The model includes curvature effects, parallel Landau damping and a collisional damping of the poloidal flows. Simulation results show a stabilization of the turbulence and a rise of the energy confinement time when the collisionality is lowered, that is when the zonal flows are weakly damped by ion-ion collisions. The mechanism responsible for the turbulence stabilization at low collisionality is identified as the non-linear upshift of the effective threshold for the ITG turbulence onset. This upshift is governed by an increase of the zonal flow shear.

Nature of the isotope effect on transport in tokamaks.

The reduction of energy and particle losses with the increasing mass of the hydrogen isotope is more pronounced under conditions of improved confinement when the dominant ion temperature gradient instability is suppressed and other channels of anomalous transport are of importance. In this Letter, we reconsider the dissipative trapped electron (DTE) instability by taking into account finite Larmor radius effects in the analysis of the ion response to perturbations. By applying the improved mixing length approximation in order to estimate the transport coefficients, it is demonstrated that DTE contribution is intrinsically dependent on the isotope mass and provides a plausible explanation for the isotope effect. Contrary to the common belief, it is shown that the DTE turbulence may be of importance for reactor plasmas of low collisionality.

Mechanism of central temperature peaking in impurity seeded plasmas

Formation of a centrally peaked profile of the ion temperature by impurity seeding has been observed in all the largest tokamaks: JET, JT-60U, TFTR. A possible explanation of this phenomenon is proposed, which takes into account the suppression of ion temperature gradient instability induced anomalous transport through increasing ion effective charge Zeff and Doppler shift of unstable modes, S⊥. The particular importance of the S⊥ component proportional to the temperature gradient, which stems from the pressure gradient and neoclassical poloidal rotation, is elucidated. It is demonstrated that this contribution grows significantly by impurity seeding when the rotation regime changes due to increased collisionality. An interrelation between the heating power density and Zeff necessary for the transition to a peaked ion temperature is found. The modification of radial profiles by impurity seeding is modelled numerically and the results are in agreement with the experimental data from JET.

Evidence for reduction of the toroidal ITG instability in the transition from saturated to improved Ohmic confinement in the tokamak TEXTOR

In high density Ohmically heated discharges in the tokamak TEXTOR a transition from the saturated Ohmic confinement (SOC) to the improved Ohmic confinement (IOC) was observed triggered by a sudden reduction of the external gas flow. The SOC–IOC transition was investigated regarding the influence of the toroidal ITG instability driven by the ion temperature gradient (ITG). The ion temperature profiles were measured with high radial resolution by means of charge-exchange recombination spectroscopy (CXRS) with a high-energetic diagnostic hydrogen beam recently installed at TEXTOR. On the basis of the measured ion temperature distributions the ηi parameter (ratio of the density and ion temperature decay lengths) and the growth rate of the toroidal ITG instability were calculated. After the SOC–IOC transition ηi drops and lies in a noticeably smaller radial region over the threshold for the toroidal ITG. In consequence of it, the IOC regime is characterized by a clear reduction of the ITG growth rate γITG which was calculated including finite Larmor radius effects. The steepening of the plasma density profile after the decrease of the external gas flow is the main reason for the reduction of the ITG growth rate and the subsequent confinement transition to the IOC regime.

Hall magnetohydrodynamic ballooning instability in the magnetotail

The ballooning stability of the magnetotail is considered within the framework of Hall magnetohydrodynamics (MHD). In particular, the extent to which Hall MHD effects modify ideal MHD ballooning modes is explored extensively. It is shown that Hall MHD effects primarily enter the stability analysis through changes introduced in the plasma compressibility. Hence, the incompressible ideal MHD modes are not affected, while the compressible ideal MHD modes are altered both quantitatively and qualitatively. In addition to modifying the growth rate of the compressible ideal MHD mode, Hall effects also introduce a new instability, called the entropy interchange instability, which is a variant of the ion temperature gradient instability, when the gradient ratio η≡d ln Ti/d ln ρ of the configuration becomes greater than 2/3, where Ti is the ion temperature and ρ is the plasma density. The theory is applied to two types of magnetotail configurations—analytic equilibria developed by Voigt [in Solar Wind-Magnetosphere Coupling, edited by Y. Kamide and J. A. Slavin (Terra Scientific, Tokyo, 1986), pp. 233–273], and more realistic magnetotail configurations containing thin current sheets obtained from Hall MHD simulations of substorm dynamics by Ma and Bhattacharjee [Geophys. Res. Lett. 25, 3277 (1998)].

Electromagnetic ion temperature gradient modes of tearing mode parity in high β sheared slab plasmas

The ion temperature gradient modes of tearing mode parity are investigated for arbitrary β (=plasma pressure/magnetic pressure) plasmas in a sheared slab. Under the low β limit, the results agree with Reynders’ conclusion that the lowest order (l=1) mode of tearing mode parity persists after the fundamental mode (l=0) of drift mode parity is completely stabilized by finite β [J. V. M. Reynders, Phys. Plasmas 1, 1953 (1994)]. However, when the effects of the magnetic gradient drift and the coupling to the compressional Alfvén waves are included, the l=0 mode is more difficult to stabilize than the l=1 mode. It is also shown that the l=1 mode is much easier to stabilize by the magnetic shear than the l=0 mode. Generally, the l=1 mode grows faster in the low magnetic shear and low β regime while the l=0 mode is the dominant eigenmode of ion temperature gradient instability in high β plasmas.

Instability of convective cells in ion temperature gradient turbulence

It has been demonstrated using numerical simulation of two-dimensional ion temperature gradient (ITG) equations that a periodic array consisting of large scale convective cells is subject to shear flow instability. A dynamically global and self-consistent evolution of linearly unstable modes, close to marginal instability, leads to the formation of poloidal shear flow through the process of peeling-instability. The saturated state thus comprises radially localized and polloidally extended length scales, namely, zonal flows. The zonal flows are predominantly led by the perturbed shear flow, whose growth rate is larger than the linear ITG instability.

Physicists Honored by APS

Physicists Honored by APS

Measurement of poloidal flow, radial electric field and E × B shearing rates at ASDEX Upgrade

The theoretical model of transport reduction by E × B shear decorrelation is tested experimentally for ASDEX Upgrade discharges. The radial force balance is used to determine the radial electric field from charge exchange recombination spectroscopy measurements. As the effective rate coefficient for photon emission of the charge exchange process depends on the collision energy, the alignment of the lines of sight with respect to the neutral beam gives rise to apparent velocities and temperatures. In addition, the gyro-motion of the observed species along with the finite lifetime of the observed excited state leads to lineshifts in spectra measured in the poloidal direction. Both effects require corrections, which will be discussed. The corrections are tested using the measurements of a discharge with a locked mode. From the profiles of an H mode discharge with improved confinement and a discharge with an internal transport barrier (ITB) the ion heat transport coefficients, E × B shearing rates and the maximum linear growth rates of the instabilities are calculated. Comparison of these results supports the assumption that turbulent transport due to the ion temperature gradient instability is suppressed inside the transport barrier in the ITB discharge. However, due to the dominant influence of the toroidal rotation velocity on the central E × B shear, they do not prove the shear decorrelation model, because Er naturally rises during the phases with improved confinement if unbalanced neutral beam heating is applied.