Stability Of Drift Waves Research Articles

Stability of the Landau resonance for drift modes in rotating tokamak plasma

The linear stability of drift waves in a poloidally rotating tokamak plasma is considered. The derived dispersion relation features a peaking of the diamagnetic frequency which gives the drift modes an irreducible two-dimensional character. We then show that inverse Landau damping can be suppressed and even stabilized, if the flow's shear is strong. Even though the instability, excited by the Landau resonance, is stronger at a high velocity shear for positive rotation velocities, effects due to the rotation of the plasma can reverse the sign and induce damping of the two-dimensional drift modes. This stabilizing mechanism works only for positive rotation velocities. For negative rotation velocities, we show that only modes with high poloidal mode numbers are unstable.

Role of the current density profile on drift wave stability in internal transport barrier reversed magnetic shear experiments at JET and Tore Supra

The role of the current density profile on drift wave stability is investigated using a linear electrostatic gyro-kinetic code. The growth rates are shown to have a linear dependence on the normalized temperature gradients above a certain threshold. A parametric study of the threshold shows a dramatic stabilizing effect of negative magnetic shear, especially for large scale instabilities. A set of handy formulae fitting the threshold as a function of the magnetic shear and the safety factor is proposed. Analysis of reversed magnetic shear discharges with internal transport barrier (ITB) in JET shows that ion ITBs can be triggered by the negative magnetic shear in the core of the plasma. Subsequently, the increase of the E×B shearing rate allows for the expansion of the ITB, despite the increase of the linear growth rates due to the temperature gradient peaking. In the case of the electron ITB obtained in the Tore Supra LHEP mode, the central increase of the confinement is associated with the stabilization of large scale trapped electron modes by the negative magnetic shear effect, whereas the steep electron temperature gradient destabilizes the small scale electron temperature gradient modes, which prevent the electron heat transport to reach neoclassical levels.

Krook collisional models of the kinetic susceptibility of plasmas.

An assessment is made of Krook collisional models used to describe the kinetic behavior of collective oscillations, i.e., when Landau damping and collisions must be considered, as is often the case for low-frequency waves. The study focuses on an early energy-conserving model [B. D. Fried, A. N. Kaufman, and D. L. Sachs, Phys. Fluids 9, 292 (1966)] that is shown to be identical to a more modern version used in drift-wave stability studies [G. Rewoldt, W. M. Tang, and R. J. Hastie, Phys. Fluids 29, 2893 (1986)]. The inadequacy of the simpler, and often used, nonconserving model is illustrated. Comparisons are established with recent collisional studies of ion acoustic waves [V. Yu. Bychenkov, J. Myatt, W. Rozmus, and V. T. Tikhonchuk, Phys. Plasmas 1, 2419 (1994)] and electron plasma waves [C. S. Ng, A. Bhattacharjee, and F. Skiff, Phys. Rev. Lett. 83, 1974 (1999)]. A connection is also established with contemporary studies of condensed matter and quantum liquids [K. Morawetz and U. Fuhrmann, Phys. Rev. E 61, 2272 (2000); 62, 4382 (2000)]. A useful empirical fit is found that corrects the Braginskii susceptibility to incorporate the kinetic behavior associated with the Krook kinetic susceptibility.

Nonlocal theory of drift type waves in a collisionless dusty plasma

A nonlocal theory is formulated to study drift waves in a collisionless multicomponent (dusty) plasma in a sheared slab geometry. The dynamics of dust particles and ions are treated by fluid models, whereas the electrons are assumed to follow the Boltzmann distribution. It is found that the usual stability of drift waves in a sheared slab geometry is destroyed by the presence of dust particles. A drift wave is excited which propagates with a new characteristic frequency modified by dust particles. This result is similiar to our earlier work for the collisional dusty plasma [Chakraborty et al., Phys. Plasmas 8, 1514 (2001)].

A comparison of drift wave stability in stellarator and tokamak geometry

The influence of plasma geometry on the linear stability of electrostatic ion-temperature-gradient driven drift modes (ITG or ηi=Ln/LTi modes) is investigated. An advanced fluid model is used for the ions together with Boltzmann distributed electrons. The derived eigenvalue equation is solved numerically. A comparison is made between an H–1NF [Fusion Technol. 17, 123 (1990)] like stellarator equilibrium, a numerical tokamak equilibrium and the analytical ŝ−α equilibrium. The numerical and the analytical tokamak are found to be in good agreement in the low inverse aspect ratio limit. The growth rates of the tokamak and stellarator are comparable whereas the modulus of the real frequency is substantially larger in the stellarator. The threshold in ηi for the stellarator is found to be somewhat larger. In addition, a stronger stabilization of the ITG mode growth is found for large εn(=Ln/R) in the stellarator case.

Electrostatic drift modes in a closed field line configuration

The stability of electrostatic drift waves in a closed field line configuration in collisionality regimes ranging from collisional to collisionless is compared. The maximum sustainable pressure gradient is found to be dependent on the ratio of the temperature and density gradients (η≡d ln T/d ln n). The eigenmodes are seen to be flute-like. The stability boundary was found to be similar when both ions and electrons are collisional, when they are collisionless, and for collisional electrons and collisionless ions. The largest stable pressure gradients are obtained for η⩾2/3. As the collisionality is reduced one observes some reduction of the region of stability.

Local magnetic shear and drift waves in stellarators

A study of the effect of local magnetic shear on the drift wave stability is presented. The eigenvalue problem for the drift wave equation is solved numerically in fully three-dimensional stellarator plasma using the ballooning mode formalism. It is found that negative local magnetic shear has a stabilizing effect on the drift wave instability and positive local shear is destabilizing. This is in agreement with the effect of negative global magnetic shear in tokamaks and also agrees with the simple estimates. As a consequence the highly unstable modes found on a specific magnetic surface are localized in the region of positive local magnetic shear.

Geometric effects on drift wave stability in advanced stellarators

The linear stability of electrostatic drift waves in three-dimensional helical advanced stellarator (Helias) configurations is investigated. Effects of local geometrical properties and optimization due to reduction of Pfirsch–Schlüter currents on drift waves are discussed in a comparative numerical study for various configurations of Helias stellarators. The ballooning mode representation is used both for a basic approach with arbitrary nonadiabaticity and perturbatively for the more realistic dissipative trapped electron regime. Mode number spectra and linear growth rates are obtained with an eigenvalue code for three-dimensional equilibria. Local shear properties are found to have considerable influence on stability.

Drift wave stability of PEP discharges in Tore Supra

The drift wave stability of pellet enhanced performance modes in Tore Supra has been investigated. It is found that these discharges are characterized by a combination of three different stabilizing mechanisms: density peaking, E × B shear and magnetic shear. Drift wave stability appears to be very sensitive to magnetic shear, with the most favourable configuration corresponding to a slightly negative magnetic shear. The conclusions are compatible with the results from JET and TFTR.

Coherent Structures in Sheared Flow of Magnetized Plasmawith Magnetic Shear

Nonlinear equations describing electrostatic drift waves in aspatially non-uniform plasma with a background shear flow and magneticshear are derived. Various analytical and numerical solutions in theform of vortex chains, periodic along the plasma flow and localized inthe perpendicular direction are found. In plasmas with shear flow andsteep density gradient the standard magnetic shear stability of driftwaves is severely restricted which makes such systems prone to aninstability, and the strongly nonlinear solutions presented here mayarise as the final stage in the development of instability of driftwaves in such plasma configurations.

Improved High-Confinement Mode with Neon Injection in the DIII-D Tokamak

The first observation of a high-confinement mode with reduced energy transport in both the center and the edge induced by the injection of neon impurities is reported in this paper. This improved high mode develops from an improved low-confinement mode. Linear growth rate calculations indicate that a new theoretical mechanism, the stabilization of high wave number drift waves by impurities, is at work, combined with $\mathbf{E}\ifmmode\times\else\texttimes\fi{}\mathbf{B}$ velocity shear suppression of low wave number instabilities.

開放端磁場プラズマの物理 2.ミラープラズマの安定性

The stability of mirror-confined plasmas is reviewed. The equilibrium of mirror-confined plasmas is first briefly discussed. Then, MHD stability is studied based on an energy priciple with the paraxial approximation and flute and ballooning interchange-mode equations are derived. The effects of E×B rotation due to an ambipolar electric field and the finite Larmor radius of ions on MHD stability are briefly described. Alfven ion cyclotron instability driven by the temperature anisotropy of ions, and E×B drift shear stabilization of electrostatic drift waves due to an ambipolar electric field are reported.

Drift waves in plasmas with sheared flows

In the standard approach to the problem of shear stabilization of drift waves the diamagnetic drift velocity v* is regarded as a constant, which is usually not satisfied at the edge of a tokamak plasma. In configurations of this type, with a steep density gradient and radially sheared transverse velocity field, the magnetic shear stabilization criteria are severely restricted, and the velocity profile curvature v0″(x) is found to play a crucial role. In the strongly nonlinear regime, unstable drift waves may saturate into stationary coherent vortex-type structures. The latter include a tripolar vortex.

Sheared rotation effects, ion- and electron-temperature fluctuations, and generalized form factors on drift waves

The effect of inhomogeneous azimuthal flows in cylindrical geometry on drift waves with non-Boltzmann density response is investigated. Stabilization of dissipative drift waves by the inhomogeneous flow is also analyzed. Convective cells are shown to be destabilized by the discontinuous flow. Next, ion- and electron-temperature fluctuations in a resistive plasma are investigated in the slab approximation, allowing for the self-consistently stationary system parameters (electron- and ion-temperature inhomogeneities, magnetic shear, and plasma currents). Their magnitude, their propagation directions, and the dependence of their stability characteristics on the system parameters are identified, distinguishing between the weakly and the strongly collisional regions. Finally, the generalized form factor for density fluctuations in ion-temperature gradient modes is calculated. The resulting broad frequency spectrum is shown to stem from the fact that the linear growth rate is comparable to the real wave frequency.

Effects of a poloidally asymmetric ionization source on toroidal drift wave stability and the generation of sheared parallel flow

The effects of a poloidally asymmetric ionization source on both dissipative toroidal drift wave stability and the generation of mean sheared parallel flow are examined. The first part of this work extends the development of a local model of ionization-driven drift wave turbulence [Phys. Fluids B 4, 877 (1992)] to include the effects of magnetic shear and poloidal source asymmetry, as well as poloidal mode coupling due to both magnetic drifts and the source asymmetry. Numerical and analytic investigation confirm that ionization effects can destabilize collisional toroidal drift waves. However, the mode structure is determined primarily by the magnetic drifts, and is not overly effected by the poloidal source asymmetry. The ionization source drives a purely inward particle flux, which can explain the anomalously rapid uptake of particles which occurs in response to gas puffing. In the second part of this work, the role poloidal asymmetries in both the source and turbulent particle diffusion play in the generation of sheared mean parallel flow is examined. Analysis indicates that predictions of sonic parallel shear flow [v∥(r)∼cs] are an unphysical result of the assumption of purely parallel flow (i.e., v⊥=0) and the neglect of turbulent parallel momentum transport. Results indicate that the flow produced is subcritical to the parallel shear flow instability when diamagnetic effects are properly considered.

Impurity effects on drift wave stability and impurity transport

A numerical linear stability analysis of electrostatic ion temperature gradient (ITG) and dissipative trapped electron (DTE) modes in a three-component plasma (electrons, primary ions and impurity ions) is performed using a fully kinetic, sheared slab model. The quasi-linear particle and energy fluxes for each species are also computed. For the ITG mode, it is found that increasing plasma dilution (increasing Zeff) as well as increasing peakedness of the Zeff profile are strongly stabilizing. The quasi-linear calculations of the total anomalous energy flow driven by ITG mode turbulence shows that for Zeff profiles that are nearly flat and of moderately low value (Zeff ≲ 2), an energy 'pinch' is possible. A possible connection of this result with recent DIII-D off-axis heating experiments is discussed. A concomitant feature of this inward energy flow is an inward flow of primary ion particles, and an outward flow of impurity ion particles that greatly exceeds the neoclassical level. The impurity effects on the DTE mode are opposite, i.e. increasing dilution and Zeff profile peakedness are strongly destabilizing. As a result, quasi-linear theory predicts a large increase in the anomalous electron energy flux and much smaller effects on the anomalous fluxes of the ion species

Atomic physics effects on dissipative toroidal drift wave stability

The effects of atomic physics processes such as ionization, charge exchange, and radiation on the linear stability of dissipative drift waves are investigated in toroidal geometry, both numerically and analytically. For typical Tokamak Fusion Test Reactor (TFTR) [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (IAEA, Vienna, 1987), Vol. 1, p. 51] and Texas Experimental Tokamak (TEXT) [Nucl. Technol. Fusion 1, 479 (1981)] edge parameters, overall linear stability is determined by the competition between the destabilizing influence of ionization and the stabilizing effect due to the electron temperature gradient. An analytical expression for the linear marginal stability condition, ηcrite, is derived. The instability is most likely to occur at the extreme edge of tokamaks with a significant ionization source and a steep electron density gradient.

Frequency spectrum in drift wave turbulence

The frequency spectrum of drift wave turbulence is examined, with emphasis on the underlying dynamics, the nonlinear frequency shift, and the reliability of analytical techniques. It is found that the frequency spectrum can depend on three different effects, each of which contribute both a broadening and shift to the spectrum. First is the usual ‘‘eddy-damping’’ mechanism, which is derived here from a direct interaction approximation (DIA) analysis. Spectral broadening from the eddy-damping mechanism tends to be important at longer wavelengths, and gives a frequency broadening and a downshift, coming, respectively, from the real and imaginary parts of the renormalized diffusivity. A second effect that contributes to the frequency spectrum is the incoherent nonlinear drive, revealed by a DIA solution but often neglected in Markovian approximations. The nonlinear drive also tends to be important at longer wavelengths, and contributes both to the spectral width (from broadband driving), and a frequency downshift (from off-frequency driving). A third effect comes from turbulent fluctuations of the density gradient, which add to the equilibrium density gradient and thereby cause fluctuations in the linear drift frequency. This mechanism tends to become important at short wavelengths, contributing both a frequency broadening as revealed by a DIA analysis, and a frequency upshift, as revealed by a weak turbulence analysis. The relation of these results to the fluctuation–dissipation theorem, and the impact on drift wave stability are discussed.

Stabilization of collisional drift waves by kinetic Alfvén waves

We have investigated a mode-coupling mechanism between kinetic Alfvén waves and a collisional drift wave in an inhomogeneous cylindrical plasma. Drift waves satisfying the condition k⊥D > 1/r0 (where r0 is the radius of the plasma cylinder) are stabilized by the low-frequency ponderomotive force generated by the kinetic Alfvén waves. For typical plasma parameters and a moderate level of Alfven-wave intensity the stabilization factor is comparable to the destabilization mechanism due to collisions.

Numerical analysis of the stability of drift waves

Numerical analysis of the stability of drift waves