Unstable Drift Waves Research Articles

Nonlinear dynamics of low-frequency drift waves

The nonlinear behaviour of unstable drift waves in magnetized plasmas is analysed analytically. Most attention is paid to low-frequency waves created in electron density and temperature gradients of opposite sign. This situation is typically encountered in radiofrequency-produced discharges. The model developed explains nonlinear features such as mode competition, amplitude saturation and magnetic field hysteresis, which are observed experimentally.

Electron-temperature-gradient-driven drift waves and anomalous electron energy transport

By means of a kinetic description for ions and Braginskii's fluid model for electrons, we derive three coupled nonlinear equations governing the dynamics of low-frequency short-wavelength electrostatic waves in the presence of equilibrium density, temperature and magnetic-field gradients in a two-component magnetized plasma. In the linear limit we present a dispersion relation that admits new instabilities of drift waves. An estimate of the anomalous electron energy transport due to non-thermal drift waves is obtained by making use of the saturated wave potential, which is deduced from the mixing-length hypothesis. We also present stationary solutions of the nonlinear equations governing the interaction of linearly unstable drift waves. The relevance of our investigation to wave phenomena in space and laboratory plasmas is pointed out.

Unstable drift waves in a self-consistent stationary state with saturated magnetic shear

The stability of dissipative drift wave eigenmodes in a stationary state is investigated. Small magnetic shear, generated self-consistently by an electron plasma current through Ampère’s law, is included. This magnetic shear is found to be stabilizing (destabilizing) if the electron drift consistent with this is antiparallel (parallel) to the propagation direction of the drift waves. As a result, it is concluded that the introduction of magnetic shear does not effectively stabilize the drift wave instability.

Turbulent stabilization of the tearing mode in tokamak plasmas

The effect of turbulent electron diffusion from stochastic electron orbits on the stability of low-beta fluctuations is considered through the use of the normal stochastic approximation. A set of coupled, self-adjoint equations is derived for the fluctuation potentials φ̃ and Ã∥. Solutions to this set of equations describe both unstable finite-β drift waves when analyzed for high-m modes and the tearing mode when analyzed for low-m modes. For the tearing mode, it is shown that stability is obtained for sufficiently large values of the diffusion coefficient. Provided De∼1/n, this implies that a density threshold must be surpassed before the tearing mode is observed. Physically, turbulent electron diffusion prohibits the formation of a perturbed current within a finite region about the rational surface. At higher densities, the inclusion of a finite electrostatic potential φ̃ gives an additional stabilizing term to the dispersion relation, which physically represents ion inertial effects. This ion inertial effect implies that, in the absence of diffusion, the tearing mode is stabilized for ion betas βi above some critical value.

Self-Organization in Dissipative Plasmas

A nonlinear analysis of the dynamic behavior of dissipative drift-waves is developed. Near the neutral stable point, the time-dependent Ginzburg-Landau equation with complex coefficients is derived from the two-fluid equations which describe the dissipative drift-waves, by means of reductive perturbation. The convective cell excited by the nonlinear self-interaction of a linearly stable drift-wave is undamped and is adiabatically enslaved by the drift-wave. The system composed of the drift-wave and convective cell self-organizes as the external magnetic field exceeds a certain critical value and tends asymptotically to a stable nonequilibrium state (nonlinear saturation). The saturation level of a single, linearly unstable drift-wave in a non-isothermal plasma is obtained as a function of critical wavenumber, density gradient scale length, plasma temperature and magnetic field.

Electrostatic plasma wave propagation in a density modulated plasma

A model which treats the formation of wave sidebands on a propagating electron plasma wave in the case where the plasma density is modulated by a low-frequency perturbation is developed. A new mechanism for production of an asymmetric distribution of sidebands appears, and circumstances under which the original wave may reconstitute itself are described. An experimental study of electrostatic plasma waves in a weakly ionized plasma, where the density is modulated either by external means or by the presence of an unstable drift wave, is in agreement with the model.

Convective cell turbulence and anomalous plasma diffusion

We present a simple physical mechanism for maintaining a steady turbulent state consisting of convection cells and drift waves. In this mechanism, energy is transferred from the unstable short-wavelength drift waves to the longer wave-length convection cells by a decay process. Stationarity is achieved by the viscous dissipation of the convection cell energy. Dual cascading in the convective cell turbulence, as well as the enhanced cross-field plasma diffusion, are examined.

Nonlinear development of drift waves

This note presents a model equation which describes nonlinear evolution of finite amplitude drift waves in a non-uniform plasma. Significant nonlinearities originate from the ion polarization drift and the electron temperature gradient. Modulational instability and possible final state of unstable drift waves are investigated.

Stabilization of drift waves by lower hybrid waves of finite wavenumber

The lower hybrid waves of finite wavenumber k0 are shown to be able to quench the entire k spectrum of unstable drift waves in tokamak plasmas for k0 greater than k, where k0 is perpendicular to k. In relatively cold plasmas, where k0 may become less than k, one needs to invoke the ion damping to stabilize the whole spectrum. The analysis explains very well the experimental results of Gore, Grun, and Lashinsky on the suppression of whole drift wave spectrum in a Q machine by a lower hybrid electric field.

ON THE LOW FREQUENCY DRIFT WAVE AND THE PSEUDOCLASSICAL DIFFUSION

In this paper, the relationship between the low frequency drift wave and the empirical law of anomalous transport in Tokamak the pseudo-classical diffusion is discussed. We show that, it is the collisionless drift wave, rather than the dissipative one, which corresponds to the pseudoelassical diffusion. If the linear unstable collision-less drift wave is saturated mainly by the quasi-linear relaxation process, it can lead to a diffusion of the pseudo-classical type. The estimated diffusion coefficient agrees with experiment within an order of magnitude. The range of the parameters in which the above mentioned mechanism may be effective is discussed.

Unstable Drift Waves in a Sheared Magnetic Field

Electrostatic collisionless drift waves in a sheared magnetic field have been studied extensively with use of particle-code simulations. When the shear is strong, we have found that the plasma is dominated by spatially uncorrelated small-amplitude oscillations with frequencies close to those prescribed by the local dispersion relation. With a weaker shear, spatially correlated large-amplitude waves with a well-defined frequency have been observed. Theoretically predicted eigenmodes are not the dominant feature of the fluctuation spectrum.

Numerical Analysis of Nonlinear Collisional Drift Instability

Nonlinear evolution of collisional drift wave instability is studied numerically. The model equations of quasilinear type are used which describe the modification of background density and the amplitude of unstable drift wave. Their solutions are classified according to the value of a parameter η which is proportional to the ratio of ion viscous damping to linear growth rate γ L . In the vicinity of marginal stability the unstable drift waves are shown to be saturated by flattening of the background density. As η decreases further we first obtain periodic and latter aperiodic solutions. The wave associated diffusion coefficient is obtained numerically as a function of η and found to be much less than the usual estimate γ L / k ⊥ 2 .

Asymptotic Expansion of Nonlinear Unstable Collisional Drift Wave

Nonlinear evolution equation for the collisional drift wave is obtained in a stab model based on the two fluid equations where the ton inertia, finite gyroradius and viscosity are included. A systematic expansion is introduced by taking e =|κ| l as a smallness parameter where κ is the degree of density gradient and l is the linear scale of the stab along the density gradient. A set of the model equations is proposed to describe the evolution of the nonlinear drift wave.

Drift wave anomalous transport in axisymmetric toroidal plasmas

A quasi-linear theory of the anomalous transport properties of an axisymmetric toroidal plasma caused by unstable drift waves has been developed. Both particle and kinetic energy fluxes across magnetic surfaces are derived and discussed. Applications of the results have been made to several drift instabilities which are likely to be present in actual toroidal devices. Estimates and comparisons for such devices show that the derived anomalous fluxes are likely to be higher than classical values even for small fluctuation levels.

Nonlinear Coupling between Drift Wave and Externally Excited Ion-Acoustic Wave

Effects of an alternating electric field on collisionless drift waves driven by density gradient are investigated theoretically. The alternating electric field is applied along the magnetic field, the frequency of which is close to that of the drift wave. It is assumed that the electron temperature is much greater than that of ions. The applied field is treated as a perturbation like ion-acoustic wave. The contribution of the “nonlinear Landau damping” due to the coupling between the drift and ion-acoustic waves to the damping coefficient, as well as the effect of the frequency shift, is calculated. It is found that the unstable drift waves can be stabilized for the suitable applied intensities. The damping mechanism is caused mainly by the increasing of the frequency of the drift wave. The results are compared with experimental observations.

Possibility of unstable collisional drift waves in lithium arc plasmas

The production of a high density ( approximately 5.1012/cm3) fully ionized lithium plasma by a reflex arc discharge in a mirror magnetic field has been reported by Fumelli (1963). This device has subsequently been used to study the dissociation of H2+ and H3+ in a lithium plasma, and to determine the energy loss of fast test ions in a plasma. The reports of anomalous losses and fluctuations have prompted the author to study the stability of such a plasma. He considers the collisional drift wave analysis of Hendel et al. (1968). After slight modifications are made to account for unequal electron and ion temperatures he shows that the lithium arc plasma may be susceptible to the onset of such a collisional drift instability. Furthermore, the possible existence of such an instability may account for the anomalous losses and fluctuations observed.

Effect of Shear on Resistive Drift Waves in the Spherator

Observations of marginally unstable resistive drift waves in a hydrogen plasma immersed in the sheared magnetic field of the Princeton spherator are reported. A theoretical treatment based on the nonlocal normal mode is proposed, which predicts the wave parameters of the most unstable mode, and provides a new stability criterion. The experimental wave parameters and observed stabilization of the resistive drift waves are found to agree well with the predicted values.

Dynamic stabilization of drift waves by electron temperature modulation

The effect of a small, periodic, time-dependent modulation of the electron temperature on the linear stability of a weakly inhomogeneous magnetoplasma is considered. Such a modulation may be produced by microwave heating of electrons. First, a general theory of the instability of collisionless drift waves with a small periodic modulation of the distribution function is derived. This is then used to deduce conditions for the dynamic stabilization of a variety of drift instabilities. It is found that the collisionless instabilities may be stabilized when the beating of an unstable drift wave with the temperature modulation is subject to an additional damping mechanism. No stabilizing effect has been found for the resistive drift mode described by a fluid approximation.

Noise in collision-free alkali metal plasmas

Oscillations in alkali metal plasmas generated by contact ionization have been attributed to unstable drift waves both in collision-free and collision-dominated plasmas. In the early experiments, however, the influence of the radial electric field Er in causing rotation of the plasma column was ignored. In later work with collisional plasmas, measured Er values were used to calculate frequencies in the rest-frame of the plasma and so demonstrate unstable collisional driftwaves.Measurements are reported on collision-free potassium and caesium plasmas. The radial electric field causes a Doppler shift comparable with the frequencies observed and often larger than the predicted frequency of the fastest growing drift wave. When this is taken into account the frequencies observed in potassium are within a factor of two of those predicted for the collisionless drift instability and the radial distribution of the density fluctuations shows a peak away from the edge of the column. Other features are consistent with the interpretation of the noise in potassium as due to the drift instability. In caesium edge effects predominate and the cause of the enhanced noise is not the drift instability.

Plasma Waves and Rotation in the Gas-Fed Hollow-Cathode Arc

Mass rotation and azimuthally propagating waves have been observed in gas-fed hollow-cathode arcs having ne ≈ 1014cm−3, Te ≈ 1 eV, Ti = 3 to 30 eV, and Bz = 1 to 6 kG. The column rotates as a rigid body at an angular velocity of 12 ωci; it is shown theoretically that at this velocity the radial density gradient has the maximum value at which equilibrium is possible in the absence of a radial electric field. This maximum gradient corresponds to an exp [− r2/(2ρi)2] dependence of density on radius, where ρi is the ion Larmor radius. The observed waves propagate in the electron drift direction exactly perpendicular to the axis of the arc, but have nonzero k‖ because of the azimuthal field of the arc current. They are identified as resistively unstable drift waves, modified torsional Alfvén waves, and ion cyclotron waves. The drift and ion cyclotron waves occur as coherent oscillations with phase-locked harmonics, while the Alfvén waves are noncoherent. Because of the dependence of the density gradient on Bz, the drift wave frequency is proportional to Bz and the Alfvén wave frequency is independent of Bz. The Alfvén and ion cyclotron waves are excited by a feedback mechanism involving electron flow across the anode sheath.