Electrostatic Drift Waves Research Articles

Nonlinear dust drift Alfvén waves in rotating planetary magnetospheres

Linear and nonlinear electromagnetic waves are investigated in the dusty magnetospheres of rotating planets. In the presence of heavy dust, the plasma may support very low frequency waves that can be affected by the plasma rotation. It is also shown that Alfvén waves can couple with the electrostatic dust drift waves induced by the planetary rotation. A comparison of the results with a previous work has also been made in the electrostatic limit. The electromagnetic vortex structures can be formed in rotating planetary dusty plasmas in the nonlinear regime. An application of this theory to dusty plasmas of the magnetospheres of Saturn and Jupiter is pointed out.

Drift wave instability in the presheath of a fully ionized collisional plasma

It is shown that a presheath near a wall in fully ionized collisional plasma is unstable due to resistive excitation of electrostatic drift waves. The instability depends on the plasma inhomogeneity and resistivity but is independent of the particle flows to the wall. The wave spectrum and growth rate were calculated using a fluid model of the plasma and the Wentzel–Kramers–Brillouin approximation. The electron-wave collision frequency and the additional diffusion flux of the particles were calculated. The resistive instability may be a cause of the fluctuations in plasma parameters observed in transporting vacuum arc plasma beams through magnetized ducts.

Electron drift waves in an advanced tokamak plasma

The influence of details of an international thermonuclear experimental reactor (ITER)-like geometry on drift wave stability is studied. The eigenvalue problem for electrostatic electron drift waves is solved numerically by following the ballooning mode formalism and using a standard shooting technique. The real frequencies and growth rates of the most unstable modes and their eigenfunctions are calculated for two specific magnetic flux surfaces. For the equilibrium under investigation, the modes are found to be unstable for peak density profiles and their stability is found to be strongly affected by the local magnetic shear (LMS). The presence of positive LMS is found to be destabilizing on the magnetic surface where global magnetic shear is reverse. The stability behaviour is however different for a positive magnetic shear surface where the effect of large positive LMS is found to be stabilizing. The eigenfunctions are more localized in the regions where normal curvature is bad and magnetic field is weak.

Multitude of Core-Localized Shear Alfvén Waves in a High-Temperature Fusion Plasma

Evidence is presented for a multitude of discrete frequency Alfvén waves in the core of magnetically confined high-temperature fusion plasmas. Multiple diagnostic instruments confirm wave excitation over a wide spatial range from the device size at the longest wavelengths down to the thermal ion Larmor radius. At the shortest scales, the poloidal wavelengths are comparable to the scale length of electrostatic drift wave turbulence. Theoretical analysis confirms a dominant interaction of the modes with particles in the thermal ion distribution traveling well below the Alfvén velocity.

Multiscale interaction of a tearing mode with drift wave turbulence: A minimal self-consistent model

A minimal self-consistent model of the multiscale interaction of a tearing mode with drift wave turbulence is presented. A tearing instability in a cylindrical plasma interacting with electrostatic drift waves is considered, for reasons of simplicity. Wave kinetics and adiabatic theory are used to treat the feedback of tearing mode flows on the drift waves via shearing and radial advection. The stresses exerted by the self-consistently evolved drift wave population density on the tearing mode are calculated by mean field methods. The principal effect of the drift waves is to pump the resonant low-m mode via a negative viscosity, consistent with the classical notion of an inverse cascade in quasi-two-dimensional turbulence. This process can occur alone or in synergy with current gradient drive of the low-m mode. Speculations of the relation of this multiscale process to the more general issue of the fate of energy transferred to large scales by an inverse cascade are presented. The existence of nonlinearly driven vortices pinned to low-q surfaces as a class of highly anisotropic dissipative structures which terminate the inverse cascade is proposed. The evolution of a finite size magnetic island is discussed.

Drift wave instability in the Helimak experiment

Electrostatic drift wave linear stability analysis is carried out for the Helimak configuration and compared against experimental data. Density fluctuation and cross-spectrum measurements show evidence of a coherent mode propagating perpendicular to the magnetic field which becomes unstable at k⊥ρs∼0.15. By comparing the experimental results with the wave characteristic of linear two-fluid theory, this mode is identified as an unstable resistive drift wave driven by the density gradient and magnetic grad-B/curvature present in an otherwise magnetohydrodynamic stable steady-state equilibrium.

Investigation of electron heat pinch in ASDEX-Upgrade

The existence of an electron heat pinch has been experimentally investigated in ASDEX-Upgrade in plasmas with strong off-axis electron cyclotron heating (ECH). Localization of 1.6 MW of ECH power at ρdep = 0.65 in plasmas with low Ohmic power (<100 kW) still resulted in peaked electron temperature (Te) profiles at densities ne0 ∼ 2.7 × 1019 m−3. Two out of four gyrotrons were modulated in order to study convective effects also on the Te transient response at different frequencies. Peculiar profiles of the modulation amplitude have been measured, very flat in the region just inside ρdep (0.3 < ρtor < 0.65) or even increasing rather than decreasing away from ρdep on the inner side. The phase profiles instead regularly indicate the propagation of the heat wave in both directions away from ρdep. Power balance analysis shows that the heat flux in the core region is very close to zero, but uncertainties do not allow a clear determination of its sign. Modelling steady-state and modulation results with an empirical model featuring a diffusive term characterized by a critical gradient length (LTe = −Te/∇Te) behaviour and a constant Gaussian shaped heat pinch profile allows good reproduction of the data when the region just inside ρdep is close to the critical threshold and oscillates around it, and a small convective term U ∼ 1–2 m s−1 is present in the same region. At higher density the Te profile becomes flatter and the amplitude profiles recover the usual shape with stronger decay inside with respect to outside ρdep. In this case no heat pinch is needed and the plasma goes below the critical threshold inside ρdep. The results are consistent with the theoretical prediction of a turbulence regulated by a threshold in R/LTe and a small turbulence generated electron heat pinch term. However initial attempts to perform first principle-based simulations using the quasi-linear electrostatic drift wave Weiland model have failed to reproduce the experimental results.

Solar wind interaction with the stationary dust can produce drift waves to form nonlinear structures

Solar wind electrons and ions penetrating with shear flow into the stationary dust can introduce electrostatic drift wave in plasmas of cometary and planetary environments. The drift wave becomes linearly unstable in the presence of shear flow. The background current also produces shear in the static magnetic field which does not allow the Shukla-VarmaPhys. Fluids B [5, 236 (1993)] mode to exist in such a system. The vortex structures can be formed in nonlinear regime. The relevance of this investigation to space plasmas is pointed out.

Self-gravitation effect on the nonlinear dynamics of an electron–positron–ion magnetoplasma

A new set of nonlinear equations governing the dynamics of low-frequency electrostatic drift waves in a self-gravitating electron–positron–ion (e–p–i) magnetoplasma with equilibrium density, temperature, magnetic field and velocity gradients has been derived. It is shown that possible stationary solutions of the nonlinear equations can be represented in the form of dipolar and tripolar vortices of gravitational potential. The results of the present investigation are useful to understand the nonlinear dynamics of low-frequency gravitational-drift waves in laboratory and astrophysical e–p–i magnetoplasmas.

Ion temperature gradient-driven dipolar vortices in dusty plasmas

The nonlinear dynamics of the ion temperature gradient (ITG) mode is investigated in a dusty plasma assuming the dust grains to be tiny and highly charged. The electrostatic drift waves cannot be ignored in the linear dispersion relation if polarization drifts of ions and dust are taken into account. The dipolar vortices are predicted to be formed in the nonlinear regime. The relevance of this study to space and astrophysical plasmas is pointed out.

Drift wave driven zonal flows in plasmas

The generation of large-scale zonal flows by small-scale electrostatic drift waves in a plasma is considered. The generation mechanism is based on the parametric excitation of convective cells by finite amplitude drift waves. To describe this process a generalized Hasegawa–Mima equation containing both vector and scalar nonlinearities is used. The drift waves are supposed to have arbitrary wavelengths (as compared with the ion Larmor radius). A set of coupled equations describing the nonlinear interaction of drift waves and zonal flows is deduced. The generation of zonal flows turns out to be due to Reynolds stresses produced by finite amplitude drift waves. It is found that the wave vector of the fastest growing mode is perpendicular to that of the drift pump wave. Explicit expressions for the maximum growth rate as well as for the optimal spatial dimensions of the zonal flows are obtained. A comparison with previous results is carried out. The present theory can be used for interpretations of drift wave observations in laboratory plasmas.

Magnetic electron drift waves in electron magnetohydrodynamic plasmas

The dynamics of nonuniform, magnetized, cold electron plasma in a stationary charge neutral ion background is considered. In the high frequency limit, electromagnetic modification of electron plasma oscillation is obtained in homogeneous plasma, whereas in inhomogeneous plasma in the low frequency regime a driftlike mode is found. Nonlinear evolution of this mode is derived to describe the two-dimensional (2D) dynamics. The equation has a close resemblance to 2D electrostatic collisionless drift wave equation thereby called as “magnetic electron drift” wave. In addition to the usual small amplitude dispersive modes the stationary state nonlinear vortexlike solutions are also discussed. The magnetic electron drift wave in the electron magnetohydrodynamic regime can find applications in laboratory as well as in space plasmas.

Sheared-flow-driven ion-acoustic drift-wave instability and the formation of quadrupolar vortices in a nonuniform electron–positron–ion magnetoplasma

A system of nonlinear equations which governs the dynamics of low-frequency (in comparison with the ion gyrofrequency) electrostatic waves in a nonuniform electron–positron–ion (e-p-i) magnetoplasma with sheared ion flows is presented. In the linear limit, a dispersion relation is obtained that admits new instabilities of drift-waves. It is found that ion-acoustic and electrostatic drift waves can become unstable due to ion sheared flow. Furthermore, the nonlinear interactions between these finite amplitude short-wavelength waves give rise to quadrupolar vortices. The relevance of the investigation to laboratory and astrophysical plasmas is pointed out.

Spatial mode structures of electrostatic drift waves in a collisional cylindrical helicon plasma

In a cylindrical helicon plasma, mode structures of coherent drift waves are studied in the poloidal plane, the plane perpendicular to the ambient magnetic field. The mode structures rotate with a constant angular velocity in the direction of the electron diamagnetic drift and show significant radial bending. The experimental observations are compared with numerical solutions of a linear nonlocal cylindrical model for drift waves [Ellis et al., Plasma Phys. 22, 113 (1980)]. In the numerical model, a transition to bended mode structures is found if the plasma collisionality is increased. This finding proves that the experimentally observed bended mode structures are the result of high electron collisionality.

Comparison of electron drift waves in numerical and analytical tokamak equilibria

In this paper, we demonstrate the importance of the details of the equilibria on the stability of electron drift waves. A comparison of electrostatic electron drift waves in numerical and analytical tokamak equilibria is presented in fully three-dimensional circular and non-circular tokamaks. The numerical equilibria are obtained using the variational moments equilibrium code and the analytical equilibria used is the generalized model. An eigenvalue equation for the model is derived using the ballooning mode formalism and solved numerically using a standard shooting technique. The stability and the localization of the electron drift wave is found to be strongly dependent on the local shear of the magnetic field. Large values of the local shear are found to be stabilizing. A disagreement in the results is found between analytical and numerical equilibria at aspect ratios of typical tokamaks, suggesting that the latter approach should be used in the transport calculations. The effects of the local shaping of the magnetic surfaces are complicated and can be both stabilizing and destabilizing, depending on the details of the equilibria.

Electrostatic instabilities and nonlinear structures of low-frequency waves in nonuniform electron–positron–ion plasmas with shear flow

It is found that the low-frequency ion acoustic and electrostatic drift waves can become unstable in uniform electron–ion and electron–positron–ion plasmas due to the ion shear flow. In a collisional plasma a drift-dissipative instability can also take place. In the presence of collisions the temporal behavior of nonlinear drift-dissipative mode can be represented in the form of well-known Lorenz and Stenflo type equations that admit chaotic trajectories. On the other hand, a quasi-stationary solution of the mode coupling equations can be represented in the form of monopolar vortex. The results of the present investigation can be helpful in understanding electrostatic turbulence and wave phenomena in laboratory and astrophysical plasmas.

Micro-stability and transport modelling of internal transport barriers on JET

The physics of internal transport barrier (ITB) formation in JET has been investigated using micro-stability analysis, profile modelling and turbulence simulations. The calculation of linear growth rates shows that magnetic shear plays a crucial role in the formation of the ITB. Shafranov shift, ratio of the ion to electron temperature, and impurity content further improve the stability. This picture is consistent with profile modelling and global fluid simulations of electrostatic drift waves. Turbulence simulations also show that rational q values may play a special role in triggering an ITB. The same physics also explains how double internal barriers can be formed.

Multigrid particle-in-cell simulations of plasma microturbulence

A new scheme to accurately retain kinetic electron effects in particle-in-cell (PIC) simulations for the case of electrostatic drift waves is presented. The splitting scheme, which is based on exact separation between adiabatic and nonadiabatic electron responses, is shown to yield more accurate linear growth rates than the standard δf scheme. The linear and nonlinear elliptic problems that arise in the splitting scheme are solved using a multigrid solver. The multigrid PIC approach offers an attractive path, both from the physics and numerical points of view, to simulate kinetic electron dynamics in global toroidal plasmas.

Vortices in a Strongly Magnetized Electron–Positron–Ion Plasma

A theoretical investigation has been presented for the linear and nonlinear properties of obliquely propagating coupled low-frequency electrostatic drift and ion-acoustic (ED-IA) waves in a strongly magnetized nonuniform electron–positron–ion plasma in the presence of sheared ion flow. A result from our linear analysis is that the ED-IA waves can be unstable due to the ion sheared flow. In addition, it is shown that the nonlinear equations governing the dynamics of weakly interacting ED-IA waves admit vortex solutions of two different classes viz. a vortex chain and a double vortex.

Measurements of anomalous particle and energy fluxes in a magnetized plasma.

Electrostatic probe measurements of low frequency plasma fluctuations and anomalous particle and energy flux densities in a magnetized plasma are presented. A method allowing the simultaneous recording of instantaneous electric field, electron density, and temperature is invoked. The method is applied to flux density measurements in a weakly ionized, low beta plasma created in a toroidal device without magnetic rotational transform. It is also used to identify modes belonging to different dispersion branches and to obtain the dispersion relations for these modes. For the plasma states studied, the phase velocities and the cross phase between the electron density and electric field agree with those predicted from a local, linear stability analysis for electrostatic flute modes and drift waves. The instability threshold, however, is one order of magnitude higher than predicted by theory for unsheared flow. The fluxes measured are consistent with the estimated ionization rate.