Ion Landau Damping Research Articles

One-dimensional Vlasov simulations of Langmuir solitons

Interactions of Langmuir solitons with plasma are simulated using a one-dimensional electrostatic Vlasov code, including both electrons and ions. The Zakharov’s solutions are used as initial conditions. The wave is found to transfer energy into electrons during the heating process due to the interaction of resonant electrons with high-frequency electric fields. For Te≫Ti, the temporal evolution of the electron distribution function shows different heating behaviors depending on whether the electrons are interacting with a single soliton or many solitons. In single-soliton interactions, the final electron distribution function approaches an exponential form, f(v)∝exp(−6v/vte). However, for multisoliton interactions, the final stage of the heated electrons establishes a power-law distribution function, f(v)∝v−4, which agrees with that of Gorev and Kingsep [Sov. Phys. JETP 39, 1008 (1974)]. Simulation results for soliton motion show strong ion Landau damping, such that the solitons dissipated quickly when Ti=Te. Analyses indicate that nonlinear damping of Langmuir solitons by thermal ions for vg≤vti plays the most important role in slowing down the moving solitons. A double-hump structure was also found in the near-sonic soliton motion.

Stability Analysis of Toroidicity-Induced Alfvén Eigenmodes in TFTR Deuterium-Tritium Experiments

The toroidicity-induced Alfven eigenmodes (TAE) are found to be stable in the Tokamak Fusion Test Reactor (TFTR) deuterium-tritium plasmas. The dominant stabilizing mechanisms are beam ion Landau damping and radiative damping. A core localized TAE mode is shown to exist near the center of the plasma at small magnetic shear and finite plasma beta, which can be destabilized by energetic alpha particles in future TFTR DT experiments. With additional instability drive from fast minority ions powered by ion cyclotron radio frequency, both the global and core localized TAE modes can be readily destabilized.

Influence of parallel viscosity on tearing mode stability

The influence of parallel viscosity on the linear stability of tearing modes is analyzed. The parallel viscosity is introduced as a fluid approximation of ion Landau damping. Solution of the resistive layer equations shows that the toroidal stabilization resulting from favorable averaged curvature is rather robust and is only weakly reduced by the parallel viscosity.

Stabilization of ideal modes by resistive walls in tokamaks with plasma rotation and its effect on the beta limit

It is shown that pressure-driven, ideal external modes in tokamaks can be fully stabilized by resistive walls with plasma rotation. For wall stabilized plasmas, there are two types of potentially unstable external modes: (i) the ‘‘resistive wall modes’’ that penetrate, and are nearly locked to the wall, and (ii) modes that rotate with the plasma and for which the wall acts as a good conductor. For the quickly rotating modes, the stabilizing effect of the wall increases when the wall is brought closer to the plasma, while for the resistive wall modes, the stabilization improves with increasing wall distance. When the plasma rotates at some fraction of the sound speed, there is a window of stability to both the wall-locked and the rotating mode. The stabilization depends principally on the toroidal coupling to sound waves and is affected by ion Landau damping. Two-dimensional stability calculations are presented to evaluate the gains in beta limit resulting from this wall stabilization for different equilibria and rotation speeds. Results are shown for advanced tokamak configurations with bootstrap fractions of ≊100%.

Damping and structure of dissipative toroidal drift waves in the presence of a velocity field

The eigenmode equation describing ballooning collisional drift instabilities is analysed in the presence of a radially varying poloidal velocity. The instability is found to be stabilized by an H-mode-type velocity profile. The radial mode structure is found to be more extended than its conventional localized Gaussian form. Electron Landau damping (contrary to the usual ion Landau damping of the corresponding slab problem) is conjectured as the possible sink of the outgoing energy.

Stabilization of external modes in tokamaks by resistive walls and plasma rotation.

It is shown that low n, pressure-driven, external modes in tokamaks can be fully stabilized by resistive walls when the plasma rotates at some fraction of the sound speed. The stabilization depends on toroidal coupling to sound waves and is affected by ion Landau damping. Two-dimensional stability calculations are presented to show the resulting gains in the beta limit.

Destabilized ion acoustic transit mode and anomalous transport in tokamaks

Kinetic and hydrodynamic analyses both predict that long wavelength electrostatic modes in tokamaks may be categorized as a destabilized ion acoustic mode. Ion Landau damping is essentially nullified by the ion magnetic drift for modes propagating in the electron diamagnetic drift (ω > 0). The anomalous electron thermal diffusivity estimated in terms of the mixing length theory scales with the safety factor q and resembles the ion diffusivity in the plateau regime varies as χe varies as 1/BθBϕ

Plasma wave modes in cooling flows in clusters of galaxies

We study the relevance of plasma microturbulences in the evolution of cooling flows in clusters of galaxies. The source of plasma instabilities is the temperature gradient which exists in the intracluster medium (ICM) of these clusters. Here we discuss in greater detail the effects of the ion acoustic turbulence (IAT). The study includes the effects of quasilinear interaction of particles with microturbulent fields, of nonlinear ion Landau damping process, and of heating of resonant ions. The main consequences of the IAT considered are those related to the reduction of the thermal conductivity due to anomalous effects, the formation of thermally insulated blobs of gas, and the hydrodynamical instability. We show that the ion acoustic mode can explain a reduction of at most around one order of magnitude in the thermal conductivity. We suggest, however, that such a mode can be perhaps one of the main microscopic processes determining the evolution of important macroscopic features of the ICM. 41 refs.

Destabilized ion acoustic mode in toroidal plasmas

An unstable long-wavelength electrostatic mode well described by ω≂ωs (the ion acoustic transit frequency) has been identified in an isothermal (Ti≂Te) tokamak. The ion Landau damping is prohibited by the ion magnetic drift provided ω≳0. For realistic discharge parameters, the mode frequency exceeds the diamagnetic frequency by a factor 2 to 3 at the stability boundary.

Weak turbulence theory of collisionless trapped electron driven drift instability in tokamaks

The toroidal collisionless trapped electron modes are analyzed in the weak turbulence regime treating both ions and trapped electrons nonlinearly in the presence of ion and electron temperature gradients. The spectral intensity of the density fluctuations in the nonlinearly saturated state is analytically obtained from the steady-state solution of the wave-kinetic equation. Distant nonlinear interactions between low-kθ and high-kθ modes of similar frequencies via trapped electron scattering (the resonance between the beat wave and the trapped electron precession drift frequencies) suppress the low-kθ [kθρs ≪(Ln/R)1/2] modes while close interactions via ion Compton scattering (nonlinear ion Landau damping) produce a monotonically decreasing spectrum from kθρs ≂(Ln/R)1/2 to kθρs≂1 according to an approximate power law k−3θ. Various fluctuation amplitudes at saturation and the fluctuation-induced anomalous particle and heat fluxes are found to be smaller than the mixing length estimates. The plasma confinement is predicted to improve with higher Ti/ Te, more peaked density profile, larger aspect ratio, and higher plasma current. Also, a significant dependence of transport on the electron temperature gradient is found which could contribute to the rigidity of the electron temperature profile often experimentally observed.

Inclusion of poloidal potential variation in neoclassical transport

Inclusion of the electrostatic potential is found to increase the electron neoclassical heat flux by an order of magnitude, while producing only a modest increase in the ion heat flux. The analysis is done for the plateau regime, though a similar behavior is expected in the banana regime. The poloidally varying potential, determined by quasineutrality, is predominantly due to ion Landau damping. The resulting E×B drift introduces terms into the electron heat flux that are comparable to those previously derived for the ion heat flux. Similar terms enter the particle flux, but here they cancel due to momentum balance.

Sheared field tearing mode instability and creation of flux ropes in the Earth magnetotail

Spontaneous disruptions of magnetotail energy are supposed to be caused by a tearing mode instability. We show how the tail current sheet becomes unstable in the presence of a sufficiently large magnetic shear. The instability occurs because the magnetic shear removes the stabilizing influence of the gyroscopic electrons. Ion Landau damping determines the growth rate of the instability. A violation of the magnetic line conservation in a narrow region due to finite electron inertia would allow three—dimensional reconnection and flux rope formation. The resulting flux topes are smaller in size and cause, therefore, weaker and more localized perturbations of the magnetosphere.

The effect of the ion transit resonance on the resistive magnetohydrodynamic modes

The stability of resistive interchange and ballooning modes is analyzed taking into account the kinetic effects associated with the ion transit resonance. In the parallel compressible limit, it is found that kinetic effects yield an unstable localized mode driven by inverse ion Landau damping. In addition, no threshold is found for the resistive ballooning mode even in the presence of average good curvature, with the effect of the ion transit resonance being destabilizing.

Landau damping in a magnetic quadrupole

Electrostatic waves with a frequency which is small compared to the ion cyclotron frequency in a plasma confined by a magnetic quadrupole are considered. An equation is derived for the growth or damping rate due to wave-particle (Landau) resonances with the effects of temperature gradients and finite Larmor radius included. Ion Landau damping of the fundamental drift mode in the UMIST quadrupole is calculated and its effect on the net growth rate is shown.

Decay instability of an upper-hybrid wave in a plasma cylinder

A nonlocal theory of parametric decay of an upper-hybrid wave into an ion-acoustic wave and an upper-hybrid sideband reveals that an axially symmetric pump tends to excite axially symmetric modes. The growth rate falls off with the frequency ω0 of the pump and the azimuthal model number l of the decay waves. In cases where ion and electron temperatures are nearly equal the decay process goes over to nonlinear ion Landau damping; however, the behavior of the growth rate with ω0 and l remains the same. The resonant and nonresonant decay via ion-cyclotron modes also show similar behavior, although with a smaller growth rate.

Ray Tracing Analyses of Lower Hybrid Waves in Heliotron/Torsatron

Lower hybrid (LH) wave propagation and absorption caused by ion Landau damping and electron Landau damping in the heliotron/torsatron were studied for ion heating, electron heating and current drive. The analyses are based on the ray tracing method using the electromagnetic plasma dispersion relation, including warm plasma effects. In the heliotron/torsatron, the magnetic field has large ripples along the magnetic field line produced by external helical coils. This property changes the cross-sectional shape of the LH resonance layer from a circular shape in tokamaks. The refractive indices N ⊥ and N // , perpendicular and parallel to the magnetic field line, respectively, also change in oscillation along the ray trajectory. LH waves are absorbed at the places where the refractive index is large or at the high-field side near the helical coils.

Experimental Srudy of an Ion-Acoustic Soliton with Dissipation

The propagation of an ion-acoustic soliton in an Ar (or Ar–He) plasma is investigated experimentally in a double plasma device. The various patterns of signals propagating from the separation grid into the target region are classified into three types, Besides the normal soliton pattern, there appear signals with either a shallow dip or a deep valley. The K–dV equation with a term expressing the effect of ion Landau damping is solved numerically with parameters corresponding to the experimental conditions. One of the types observed in the experiment (with a shallow dip) is fully reproduced theoretically with the corresponding plasma parameters. Effects of the initial height of the perturbation on the evolution of the signal are investigated experimentally and theoretically. The minority He ion which causes an increase of the ion Landau damping rate had the same effect as the decrease of the initial height of the signal.

Growth rate, saturation, and radial transport measurements for the trapped ion instability

The dissipative trapped ion instability (DTII) is observed as an m=1 mode localized to the mirror cell of the Columbia Linear Machine (CLM) [Plasma Phys. 24, 185 (1982)]. A gated feedback diagnostic allows the direct measurement of the DTII linear growth rate. The DTII growth rate is measured as a function of trapped fraction, keeping all other parameters fixed, and clearly displays the scaling with trapped fraction predicted by the radially local linear dispersion relation, including ion Landau damping. The saturated DTII mode amplitude is measured concurrently with the growth rate. The saturated amplitude displays a nearly linear dependence on the measured growth rate, normalized to the DTII real frequency, and is nearly proportional to the square root of the measured growth rate. A striped particle collector is used to measure the ambipolar radial plasma flux as the trapped fraction is varied. Radial diffusion coefficients are calculated from the measured radial particle fluxes and display a scaling intermediate between the Kadomtsev weak and strong turbulence predictions.

Effects of an Ambipolar Field on Stability of Electrostatic Drift Waves in Sheet Plasmas

The effects of an ambipolar field on the stability of electrostatic drift waves in sheet plasmas are investigated numerically. The analysis is based on an integral equation in the wave number space derived from the profiles of Gaussian density and parabolic ambipolar potential. The ambipolar field dependence of the eigenfrequency and eigenfunction of the drift waves is obtained. It is found that the drift waves are stabilized for a strong ambipolar potential of both the hill-type and well-type. The stabilization is due to the ion Landau damping caused by the velocity shear effect of the E × B drift. Purely growing (zero real frequency) drift modes are also found in the case of a hill-type ambipolar potential.

High-frequency emissions during the propagation of an electron beam in high-density plasma

A relativistic annular electron beam passing through a high-density plasma excites Langmuir waves via Cerenkov interaction. The Langmuir waves are backscattered off ions via nonlinear ion Landau damping. At moderately high amplitudes these waves are parametrically up-converted by the beam into high-frequency electromagnetic radiation, as observed in some recent experiments. A nonlocal theory of this process is developed in a cylindrical geometry. It is seen that the growth rate of the Langmuir wave scales as one-third the power of beam density. The growth rate of parametric instability scales as one-fourth the power of beam density and the square root of beam thickness.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>