Ion Landau Damping Research Articles

Stabilization of resistive wall modes in ITER by active feedback and toroidal rotation

Two approaches are examined for stabilization of the resistive wall mode (RWM) of toroidal mode number n = 1 in an advanced ITER scenario. Active feedback control, with the present coil design and poloidal sensors placed just inside the inner wall, can be very efficient in stabilizing the RWM. Within the voltage limit of the present design for the feedback coils and conservative constraints on performance, the plasma pressure can be increased up to at least 70% between the no-wall and ideal-wall beta limits. Stabilization of the RWM by toroidal plasma rotation depends on the rotation profile as well as on the model for ion Landau damping. Feedback control of rotating plasmas for the advanced scenario is considered. The effect of the blanket is also studied using a simplified model.

Effects of ion trapping on crossed-laser-beam stimulated Brillouin scattering

An analysis of the effects of ion trapping on ion acoustic waves excited by the stimulated Brillouin scattering of crossing intense laser beams is presented. Ion trapping alters the dispersion of ion acoustic waves by nonlinearly shifting the normal mode frequency and by reducing the ion Landau damping. This in turn can influence the energy transfer between two crossing laser beams in the presence of plasma flows such that stimulated Brillouin scattering (SBS) occurs. The same ion trapping physics can influence the saturation of SBS in other circumstances. A one-dimensional analytical model is presented along with reasonably successful comparisons of the theory to results from particle simulations and laboratory experiments. An analysis of the vulnerability of the National Ignition Facility Inertial Confinement Fusion point design [S. W. Haan et al., Fusion Sci. Technol. 41, 164 (2002)] is also presented.

Study of thermonuclear Alfvén instabilities in next step burning plasma proposals

The stability of α-particle driven shear Alfvén eigenmodes (AE) for nominal burning plasma (BP) parameters in the proposed international tokamak experimental reactor (ITER), fusion ignition research experiment (FIRE) and IGNITOR tokamaks is studied. JET plasma, where fusion αs were generated in tritium experiments, is also studied to compare the numerical predictions with the existing experiments. An analytic assessment of toroidal AE (TAE) stability is first presented, where the α-particle β due to the fusion reaction rate and electron drag is simply and accurately estimated in plasmas with central temperature in the range of 7–20 keV. In this assessment the hot particle drive is balanced against ion-Landau damping of the background deuterons, and electron collision effects and stability boundaries are determined. Then two numerical studies of AE instability are presented. In one, the HIgh-n STability (HINST) code is used to predict the instabilities of low and moderately high frequency Alfvén modes. HINST computes the non-perturbative solutions of the AE including effects of ion finite Larmor radius, orbit width, trapped electrons etc. The stability calculations are repeated using the global code NOVAK. We show that for these plasmas the spectrum of the least stable AE modes is at medium-/high-n numbers. In HINST, TAEs are locally unstable due to the α pressure gradient in all the devices under consideration except IGNITOR. However, NOVAK calculations show that the global mode structure enhances the damping mechanisms and produces stability for the nominal FIRE proposal and near-marginal stability for the nominal ITER proposal. NBI ions produce a strong stabilizing effect for JET. However, in ITER, the beam energies needed to penetrate to the core must be high (∼1 MeV) so that a diamagnetic drift frequency comparable to that of α-particles is produced by the beam ions which induces a destabilizing effect. A serious question remains whether the perturbation theory used in NOVAK overestimates the stability predictions, so that it is premature to conclude that the nominal operation of all three BP proposals without neutral beam injection are stable (or marginally stable) to AEs.

Experimental test of damping models for n = 1 toroidal Alfvén eigenmodes in JET

The damping rate of the n = 1 toroidal Alfvén eigenmodes (TAE) mode in Ohmic-heated JET plasmas has been measured and compared with the prediction of the kinetic NOVA-K code, which includes electron and ion Landau damping of the global shear-Alfvén wave field, collisional damping, and radiative damping. It was found that the calculated damping rate is too small to account for the measured value under these experimental conditions. A relatively weak dependence of the damping rate on the normalized Larmor radius is observed experimentally.

Slow wave ion heating in the HELIX helicon source

Ion temperature measurements have been made at multiple axial and radial locations in a helicon source for a range of magnetic field strengths and RF frequencies. The observed temperature gradient along the axis suggests limited thermal transport along the magnetic field. The radial profiles are flat near the axis and in some cases peak near the edge of the plasma. The ion temperature measurements combined with calculations of the perpendicular wave numbers for the slow wave or `Trivelpiece–Gould' mode are consistent with ion heating due to ion Landau damping of the slow wave at the edge of the plasma.

RF absorption and ion heating in helicon sources.

Experimental data are presented that are consistent with the hypothesis that anomalous rf absorption in helicon sources is due to electron scattering arising from parametrically driven ion-acoustic waves downstream from the antenna. Also presented are ion temperature measurements demonstrating anisotropic heating (T( perpendicular)>T(parallel)) at the edge of the discharge. The most likely explanation is ion-Landau damping of electrostatic slow waves at a local lower-hybrid-frequency resonance.

Low frequency oscillations in a plasma with spatially variable field-aligned flow

The effects of a transverse gradient in the plasma flow velocity parallel to the ambient magnetic field are analyzed. A transverse velocity gradient in the parallel ion flow, even in small magnitude, can increase the parallel phase speed of the ion-acoustic waves sufficiently to reduce ion Landau damping. This results in a significantly lower threshold current for the current driven ion acoustic instability. Ion flow gradients can also give rise to a new class of ion cyclotron waves via inverse cyclotron damping. A broadband wave spectrum with multiple cyclotron harmonics is possible. A combination of the multiple cyclotron harmonic waves can result in spiky electric field structures with their peaks separated by an ion cyclotron period. A spatial gradient in the parallel electron flow is also considered but it is found to play a minimal role in the low frequency regime. Relevance of these to natural plasma environments is discussed.

Isotope effects in an electron cyclotron resonance ion source inmixtures of 15N/14N

Isotope effects in an electron cyclotron resonance ion source areinvestigated in mixtures of 15N and 14N. The ratio of the extractedcurrents I(15Nq + )/I(14Nq + ) increases with increasingcharge state q. This so-called `isotope anomaly' proves to be dependent onboth the mixture ratio of the gases as well as the microwave power fed intothe discharge. It is shown that the often-utilized `ion cooling' model cannotsolely explain the observed isotope effects as long as the temperature isassumed to be equal for all ion species. Since we observed the occurrence oflow-frequency noise in correlation with the isotope anomaly, we suggest thatthe ions are additionally heated by ion Landau damping. Due to the massdependence of this process, the lighter ion species will be heatedpredominantly. This results in an enhanced transport of lighter ions out ofthe plasma and a better confinement for the heavier component, which,consequently, may be more effectively ionized to higher charges states.

Identification of Mercier instabilities in Alcator C-Mod tokamak

During current ramp-up discharges, highly localized magnetohydrodynamic (MHD) fluctuations were observed on the electron cyclotron emission diagnostics of Alcator C-Mod tokamak [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)]. The electron temperature profile was hollow, while the density profile was weakly decreasing. Assuming that the equilibration time was short enough to quickly thermalize ions the pressure profile was also found to be hollow. Using this pressure profile as an additional constraint to the EFIT program, an equilibrium with reversed shear was constructed having a q(0)≫1. The localized MHD activity was observed near the inner q=5 rational surface in this reconstructed equilibrium, where the Mercier criterion for ideal MHD stability was violated because of the reversed pressure gradient (dp/dr>0), q>1 and moderate shear. When kinetic effects were added, the ideal Mercier mode was finite ion Larmor radius stabilized. However, ion Landau damping was found to be strong enough to drive a kinetic Mercier instability.

Ion-collisional effects on ion-acoustic waves: an eigenvalue technique via moment expansion

A numerical solution to the linearized ion Fokker-Planck (FP) equation is presented. By reducing the FP equation to an eigenvalue problem via moment expansion of a perturbed ion distribution function, the frequencies and damping rates of ion-acoustic waves and the specific heat ratio are calculated. Numerical calculation shows that this technique is very efficient, as ion Landau damping is negligible in comparison with collisional damping.

The effect of plasma flow, compressibility, and Landau damping on resistive wall modes

A uniform compressible plasma with a uniform flow along the magnetic field in the presence of a resistive wall is shown to be subject to two instabilities. For the first instability, the flow velocity is required to exceed the Alfvén speed, whereas for the second it need only exceed the sound speed. For a sufficiently high ion temperature, ion Landau damping is shown to stabilize the second instability associated with the sound speed.

Ion heating effects in LHCD sustained low density tokamak plasmas

In low density (similar 1018 cm-3) plasmas sustained by lower hybrid current drive in the high magnetic field superconducting tokamak Triam-1M (Kyushu University, Japan), high ion temperature has been frequently observed by an NEA diagnostic. The experimental phenomena are briefly described and analyzed in the paper. It is suggested by the analysis that the high ion temperature of the low density tokamak plasmas is attributed to ion Landau damping of lower hybrid wave.

Electrostatic Particle-in-Cell Simulation Technique for Quasineutral Plasma

We have developed a simulation method withbothelectrons and ions represented as particles-in-cell, in which the electrostatic field is determined from the requirement of quasineutrality rather than from Poisson's equation. This approach permits self-consistent calculation of the potential, in quasineutral situations where statistical fluctuations in the charge density frustrate the use of Poisson's equation. Time steps may be orders of magnitude longer than the plasma period, and mesh cells orders or magnitude longer than the Debye length, since electron plasma oscillations do not appear in the model and the Debye length is essentially set to zero. The simulation technique correctly represents kinetic features such as electron and ion Landau damping. The method is demonstrated by application to several simple test problems, including free expansion of a plasma, and linear and nonlinear ion sound. In the case of a plasma with strongly magnetized electrons, we apply the technique to determine the parallel electric field and parallel transport within the plasma. Quasineutral techniques for representing cross-field transport, and edge effects in bounded plasmas, will be discussed in subsequent publications.

Experiments on drift wave launching: I. Dispersion curves and damping rates

We describe experiments on the launching of drift waves in the UMIST Quadrupole GOLUX, presenting the general principles of successful launching and showing how these are applied to launch both the unstable drift waves which occur spontaneously in the device, and other stable modes representing different branches of the drift wave dispersion relation. In each case the measured dispersion curves are presented and compared with theory. All the waves appear to be spatially damped, including those known to be unstable; we propose that this is due to systematic error in the detection system. The results suggest that only if the measured decay constant exceeds about can we be certain that the waves are actually damped. This is the case at low frequencies, where the dissipation is due to ion Landau damping, and again at high wavenumbers where no suitable dissipative process has been discovered. We conjecture that the effect is due to radiative damping, associated with the breakdown of the one-dimensional propagation assumed in the theory.

Analysis of alpha particle-driven toroidal Alfvén eigenmodes in Tokamak Fusion Test Reactor deuterium–tritium experiments

The toroidal Alfvén eigenmodes (TAE) are calculated to be stable in the presently obtained deuterium–tritium plasmas in the Tokamak Fusion Test Reactor (TFTR) [Plasma Phys. Controlled Nucl. Fusion Res. 26, 11 (1984)]. However, the core localized TAE mode can exist and is less stable than the global TAE modes. The beam ion Landau damping and the radiative damping are the two main stabilizing mechanisms in the present calculation. In future deuterium–tritium experiments, the alpha-driven TAE modes are predicted to occur with a weakly reversed shear profile.

Search for alpha driven TAEs at lowered ion temperature in TFTR DT discharges

An experiment was performed in TFTR DT plasmas in an attempt to destabilize the alpha particle driven toroidicity-induced Alfven eigenmodes (TAEs) by reducing their thermal ion Landau damping. The thermal ion Landau damping was reduced by transiently lowering the ion temperature using either helium (He) gas puffs or deuterium (D) or lithium (Li) pellet injection during neutral beam injection (NBI) into DT supershots. The ion temperature was successfully lowered from Ti(0) approximately=20 keV to Ti(0) approximately=10 keV in about 0.2 s; however, no alpha driven TAEs were observed. Theoretical analyses of the TAE instability of these DT discharges indicate that the alpha pressure required for TAE stability still remained greater than that actually obtained in this experiment, mainly because of the effects of beam ion Landau damping

Inertia and ion Landau damping of low-frequency magnetohydrodynamical modes in tokamaks

The inertia and Landau damping of low-frequency magnetohydrodynamical modes are investigated using the drift-kinetic energy principle for the motion along the magnetic field. Toroidal trapping of the ions decreases the Landau damping and increases the inertia for frequencies below (r/R)1/2vthi/qR. The theory is applied to toroidicity-induced Alfvén eigenmodes and to resistive wall modes in rotating plasmas. An explanation of the beta-induced Alfvén eigenmode is given in terms of the Pfirsch–Schlüter-like enhancement of inertia at low frequency. The toroidal inertia enhancement also increases the effects of plasma rotation on resistive wall modes.

An Adiabatic Fluid Electron Particle-in-Cell Code for Simulating Ion-Driven Parametric Instabilities

A hybrid particle-in-cell (PIC) method is presented in which the electrons are modeled as an adiabatic fluid with an arbitrary ratio of specific heats γ. The electromagnetic field model is based on a temporal Wentzel–Krammers–Brillouin approximation. The method is a new tool for simulating ion-driven parametric instabili?ties which often exist in laser-produced plasmas. The method is general and does not depend on the number of spatial dimensions. The method will model the plasma behavior correctly even in situations where the electron Debye shielding is not negligible. Test simulations of ion Landau damping in both one and two dimensions are performed, and the results are in excellent agreement with linear Vlasov theory. Test simulations of stimulated Brillouin scattering (SBS) in one and two dimensions are performed, and the results indicate that when the intensity of the driving electromagnetic field is sufficiently high, backscatter SBS is dominant at early time while side-scatter SBS is dominant at late time. For the test cases in which a high-frequency driving electromagnetic field is present, our hybrid PIC method offers a substantial saving in computational time over explicit PIC methods that require the time scale of the driving electromagnetic field to be resolved.

TAE mode stability in JT-60SU steady state plasmas

The stability of toroidal Alfven eigenmodes (TAEs) is presented for steady state plasmas in the JT-60 Super Upgrade (JT-60SU). Studies are carried out by using the ACCOME code for calculating self-consistent MHD equilibria and by using the NOVA-K code for analysing the TAE stability. Characteristics of the TAE stability are obtained for non-inductive steady state plasmas (3 MA/3 T) with a large bootstrap current and a 500 keV neutral beam (NB) current. Above the density value corresponding to VhVA~1, the TAE becomes unstable owing to the large pressure gradient, ΔPh, and the large β of the hot particles, (βh). Here, VhVA is the ratio of the hot particle velocity to the Alfven velocity. As the density and the temperature increase, the bootstrap current increases so that the NB power required for the current drive decreases. Consequently, both ΔPh and (βh) decrease and the TAEs are stabilized by ion Landau damping. In the high current and high toroidal field plasma (10 MA/6.25 T) case, because ΔPh is small, owing to high density, and (βh) is small, owing to high toroidal field, the TAE is stable for low n to medium n (⩽15)

External kink modes in a tokamak with a resistive wall and a high-beta rotating plasma

The effect of the toroidal plasma rotation on the external kink mode instability driven by the wall resistivity is studied theoretically. It is suggested that this effect is related to the presence of side-band poloidal harmonics with singular points lying inside the plasma. Near the singular points we allow for plasma inertia and related toroidal effects. The ion Landau damping and its weakening due to the toroidal trapping and taken into account. High-beta effects near the singular points are allowed for. They cause the finiteness of the Mercier index s. It is shown that the influence of the plasma rotation on the external kink modes is most significant for s<0, i.e., in the situation favouring the development of instability in a non-rotating plasma.