Ion Landau Damping Research Articles

Validation study of RWM stability in DIII-D high-βN plasmas

Abstract The n = 1 (n is the toroidal mode number) resistive wall mode (RWM) stability is numerically investigated for two DIII-D high-β N discharges 176440 and 172461, utilizing the MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) and MARS-K (Liu et al 2008 Phys. Plasmas 15 112503) codes. Systematic validation efforts are attempted, for the first time, for discharges with very slow or vanishing toroidal flow for a large fraction of the plasma volume. While gaining physics insights in accessing stable operation regime at β N exceeding the Troyon no-wall limit in these slow-rotation experiments, the predictive capability of fluid and non-perturbative magnetohydrodynamic-kinetic hybrid models for the RWM is further confirmed. The MARS-F fluid model, with a strong but numerically tunable viscosity mimicking ion Landau damping of parallel sound waves, finds complete stabilization of the n = 1 RWM in the considered DIII-D plasmas under the experimental flow conditions. Similarly, either full stabilization (for discharge 176440) or marginal stability (for discharge 172461) of the mode is computed by the MARS-K hybrid model, which is first-principle based without free model parameters. In particular, all drift kinetic resonances, including those of thermal and energetic particles, are found to synergistically act to marginally stabilize the RWM in discharge 172461. These MARS-F/K modeling results explain the experimentally observed stable operational regime in DIII-D, as far as the RWM stability is concerned. Extensive numerical sensitivity studies, with respect to the plasma toroidal flow speed as well as the radial location of the resistive wall, are also carried out to further support the validation study.

Predictive modeling of Alfvén eigenmode stability in inductive scenarios in JT-60SA

The JT-60SA device offers unique conditions before ITER for the study of the interaction of energetic particles with plasma waves. With similar dimensions to JET, e.g., a major radius but with a slightly more elongated plasma volume, JT-60SA is used as a high-power device where additional heating power (including 10 MW of the 500 keV Neutral Beam Injection) of up to 41 MW and the potential for high non-inductive plasma current operation pave the path for numerous challenges in physics on MHD stability, in particular, when considering the effects of energetic particles. Several operational scenarios with ITER and DEMO-relevant plasma regimes, in terms of non-dimensional plasma parameters, are anticipated. In this work, the stability of Alfvén eigenmodes (AEs) in variants of two of the most relevant operational scenarios with single null is analyzed: a full Ip inductive scenario at high density (1.1 × 1020 m−3 on-axis electron density) and 5.48MA/2.05T toroidal plasma current and magnetic field, and an advanced (hybrid) scenario with an ion energy transport barrier (ITB) and 3.5MA/2.28T toroidal plasma current and magnetic field. The workflow included the CRONOS code to establish the scenario, the ASCOT code to calculate the slowing-down energetic particle distributions for a positive/negative ion source-based neutral beam, and the MISHKA/CASTOR-K suite to calculate the MHD spectra of AEs and the associated drive/damping contributions from the NBI energetic ions, as well as the thermal ion landau damping. The systematic analysis, over a large Fourier space of the toroidal mode number/mode frequency, provides evidence that although a significant fraction of supra-Alfvénic particles stemming from the negative ion source-based neutral beam (500 keV) can, in some cases, drive to AEs in both scenarios, it is not enough to overcome the thermal ion landau damping. In addition, the advanced scenario with ITB is shown to be stable against AEs localized in the vicinity of the barrier as well, offering good prospects of sustainability of the plasma performance and of ITB. Finally, some sensitivity scan results are shown on the influence of fast ion density and q-profile on the AE mode spectra and stability.

Toroidal Alfvén eigenmodes observed in low power JET deuterium–tritium plasmas

The Joint European Torus recently carried out an experimental campaign using a plasma consisting of both deuterium (D) and tritium (T). We observed a high-frequency mode using a reflectometer and an interferometer in a D-T plasma heated with low power neutral beam injection, . This mode was observed at a frequency and was located at major radii . The observed mode was identified as a toroidal Alfvén eigenmode (TAE) using the linear MHD code, MISHKA. Beam ions and fusion-born alpha particles were modelled using the full orbit particle tracking code LOCUST, which produces smooth distribution functions suitable for stability calculations without analytical fits or the use of moments. We calculated the stability of the 21 candidate modes using the HALO code. These calculations revealed that beam ions can drive TAEs with toroidal mode numbers with linear growth rates , while TAEs with n < 8 are damped by the beam ion population. Alpha particles drive modes with significantly smaller linear growth rates, due to the low alpha power generated almost exclusively by beam-thermal fusion reactions. Non-ideal effects were calculated using complex resistivity in the CASTOR code, leading to an assessment of radiative, collisional, and continuum damping for all 21 candidate modes. Ion Landau damping was modelled using Maxwellian distribution functions for bulk D and T ions in HALO. Radiative damping, the dominant bulk damping mechanism, suppresses modes with high toroidal mode numbers. Comparing the drive from energetic particles with damping from thermal particles, we find all but one of the candidate modes are damped. The single net-driven n = 9 TAE with a net growth rate matches experimental observations with a lab frequency and location . The TAE was driven by co-passing particles through the resonance. Both co- and counter-passing alpha particles drive the TAE through the resonance. Additional sideband resonances contribute significant drive for both beam and alpha particles.

Growth mechanism and characteristics of electron drift instability in Hall thruster with different propellant types

The existence of a significant electron drift instability (EDI) in the Hall thruster is considered as one of the possible causes of the abnormal increase in axial electron mobility near the outlet of the channel. In recent years, extensive simulation research on the characteristics of EDI has been conducted, but the excitation mechanism and growth mechanism of EDI in linear stage and nonlinear stage remain unclear. In this work, a one-dimensional PIC model in the azimuthal direction of the thruster near-exit region is established to gain further insights into the mechanism of the EDI in detail, and the effects of different types of propellants on EDI characteristics are discussed. The changes in axial electron transport caused by EDI under different types of propellants and electromagnetic field strengths are also examined. The results indicate that EDI undergoes a short linear growth phase before transitioning to the nonlinear phase and finally reaching saturation through the ion Landau damping. The EDI drives a significant ion heating in the azimuthal direction through electron–ion friction before entering the quasi-steady state, which increases the axial mobility of the electrons. Using lighter atomic weight propellant can effectively suppress the oscillation amplitude of EDI, but it will increase the linear growth rate, frequency, and phase velocity of EDI. Compared with the classical mobility, the axial electron mobility under the EDI increases by three orders of magnitude, which is consistent with experimental phenomena. The change of propellant type is insufficient to significantly change the axial electron mobility. It is also found that the collisions between electrons and neutral gasescan significantly affect the axial electron mobility under the influence of EDI, and lead the strength of the electric field to increase and the strength of the magnetic field to decrease, thereby both effectively suppressing the axial transport of electrons.

The competing effects of wave amplitude and collisions on multi-ion species suppression of stimulated Brillouin scattering in inertial confinement fusion Hohlraums

Reduction in stimulated Brillouin scattering (SBS) from National Ignition Facility Hohlraums has been predicted through the use of multi-ion species materials on Hohlraum walls. This approach to controlling SBS is based upon introducing a lighter ion species to the heavier ion species Hohlraum wall in order to greatly increase the ion Landau damping of ion acoustic waves (IAWs). In a collisionless plasma, if the IAWs driven by SBS reach sufficient amplitudes, this increased damping is reduced or even eliminated by ion trapping in the IAWs. Here, the nonlinear behavior of IAWs is simulated with a multi-ion species Vlasov code, including interspecies ion–ion collisions, self-collisions, and electron–ion pitch-angle collisions. The effect of collisions on the trapping of ions and electrons in a large-amplitude IAW is studied in a regime of relevance to current Inertial Confinement Fusion experiments. Our simulations show that collisions can scatter trapped particles out of resonance with the IAW, suppressing trapping and helping to maintain an effective Landau damping of the IAW. The IAW amplitude required to trap particles in the presence of strong collisions is estimated analytically. These estimates are tested for strongly damped IAWs in tantalum oxide and pure helium plasmas. Our simulations show that, above a threshold amplitude, the damping is reduced by an amount inversely proportional to the wave amplitude. Thus, the success of controlling SBS using a multispecies plasma may depend sensitively on laser power and pulse length.

Thermal ion kinetic effects and Landau damping in fishbone modes

The kinetic–magnetohydrodynamic (MHD) hybrid simulation approach for macroscopic instabilities in plasmas can be extended to include the kinetic effects of both thermal ions and energetic ions. The new coupling scheme includes synchronization of the density and parallel velocity between thermal ions and MHD, in addition to pressure coupling, to ensure the quasineutrality condition and avoid numerical errors. The new approach has been implemented in the kinetic-MHD code M3D-C1-K, and was used to study the thermal ion kinetic effects and Landau damping in fishbone modes in both DIII-D and NSTX. It is found that the thermal ion kinetic effects can cause an increase of the frequencies of the non-resonant $n=1$ fishbone modes driven by energetic particles for $q_\mathrm {min}&gt;1$ , and Landau damping can provide additional stabilization effects. A nonlinear simulation for $n=1$ fishbone mode in NSTX is also performed, and the perturbation on magnetic flux surfaces and the transport of energetic particles are calculated.

Core localized alpha-channeling via low frequency Alfvén mode generation in reversed shear scenarios

A novel channel for fuel ions heating in tokamak core plasma is proposed and analyzed using nonlinear gyrokinetic theory. The channel is achieved via spontaneous decay of reversed shear Alfvén eigenmode (RSAE) into low frequency Alfvén modes, which then heat fuel ions via collisionless ion Landau damping. The conditions for RSAE spontaneous decay are investigated, and the saturation level and the consequent fuel ion heating rate are also derived. The channel is expected to be crucial for future reactors operating under reversed shear configurations, where fusion alpha particles are generated in the tokamak core with the magnetic shear being, typically, reversed, and there is a dense RSAE spectrum due to the small alpha particle characteristic dimensionless orbits.

Hybrid simulation of Alfvén wave parametric decay instability in a laboratory relevant plasma

Large-amplitude Alfvén waves are subject to parametric decays, which can have important consequences in space, astrophysical, and fusion plasmas. Although the Alfvén wave parametric decay instability (PDI) was predicted decades ago, observational evidence is limited, stimulating considerable interest in laboratory demonstration of the instability and associated numerical modeling. Here, we report an important step toward direct hybrid simulation of the Alfvén wave PDI in a laboratory plasma, using antenna-like wave injection of a circularly polarized wave and realistic wave-plasma parameters. Considering collisionless damping, we identify the threshold Alfvén wave amplitudes and frequencies required for triggering the instability. These threshold behaviors are corroborated by simple theoretical analysis, considering the balance between PDI growth and ion Landau damping and PDI development in a bounded plasma. Other effects not included in the present model such as finite transverse wave scale and ion–neutral collisions are briefly discussed. These hybrid simulations promise to be a useful tool for investigating laboratory Alfvén wave dynamics and may provide guidance for future laboratory demonstration of the PDI process.

Gyrokinetic simulations of momentum flux parasitic to free-energy transfer

Ion Landau damping interacts with a portion of the E × B drift to cause a nondiffusive outward flux of co-current toroidal angular momentum. Quantitative evaluation of this momentum flux requires nonlinear simulations to determine fL, the fraction of fluctuation free energy that passes through ion Landau damping, in fully developed turbulence. Nonlinear gyrokinetic simulations with the GKW code confirm the presence of the systematic symmetry-breaking momentum flux. For simulations with adiabatic electrons, fL scales inversely with the ion temperature gradient, because only the ion curvature drift can transfer free energy to the electrostatic potential. Although kinetic electrons should, in principle, relax this restriction, the ion Landau damping measured in collisionless kinetic-electron simulations remained at low levels comparable with ion-curvature-drift transfer, except when magnetic shear ŝ was strong. A set of simulations scanning the electron pitch-angle scattering rate showed only a weak variation of fL with the electron collisionality. However, collisional-electron simulations with electron temperature greater than ion temperature unambiguously showed electron-curvature-drift transfer supporting ion Landau damping, leading to a corresponding enhancement of the symmetry-breaking momentum flux.

The effects of multispecies Hohlraum walls on stimulated Brillouin scattering, Hohlraum dynamics, and beam propagation

Experiments and simulations have been conducted to investigate the efficacy of Ta2O5-lined Hohlraum walls at reducing stimulated Brillouin backscattering (SBS) as well as any subsequent effects on the Hohlraum dynamics and capsule implosions in indirect drive experiments at the National Ignition Facility. Using a 1.1 MJ 400 TW, 351 nm, shaped laser pulse, we measure a 5× reduction in SBS power in the peak of the pulse from the wall on the outer 50° cone beams. The SBS spectrum indicates a reduction in the high-Z spectral signature when using multispecies wall materials. Detailed hydrodynamic simulations were performed using different heat conduction models with flux limiters. Additional simulations were performed on the plasma maps using the 3D parallel paraxial code pF3D to compare backscatter powers between the pure Au and Ta2O5-lined Hohlraums. Further analysis, using hydrodynamically equivalent plasmas, shows that the SBS reduction is clearly a result of the added ion Landau damping caused by the oxygen ions and not from differences in plasma conditions. The experimental and simulation results also show an increase in the wall plasma expansion when using the Ta2O5 liner leading to a 70% more oblate implosion.

Ion Acoustic Peregrine Soliton Under Enhanced Dissipation

The effect of enhanced Landau damping on the evolution of ion acoustic Peregrine soliton in multicomponent plasma with negative ions has been investigated. The experiment is performed in a multidipole double plasma device. To enhance the ion Landau damping, the temperature of the ions is increased by applying a continuous sinusoidal signal of frequency close to the ion plasma frequency ∼1 MHz to the separation grid. The spatial damping rate of the ion acoustic wave is measured by interferometry. The damping rate of ion acoustic wave increases with the increase in voltage of the applied signal. At a higher damping rate, the Peregrine soliton ceases to show its characteristics leaving behind a continuous envelope.

The combined kinetic effects of the ion temperature gradient and the velocity shear of a plasma flow parallel to the magnetic field on the drift-Alfven instabilities

The drift-Alfvén instabilities of the sheared flow along the magnetic field of a finite beta (1&amp;gt;β≫me/mi) plasma with comparable inhomogeneous ion temperature and homogeneous electron temperature are examined by the numerical analysis of the derived linear dispersion equation. Accounting for the electromagnetic ion kinetic response, which has been neglected in conventional discussions of the drift-Alfvén instabilities of a steady plasma, a new kinetic drift-Alfvén instability has been found. It develops in a plasma shear flow due to the coupled action of the ion temperature gradient, the flow velocity shear, and the inverse ion Landau damping.

Multisatellite MMS Analysis of Electron Holes in the Earth's Magnetotail: Origin, Properties, Velocity Gap, and Transverse Instability

AbstractWe present a statistical analysis of more than 2,400 electrostatic solitary waves interpreted as electron holes (EH) measured aboard at least three Magnetospheric Multiscale (MMS) spacecraft in the Earth's magnetotail. The velocities of EHs are estimated using the multispacecraft interferometry. The EH velocities in the plasma rest frame are in the range from just a few km/s, which is much smaller than ion thermal velocity VTi, up to 20,000 km/s, which is comparable to electron thermal velocity VTe. We argue that fast EHs with velocities larger than about 0.1VTe are produced by bump‐on‐tail instabilities, while slow EHs with velocities below about 0.05VTe can be produced by warm bistream and, probably, Buneman‐type instabilities. We show that typically fast and slow EHs do not coexist, indicating that the instabilities producing EHs of different types operate independently. We have identified a gap in the distribution of EH velocities between VTi and 2VTi, which is considered to be the evidence for self‐acceleration (Zhou &amp; Hutchinson, 2018) or ion Landau damping of EHs. Parallel spatial scales and amplitudes of EHs are typically between λD and 10 λD and between 10−3 Te and 0.1 Te, respectively. We show that electrostatic potential amplitudes of EHs are below the threshold of the transverse instability and highly likely restricted by the nonlinear saturation criterion of electron streaming instabilities seeding electron hole formation: , where ϖ = min(γ, 1.5 ωce), where γ is the increment of instabilities seeding EH formation, while ωce is electron cyclotron frequency. The implications of the presented results are discussed.

Gyrokinetic investigation of the damping channels of Alfvén modes in ASDEX Upgrade

The linear destabilization and nonlinear saturation of energetic-particle driven Alfvénic instabilities in tokamaks strongly depend on the damping channels. In this work, the collisionless damping mechanisms of Alfvénic modes are investigated within a gyrokinetic framework by means of global simulations with the particle-in-cell code ORB5 and compared with the eigenvalue code LIGKA and reduced models. In particular, the continuum damping and the Landau damping (of ions and electrons) are considered. The electron Landau damping is found to be dominant compared to the ion Landau damping for experimentally relevant cases. As an application, the linear and nonlinear dynamics of toroidicity induced Alfvén eigenmodes and energetic-particle driven modes in ASDEX Upgrade is investigated theoretically and compared with experimental measurements.

Modeling Imbalanced Collisionless Alfvén Wave Turbulence with Nonlinear Diffusion Equations

Abstract A pair of nonlinear diffusion equations in Fourier space is used to study the dynamics of strong Alfvén wave turbulence, from MHD to electron scales. Special attention is paid to the regime of imbalance between the energies of counter-propagating waves commonly observed in the solar wind (SW), especially in regions relatively close to the Sun. In the collisionless regime where dispersive effects arise at scales comparable to or larger than those where dissipation becomes effective, the imbalance produced by a given injection rate of generalized cross-helicity (GCH), which is an invariant, is much larger than in the corresponding collisional regime described by the usual (or reduced) magnetohydrodynamics. The combined effect of high imbalance and ion Landau damping induces a steep energy spectrum for the transverse magnetic field at sub-ion scales. This spectrum is consistent with observations in highly Alfvénic regions of the SW, such as trailing edges, but does not take the form of a transition range continued at smaller scales by a shallower spectrum. This suggests that the observed spectra displaying such a transition result from the superposition of contributions originating from various streams with different degrees of imbalance. Furthermore, when imbalanced energy injection is supplemented at small scales in an already fully developed turbulence, for example under the effect of magnetic reconnection, a significant enhancement of the imbalance at all scales is observed.

Molecular dynamics simulations of wake structures behind a microparticle in a magnetized ion flow. II. Effects of velocity spread and ion collisions

The influence of velocity spread and ion-neutral collisions on the wake of a microparticle in a collisional magnetized ion flow is explored by means of molecular dynamics simulations. The ion flow is described in the constant-mean-free-path limit. A constant electric field is superimposed that maintains the ion drift at the Bohm speed and approximates conditions in the plasma sheath. The contribution of ion Landau damping to the wake structure is separated by simulations with a collisionless drift distribution. It is found that ion Landau damping and collisions have a counteracting effect on the ion density in the focus region. The dynamic shadows that are a typical feature of collisionless magnetized wakes with cold ion beams are damped by the velocity spread and vanish by a collision-enhanced ion density in the wake. Dynamic shadows reappear only at very high magnetic fields, B ≈ 10 T. In two-particle arrangements, the full collisional model shows that horizontal attractive forces persist up to B = 4 T but become repulsive for higher magnetization.

Dynamics of a slow electron hole coupled to an ion-acoustic soliton

This paper demonstrates stable embedding of an electron phase-space hole into an ion-acoustic soliton simulated using one-dimensional Particle-In-Cell simulation, forming a stable Coupled Hole-Soliton pair, which is a coupled state of a fluid soliton and a Bernstein-Green-Kruskal mode electron phase-space hole. Collision tests reveal that its collisional dynamics are a hybrid of soliton collision and electron hole merging. This hybrid state is separated from the classical free electron hole branch by a gap in their ion-frame velocities. Transition is possible from the coupled state to the free state by ion Landau damping and in the opposite direction by hole growth. Buneman instability simulation is performed, showing generation of both types of electron holes depending on the ion temperature. The results from our work can be readily applied to better understand the electrostatic solitary wave observations in space plasmas.

Interplanetary ion acoustic wave in solar wind plasma

The ion acoustic wave (IAW) and Landau damping in drifting solar wind (SW) plasma are studied kinetically. The derived dispersion relationship and Landau damping have been sketched using the Solar-Terrestrial Relations Observatory spacecraft data. In comparison to the plasma density and temperature, the plasma streaming speed is found to significantly increase the IAW phase speed. The Landau damping is found to strongly depend on the plasma density and temperature and has no dependency on the streaming speed. This study could be helpful in understanding the interplanetary IAW propagation in drifting SW plasma.

NIMROD calculations of energetic particle driven toroidal Alfvén eigenmodes

Toroidal Alfvén eigenmodes (TAEs) are gap modes induced by the toroidicity of tokamak plasmas in the absence of continuum damping. They can be excited by energetic particles (EPs) when the EP drive exceeds other dampings, such as electron and ion Landau damping, and collisional and radiative damping. A TAE benchmark case, which was proposed by the International Tokamak Physics Activity group, is studied in this work. The numerical calculations of linear growth of TAEs driven by EPs in a circular-shaped, large aspect ratio tokamak have been performed using the Hybrid Kinetic-MHD (HK-MHD) model implemented in the NIMROD code. This HK-MHD model couples a δf particle-in-cell representation of EPs with the 3D MHD representation of the bulk plasma through moment closure for the momentum conservation equation. Both the excitation of TAEs and their transition to energetic particle modes (EPMs) have been observed. The influence of EP density, temperature, density gradient, and position of the maximum relative density gradient, on the frequency and the growth rate of TAEs are obtained, which are consistent with those from the eigen-analysis calculations, kinetic-MHD, and gyrokinetic simulations for an initial Maxwellian distribution of EPs. The relative pressure gradient of EP at the radial location of the TAE gap, which represents the drive strength of EPs, can strongly affect the growth rate of TAEs. It is demonstrated that the mode transition due to EP drive variation leads to not only the change of frequency but also the change of the mode structure. This mechanism can be helpful in understanding the nonlinear physics of TAE/EPM, such as frequency chirping.

Ions shear flow and electron field-aligned current produce ion acoustic waves in the oxygen-hydrogen ionospheric plasma

It is pointed out that the ion acoustic waves (IAWs) are excited either by field-aligned shear flows or electron parallel current in oxygen-hydrogen (O-H) plasma of upper ionosphere. The purely growing D'Angelo instability becomes ion acoustic wave instability in the presence of second kind of ions within the framework of multi-fluid plasma model. On the other hand, kinetic theory is used to show that the growth rate of current driven ion acoustic wave overcomes the ion Landau damping. Out of four real roots corresponding to negative shear flow, the two roots can become unstable. Thus, ion acoustic waves at different but very low real frequencies appear in O-H plasma of ionosphere due to parallel shear flow and current, which is in agreement with satellite observations.