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Alfven waves are of fundamental importance in magnetized plasmas. This project aims to advance our understanding of the basic physics of the parametric instabilities of Alfven waves using advanced computer simulations. The results will have implications for important processes in the heliosphere involving Alfven waves, such as coronal heating and solar wind heating.
Recently, it has been realized that magnetic plasma turbulence and magnetic field reconnection are inherently related phenomena. Turbulent fluctuations generate regions of sheared magnetic field that become unstable to the tearing instability and reconnection, thus modifying turbulence at the corresponding scales. In this contribution, we give a brief review of some recent results on tearing-mediated magnetic turbulence.We illustrate the main ideas of this rapidly developing field of study by concentrating on two important examples—magnetohydrodynamic Alfven turbulence and small-scale kinetic-Alfven turbulence. Due to various potential applications of these phenomena in space physics and astrophysics, we specifically try not to overload the text by heavy analytical derivations but rather present a qualitative discussion accessible to a non-expert in the theories of turbulence and reconnection.
The FAR3d model calculates the linear and nonlinear stability properties of energetic particle driven Alfven instabilities for both tokamak and stellarator plasma confinement devices using gyro-landau closure methods. This is an important fundamental physics problem for existing fusion energy experiments and for future fusion reactors.
Fusion-born alpha particles in ITER disruption simulations are investigated as a possible drive of Alfvénic instabilities. The ability of these waves to expel runaway electron (RE) seed particles is explored in the pursuit of a passive, inherent RE mitigation scenario. The spatiotemporal evolution of the alpha particle distribution during the disruption is calculated using the linearized Fokker–Planck solver CODION coupled to a fluid disruption simulation. These simulations are done in the limit of no alpha particle transport during the thermal quench, which can be seen as a most pessimistic situation where there is also no RE seed transport. Under these assumptions, the radial anisotropy of the resulting alpha population provides free energy to drive Alfvénic modes during the quench phase of the disruption. We use the linear gyrokinetic magnetohydrodynamic code LIGKA to calculate the Alfvén spectrum and find that the equilibrium is capable of sustaining a wide range of modes. The self-consistent evolution of the mode amplitudes and the alpha distribution is calculated utilizing the wave-particle interaction tool HAGIS. Intermediate mode number (n = 7–15, 22–26) toroidal Alfvén eigenmodes are shown to saturate at an amplitude of up to δB/B ≈ 0.1% in the spatial regimes crucial for RE seed formation. We find that the mode amplitudes are predicted to be sufficiently large to permit the possibility of significant radial transport of REs.
Initial computational plasma physics scoping and a finite element method antenna modeling design workflow for a symmetric center-fed high-field side high harmonic fast wave traveling wave array (TWA) antenna are reported here. The TWA is designed to generate a test population of fast deuterium ions in an existing D–D tokamak by heating neutral beam deuterium ions, accelerating them from 80 keV to several hundred keV. The resulting fast particles are tailored to mimic key reactor energetic particle parameters with regards to exciting Alfven eigenmode instabilities, allowing for a D–D tokamak like DIII-D or ASDEX-U to replicate reactor-relevant conditions experimentally. Initial scenario scoping for high single-pass absorption as well as good preferential fast ion damping relative to electron damping was completed using the ray-tracing/Fokker–Planck codes GENRAY and CQL3D. Python RF network analysis packages were used to create a custom TWA optimization tool to inform a COMSOL flat antenna design, and Petra-M was used to study cold plasma effects. The TWA produced by this workflow has several novel features when compared to previous TWA studies, including symmetric center feeding, and passive end straps for image current cancellation for reduced impurity production. We show here that the antenna design workflow can readily produce TWA antennas optimized for reflection coefficient, image current cancellation, and launched power spectrum shape; and that a population of fast ions can be generated in the correct region of parameter space, warranting future more detailed studies.
Instabilities driven by energetic particles normally reduce fusion power but recent studies find Alfven eigenmode instabilities can drive ``zonal" flows and currents that reduce thermal transport, improving overall performance. Motional Stark effect (MSE) data from the DIII-D tokamak reveal changes in magnetic pitch angle during the phase when Alfven-eigenmode nonlinearity drives zonal flows, suppresses microturbulence, and increases the electron and ion temperatures. Finally, measured changes in safety factor of ∆q/q ≃ 5% occur in roughly 20 ms, consistent with a rough estimate based on the measured zonal flow.
A comprehensive numerical study has been conducted in order to investigate the stability of beam-driven, sub-cyclotron frequency compressional (CAE) and global (GAE) Alfven Eigenmodes in low aspect ratio plasmas for a wide range of beam parameters. The presence of CAEs and GAEs has previously been linked to anomalous electron temperature profile flattening at high beam power in NSTX experiments, prompting further examination of the conditions for their excitation. Linear simulations are performed with the hybrid MHD-kinetic initial value code HYM in order to capture the general Doppler-shifted cyclotron resonance that drives the modes. Three distinct types of modes are found in simulations -- co-CAEs, cntr-GAEs, and co-GAEs -- with differing spectral and stability properties. The simulations reveal that unstable GAEs are more ubiquitous than unstable CAEs, consistent with experimental observations, as they are excited at lower beam energies and generally have larger growth rates. Local analytic theory is used to explain key features of the simulation results, including the preferential excitation of different modes based on beam injection geometry and the growth rate dependence on the beam injection velocity, critical velocity, and degree of velocity space anisotropy. The background damping rate is inferred from simulations and estimated analytically for relevant sources not present in the simulation model, indicating that co-CAEs are closer to marginal stability than modes driven by the cyclotron resonances.
Abstract Energetic particle (EP) destabilized Alfvén eigenmode (AE) instabilities are simulated for a DIII-D experimental case with a pulsed neutral beam using a gyro-Landau moments model which introduces EP phase-mixing effects through closure relations. This provides a computationally efficient reduced model which is applied here in the nonlinear regime over timescales that would be difficult to address with more complete models. The long timescale nonlinear evolution and related collective transport losses are examined including the effects of zonal flow/current generation, nonlinear energy cascades, and EP profile flattening. The model predicts frequencies and mode structures that are consistent with experimental observations. These calculations address issues that have not been considered in previous modelling: the EP critical gradient profile evolution in the presence of zonal flows/currents, and the dynamical nature of the saturated state. A strong level of intermittency is present in the predicted instability-driven transport; this is connected to the zonal flow growth and decay cycles and nonlinear energy transfers. Simulation of intermittent AE-enhanced EP transport will be an important issue for the protection of plasma facing components in the next generation of fusion devices.
Instabilities of Alfvén eigenmodes (AEs) are of significant concern because they can enhance the cross-field transport of fusion-born alpha particles beyond the neoclassical level in magnetic fusion plasmas. The threshold value of alpha-particle pressure for exciting AEs depends critically on the damping rate of AEs. The damping mechanisms include kinetic damping due to interactions with thermal particles, continuum damping due to AE frequency crossing Alfvén continuum, and radiative damping due to emitting kinetic Alfvén waves (KAWs). The radiative damping is substantial and can even prevail in high-temperature burning plasmas [1]. We revisit the radiative damping analytic theory for TAE in plasmas with low positive magnetic shear, considering TAE with an eigenfrequency near the bottom of TAE-gap and with poloidal harmonics of the same sign (even TAE). In contrast to earlier papers, we provide the damping calculations in real space rather than Fourier space. This approach is straightforward technically and more enlightening from a physics standpoint for benchmarking numerical calculations of radiative damping. The parametric dependence of the resulting damping rate agrees with that of Refs. [2-5], but it has a smaller numerical factor in front of it.
Fast ion phase-space flow, driven by Alfven eigenmodes (AEs), is measured by an imaging neutral particle analyzer in the DIII-D tokamak. The flow firstly appears near the minimum safety factor at the injection energy of neutral beams, and then moves radially inward and outward by gaining and losing energy, respectively. The flow trajectories in phase space align well with the intersection lines of the constant magnetic moment surfaces and constant E – (ω/n)P ζ surfaces, where E, P ζ are energy and toroidal canonical momentum of ions; ω and n are angular frequencies and toroidal mode numbers of AEs. It is found that the flow is so destructive that the thermalization of fast ions is no longer observed in regions of strong interaction. Here, the measured phase-space flow is consistent with nonlinear hybrid kinetic-magnetohydrodynamics simulation. Calculations of the relatively narrow phase-space islands reveal that fast ions must transition between different flow trajectories to experience large-scale phase-space transport.
The Kelvin-Helmholtz (KH) instability of magnetohydrodynamic surface waves at the low latitude boundary layer is examined using both an eigenfrequency analysis and a time-dependent wave simulation. The analysis includes the effects of sheared flow and Alfven velocity gradient. When the magnetosheath flows are perpendicular to the ambient magnetic field direction, unstable KH waves that propagate obliquely to the sheared flow direction occur at the sheared flow surface when the Alfv\'en Mach number is higher than an instability threshold. Including a shear transition layer between the magnetosphere and magnetosheath leads to secondary KH waves (driven by the sheared flow) that are coupled to the resonant surface Alfven wave. There are remarkable differences between the primary and the secondary KH waves including wave frequency, the growth rate, and the ratio between transverse and the compressional component. The secondary KH wave energy is concentrated near the shear Alfven wave frequency at the magnetosheath with a lower frequency than the primary KH waves. Although the growth rate of the secondary KH waves is lower than the primary KH waves, the threshold condition is lower, so it is expected that these types of waves will dominate at lower Mach number. Because the transverse component of the secondary KH waves is stronger than the primary KH waves, more efficient wave energy transfer from the boundary layer to the inner magnetosphere is also predicted.
Magnetohydrodynamics (MHD) provides a useful model to describe the crucial plasma macroscopic equilibrium and stability behaviors in toroidal tokamak devices by considering the plasma as a conducting fluid interacting with a surrounding confining electromagnetic field. MHD is the most basic plasma model, incorporating most large-scale phenomena, including plasma equilibrium and all major instabilities. MHD equations are obtained by taking moments of the Boltzmann equations for different plasma species. They provide a set of comprehensive physics constrains to compute and optimize the equilibrium plasma shape and pressure and current profiles that are critical to its stability and performance. In the ideal case, the equations have special properties that lead to efficient numerical calculation schemes, the most important of which is the ideal MHD energy principle for linear stability against small departures from equilibrium. In a tokamak plasma, equilibrium pressure is mostly destabilizing for MHD modes, whereas equilibrium current is also often a major driving force. Plasma resistivity creates new freedom for a MHD instability to grow, but there are also cases where the plasma resistivity plays a stabilizing role. Equilibrium toroidal flow and/or flow shear can affect MHD instabilities. Principal MHD instabilities include the internal kink mode, sawtooth, fishbone, external kink, resistive wall mode, resistive interchange, tearing and neoclassical tearing modes (NTMs), locked modes, toroidal Alfven eigenmodes (TAEs), and edge localized modes (ELMs). Fast-growing MHD instabilities can lead to an abrupt plasma disruption and termination that can potentially damage the device plasma facing components (PFCs) and in-vessel structures. Furthermore, an important MHD application is to develop robust techniques to mitigate and control MHD instabilities.
The new regimes of Alfvén eigenmode (AE) induced fast ion transport in tokamak plasmas are reported, in which microturbulence plays the role of a mediator of fast ion relaxation. Coulomb collisional scattering alone leads to small AE amplitudes and does not reproduce the steady state regimes observed in experiments. We show that in nonlinear regimes the sufficiently large effective pitch angle scattering due to microturbulence can lead to steady state AE amplitude evolution. This indicates a new route for fast ion losses, which is beyond the scenarios described in “Energetic ion transport by microturbulence is insignificant in tokamaks”. As a result, microturbulence can significantly increase the amplitude of AEs in predictive simulations of burning plasma experiments such as ITER.
Objectives: To establish, for lab & space conditions, EM-IEDDI’s (electromagnetic shear-driven instability's) dispersion relation, unstable range, instability threshold, and mode characteristics, we need LAPD’s Alfven-wave-favorable electromagnetic-style conditions, including higher "beta" (0.001 < beta ≤ 0.3) and low-collisionality. Also, we attempted to intentionally launch or spontaneously destabilize compressional and shear Alfven waves in the strong, localized, perpendicular-velocity-shear region at the interface between coaxial plasmas (one plasma cylinder inside an outer, otherwise hollow, tube, each having a different, controllable, value of plasma electrostatic potential, i.e., “space” potential (not to be confused with the temperature-dependent “floating” potential of an object immersed in the plasma). Nonlinear wave-wave interactions between same-family (EM-IEDD or Alfven) and cross-family (EM-IEDD-with-Alfven) fluctuations were targeted for documentation over a range of spectral overlap. Although laboratory experiments were conducted, the following theoretical work was left unfinished: Analytical non-modal prediction Computational non-modal prediction Check to see if Mikhailenko’s theory formulation leads to his published graphs
In order to study the distribution and evolution of the transient heat flux on HL-2A during edge-localized-mode (ELM) bursts, the BOUT++ electromagnetic six-field two-fluid model is used to simulate the pedestal collapse under the lower single-null divertor geometry. The equilibrium profiles of HL-2A ELMy H-mode discharge No. 24 953 are adopted as the initial condition in the original case. In this instance, linear analysis shows that the resistive ballooning mode (RBM) and drift-Alfven wave are unstable to this equilibrium, and RBM is the dominant instability. The evolutions of the radial heat fluxes at the outer mid-plane and heat fluxes to the inner and outer targets during the ELM event are presented. Six more equilibria are constructed based on the original case to find out the influence of the pedestal profiles on the peak electron heat flux. The results indicate that the heat flux increases with temperature and/or density, and the theoretical analysis and simulation results consistently show that the heat flux q ∥e is proportional to n e0,SEP $T^{\frac32}_{e0,SEP}$.
Abstract A feature of Earth's storm‐time magnetosphere outside the plasmapause is the occurrence of broad‐spectrum Alfvénic fluctuations. In this letter observations from the Van Allen Probes are compared with 3‐D fluid‐kinetic simulations of an evolving convective flow channel to investigate the mechanisms generating the observed spectrum. It is shown how narrow channels of fast convection are unstable to the Kelvin‐Helmholtz instability which on closed field‐lines initiates a cascade to small scales. Sustained driving of the flow combined with reflection from the topside ionosphere leads to the generation of an intensified spectrum of electromagnetic structures having similar spectral and morphological characteristics to those observed. This process couples enhanced magnetospheric convection to kinetic scale electromagnetic fluctuations that drive particle transport, scattering and energization through the outer radiation belt and ring current during geomagnetic storms.
Recently, the numerical scheme presented by Mishchenko et al. enabled explicit gyrokinetic simulations of low-frequency electromagnetic instabilities in tokamaks at experimentally relevant values of plasma β. This scheme resolved the long-standing cancellation problem that previously hindered gyrokinetic particle-in-cell code simulations of magnetohydrodynamic phenomena with inherently small parallel electric fields. Moreover, the scheme did not employ approximations that eliminate critical tearing-type instabilities. Here, we report on the implementation of this numerical scheme in the global gyrokinetic particle-in-cell code GTS. This implementation allows for a more complete and accurate picture of interaction between small scale turbulence and MHD modes in tokamaks. Additionally, we present a comprehensive set of verification simulations of numerous electromagnetic instabilities relevant to present-day tokamaks. These simulations encompass the kinetic ballooning mode, the internal kink mode, the tearing mode, the micro-tearing mode, and the toroidal Alfven eigenmode destabilized by energetic ions, which are all instrumental in understanding tokamak physics. We will also showcase the preliminary nonlinear simulations of kinetic ballooning instabilities and (2,1) island formation due to tearing mode instability. These simulations validate the accuracy of the scheme implementation and pave the way for studying how these instabilities affect plasma confinement and performance.
Results from a laboratory experiment are presented in which, for the first time, a shear Alfvén wave is launched using an antenna in a current-carrying plasma column that is tailored to be either stable or unstable to the kink oscillation. As the plasma is driven kink unstable, the frequency power spectrum of the Alfvén wave evolves from a single peak to a peak with multiple sidebands separated by integer multiples of the kink frequency. The main sidebands (one on either side of the launched wave peak in the power spectrum) are analyzed using azimuthal wavenumber matching, perpendicular and parallel wavenumber decomposition, and bispectral time series analysis. The dispersion relation and three-wave matching conditions are satisfied, given each sideband is a propagating Alfvén wave that results from the interaction of the pump Alfvén wave and the co-propagating component of a half-wavelength, standing kink mode. The interaction is shown to generate smaller perpendicular wavelength Alfvén waves that drive energy transport to scales that will approach the dissipation scale of k⊥ρs=1, with k⊥ being the perpendicular wavenumber and ρs being the ion gyroradius at the electron temperature.