Gyroradius Scale Research Articles

Overview of multiscale turbulence studies covering ion-to-electron scales in magnetically confined fusion plasma

Turbulent transport in magnetically confined fusion plasma has conventionally been analyzed at the ion gyroradius scale based on the microturbulence theory. However, ion-scale turbulence analysis sometimes fails to predict the turbulent transport flux observed experimentally. Microturbulence at the electron gyroradius scale and cross-scale interactions between disparate-scale turbulences are possible mechanisms to resolve this issue. This overview discusses the recent progress in multiscale turbulence studies and presents future perspectives from recent experimental, theoretical, and numerical investigations. The following aspects are highlighted: (1) the importance of electron-scale effects in experiments, (2) the physical mechanisms of cross-scale interactions, (3) modeling electron-scale effects in quasilinear transport models, and (4) the impacts of cross-scale interactions on burning plasmas. Understanding multiscale turbulence is necessary to improve performance prediction and explore optimal operations for future burning plasmas.

Multipoint Cluster Observations of Kinetic Alfvén Waves, Electron Energization, and O+ Ion Outflow Response in the Mid‐Altitude Cusp Associated With Solar Wind Pressure and/or IMF BZ Variations

AbstractWe report the properties of low frequency (LF) electromagnetic fluctuations (≤11 Hz) in relation to input electron and ion outflow response observed by Cluster in the mid‐altitude cusp during high solar wind dynamic pressure PSW and active magnetospheric conditions (Kp = 4+). The multipoint observations reveal the dynamic interplay between the spatial‐temporal properties of the wave and electron inputs and the ion outflow response enabling an assessment of causal connections. The LF waves are identified as ingoing traveling Alfvén waves that become dispersive at the ion gyroradius scale (i.e., kinetic Alfvén waves KAWs). The KAWs are collocated with ingoing field‐aligned electrons and ion outflow at keV energies and below. The KAWs are associated with earthward directed Poynting fluxes and energy densities with peak amplitudes occurring at multiple energy enhancements (“step‐ups”) exhibited in the electrons and ions, attributed to IMF BZ and/or PSW variations. Indicative of a causal connection, KAW Poynting fluxes and energy densities are strongly correlated with precipitating electron energy fluxes and outflowing O+ energies and energy fluxes. These yield mid‐altitude cusp empirical relationships that can be incorporated into or constrain cusp transport models. These results demonstrate the important role played by KAWs in enhancing electron precipitation into the cusp ionosphere and subsequent O+ energization upward along the magnetic field into the mid‐altitude cusp and beyond. The results also suggest the importance of PSW and/or IMF BZ variations in driving/controlling the reconnection source Alfvén wave and electron inputs into the cusp that significantly impact the ion outflow process.

Design considerations for an ultrahigh-bandwidth Phase Contrast Imaging system applied to fusion grade devices

The PCI diagnostic is an internal reference interferometer that creates an image of absolutely calibrated electron density fluctuations integrated along the line of sight of the probing light beam. While conventional PCI diagnostics installed on fusion experiments worldwide employ light of wavelength equal to 10.59 μm, the same system using light at 1.55 μm wavelength would extend the spectral response in wave-number and frequency by factors of seven and over one hundred, respectively, thereby potentially providing quantitative measurements of the internal structure of density perturbations induced by either turbulent or radio-frequency waves, simultaneously covering ion to electron gyro-radius scales up to the GHz frequency region. Based on a previously developed 1.55 μm PCI prototype system, constraints to the design for such a diagnostic in fusion grade devices are presented and compared to those faced with the conventional method.

An ultrahigh-bandwidth Phase Contrast Imaging system for fusion plasmas

A novel Phase Contrast Imaging system that uses probing light in the near infrared region has been developed to image electron density fluctuations in fusion plasmas. As compared to standard systems operating in the mid infra-red region, the spectral response of the system is extended in wave-number and frequency response by 7 and 100 times, respectively. The internal structure of turbulence and radio-frequency waves is therefore accessible across an unprecedented wavelength and frequency range, extending into the electron gyro-radius scale and the GHz frequency region.

Magnetotail Ion Structuring by Kinetic Ballooning-Interchange Instability.

By combining three‐probe THEMIS observations and 3‐D Particle‐in‐Cell simulations, we identify key structures on the ion gyroradius scale that occur in connection with ballooning‐interchange instability heads in the Earth's magnetotail. The mesoscale structures occur at sites of strong ion velocity shear and vorticity where the thermal ion Larmor radius is about half of the width of the head. Finer structures occur at the smaller scales characterizing the wavelength of the electromagnetic ion cyclotron waves generated at the heads. These two processes act to erode and thin the current sheet, thereby forming a local magnetotail configuration that is favorable for reconnection.

Two Correlations with Enhancement Near the Proton Gyroradius Scale in Solar Wind Turbulence: Parker Solar Probe (PSP) and Wind Observations

Abstract Based on the Parker Solar Probe mission, this paper presents the observations of two correlations in solar wind turbulence near the Sun for the first time, demonstrating the clear existence of the following two correlations. One is positive correlation between the proton temperature and turbulent magnetic energy density. The other is negative correlation between the spectral index and magnetic helicity. It is found that the former correlation has a maximum correlation coefficient (CC) at the wavenumber k ρ p ≃ 0.5 (ρ p being the proton thermal gyroradius), and the latter correlation has a maximum absolute value of CC at k ρ p ≃ 1.8. In addition, investigations based on 11 yr of Wind observations reveal that the dimensionless wavenumbers (k ρ p ) corresponding to the maximum (absolute) values of CC remain nearly the same for different data sets. These results tend to suggest that the two correlations enhanced near the proton gyroradius scale would be a common feature of solar wind turbulence.

Turbulent Acceleration of Interstellar Pickup Ions at the Heliospheric Termination Shock Forms the Global ENA Spectrum

Abstract The heliospheric energetic neutral atom spectrum observed by the Interstellar Boundary Explorer (IBEX) reveals that the heliosheath proton distribution is consistent with a power law. The origin of the spectrum is likely from interstellar pickup ions (PUIs) accelerated at the heliospheric termination shock (HTS). We present an explanation of the proton spectrum origin using a test particle simulation of PUIs accelerated at the HTS. PUIs experience preferential heating by the motional electric field in the shock foot, but do not develop a power-law tail without the presence of turbulence at wavenumbers (k) close to the PUI gyroradius scale (R g). Voyager 2 observations of the magnetic field downstream of the HTS indicate a moderate amount of turbulence at kR g ≅ 1, δ B / B 0 2 ≅ 0.01 , which we find to be sufficient for producing a downstream suprathermal PUI tail but not at intensities observed by IBEX. Within the shock ramp, however, Voyager observed the turbulence power at much smaller scales to be nearly 100 times stronger, suggesting the possibility of strong turbulence at the PUI gyroradius scale. We show that a proton distribution can develop a power law downstream of the HTS consistent with IBEX observations if δ B / B 0 2 ≳ 0.1 at kR g ≅ 1 in the shock foot. Shock drift acceleration of PUIs by the motional electric field is aided by interactions with turbulence upstream of the shock overshoot. Steepening of the IBEX proton spectrum in directions farther from the heliospheric nose suggests the HTS compression ratio and/or turbulence power weakens near the heliotail.

Dissipation in the magnetic turbulence of reversed field pinch plasmas

Reversed field pinch (RFP) plasmas are subject to tearing instability that creates a broad spectrum of magnetic fluctuations. The dominant fluctuations have poloidal and toroidal mode numbers (m,n)=(1,6−10) and can grow to 2–3% of the mean magnetic field. Through nonlinear coupling, this growth culminates in a strong reconnection event and broadening of the magnetic spectrum extending to the ion gyroradius scale. Multiple developments occur during the reconnection stage: ions and electrons are energized, magnetic fluctuation amplitudes increase, plasma flow is halted, and the toroidal magnetic flux increases in a sawtooth-like fashion as the RFP dynamo becomes stronger. Magnetic fluctuations are measured in the plasma edge at multiple radial locations from r/a = 0.75 to 0.96 to assess and characterize the magnetic turbulence. The measured spectrum perpendicular to the mean field, S(k⊥), can be fit to a model spectrum consisting of power-law and exponential component with one free parameter that characterizes dissipation. The measured dissipation is much larger than estimated from classical viscous or resistive dissipation, but it is consistent with a flow damping measurement of anomalous viscosity. The measurements show an evolution of the spectrum during which fluctuation power builds up in the smallest wavenumbers and cascades to the larger wavenumber due to the nonlinear coupling between the linear (m, n) = (1, > 6) and the nonlinear (m, n) = (0, 1) tearing modes.

Efficient generation of turbulent collisionless shocks in laser-ablated counter-streaming plasmas

Laser-ablated high-energy-density (HED) plasmas offer a promising route to study astrophysically relevant processes underlying collisionless shock formation, magnetic field amplification, and particle acceleration in the laboratory. Using large-scale, multi-dimensional particle-in-cell simulations, we explore the interpenetration of laser-ablated counter-streaming plasmas for realistic experimental flow profiles. We find that the shock formation and its structure are substantially different from those of more idealized and commonly considered uniform flows: shock formation can be up to 10 times faster due to the transition from small-angle scattering to magnetic reflection and the shock front develops strong corrugations at the ion gyroradius scale. These findings have important consequences for current experimental programs and open exciting prospects for studying the microphysics of turbulent collisionless shocks with currently available high-energy laser systems.

Effects of ion polarization and finite-β on heat transport in slab electron-temperature-gradient driven turbulence

Effects of kinetic ions and electromagnetic fluctuations on slab electron-temperature-gradient (ETG) driven turbulence are investigated by means of gyrokinetic simulations covering scales from electron gyroradius to ion gyroradius and electron skin depth. Linear growth rates of electrostatic ETG modes are enhanced by the ion polarization at ion gyroradius scale. Nonlinear simulations show that this low-poloidal-wavenumber instability induces ion-scale eddies which cause heat transport higher than that in the adiabatic ion model. In finite-β plasma, electromagnetic fluctuations stabilize the low-wavenumber modes, and suppress the turbulent heat transport. Additionally, electromagnetic effects also weaken zonal flow generation, which slightly enhances turbulent transport than that in the electrostatic adiabatic ion model.

Direct Multipoint Observations Capturing the Reformation of a Supercritical Fast Magnetosonic Shock

Abstract Using multipoint Magnetospheric Multiscale (MMS) observations in an unusual string-of-pearls configuration, we examine in detail observations of the reformation of a fast magnetosonic shock observed on the upstream edge of a foreshock transient structure upstream of Earth's bow shock. The four MMS spacecraft were separated by several hundred kilometers, comparable to suprathermal ion gyroradius scales or several ion inertial lengths. At least half of the shock reformation cycle was observed, with a new shock ramp rising up out of the “foot” region of the original shock ramp. Using the multipoint observations, we convert the observed time-series data into distance along the shock normal in the shock's rest frame. That conversion allows for a unique study of the relative spatial scales of the shock's various features, including the shock's growth rate, and how they evolve during the reformation cycle. Analysis indicates that the growth rate increases during reformation, electron-scale physics play an important role in the shock reformation, and energy conversion processes also undergo the same cyclical periodicity as reformation. Strong, thin electron-kinetic-scale current sheets and large-amplitude electrostatic and electromagnetic waves are reported. Results highlight the critical cross-scale coupling between electron-kinetic- and ion-kinetic-scale processes and details of the nature of nonstationarity, shock-front reformation at collisionless, fast magnetosonic shocks.

Model of imbalanced kinetic Alfvén turbulence with energy exchange between dominant and subdominant components

ABSTRACT Alfvénic turbulence in the fast solar wind is imbalanced: the energy of the (dominant) waves propagating outward from the Sun is much larger than energy of inward-propagating (subdominant) waves. At large scales Alfvén waves are non-dispersive and turbulence is driven by non-linear interactions of counter-propagating waves. Contrary to this, at kinetic scales Alfvén waves become dispersive and non-linear interactions become possible among co-propagating waves as well. The study of the transition between these two regimes of Alfvénic turbulence is important for understanding of complicated dynamics of imbalanced Alfvénic turbulence. In this paper, we present a semiphenomenological model of the imbalanced Alfvénic turbulence accounting for the energy exchange between the dominant and subdominant wave fractions. The energy transfer becomes non-negligible at sufficiently small yet still larger than the ion gyroradius scales and is driven by the non-linear beatings between dispersive dominant(subdominant) waves pumping energy into the subdominant(dominant) component. Our results demonstrate that the turbulence imbalance should decrease significantly in the weakly dispersive wavenumber range.

Comparing electromagnetic instabilities in global gyrokinetic simulations with local and MHD models

We perform a study of system-scale to gyro-radius scale electromagnetic modes in a pedestal-like equilibrium using a gyrokinetic code ORB5, along with a comparison to the results of wimulations in a local gyrokinetic code, GS2, and an MHD energy principle code, MISHKA. In the relevant large-system, short wavelength regime, good agreement between the gyrokinetic codes is found. For global-scale modes, reasonable agreement between MHD and the global gyrokinetic code is observed. There are various formulational and implementational issues with using standard gyrokinetic codes in this limit, so even this level of agreement is promising. In order to correctly model the physics it is important to keep the effect of magnetic field strength fluctuations (which are not directly included in ORB5) in this case, where the gradient of β is large. The pressure stability threshold does not change substantially between the MHD and global gyrokinetic simulations, for the conditions present in this paper. It is also noted that the main stabilising mechanism at short wavelength is the diamagnetic drift, for which a two-fluid (rather than gyrokinetic) formulation would be sufficient.

Dynamo in Weakly Collisional Nonmagnetized Plasmas Impeded by Landau Damping of Magnetic Fields.

We perform fully kinetic simulations of flows known to produce dynamo in magnetohydrodynamics (MHD), considering scenarios with low Reynolds number and high magnetic Prandtl number, relevant for galaxy cluster scale fluctuation dynamos. We find that Landau damping on the electrons leads to a rapid decay of magnetic perturbations, impeding the dynamo. This collisionless damping process operates on spatial scales where electrons are nonmagnetized, reducing the range of scales where the magnetic field grows in high magnetic Prandtl number fluctuation dynamos. When electrons are not magnetized down to the resistive scale, the magnetic energy spectrum is expected to be limited by the scale corresponding to magnetic Landau damping or, if smaller, the electron gyroradius scale, instead of the resistive scale. In simulations we thus observe decaying magnetic fields where resistive MHD would predict a dynamo.

Stochastic ion and electron heating on drift instabilities at the bow shock

Abstract The analysis of the wave content inside a perpendicular bow shock indicates that heating of ions is related to the lower hybrid drift (LHD) instability, and heating of electrons is related to the electron cyclotron drift (ECD) instability. Both processes represent stochastic acceleration caused by the electric field gradients on the electron gyroradius scales, produced by the two instabilities. Stochastic heating is a single-particle mechanism where large gradients break adiabatic invariants and expose particles to direct acceleration by the direct current and wave fields. The acceleration is controlled by function $\chi = m_iq_i^{-1} B^{-2}$div(E), which represents a general diagnostic tool for processes of energy transfer between electromagnetic fields and particles, and the measure of the local charge non-neutrality. The identification was made with multipoint measurements obtained from the Magnetospheric Multiscale spacecraft. The source for the LHD instability is the diamagnetic drift of ions, and for the ECD instability the source is ExB drift of electrons. The conclusions are supported by laboratory diagnostics of the ECD instability in Hall ion thrusters.

Discovery of an Electron Gyroradius Scale Current Layer: Its Relevance to Magnetic Fusion Energy, Earth's Magnetosphere, and Sunspots

In the Earth’s magnetosphere, sunspots and magnetic cusp fusion devices, the boundary between the plasma and the magnetic field is marked by a diamagnetic current layer with a rapid change in plasma pressure and magnetic field strength. First principles numerical simulations were conducted to investigate this boundary layer with a spatial resolution beyond electron gyroradius while incorporating a global equilibrium structure. The boundary layer thickness is discovered to be on the order of electron gyroradius scale due to a self-consistent electric field suppressing ion gyromotion at the boundary. Formed at the scale of the electron gyroradius, the electric field plays a critical role in determining equilibrium structure and plasma transport. The discovery highlights the necessity to incorporate electron gyroradius scale physics in studies aimed at advancing our understanding of fusion devices, the magnetosphere and sunspots.

Experimental energy confinement time scaling with dimensionless parameters in C-Mod I-mode plasmas

The dependence of energy confinement time on gyroradius, , and normalized collisionality in I-mode plasmas is investigated through dedicated C-Mod experiments scanning dimensionless parameters with constant safety factor. The gyroradius scaling is calculated to be , which suggests core transport may scale with gyro–Bohm physics, indicating favorable extrapolation of the I-mode regime to future devices at low . The scaling exponent for is calculated to be small, but positive (), and the exponent for is deemed inconclusive () due to high correlation with the other two dimensionless variables in the dataset, and therefore requires further investigation. The individual dimensionless parameter scaling is compared to calculations from larger C-Mod I-mode datasets as well as multi-machine scaling laws for ELMy H-mode and L-mode plasmas. Multiple regression techniques and principal component analysis are used to clarify the single parameter scalings and analyze parameter significance within the dataset.

Gyrokinetic particle simulation of electrostatic microturbulence with impurity ions

Impurity is an important factor that can affect significantly turbulent transport in tokamaks. In order to study the impurity physics, we implement a new impurity module in the gyrokinetic particle simulation code GTC (Gyrokinetic Toroidal Code). With an improved numerical scheme, we expand the validity of gyrokinetic Poisson equation in the GTC to the short wavelength region, for both non-zonal and zonal parts of the perturbed Poisson equation. Verifications of this new scheme are carried out on the linear instability and zonal flow response. The linear simulation of the ion temperature gradient (ITG) instability including the impurity ions shows that the new Poisson solver can obtain the correct linear growth rate and frequency at the thermal ion gyro-radius scale. The residual zonal flow with impurities obtained via the new zonal flow solver is consistent with the numerical and analytical predictions in the large aspect-ratio limit. The nonlinear simulation of the ITG turbulence shows that the turbulent transport is significantly reduced by the impurity ions through decreasing the linear growth rate of the instability.

On the Full-range β Dependence of Ion-scale Spectral Break in the Solar Wind Turbulence

Abstract The power spectrum of magnetic fluctuations has a break at the high-frequency end of the inertial range. Beyond this break, the spectrum becomes steeper than the Kolmogorov law f −5/3. The break frequency was found to be associated with plasma beta (β). However, the full-range β dependence of the ion-scale spectral break has not been presented before in observational studies. Here we show the continuous variation of the break frequency on full-range β in the solar wind turbulence. By using measurements from the WIND and Ulysses spacecraft, we show the break frequency (f b ) normalized, respectively, by the frequencies corresponding to ion inertial length (f di ), ion gyroradius ( ), and cyclotron resonance scale (f ri ) as a function of β for 1306 intervals. Their β values spread from 0.005 to 20, which nearly covers the full β range of the observed solar wind turbulence. It is found that ( ) generally decreases (increases) with β, while is nearly a constant. We perform a linear fit on the statistical result, and obtain the empirical formulas , , and to describe the relation between f b and β. We also compare our observations with a numerical simulation and the prediction by ion cyclotron resonance theory. Our result favors the idea that the cyclotron resonance is an important mechanism for energy dissipation at the spectral break. When β ≪ 1 and β ≫ 1, the break at f di and may also be associated with other processes.

A hybrid gyrokinetic ion and isothermal electron fluid code for astrophysical plasma

This paper describes a new code for simulating astrophysical plasmas that solves a hybrid model composed of gyrokinetic ions (GKI) and an isothermal electron fluid (ITEF) Schekochihin et al. (2009) [9]. This model captures ion kinetic effects that are important near the ion gyro-radius scale while electron kinetic effects are ordered out by an electron–ion mass ratio expansion. The code is developed by incorporating the ITEF approximation into AstroGK, an Eulerian δf gyrokinetics code specialized to a slab geometry Numata et al. (2010) [41]. The new code treats the linear terms in the ITEF equations implicitly while the nonlinear terms are treated explicitly. We show linear and nonlinear benchmark tests to prove the validity and applicability of the simulation code. Since the fast electron timescale is eliminated by the mass ratio expansion, the Courant–Friedrichs–Lewy condition is much less restrictive than in full gyrokinetic codes; the present hybrid code runs ∼2mi/me∼100 times faster than AstroGK with a single ion species and kinetic electrons where mi/me is the ion–electron mass ratio. The improvement of the computational time makes it feasible to execute ion scale gyrokinetic simulations with a high velocity space resolution and to run multiple simulations to determine the dependence of turbulent dynamics on parameters such as electron–ion temperature ratio and plasma beta.