Field-particle Correlation Research Articles

The velocity-space signature of transit-time damping

Transit-time damping (TTD) is a process in which the magnetic mirror force – induced by the parallel gradient of magnetic field strength – interacts with resonant plasma particles in a time-varying magnetic field, leading to the collisionless damping of electromagnetic waves and the resulting energization of those particles through the perpendicular component of the electric field, $E_\perp$ . In this study, we utilize the recently developed field–particle correlation technique to analyse gyrokinetic simulation data. This method enables the identification of the velocity-space structure of the TTD energy transfer rate between waves and particles during the damping of plasma turbulence. Our analysis reveals a unique bipolar pattern of energy transfer in the velocity-space characteristic of TTD. By identifying this pattern, we provide clear evidence of TTD's significant role in the damping of strong plasma turbulence. Additionally, we compare the TTD signature with that of Landau damping (LD). Although they both produce a bipolar pattern of phase-space energy density loss and gain about the parallel resonant velocity of the Alfvénic waves, they are mediated by different forces and exhibit different behaviours as the perpendicular velocity $v_\perp \to 0$ . We also explore how the dominant damping mechanism varies with ion plasma beta $\beta _i$ , showing that TTD dominates over LD for $\beta _i > 1$ . This work deepens our understanding of the role of TTD in the damping of weakly collisional plasma turbulence and paves the way to seek the signature of TTD using in situ spacecraft observations of turbulence in space plasmas.

Characterizing the velocity-space signature of electron Landau damping

Plasma turbulence plays a critical role in the transport of energy from large-scale magnetic fields and plasma flows to small scales, where the dissipated turbulent energy ultimately leads to heating of the plasma species. A major goal of the broader heliophysics community is to identify the physical mechanisms responsible for the dissipation of the turbulence and to quantify the consequent rate of plasma heating. One of the mechanisms proposed to damp turbulent fluctuations in weakly collisional space and astrophysical plasmas is electron Landau damping. The velocity-space signature of electron energization by Landau damping can be identified using the recently developed field–particle correlation technique. Here, we perform a suite of gyrokinetic turbulence simulations with ion plasma beta values$\beta _i = 0.01, 0.1, 1$and$10$and use the field–particle correlation technique to characterize the features of the velocity-space signatures of electron Landau damping in turbulent plasma conditions consistent with those observed in the solar wind and planetary magnetospheres. We identify the key features of the velocity-space signatures of electron Landau damping as a function of varying plasma$\beta _i$to provide a critical framework for interpreting the results of field–particle correlation analysis ofin situspacecraft observations of plasma turbulence.

Isolation and phase-space energization analysis of the instabilities in collisionless shocks

We analyse the generation of kinetic instabilities and their effect on the energization of ions in non-relativistic, oblique collisionless shocks using a 3D-3V (three spatial with three velocity components) simulation by dHybridR, a hybrid particle-in-cell code. At sufficiently high Mach number, quasi-perpendicular and oblique shocks can experience rippling of the shock surface caused by kinetic instabilities arising from free energy in the ion velocity distribution due to the combination of the incoming ion beam and the population of ions reflected at the shock front. To understand the role of the ripple on particle energization, we devise a new instability isolation method to identify the unstable modes underlying the ripple and interpret the results in terms of the governing kinetic instability. We generate velocity-space signatures using the field–particle correlation technique to look at energy transfer in phase space from the isolated instability driving the shock ripple, providing a viewpoint on the different dynamics of distinct populations of ions in phase space. Together, the field–particle correlation technique and our new instability isolation method provide a unique viewpoint on the different dynamics of distinct populations of ions in phase space and allow us to completely characterize the energetics of the collisionless shock under investigation.

Phase-space Energization of Ions in Oblique Shocks

Examining energization of kinetic plasmas in phase space is a growing topic of interest, owing to the wealth of data in phase space compared to traditional bulk energization diagnostics. Via the field-particle correlation (FPC) technique and using multiple means of numerically integrating the plasma kinetic equation, we have studied the energization of ions in phase space within oblique collisionless shocks. The perspective afforded to us with this analysis in phase space allows us to characterize distinct populations of energized ions. In particular, we focus on ions that reflect multiple times off the shock front through shock-drift acceleration, and how to distinguish these different reflected populations in phase space using the FPC technique. We further extend our analysis to simulations of three-dimensional shocks undergoing more complicated dynamics, such as shock ripple, to demonstrate the ability to recover the phase-space signatures of this energization process in a more general system. This work thus extends previous applications of the FPC technique to more realistic collisionless shock environments, providing stronger evidence of the technique’s utility for simulation, laboratory, and spacecraft analysis.

Revolutionizing Our Understanding of Particle Energization in Space Plasmas Using On-Board Wave-Particle Correlator Instrumentation

A leap forward in our understanding of particle energization in plasmas throughout the heliosphere is essential to answer longstanding questions in heliophysics, including the heating of the solar corona, acceleration of the solar wind, and energization of particles that lead to observable phenomena, such as the Earth’s aurora. The low densities and high temperatures of typical heliospheric environments lead to weakly collisional plasma conditions. Under these conditions, the energization of particles occurs primarily through collisionless interactions between the electromagnetic fields and the individual plasma particles with energies characteristic of a particular interaction. To understand how the plasma heating and particle acceleration impacts the macroscopic evolution of the heliosphere, impacting phenomena such as extreme space weather, it is critical to understand these collisionless wave-particle interactions on the characteristic ion and electron kinetic timescales. Such understanding requires high-cadence measurements of both the electromagnetic fields and the three-dimensional particle velocity distributions. Although existing instrument technology enables these measurements, a major challenge to maximize the scientific return from these measurements is the limited amount of data that can be transmitted to the ground due to telemetry constraints. A valuable, but underutilized, approach to overcome this limitation is to compute on-board correlations of the maximum-cadence field and particle measurements to improve the sampling time by several orders of magnitude. Here we review the fundamentals of the innovative field-particle correlation technique, present a formulation of the technique that can be implemented as an on-board wave-particle correlator, and estimate results that can be achieved with existing instrumental capabilities for particle velocity distribution measurements.

Observing particle energization above the Nyquist frequency: An application of the field-particle correlation technique

The field-particle correlation technique utilizes single-point measurements to uncover signatures of various particle energization mechanisms in turbulent space plasmas. The signature of Landau damping by electrons has been found in both simulations and in situ data from Earth's magnetosheath using this technique, but instrumental limitations of spacecraft sampling rates present a challenge to discovering the full extent of the presence of Landau damping in the solar wind. Theory predicts that field-particle correlations can recover velocity space energization signatures even from data that is undersampled with respect to the characteristic frequencies at which the wave damping occurs. To test this hypothesis, we perform a high-resolution gyrokinetic simulation of space plasma turbulence, confirm that it contains signatures of electron Landau damping, and then systematically reduce the time resolution of the data to identify the point at which the signatures become impossible to recover. We find results in support of our theoretical prediction and look for a rule of thumb that can be compared with the measurement capabilities of spacecraft missions to inform the process of applying field-particle correlations to low time resolution data.

Characterizing velocity–space signatures of electron energization in large-guide-field collisionless magnetic reconnection

Magnetic reconnection plays an important role in the release of magnetic energy and consequent energization of particles in collisionless plasmas. Energy transfer in collisionless magnetic reconnection is inherently a two-step process: reversible, collisionless energization of particles by the electric field, followed by collisional thermalization of that energy, leading to irreversible plasma heating. Gyrokinetic numerical simulations are used to explore the first step of electron energization, and we generate the first examples of field–particle correlation signatures of electron energization in 2D strong-guide-field collisionless magnetic reconnection. We determine these velocity space signatures at the x-point and in the exhaust, the regions of the reconnection geometry in which the electron energization primarily occurs. Modeling of these velocity–space signatures shows that, in the strong-guide-field limit, the energization of electrons occurs through bulk acceleration of the out-of-plane electron flow by the parallel electric field that drives the reconnection, a non-resonant mechanism of energization. We explore the variation of these velocity–space signatures over the plasma beta range 0.01≤βi≤1. Our analysis goes beyond the fluid picture of the plasma dynamics and exploits the kinetic features of electron energization in the exhaust region to propose a single-point diagnostic, which can potentially identify a reconnection exhaust region using spacecraft observations.

A field-particle correlation analysis of magnetic pumping

Spacecraft measurements of the solar wind have observed suprathermal tails in the energy distribution of particles. While the mechanism for this energization is still unsettled, recent work has suggested that magnetic pumping may be able to account for this energization. The newly devised field-particle correlation technique employs single-point measurements of the particle velocity distributions and electromagnetic fields to generate a characteristic velocity-space signature that can be used to identify the mechanism of particle energization. Here, we apply this technique to an analytical model of magnetic pumping to predict the velocity-space signature of magnetic pumping, as a function of the plasma collisionality and the amplitude of the magnetic field magnitude fluctuations, that can be used to seek evidence of magnetic pumping in kinetic numerical simulations or spacecraft measurements of heliospheric plasmas.

Coherence of Ion Cyclotron Resonance in Damped Ion Cyclotron Waves in Space Plasmas

Abstract Ion cyclotron resonance is one of the fundamental energy-conversion processes through field–particle interaction in collisionless plasmas. However, the key evidence for ion cyclotron resonance (i.e., the coherence between electromagnetic fields and the ion phase-space density) and the resulting damping of ion cyclotron waves (ICWs) has not yet been directly observed. Investigating the high-quality measurements of space plasmas by the Magnetospheric Multiscale (MMS) satellites, we find that both the wave electromagnetic field vectors and the bulk velocity of the disturbed ion velocity distribution rotate around the background magnetic field. Moreover, we find that the absolute gyrophase angle difference between the center of the fluctuations in the ion velocity distribution functions and the wave electric field vectors falls in the range of (0, 90)°, consistent with an ongoing energy conversion from wave fields to particles. By invoking plasma kinetic theory, we demonstrate that the field–particle correlation for the damped ICWs in our theoretical model matches well with our observations. Furthermore, the wave electric field vectors ( δ E wave , ⊥ ′ ), ion current density (δ J i,⊥), and energy transfer rate ( δ J i , ⊥ · δ E wave , ⊥ ′ ) exhibit quasiperiodic oscillations, and the integrated work done by the electromagnetic field on the ions is positive, indicating that ions are mainly energized by the perpendicular component of the electric field via cyclotron resonance. Therefore, our combined analysis of MMS observations and kinetic theory provides direct, thorough, and comprehensive evidence for ICW damping in space plasmas.

A field–particle correlation analysis of a perpendicular magnetized collisionless shock

Using the field–particle correlation technique, we examine the particle energization in a three-dimensional (one spatial dimension and two velocity dimensions; 1D-2V) continuum Vlasov–Maxwell simulation of a perpendicular magnetized collisionless shock. The combination of the field–particle correlation technique with the high-fidelity representation of the particle distribution function provided by a direct discretization of the Vlasov equation allows us to ascertain the details of the exchange of energy between the electromagnetic fields and the particles in phase space. We identify the velocity-space signatures of shock-drift acceleration of the ions and adiabatic heating of the electrons arising from the perpendicular collisionless shock by constructing a simplified model with the minimum ingredients necessary to produce the observed energization signatures in the self-consistent Vlasov–Maxwell simulation. We are thus able to completely characterize the energy transfer in the perpendicular collisionless shock considered here and provide predictions for the application of the field–particle correlation technique to spacecraft measurements of collisionless shocks.

Determining Threshold Instrumental Resolutions for Resolving the Velocity‐Space Signature of Ion Landau Damping

AbstractUnraveling the physics of the entire turbulent cascade of energy in space and astrophysical plasmas from the injection of energy at large scales to the dissipation of that energy into plasma heat at small scales, represents an overarching, open question in heliophysics and astrophysics. The fast cadence and high phase‐space resolution of particle velocity distribution measurements on modern spacecraft missions, such as the recently launched Parker Solar Probe, presents exciting new opportunities for identifying turbulent dissipation mechanisms using in situ measurements of the particle velocity distributions and electromagnetic fields. Here we demonstrate how to use data from kinetic numerical simulations of plasma turbulence to create synthetic spacecraft data; this data set can then be used to determine instrumental requirements to identify specific particle energization mechanisms. Using such synthetic data, downsampled to the velocity phase‐space resolution available from the plasma instruments on several past and present missions, we compute the resulting velocity‐space signature of ion Landau damping using the recently developed Field‐Particle Correlation (FPC) technique. We find that only recent missions have sufficiently fine phase‐space resolution to resolve the characteristic resonant features of the ion Landau damping signature. Coupled with numerical determinations of the velocity‐space signatures of different proposed particle energization mechanisms, this strategy enables the specification of instrumental capabilities required to achieve science goals on the topic of plasma heating and particle acceleration in turbulent heliospheric plasmas.

PATCH: Particle Arrival Time Correlation for Heliophysics

AbstractThe ability to understand the fundamental nature of the physics that governs the heliosphere requires spacecraft instrumentation to measure energy transfer at kinetic scales. This translates to a time cadence resolving the proton kinetic timescales, typically of the order of the proton gyrofrequency. The downlinked survey‐mode data from modern spacecraft are often much lower resolution than this criterion, meaning that the higher resolution, burst‐mode data must be captured to study an event at kinetic time scales. Telemetry restrictions, however, prohibit a sizable fraction of this burst‐mode data from being downlinked to the ground. The field‐particle correlation (FPC) technique can quantify kinetic‐scale energy transfer between electromagnetic fields and charged particles and identify the mechanisms responsible for mediating the transfer. In this study, we adapt the FPC technique for calculating wave‐particle energy transfer onboard modern spacecraft using time‐tagged particle counts simultaneous with electromagnetic field measurements. The newly developed procedure, called Particle Arrival Time Correlation for Heliophysics (PATCH), is tested using synthetic spacecraft data, where output from a gyrokinetic plasma turbulence simulation was downsampled to Parker Solar Probe (PSP) energy‐angle resolution. We assess the ability of the PATCH algorithm to recover the qualitative and quantitative features of the resulting velocity‐space signatures, such as ion‐Landau damping, that can be used to distinguish different kinetic mechanisms of particle energization. Ultimately, we demonstrate a proof‐of‐concept that the PATCH method could enable calculations of onboard wave‐particle correlations, with the intent of enhancing spacecraft data return by several orders of magnitude.

Electron Landau damping of kinetic Alfvén waves in simulated magnetosheath turbulence

Turbulence is thought to play a role in the heating of the solar wind plasma, though many questions remain to be solved regarding the exact nature of the mechanisms driving this process in the heliosphere. In particular, the physics of the collisionless interactions between particles and turbulent electromagnetic fields in the kinetic dissipation range of the turbulent cascade remains incompletely understood. A recent analysis of an interval of Magnetospheric Multiscale (MMS) observations has used the field–particle correlation technique to demonstrate that electron Landau damping is involved in the dissipation of turbulence in the Earth's magnetosheath. Motivated by this discovery, we perform a high-resolution gyrokinetic numerical simulation of the turbulence in the MMS interval to investigate the role of electron Landau damping in the dissipation of turbulent energy. We employ the field–particle correlation technique on our simulation data, compare our results to the known velocity–space signatures of Landau damping outside the dissipation range, and evaluate the net electron energization. We find qualitative agreement between the numerical and observational results for some key aspects of the energization and speculate on the nature of disagreements in light of experimental factors, such as differences in resolution, and of developing insights into the nature of field–particle interactions in the presence of dispersive kinetic Alfvén waves.

Diagnosing collisionless energy transfer using field–particle correlations: Alfvén-ion cyclotron turbulence

We apply field–particle correlations – a technique that tracks the time-averaged velocity-space structure of the energy density transfer rate between electromagnetic fields and plasma particles – to data drawn from a hybrid Vlasov–Maxwell simulation of Alfvén-ion cyclotron turbulence. Energy transfer in this system is expected to include both Landau and cyclotron wave–particle resonances, unlike previous systems to which the field–particle correlation technique has been applied. In this simulation, the energy transfer rate mediated by the parallel electric field $E_{\Vert }$ comprises approximately 60 % of the total rate, with the remainder mediated by the perpendicular electric field $E_{\bot }$ . The parallel electric field resonantly couples to protons, with the canonical bipolar velocity-space signature of Landau damping identified at many points throughout the simulation. The energy transfer mediated by $E_{\bot }$ preferentially couples to particles with $v_{tp}\lesssim v_{\bot }\lesssim 3v_{tp}$ , where $v_{tp}$ is the proton thermal speed, in agreement with the expected formation of a cyclotron diffusion plateau. Our results demonstrate clearly that the field–particle correlation technique can distinguish distinct channels of energy transfer using single-point measurements, even at points in which multiple channels act simultaneously, and can be used to determine quantitatively the rates of particle energization in each channel.

Collisionless energy transfer in kinetic turbulence: field–particle correlations in Fourier space

Turbulence is commonly observed in nearly collisionless heliospheric plasmas, including the solar wind and corona and the Earth’s magnetosphere. Understanding the collisionless mechanisms responsible for the energy transfer from the turbulent fluctuations to the particles is a frontier in kinetic turbulence research. Collisionless energy transfer from the turbulence to the particles can take place reversibly, resulting in non-thermal energy in the particle velocity distribution functions (VDFs) before eventual collisional thermalization is realized. Exploiting the information contained in the fluctuations in the VDFs is valuable. Here we apply a recently developed method based on VDFs, the field–particle correlation technique, to a $\unicode[STIX]{x1D6FD}=1$ , solar-wind-like, low-frequency Alfvénic turbulence simulation with well-resolved phase space to identify the field–particle energy transfer in velocity space. The field–particle correlations reveal that the energy transfer, mediated by the parallel electric field, results in significant structuring of the VDF in the direction parallel to the magnetic field. Fourier modes representing the length scales between the ion and electron gyroradii show that energy transfer is resonant in nature, localized in velocity space to the Landau resonances for each Fourier mode. The energy transfer closely follows the Landau resonant velocities with varying perpendicular wavenumber $k_{\bot }$ and plasma $\unicode[STIX]{x1D6FD}$ . This resonant signature, consistent with Landau damping, is observed in all diagnosed Fourier modes that cover the dissipation range of the simulation.

Evidence for electron Landau damping in space plasma turbulence

How turbulent energy is dissipated in weakly collisional space and astrophysical plasmas is a major open question. Here, we present the application of a field-particle correlation technique to directly measure the transfer of energy between the turbulent electromagnetic field and electrons in the Earth’s magnetosheath, the region of solar wind downstream of the Earth’s bow shock. The measurement of the secular energy transfer from the parallel electric field as a function of electron velocity shows a signature consistent with Landau damping. This signature is coherent over time, close to the predicted resonant velocity, similar to that seen in kinetic Alfven turbulence simulations, and disappears under phase randomisation. This suggests that electron Landau damping could play a significant role in turbulent plasma heating, and that the technique is a valuable tool for determining the particle energisation processes operating in space and astrophysical plasmas

Spatially localized particle energization by Landau damping in current sheets produced by strong Alfvén wave collisions

Understanding the removal of energy from turbulent fluctuations in a magnetized plasma and the consequent energization of the constituent plasma particles is a major goal of heliophysics and astrophysics. Previous work has shown that nonlinear interactions among counterpropagating Alfvén waves – or Alfvén wave collisions – are the fundamental building block of astrophysical plasma turbulence and naturally generate current sheets in the strongly nonlinear limit. A nonlinear gyrokinetic simulation of a strong Alfvén wave collision is used to examine the damping of the electromagnetic fluctuations and the associated energization of particles that occurs in self-consistently generated current sheets. A simple model explains the flow of energy due to the collisionless damping and the associated particle energization, as well as the subsequent thermalization of the particle energy by collisions. The net particle energization by the parallel electric field is shown to be spatially localized, and the nonlinear evolution is essential in enabling spatial non-uniformity. Using the recently developed field–particle correlation technique, we show that particles resonant with the Alfvén waves in the simulation dominate the energy transfer, demonstrating conclusively that Landau damping plays a key role in the spatially localized damping of the electromagnetic fluctuations and consequent energization of the particles in this strongly nonlinear simulation.

Diagnosing collisionless energy transfer using field–particle correlations: gyrokinetic turbulence

Determining the physical mechanisms that extract energy from turbulent fluctuations in weakly collisional magnetized plasmas is necessary for a more complete characterization of the behaviour of a variety of space and astrophysical plasmas. Such a determination is complicated by the complex nature of the turbulence as well as observational constraints, chiefly that in situ measurements of such plasmas are typically only available at a single point in space. Recent work has shown that correlations between electric fields and particle velocity distributions constructed from single-point measurements produce a velocity-dependent signature of the collisionless damping mechanism. We extend this work by constructing field–particle correlations using data sets drawn from single points in strongly driven, turbulent, electromagnetic gyrokinetic simulations to demonstrate that this technique can identify the collisionless mechanisms operating in such systems. The velocity-space structure of the correlation between proton distributions and parallel electric fields agrees with expectations of resonant mechanisms transferring energy collisionlessly in turbulent systems. This work motivates the eventual application of field–particle correlations to spacecraft measurements in the solar wind, with the ultimate goal to determine the physical mechanisms that dissipate magnetized plasma turbulence.

A prospectus on kinetic heliophysics.

Under the low density and high temperature conditions typical of heliospheric plasmas, the macroscopic evolution of the heliosphere is strongly affected by the kinetic plasma physics governing fundamental microphysical mechanisms. Kinetic turbulence, collisionless magnetic reconnection, particle acceleration, and kinetic instabilities are four poorly understood, grand-challenge problems that lie at the new frontier of kinetic heliophysics. The increasing availability of high cadence and high phase-space resolution measurements of particle velocity distributions by current and upcoming spacecraft missions and of massively parallel nonlinear kinetic simulations of weakly collisional heliospheric plasmas provides the opportunity to transform our understanding of these kinetic mechanisms through the full utilization of the information contained in the particle velocity distributions. Several major considerations for future investigations of kinetic heliophysics are examined. Turbulent dissipation followed by particle heating is highlighted as an inherently two-step process in weakly collisional plasmas, distinct from the more familiar case in fluid theory. Concerted efforts must be made to tackle the big-data challenge of visualizing the high-dimensional (3D-3V) phase space of kinetic plasma theory through physics-based reductions. Furthermore, the development of innovative analysis methods that utilize full velocity-space measurements, such as the field-particle correlation technique, will enable us to gain deeper insight into these four grand-challenge problems of kinetic heliophysics. A systems approach to tackle the multi-scale problem of heliophysics through a rigorous connection between the kinetic physics at microscales and the self-consistent evolution of the heliosphere at macroscales will propel the field of kinetic heliophysics into the future.

Characterizing fluid and kinetic instabilities using field-particle correlations on single-point time series

A recently proposed technique correlating electric fields and particle velocity distributions is applied to single-point time series extracted from linearly unstable, electrostatic numerical simulations. The form of the correlation, which measures the transfer of phase-space energy density between the electric field and plasma distributions and that had previously been applied to damped electrostatic systems, is modified to include the effects of drifting equilibrium distributions of the type that drive counter-streaming and bump-on-tail instabilities. By using single-point time series, the correlation is ideal for diagnosing dynamics in systems where access to integrated quantities, such as energy, is observationally infeasible. The velocity-space structure of the field-particle correlation is shown to characterize the underlying physical mechanisms driving unstable systems. The use of this correlation in simple systems will assist in its eventual application to turbulent, magnetized plasmas, with the ultimate goal of characterizing the nature of mechanisms that damp turbulent fluctuations in the solar wind.