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Oblique Propagation and Temperature Effects on the Resonant Right-Hand Ion Beam Instability

Published in Frontiers in Astronomy and Space Sciences, 2023

The resonant right-hand instability (RHI) is often the dominant mode driven by reflected ions upstream of Earth's quasi-parallel bow shock. In the tradition of Peter Gary, this paper further explores the right-hand instability using numerical solutions of the plasma dispersion relation and non-linear kinetic simulations, with parameters inspired by observations from NASA's Magnetospheric Multiscale (MMS) mission. Agreement is found between the ion distributions in the particle-in-cell simulations and Magnetospheric Multiscale spacecraft data, which show the gyrophase bunching characteristic of the instability. The non-linear structures created by right-hand instability tend to be stronger when the plasma beta is lower. These structures have sizes of around 100 to 200 ion inertial lengths perpendicular to the magnetic field, presenting planet-sized disturbances to the magnetosphere. 2D and 3D hybrid particle-in-cell simulations show that modes with a range of propagation angles oblique to the magnetic field are excited, providing a ground to understand previous statistical studies of observed foreshock waves.

Recommended citation: A. Le, L.-J. Chen, B. A. Wetherton, B. Keenan, and A. Stanier. Oblique propagation and temperature effects on the resonant right-hand ion beam instability. Frontiers in Astronomy and Space Sciences. 2023.

Generation of a Strong Parallel Electric Field and Embedded Electron Jet in the Exhaust of Moderate Guide Field Reconnection

Published in Geophysical Research Letters, 2022

Magnetospheric Multiscale observed an extended current layer concurrent with a strong parallel electric field. The current layer is embedded in the reconnection exhaust and is consistent with an extended magnetized jet expected in roughly symmetric moderate guide field reconnection. The strong parallel electric field observed at the jet balances a strong gradient in the parallel electron pressure caused by a transition between magnetized electrons with Te‖ > Te⊥ on one side of the jet and demagnetized, roughly isotropic electrons across the thin current layer. Simulation results show how this transition can occur and how the associated electron pressure gradients in Ohm’s law balance the parallel electric field.

Recommended citation: B. A. Wetherton, J. Egedal, A. Le, and W. Daughton. Generation of a strong parallel electric field and embedded electron jet in the exhaust of moderate guide field reconnection . Geophysical Research Letters. 2022.

Hybrid Particle-in-Cell Simulations of Electromagnetic Coupling and Waves from Streaming Burst Debris

Published in Physics of Plasmas, 2022

Various systems can be modeled as a point-like explosion of ionized debris into a magnetized, collisionless background plasma—including astrophysical examples, active experiments in space, and laser-driven laboratory experiments. Debris streaming from the explosion parallel to the magnetic field may drive multiple resonant and non-resonant ion–ion beam instabilities, some of which can efficiently couple the debris energy to the background and may even support the formation of shocks. We present a large-scale hybrid (kinetic ions + fluid electrons) particle-in-cell simulation, extending hundreds of ion inertial lengths from a 3D explosion, that resolves these instabilities. We show that the character of these instabilities differs notably from the 1D equivalent by the presence of unique transverse structure. Additional 2D simulations explore how the debris beam length, width, density, and speed affect debris–background coupling, with implications for the generation of quasi-parallel shocks.

Recommended citation: B. D. Keenan, A. Le, D. Winske, A. Stanier, B. A. Wetherton, M. Cowee, and F. Guo. Hybrid particle-in-cell simulations of electromagnetic coupling and waves from streaming burst debris. Physics of Plasmas. 2022.

Astrophysical Explosions Revisited: Collisionless Coupling of Debris to Magnetized Plasma

Published in Journal of Geophysical Research: Space Physics, 2021

The coupling between a rapidly expanding cloud of ionized debris and an ambient magnetized plasma is revisited with a hybrid (kinetic ion/fluid electron) simulation code that allows a study over a wide range of plasma parameters. Over a specified range of hypothetical conditions, simple scaling laws in terms of the total debris mass and explosion speed are derived and verified for the maximal size of the debris cloud and the fraction of debris that free-streams from the burst along the magnetic field. The amount of debris that escapes from the burst with minimal coupling to the background magnetic field increases with the debris gyroradius. Test cases with two different debris species—including a heavy minority species with a relatively large gyroradius—highlight how the collisionless coupling of the debris depends on the single particle trajectories as well as the overall conservation of energy and momentum.

Recommended citation: A. Le, D. Winske, A. Stanier, W. Daughton, M. Cowee, B. A. Wetherton, and F. Guo. Astrophysical explosions revisited: collisionless coupling of debris to magnetized plasma. Journal of Geophysical Research: Space Physics. 2021.

A Drift Kinetic Model for the Expander Region of a Magnetic Mirror

Published in Physics of Plasmas, 2021

We present a drift kinetic model for the free expansion of a thermal plasma out of a magnetic nozzle. This problem relates to plasma space propulsion systems, natural environments such as the solar wind, and end losses from the expander region of mirror magnetically confined fusion concepts such as the gas dynamic trap. The model incorporates trapped and passing orbit types encountered in the mirror expander geometry and maps to an upstream thermal distribution. This boundary condition and quasineutrality require the generation of an ambipolar potential drop of ∼5𝑇𝑒/𝑒, forming a thermal barrier for the electrons. The model for the electron and ion velocity distributions and fluid moments is confirmed with data from a fully kinetic simulation. Finally, the model is extended to account for a population of fast sloshing ions arising from neutral beam heating within a magnetic mirror, again resulting in good agreement with a corresponding kinetic simulation.

Recommended citation: B. A. Wetherton, A. Le, J. Egedal, C. Forest, W. Daughton, A. Stanier, and S. Boldyrev. A drift kinetic model for the expander region of a magnetic mirror. Physics of Plasmas. 2021.

Anisotropic Electron Fluid Closure Validated by in Situ Spacecraft Observations in the far Exhaust of Guide-field Reconnection

Published in Journal of Geophysical Research: Space Physics, 2021

Anisotropic electron heating predictions of the equations of state of Le et al. (2009) (the EoS) are applied to reconnection in the Earth’s magnetosheath. The model is applicable to open systems where electrons are streaming along magnetic field lines into the reconnection region, sourced by fixed external reservoirs of plasma ambient to the reconnection region. While spacecraft observations have previously shown the EoS to hold in the region near the X-line, we find that for an event observed far downstream (∼100 di) from the X-line both inflows and the exhaust follow the predictions of the EoS. Furthermore, the model underlying the EoS is extended to include additional perpendicular heating terms relevant to the considered event undergoing active magnetic compression with local electron trapping. The agreement between the spacecraft observations and the EoS emphasizes the roles of the ambient plasma sources and the dynamics of trapped and passing electrons in setting and controlling the anisotropic electron heating at large scale in naturally occurring plasma configurations.

Recommended citation: B. A. Wetherton, J. Egedal, A. Le, and W. Daughton. Anisotropic electron fluid closure validated by in situ spacecraft observations in the far exhaust of guide-field reconnection. Journal of Geophysical Research: Space Physics. 2021.

A Drift-Kinetic Method for Obtaining Gradients in Plasma Properties from Single-Point Distribution Function Data

Published in Journal of Geophysical Research: Space Physics, 2020

In this paper, we derive a new drift-kinetic method for estimating gradients in the plasma properties through a velocity space distribution at a single point. The gradients are intrinsically related to agyrotropic features of the distribution function. This method predicts the gradients in the magnetized distribution function, and can predict gradients of arbitrary moments of the gyrotropic background distribution function. The method allows for estimates on density and pressure gradients on the scale of a Larmor radius, proving to resolve smaller scales than any method currently available to spacecraft. The model is verified with a set of fully-kinetic VPIC particle-in-cell simulations.

Recommended citation: B. A. Wetherton, J. Egedal, P. Montag, A. Le, and W. Daughton. A drift-kinetic method for obtaining gradients in plasma properties from single-point distribution function data. Journal of Geophysical Research: Space Physics. 2020.

Pressure Tensor Elements Breaking the Frozen-in Law during Reconnection in Earth’s Magnetotail

Published in Physical Review Letters, 2019

Aided by fully kinetic simulations, spacecraft observations of magnetic reconnection in Earth’s magnetotail are analyzed. The structure of the electron diffusion region is in quantitative agreement with the numerical model. Of special interest, the spacecraft data reveal how reconnection is mediated by off-diagonal stress in the electron pressure tensor breaking the frozen-in law of the electron fluid.

Recommended citation: J. Egedal, J. Ng, A. Le, W, Daughton, B. A. Wetherton, J. Dorelli, D. Gershman, and A. Rager. Pressure tensor elements breaking the frozen-in law during reconnection in Earth's magnetotail. Physical Review Letters. 2019.

Validation of Anisotropic Electron Fluid Closure Through In Situ Spacecraft Observations of Magnetic Reconnection

Published in Geophysical Research Letters, 2019

A valid fluid model for electrons in collisionless space plasmas is desirable for understanding the structure and evolution of magnetic reconnection geometries. Additionally, such a fluid model would be useful for the simulation of systems too large to be tractable in a fully kinetic model. Using Magnetospheric Multiscale spacecraft observations, we provide direct confirmation of the Lê et al., 2009 equations of state for the electron pressure tensor during guide field reconnection and demonstrate how the closure can be applied in efficient numerical simulation, yielding new physical insight to the electron heating problem. Furthermore, we use the Lê et al., 2009 equations of state to predict a scaling of electron heating in the exhaust comparable to the available observational data.

Recommended citation: B. A. Wetherton, J. Egedal, A. Le, and W. Daughton. Validation of anisotropic electron fluid closure through in situ spacecraft observations of magnetic reconnection. Geophysical Research Letters. 2019.

Spacecraft Observations of Oblique Electron Beams Breaking the Frozen-In Law During Asymmetric Reconnection

Published in Physical Review Letters, 2018

Fully kinetic simulations of asymmetric magnetic reconnection reveal the presence of magnetic-field-aligned beams of electrons flowing toward the topological magnetic x-line. Within the ~6 de electron-diffusion region, the beams become oblique to the local magnetic field, providing a unique signature of the electron-diffusion region where the electron frozen-in law is broken. The numerical predictions are confirmed by in situ Magnetospheric Multiscale spacecraft observations during asymmetric reconnection at Earth’s dayside magnetopause.

Recommended citation: J. Egedal, A. Le, W. Daughton, B. A. Wetherton, P. A. Cassak, J. L. Burch, B. Lavraud, J. Dorelli, D. J. Gershman, and L. A. Avanov. Spacecraft observations of oblique electron beams breaking the frozen-in law during asymmetric reconnection. Physical Review Letters. 2018.

Impact of compressibility and a guide field on Fermi acceleration during magnetic island coalescence

Published in Physics of Plasmas, 2017

Previous work has shown that Fermi acceleration can be an effective heating mechanism during magnetic island coalescence, where electrons may undergo repeated reflections as the magnetic field lines contract. This energization has the potential to account for the power-law distributions of particle energy inferred from observations of solar flares. Here, we develop a generalized frame- work for the analysis of Fermi acceleration that can incorporate the effects of compressibility and non-uniformity along field lines, which have commonly been neglected in previous treatments of the problem. Applying this framework to the simplified case of the uniform flux tube allows us to find both the power-law scaling of the distribution function and the rate at which the power-law behavior develops. We find that a guide magnetic field of order unity effectively suppresses the development of power-law distributions.

Recommended citation: P. Montag, J. Egedal, E. Lichko, and B. A. Wetherton. Impact of compressibility and a guide field on Fermi acceleration during magnetic island coalescence. Physics of Plasmas. 2017.

The dynamics of large-scale arrays of coupled resonators

Published in Journal of Sound and Vibration, 2017

This work describes an analytical framework suitable for the analysis of large-scale arrays of coupled resonators, including those which feature amplitude and phase dynamics, inherent element-level parameter variation, nonlinearity, and/or noise. In particular, this analysis allows for the consideration of coupled systems in which the number of individual resonators is large, extending as far as the continuum limit corresponding to an infinite number of resonators. Moreover, this framework permits analytical predictions for the amplitude and phase dynamics of such systems. The utility of this analytical methodology is explored through the analysis of a system of N non-identical resonators with global coupling, including both reactive and dissipative components, physically motivated by an electromagnetically-transduced microresonator array. In addition to the amplitude and phase dynamics, the behavior of the system as the number of resonators varies is investigated and the convergence of the discrete system to the infinite-N limit is characterized.

Recommended citation: C. Borra, C. S. Pyles, B. A. Wetherton, D. D. Quinn, and J. F. Rhoads. The dynamics of large-scale arrays of coupled resonators. Journal of Sound and Vibration. 2017.

Shaping the Frequency Response of Electromechanical Resonators Using a Signal Interference Control Topology

Published in Journal of Dynamic Systems, Measurement, and Control, 2017

The recent study of signal interference circuits, which find its origins in earlier work related to active channelized filters, has introduced new methods for shaping the frequency response of electrical systems. This paper seeks to extend this thread of research by investigating the frequency response shaping of electromechanical resonators which are embedded in feedforward, signal interference control architectures. In particular, mathematical models are developed to explore the behavior of linear resonators that are embedded in two prototypical signal interference control topologies, which can exhibit a variety of qualitatively distinct frequency domain behaviors with component-level tuning. Experimental approaches are then used to demonstrate the proposed designs’ utility.

Recommended citation: B. A. Geesey, B. A. Wetherton, N. Bajaj, and J. F. Rhoads. A tunable signal interference control topology for sensing and signal processing based upon electromechanical resonators. Journal of Dynamic Systems, Measurement, and Control. 2017.

Processes setting the structure of the electron distribution function within the exhausts of anti-parallel reconnection

Published in Physics of Plasmas, 2016

In situ spacecraft observations within the exhausts of magnetic reconnection document a large variation in the velocity space structure of the electron distribution function. Multiple mechanisms help govern the underlying electron dynamics, yielding a range of signatures for collisionless reconnection. These signatures include passing beams of electrons separated by well-defined boundaries from betatron heated/cooled trapped electrons. The present study emphasizes how localized regions of non-adiabatic electron dynamics can mix electrons across the trapped/passing boundaries and impact the form of the electron distributions in the full width of the exhaust. While our study is based on 2D simulations, the described principles shaping the velocity space distributions also apply to 3D geometries making our findings relevant to spacecraft observation of reconnection in the Earth’s magnetosphere.

Recommended citation: J. Egedal, B. A. Wetherton, W. Daughton, and A. Le. Processes setting the structure of the electron distribution function within the exhausts of anti-parallel reconnection. Physics of Plasmas. 2016.

Spacecraft Observations and Analytic Theory of Crescent-Shaped Electron Distributions in Asymmetric Magnetic Reconnection

Published in Physical Review Letters, 2016

Supported by a kinetic simulation, we derive an exclusion energy parameter EX providing a lower kinetic energy bound for an electron to cross from one inflow region to the other during magnetic reconnection. As by a Maxwell demon, only high-energy electrons are permitted to cross the inner reconnection region, setting the electron distribution function observed along the low-density side separatrix during asymmetric reconnection. The analytic model accounts for the two distinct flavors of crescent-shaped electron distributions observed by spacecraft in a thin boundary layer along the low-density separatrix.

Recommended citation: J. Egedal, A. Le, W. Daughton, B. A. Wetherton, P. A. Cassak, L.-J. Chen, B. Lavraud, R. B. Torbert, J. Dorelli, D. J. Gershman, and L. A. Avanov. Spacecraft observations and analytic theory of crescent-shaped electron distributions in asymmetric magnetic reconnection. Physical Review Letters. 2016.