arXiv subjects

P. A. Cassak

Publications and source records attributed to P. A. Cassak.

At least 19 recordsLinked to original sources

arXiv2025

Factors Controlling the Statistics of Magnetic Reconnection in MHD Turbulence

We study the statistics of dynamical quantities associated with magnetic reconnection events embedded in a sea of strong background magnetohydrodynamic (MHD) turbulence using direct numerical simulations. We focus on the relationship of the reconnection properties to the statistics of global turbulent fields. For the first time, we show that the distribution in turbulence of reconnection rates (determined by upstream fields) is strongly correlated with the magnitude of the global turbulent magnetic field at the correlation scale. The average reconnection rates, and associated dissipation rates, during turbulence are thus much larger than predicted by using turbulent magnetic field fluctuation amplitudes at the dissipation or kinetic scales. Magnetic reconnection may therefore be playing a major role in energy dissipation in astrophysical and heliospheric turbulence.

physics.plasm-ph↗

arXiv2024

A Magnetic Analog of Pressure-Strain Interaction

We study the evolution equation for magnetic energy density for a non-relativistic magnetized plasma in the (Lagrangian) reference frame comoving with the electron bulk velocity. Analyzing the terms that arise due to the ideal electric field, namely perpendicular electron compression and magnetic field line bending, we recast them to reveal a quantity with a functional form analogous to the often-studied pressure-strain interaction term that describes one piece of internal energy density evolution of the species in a plasma, except with the species pressure tensor replaced by the magnetic stress tensor. We dub it the "magnetic stress-strain interaction." We discuss decompositions of the magnetic stress-strain interaction analogous to those used for pressure-strain interaction. These analogies facilitate the interpretation of the evolution of the various forms of energy in magnetized plasmas, and should be useful for a wide array of applications including magnetic reconnection, turbulence, collisionless shocks, and wave-particle interactions. We display and analyze all the terms that can change magnetic energy density in the Lagrangian reference frame using a particle-in-cell simulation of magnetic reconnection.

physics.plasm-ph↗

arXiv2023

Three-Dimensional Magnetic Reconnection Spreading in Current Sheets of Non-Uniform Thickness

Magnetic reconnection in naturally occurring and laboratory settings often begins locally and elongates, or spreads, in the direction perpendicular to the plane of reconnection. Previous work has largely focused on current sheets with a uniform thickness, for which the predicted spreading speed for anti-parallel reconnection is the local speed of the current carriers. We derive a scaling theory of three-dimensional (3D) spreading of collisionless anti-parallel reconnection in a current sheet with its thickness varying in the out-of-plane direction, both for spreading from a thinner to thicker region and a thicker to thinner region. We derive an expression for calculating the time it takes for spreading to occur for a current sheet with a given profile of its thickness. A key result is that when reconnection spreads from a thinner to a thicker region, the spreading speed in the thicker region is slower than both the Alfvén speed and the speed of the local current carriers by a factor of the ratio of thin to thick current sheet thicknesses. This is important because magnetospheric and solar observations have previously measured the spreading speed to be slower than previously predicted, so the present mechanism might explain this feature. We confirm the theory via a parametric study using 3D two-fluid numerical simulations. We use the prediction to calculate the time scale for reconnection spreading in Earth's magnetotail during geomagnetic activity. The results are also potentially important for understanding reconnection spreading in solar flares and the dayside magnetopause of Earth and other planets.

physics.plasm-ph↗

arXiv2021

Dissipation measures in weakly-collisional plasmas

The physical foundations of the dissipation of energy and the associated heating in weakly collisional plasmas are poorly understood. Here, we compare and contrast several measures that have been used to characterize energy dissipation and kinetic-scale conversion in plasmas by means of a suite of kinetic numerical simulations describing both magnetic reconnection and decaying plasma turbulence. We adopt three different numerical codes that can also include interparticle collisions: the fully kinetic particle-in-cell VPIC, the fully kinetic continuum Gkeyll, and the Eulerian Hybrid Vlasov-Maxwell (HVM) code. We differentiate between (i) four energy-based parameters, whose definition is related to energy transfer in a fluid description of a plasma, and (ii) four distribution function-based parameters, requiring knowledge of the particle velocity distribution function. There is an overall agreement between the dissipation measures obtained in the PIC and continuum reconnection simulations, with slight differences due to the presence/absence of secondary islands in the two simulations. There are also many qualitative similarities between the signatures in the reconnection simulations and the self-consistent current sheets that form in turbulence, although the latter exhibits significant variations compared to the reconnection results. All the parameters confirm that dissipation occurs close to regions of intense magnetic stresses, thus exhibiting local correlation. The distribution function-based measures show a broader width compared to energy-based proxies, suggesting that energy transfer is co-localized at coherent structures, but can affect the particle distribution function in wider regions. The effect of interparticle collisions on these parameters is finally discussed.

physics.plasm-ph↗

arXiv2020

Kinetic Entropy-Based Measures of Distribution Function Non-Maxwellianity: Theory and Simulations

We investigate kinetic entropy-based measures of the non-Maxwellianity of distribution functions in plasmas, i.e., entropy-based measures of the departure of a local distribution function from an associated Maxwellian distribution function with the same density, bulk flow, and temperature as the local distribution. First, we consider a form previously employed by Kaufmann and Paterson [{\it J.~Geophys.~Res.,} {\bf 114}, A00D04 (2009)], assessing its properties and deriving equivalent forms. To provide a quantitative understanding of it, we derive analytical expressions for three common non-Maxwellian plasma distribution functions. We show that there are undesirable features of this non-Maxwellianity measure including that it can diverge in various physical limits and elucidate the reason for the divergence. We then introduce a new kinetic entropy-based non-Maxwellianity measure based on the velocity-space kinetic entropy density, which has a meaningful physical interpretation and does not diverge. We use collisionless particle-in-cell simulations of two-dimensional anti-parallel magnetic reconnection to assess the kinetic entropy-based non-Maxwellianity measures. We show that regions of non-zero non-Maxwellianity are linked to kinetic processes occurring during magnetic reconnection. We also show the simulated non-Maxwellianity agrees reasonably well with predictions for distributions resembling those calculated analytically. These results can be important for applications, as non-Maxwellianity can be used to identify regions of kinetic-scale physics or increased dissipation in plasmas.

physics.plasm-ph↗

arXiv2019

Transition from ion-coupled to electron-only reconnection: Basic physics and implications for plasma turbulence

Using kinetic particle-in-cell (PIC) simulations, we simulate reconnection conditions appropriate for the magnetosheath and solar wind, i.e., plasma beta (ratio of gas pressure to magnetic pressure) greater than 1 and low magnetic shear (strong guide field). Changing the simulation domain size, we find that the ion response varies greatly. For reconnecting regions with scales comparable to the ion Larmor radius, the ions do not respond to the reconnection dynamics leading to ''electron-only'' reconnection with very large quasi-steady reconnection rates. The transition to more traditional ''ion-coupled'' reconnection is gradual as the reconnection domain size increases, with the ions becoming frozen-in in the exhaust when the magnetic island width in the normal direction reaches many ion inertial lengths. During this transition, the quasi-steady reconnection rate decreases until the ions are fully coupled, ultimately reaching an asymptotic value. The scaling of the ion outflow velocity with exhaust width during this electron-only to ion-coupled transition is found to be consistent with a theoretical model of a newly reconnected field line. In order to have a fully frozen-in ion exhaust with ion flows comparable to the reconnection Alfvén speed, an exhaust width of at least several ion inertial lengths is needed. In turbulent systems with reconnection occurring between magnetic bubbles associated with fluctuations, using geometric arguments we estimate that fully ion-coupled reconnection requires magnetic bubble length scales of at least several tens of ion inertial lengths.

physics.space-ph↗

arXiv2018

Localized and intense energy conversion in the diffusion region of asymmetric magnetic reconnection

We analyze a high-resolution simulation of magnetopause reconnection observed by the Magnetospheric Multiscale (MMS) mission and explain the occurrence of strongly localized dissipation with an amplitude more than an order of magnitude larger than expected. Unlike symmetric reconnection, wherein reconnection of the ambient reversed magnetic field drives the dissipation, we find the annihilation of the self-generated, out-of-plane (Hall) magnetic field plays the dominant role. Electrons flow along the magnetosheath separatrices, converge in the diffusion region, and jet past the X-point into the magnetosphere. The resulting accumulation of negative charge generates intense parallel electric fields that eject electrons along the magnetospheric separatrices and produce field-aligned beams. Many of these features match MMS observations.

physics.space-ph↗

arXiv2018

Turbulence in Three-Dimensional Simulations of Magnetopause Reconnection

We present detailed analysis of the turbulence observed in three-dimensional particle-in-cell simulations of magnetic reconnection at the magnetopause. The parameters are representative of an electron diffusion region encounter of the Magnetospheric Multiscale (MMS) mission. The turbulence is found to develop around both the magnetic X line and separatrices, is electromagnetic in nature, is characterized by a wave vector $k$ given by $kρ_e\sim(m_eT_e/m_iT_i)^{0.25}$ with $ρ_e$ the electron Larmor radius, and appears to have the ion pressure gradient as its source of free energy. Taken together, these results suggest the instability is a variant of the lower hybrid drift instability. The turbulence produces electric field fluctuations in the out-of-plane direction (the direction of the reconnection electric field) with an amplitude of around $\pm 10$~mV/m, which is much greater than the reconnection electric field of around $0.1$~mV/m. Such large values of the out-of-plane electric field have been identified in the MMS data. The turbulence in the simulations controls the scale lengths of the density profile and current layers in asymmetric reconnection, driving them closer to $\sqrt{ρ_eρ_i}$ than the $ρ_e$ or $d_e$ scalings seen in 2-D reconnection simulations, and produces significant anomalous resistivity and viscosity in the electron diffusion region.

physics.space-ph↗

arXiv2017

Localized Oscillatory Dissipation in Magnetopause Reconnection

Data from the NASA Magnetospheric Multiscale (MMS) mission are used to investigate asymmetric magnetic reconnection at the dayside boundary between the Earth's magnetosphere and the solar wind (the magnetopause). High-resolution measurements of plasmas, electric and magnetic fields, and waves are used to identify highly localized (~15 electron Debye lengths) standing wave structures with large electric-field amplitudes (up to 100 mV/m). These wave structures are associated with spatially oscillatory dissipation, which appears as alternatingly positive and negative values of J dot E (dissipation). For small guide magnetic fields the wave structures occur in the electron stagnation region at the magnetosphere edge of the EDR. For larger guide fields the structures also occur near the reconnection x-line. This difference is explained in terms of channels for the out-of-plane current (agyrotropic electrons at the stagnation point and guide-field-aligned electrons at the x-line).

physics.space-ph↗

arXiv2017

On the collisionless asymmetric magnetic reconnection rate

A prediction of the steady-state reconnection electric field in asymmetric reconnection is obtained by maximizing the reconnection rate as a function of the opening angle made by the upstream magnetic field on the weak magnetic field (magnetosheath) side. The prediction is within a factor of two of the widely examined asymmetric reconnection model [Cassak and Shay, Phys. Plasmas 14, 102114, 2007] in the collisionless limit, and they scale the same over a wide parameter regime. The previous model had the effective aspect ratio of the diffusion region as a free parameter, which simulations and observations suggest is on the order of 0.1, but the present model has no free parameters. In conjunction with the symmetric case [Liu et al., Phys. Rev. Lett. 118, 085101, 2017], this work further suggests that this nearly universal number 0.1, essentially the normalized fast reconnection rate, is a geometrical factor arising from maximizing the reconnection rate within magnetohydrodynamic (MHD)-scale constraints.

physics.plasm-ph↗

arXiv2017

A Review of the 0.1 Reconnection Rate Problem

A long-standing problem in magnetic reconnection is to explain why it tends to proceed at or below a normalized rate of 0.1. This article gives a review of observational and numerical evidence for this rate and discusses recent theoretical work addressing this problem. Some remaining open questions are summarized.

physics.plasm-ph↗

arXiv2016

Why does steady-state magnetic reconnection have a maximum local rate of order 0.1?

Simulations suggest collisionless steady-state magnetic reconnection of Harris-type current sheets proceeds with a rate of order 0.1, independent of dissipation mechanism. We argue this long-standing puzzle is a result of constraints at the magnetohydrodynamic (MHD) scale. We perform a scaling analysis of the reconnection rate as a function of the opening angle made by the upstream magnetic fields, finding a maximum reconnection rate close to 0.2. The predictions compare favorably to particle-in-cell simulations of relativistic electron-positron and non-relativistic electron-proton reconnection. The fact that simulated reconnection rates are close to the predicted maximum suggests reconnection proceeds near the most efficient state allowed at the MHD-scale. The rate near the maximum is relatively insensitive to the opening angle, potentially explaining why reconnection has a similar fast rate in differing models.

physics.plasm-ph↗

arXiv2016

Particle-in-cell simulation study of the scaling of asymmetric magnetic reconnection with in-plane flow shear

We investigate magnetic reconnection in systems simultaneously containing asymmetric (anti-parallel) magnetic fields, asymmetric plasma densities and temperatures, and arbitrary in-plane bulk flow of plasma in the upstream regions. Such configurations are common in the high-latitudes of Earth's magnetopause and in tokamaks. We investigate the convection speed of the X-line, the scaling of the reconnection rate, and the condition for which the flow suppresses reconnection as a function of upstream flow speeds. We use two-dimensional particle-in-cell simulations to capture the mixing of plasma in the outflow regions better than is possible in fluid modeling. We perform simulations with asymmetric magnetic fields, simulations with asymmetric densities, and simulations with magnetopause-like parameters where both are asymmetric. For flow speeds below the predicted cutoff velocity, we find good scaling agreement with the theory presented in Doss et al., J.~Geophys.~Res., 120, 7748 (2015). Applications to planetary magnetospheres, tokamaks, and the solar wind are discussed.

physics.plasm-ph↗

arXiv2016

Spacecraft observations and analytic theory of crescent-shaped electron distributions in asymmetric magnetic reconnection

Supported by a kinetic simulation, we derive an exclusion energy parameter $\cal{E}_X$ 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.

physics.plasm-ph↗

arXiv2016

The Effects of Turbulence on Three-Dimensional Magnetic Reconnection at the Magnetopause

Two- and three-dimensional particle-in-cell simulations of a recent encounter of the Magnetospheric Multiscale Mission (MMS) with an electron diffusion region at the magnetopause are presented. While the two-dimensional simulation is laminar, turbulence develops at both the x-line and along the magnetic separatrices in the three-dimensional simulation. The turbulence is strong enough to make the magnetic field around the reconnection island chaotic and produces both anomalous resistivity and anomalous viscosity. Each contribute significantly to breaking the frozen-in condition in the electron diffusion region. A surprise is that the crescent-shaped features in velocity space seen both in MMS observations and in two-dimensional simulations survive, even in the turbulent environment of the three-dimensional system. This suggests that MMS's measurements of crescent distributions do not exclude the possibility that turbulence plays an important role in magnetopause reconnection.

physics.space-ph↗

arXiv2016

Kinetic signatures of the region surrounding the X-line in asymmetric (magnetopause) reconnection

Kinetic particle-in-cell simulations are used to identify signatures of the electron diffusion region (EDR) and its surroundings during asymmetric magnetic reconnection. A "shoulder" in the sunward pointing normal electric field (EN > 0) at the reconnection magnetic field reversal is a good indicator of the EDR, and is caused by magnetosheath electron meandering orbits in the vicinity of the x-line. Earthward of the X-line, electrons accelerated by EN form strong currents and crescent-shaped distribution functions in the plane perpendicular to B. Just downstream of the X-line, parallel electric fields create field-aligned crescent electron distribution functions. In the immediate upstream magnetosheath, magnetic field strength, plasma density, and perpendicular electron temperatures are lower than the asymptotic state. In the magnetosphere inflow region, magnetosheath ions intrude resulting in an Earthward pointing electric field and parallel heating of magnetospheric particles. Many of the above properties persist with a guide field of at least unity.

physics.space-ph↗

arXiv2015

Asymmetric magnetic reconnection with a flow shear and applications to the magnetopause

We perform a theoretical and numerical study of anti-parallel 2D magnetic reconnection with asymmetries in the density and reconnecting magnetic field strength in addition to a bulk flow shear across the reconnection site in the plane of the reconnecting fields, which commonly occurs at planetary magnetospheres. We predict the speed at which an isolated X-line is convected by the flow, the reconnection rate, and the critical flow speed at which reconnection no longer takes place for arbitrary reconnecting magnetic field strengths, densities, and upstream flow speeds, and confirm the results with two-fluid numerical simulations. The predictions and simulation results counter the prevailing model of reconnection at Earth's dayside magnetopause which says reconnection occurs with a stationary X-line for sub-Alfvenic magnetosheath flow, reconnection occurs but the X-line convects for magnetosheath flows between the Alfven speed and double the Alfven speed, and reconnection does not occur for magnetosheath flows greater than double the Alfven speed. We find that X-line motion is governed by momentum conservation from the upstream flows, which are weighted differently in asymmetric systems, so the X-line convects for generic conditions including sub-Alfvenic upstream speeds. For the reconnection rate, while the cutoff condition for symmetric reconnection is that the difference in flows on the two sides of the reconnection site is twice the Alfven speed, we find asymmetries cause the cutoff speed for asymmetric reconnection to be higher than twice the asymmetric form of the Alfven speed. The results compare favorably with an observation of reconnection at Earth's polar cusps during a period of northward interplanetary magnetic field, where reconnection occurs despite the magnetosheath flow speed being more than twice the magnetosheath Alfven speed, the previously proposed suppression condition.

physics.space-ph↗

arXiv2015

Comparative Analysis of Dayside Reconnection Models in Global Magnetosphere Simulations

We test and compare a number of existing models predicting the location of magnetic reconnection at Earth's dayside magnetopause for various solar wind conditions. We employ robust image processing techniques to determine the locations where each model predicts reconnection to occur. The predictions are then compared to the magnetic separators, the magnetic field lines separating different magnetic topologies. The predictions are tested in distinct high-resolution simulations with interplanetary magnetic field (IMF) clock angles ranging from 30 to 165 degrees in global magnetohydrodynamic simulations using the three-dimensional Block-Adaptive Tree Solarwind Roe-type Upwind Scheme (BATS-R-US) code with a uniform resistivity, although the described techniques can be generally applied to any self-consistent magnetosphere code. Additional simulations are carried out to test location model dependence on IMF strength and dipole tilt. We find that most of the models match large portions of the magnetic separators when the IMF has a southward component, with the models saying reconnection occurs where the local reconnection rate and reconnection outflow speed are maximized performing best. When the IMF has a northward component, none of the models tested faithfully map the entire magnetic separator, but the maximum magnetic shear model is the best at mapping the separator in the cusp region where reconnection has been observed. Predictions for some models with northward IMF orientations improve after accounting for plasma flow shear parallel to the reconnecting components of the magnetic fields. Implications for observations are discussed.

physics.space-ph↗