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NASA NTRS2016

Photospheric Current Spikes and Their Possible Association with Flares - Results from an HMI Data Driven Model

A data driven, near photospheric magnetohydrodynamic model predicts spikes in the horizontal current density, and associated resistive heating rate per unit volume Q. The spikes appear as increases by orders of magnitude above background values in neutral line regions (NLRs) of active regions (ARs). The largest spikes typically occur a few hours to a few days prior to M or X flares. The spikes correspond to large vertical derivatives of the horizontal magnetic field. The model takes as input the photospheric magnetic field observed by the Helioseismic & Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO) satellite. This 2.5 D field is used to determine an analytic expression for a 3 D magnetic field, from which the current density, vector potential, and electric field are computed in every AR pixel for 14 ARs. The field is not assumed to be force-free. The spurious 6, 12, and 24 hour Doppler periods due to SDO orbital motion are filtered out of the time series of the HMI magnetic field for each pixel using a band pass filter. The subset of spikes analyzed at the pixel level are found to occur on HMI and granulation scales of 1 arcsec and 12 minutes. Spikes are found in ARs with and without M or X flares, and outside as well as inside NLRs, but the largest spikes are localized in the NLRs of ARs with M or X flares. The energy to drive the heating associated with the largest current spikes comes from bulk flow kinetic energy, not the electromagnetic field, and the current density is highly non-force free. The results suggest that, in combination with the model, HMI is revealing strong, convection driven, non-force free heating events on granulation scales, and that it is plausible these events are correlated with subsequent M or X flares. More and longer time series need to be analyzed to determine if such a correlation exists. Above an AR dependent threshold value of Q, the number of events N(Q) with heating rates greater than or equal to Q obeys a scale invariant power law distribution for each AR given by N(Q) varies Q(sup -s), where 0.40 less than or equal to S less than or equal to 0.53, with a mean and standard deviation across the 14 ARs of 0.47 and 0.045, showing there is little variation of S from one AR to another. These properties of N(Q) are in close agreement with those of the distribution N(E) for the total energy E of solar flares, determined from observations to be N(E) = constant x E(sup -alpha). From observations of nanoflares in the 0.7 to 4 MK range, and from observations of flares in hard X-rays, it is found that 0.51 less than or equal to alpha less than or equal to 0.57, and 0.4 less than or equal to alpha less than or equal to 0.6, respectively (Crosby et al. 1993, Sol. Phys., 143, 275; Aschwanden & Parnell 2002, ApJ, 572, 1048). Observations also show that, as is found here for the exponent S, there is little variation of alpha with AR (Wheatland 2000, ApJ, 532, 1209), indicating N(E) and N(Q) are largely independent of individual properties of ARs such as area, total magnetic flux, and distribution of current density (i.e. non-potentiality). Therefore the power law scaling of the photospheric heating rate Q computed here on granulation scales is essentially identical to that found for coronal observations of flare energies on scales 1-2 orders of magnitude larger. This suggests the physical mechanisms that cause Q and coronal flares are closely related. It seems likely that Q is the signature of a magnetic reconnection process in an energy range and volume orders of magnitude smaller than those of flares. In this context, at least the larger spikes in Q might be signatures of UV photospheric or lower chromospheric bombs in which plasma is heated to temperatures approximately 10(exp -5) K (Peter et al. 2014, Science 346, 1255726; Judge 2015, ApJ, 808, 116). In addition, lattice based avalanche simulations of flare energy release predict 0.4 less than or equal to alpha less than or equal to 0.5, while analytic, fractal-diffusive self-organized criticality models predict 0.4 less than or equal to alpha less than or equal to 0.67, in excellent agreement with observations, and the results presented here (Aschwanden & Parnell 2002, ApJ, 572, 1048; Aschwanden 2012, A&A, 539, A2; Aschwanden 2013, in "Self Organized Criticality Systems"; Aschwanden et al. 2016, SSR, 198, 47).

Goodman, Michael↗
NASA NTRS1990

Expanding force-free magnetized plasmoid

Some properties of a plasmoid in which magnetic field dominates are discussed. Linear expansion, which have been proposed, provides a simple model describing slow and topologically self-similar expansion of a low-beta plasmoid. An initially force-free magnetized plasmoid expanding linearly may evolve toward consecutive force-free states. The magnetic field energy of such an expansion is studied by applying the virial equation. The result indicates that the decrease of the magnetic energy of the plasmoid is exactly equal to work done expelling its external pressure. This means that there is no residue of magnetic energy if a force-free magnetized plasmoid expands linearly.

Yang, W.-H.↗
NASA NTRS2000

Propulsion Aeroelastic Analysis Developed for Flutter and Forced Response

The NASA Glenn Research Center at Lewis Field develops new technologies to increase the fuel efficiency of aircraft engines, improve the safety of engine operation, reduce emissions, and reduce engine noise. With the development of new designs for fans, compressors, and turbines to achieve these goals, the basic aeroelastic requirements are that there should be no flutter (self-excited vibrations) or high resonant blade stresses (due to forced response) in the operating regime. Therefore, an accurate prediction and analysis capability is required to verify the aeroelastic soundness of the designs. Such a three-dimensional viscous propulsion aeroelastic analysis capability has been developed at Glenn with support from the Advanced Subsonic Technology (AST) program. This newly developed aeroelastic analysis capability is based on TURBO, a threedimensional unsteady aerodynamic Reynolds-averaged Navier-Stokes turbomachinery code developed previously under a grant from Glenn. TURBO can model the viscous flow effects that play an important role in certain aeroelastic problems such as flutter with flow separation, flutter at high loading conditions near the stall line (stall flutter), flutter in the presence of shock and boundary-layer interaction, and forced response due to wakes and shock impingement. In aeroelastic analysis, the structural dynamics representation of the blades is based on normal modes. A finite-element analysis code is used to calculate these in-vacuum vibration modes and the associated natural frequencies. In an aeroelastic analysis using the TURBO code, flutter and forced response are modeled as being uncoupled. To calculate if a blade row will flutter, one prescribes the motion of the blade to be a harmonic vibration in a specified in-vacuum normal mode. An aeroelastic analysis preprocessor is used to generate the displacement field required for the analysis. The work done by aerodynamic forces on the vibrating blade during a cycle of vibration is calculated. If this work is positive, the blade is dynamically unstable, since it will extract energy from the flow, leading to an increase in the blade s oscillation amplitude. The forced-response excitations on a blade row are calculated by modeling the flow through two adjacent blade rows using the TURBO code. The blades are assumed to be rigid. As an option, a single blade row can be modeled with the upstream blade row influence represented by a time-varying disturbance (gust) at the inlet boundary. The unsteady forces on a blade row from such analyses are used in a structural analysis along with the blade structural dynamics characteristics and aerodynamic damping associated with blade vibration to calculate the resulting dynamic stresses on the blade.

Bakhle, Milind A.↗
NASA NTRS2003

Parametric Transformation Analysis

Because twisted coronal features are important proxies for predicting solar eruptive events, and, yet not clearly understood, we present new results to resolve the complex, non-potential magnetic field configurations of active regions. This research uses free-form deformation mathematics to generate the associated coronal magnetic field. We use a parametric representation of the magnetic field lines such that the field lines can be manipulated to match the structure of EUV and SXR coronal loops. The objective is to derive sigmoidal magnetic field solutions which allows the beta greater than 1 regions to be included, aligned and non-aligned electric currents to be calculated, and the Lorentz force to be determined. The advantage of our technique is that the solution is independent of the unknown upper and side boundary conditions, allows non-vanishing magnetic forces, and provides a global magnetic field solution, which contains high- and low-beta regimes and is consistent with all the coronal images of the region. We show that the mathematical description is unique and physical.

Gary, G. Allan↗
NASA NTRS2013

Computational Studies of Magnetic Nozzle Performance

An extensive literature review of magnetic nozzle research has been performed, examining previous work, as well as a review of fundamental principles. This has allow us to catalog all basic physical mechanisms which we believe underlie the thrust generation process. Energy conversion mechanisms include the approximate conservation of the magnetic moment adiabatic invariant, generalized hall and thermoelectric acceleration, swirl acceleration, thermal energy transformation into directed kinetic energy, and Joule heating. Momentum transfer results from the interaction of the applied magnetic field with currents induced in the plasma plume., while plasma detachment mechanisms include resistive diffusion, recombination and charge exchange collisions, magnetic reconnection, loss of adiabaticity, inertial forces, current closure, and self-field detachment. We have performed a preliminary study of Hall effects on magnetic nozzle jets with weak guiding magnetic fields and weak expansions (p(sub jet) approx. = P(sub background)). The conclusion from this study is that the Hall effect creates an azimuthal rotation of the plasma jet and, more generally, creates helical structures in the induced current, velocity field, and magnetic fields. We have studied plasma jet expansion to near vacuum without a guiding magnetic field, and are presently including a guiding magnetic field using a resistive MHD solver. This research is progressing toward the implementation of a full generalized Ohm's law solver. In our paper, we will summarize the basic principle, as well as the literature survey and briefly review our previous results. Our most recent results at the time of submittal will also be included. Efforts are currently underway to construct an experiment at the University of Michigan Plasmadynamics and Electric Propulsion Laboratory (PEPL) to study magnetic nozzle physics for a RF-thruster. Our computational study will work directly with this experiment to validate the numerical model, in order to study magnetic nozzle physics and optimize magnetic nozzle design. Preliminary results from the PEPL experiment will also be presented.

Ebersohn, Frans H.↗
NASA NTRS1992

High resolution observations of the magnetic and velocity field of simple sunspots

We have observed the disk passage of relatively simple round sunspots using a narrowband filter and a large format CCD detector and have created magnetograms, Dopplergrams, and continuum images nearly simultaneously. In addition the spectral resolution of the filter allows the construction of 'spectra' for all points in the field of view. The mean inclination of the magnetic field increases from 45-50 deg to 70-75 deg across the penumbra and there is a fluctuation of the inclination angle about the mean of about 4 +/- 18 deg. The variation in inclination is large enough that substantial amounts of magnetic field are parallel to the solar surface from the mid to outer penumbra. The Evershed flow tends to occur in the regions where the magnetic field is horizontal. This suggests that the Evershed flow is confined to the regions of horizontal fields. We show that a simple sunspot model with azimuthal variations in inclination but no azimuthal variations of field strength is free from azimuthal Lorentz forces. The meridional component of the currents which arise from the azimuthal variation in inclination are parallel to the field lines. This suggests that a cylindrically symmetric magnetostatic sunspot model can be perturbed into one with azimuthal variations in inclination with some adjustment in the meridional force balance.

Title, Alan M.↗
NASA NTRS2009

A CFD Approach to Modeling Spacecraft Fuel Slosh

Energy dissipation and resonant coupling from sloshing fuel in spacecraft fuel tanks is a problem that occurs in the design of many spacecraft. In the case of a spin stabilized spacecraft, this energy dissipation can cause a growth in the spacecrafts' nutation (wobble) that may lead to disastrous consequences for the mission. Even in non-spinning spacecraft, coupling between the spacecraft or upper stage flight control system and an unanticipated slosh resonance can result in catastrophe. By using a Computational Fluid Dynamics (CFD) solver such as Fluent, a model for this fuel slosh can be created. The accuracy of the model must be tested by comparing its results to an experimental test case. Such a model will allow for the variation of many different parameters such as fluid viscosity and gravitational field, yielding a deeper understanding of spacecraft slosh dynamics. In order to gain a better understanding of the dynamics behind sloshing fluids, the Launch Services Program (LSP) at the NASA Kennedy Space Center (KSC) is interested in finding ways to better model this behavior. Thanks to past research, a state-of-the-art fuel slosh research facility was designed and fabricated at Embry Riddle Aeronautical University (ERAU). This test facility has produced interesting results and a fairly reliable parameter estimation process to predict the necessary values that accurately characterize a mechanical pendulum analog model. The current study at ERAU uses a different approach to model the free surface sloshing of liquid in a spherical tank using Computational Fluid Dynamics (CFD) methods. Using a software package called Fluent, a model was created to simulate the sloshing motion of the propellant. This finite volume program uses a technique called the Volume of Fluid (VOF) method to model the interaction between two fluids [4]. For the case of free surface slosh, the two fluids are the propellant and air. As the fuel sloshes around in the tank, it naturally displaces the air. Using the conservation of mass, momentum, and energy equations, as well as the VOF equations, one can predict the behavior of the sloshing fluid and calculate the forces, pressure gradients, and velocity field for the entire liquid as a function of time.

Marsell, Brandon↗
NASA NTRS2009

Manipulating Neutral Atoms in Chip-Based Magnetic Traps

Several techniques for manipulating neutral atoms (more precisely, ultracold clouds of neutral atoms) in chip-based magnetic traps and atomic waveguides have been demonstrated. Such traps and waveguides are promising components of future quantum sensors that would offer sensitivities much greater than those of conventional sensors. Potential applications include gyroscopy and basic research in physical phenomena that involve gravitational and/or electromagnetic fields. The developed techniques make it possible to control atoms with greater versatility and dexterity than were previously possible and, hence, can be expected to contribute to the value of chip-based magnetic traps and atomic waveguides. The basic principle of these techniques is to control gradient magnetic fields with suitable timing so as to alter a trap to exert position-, velocity-, and/or time-dependent forces on atoms in the trap to obtain desired effects. The trap magnetic fields are generated by controlled electric currents flowing in both macroscopic off-chip electromagnet coils and microscopic wires on the surface of the chip. The methods are best explained in terms of examples. Rather than simply allowing atoms to expand freely into an atomic waveguide, one can give them a controllable push by switching on an externally generated or a chip-based gradient magnetic field. This push can increase the speed of the atoms, typically from about 5 to about 20 cm/s. Applying a non-linear magnetic-field gradient exerts different forces on atoms in different positions a phenomenon that one can exploit by introducing a delay between releasing atoms into the waveguide and turning on the magnetic field.

Aveline, David↗
NASA NTRS1975

Lunar electromagnetic scattering. III - Propagation at arbitrary angles to the cavity axis

An analytic theory is developed for both the steady state and the time-dependent electric and magnetic fields inside the moon and its downstream cavity for interplanetary electromagnetic field fluctuations incident at arbitrary angles to the cavity axis. The moon model has an electrical conductivity, electrical permittivity, and magnetic permeability which vary arbitrarily with radius. The cavity downstream of the moon in the solar wind is assumed to be an infinitely long nonconducting cylinder. If the interplanetary field fluctuations propagate parallel to the cavity, the far cavity field is a single cylindrical transverse electric mode propagating downstream with the same frequency, wavelength, and phase velocity as the interplanetary field. The far cavity field is the result of a forced surface wave on the cylindrical boundary of the void. When the interplanetary fluctuations are incident at an arbitrary angle to the cavity axis, the far cavity field is a superposition of an infinite number of cylindrical TE and TM modes.

Horning, B. L.↗
NASA NTRS1993

An improved far field drag calculation method for nonlinear CFD codes

An improved method to calculate drag based on far field conditions is presented and demonstrated. The method is illustrated using two CFD codes, PARC and CFL3D, and examining their ability to preserve lift and drag coefficients along grid line defined integration paths. The flow fields were generated by solving the Euler equations for a NACA 0012 airfoil at a free stream Mach number of 0.8 and angle of attack of 1.25 degrees. In comparison to force coefficients obtained by surface pressure integration, neither code acceptably preserved both force coefficients throughout the near and far fields. An investigation into the relationship between numerical prediction error and calculated force coefficients revealed a direct connection between solution mass conservation error and force coefficients error. A method to correct the predicted force coefficients based on integrated mass conservation error is described and demonstrated. The corrected force coefficients for both codes are shown to be more accurate than the uncorrected values. The correction method is applicable to both two and three dimensions and is independent of the algorithm used to generate the flow field.

Sirbaugh, James R.↗
NASA NTRS1991

The equilibria and evolutions of magnetized, rotating, isothermal clouds. V - The effect of the toroidal field

The structures of magnetized clouds are studied from a standpoint of magnetohydrostatic equilibrium between the self-gravity and magnetic and thermal pressure forces. Toroidal as well as poloidal magnetic field is taken into account. Poloidal current flowing along the poloidal magnetic field forms a toroidal field which causes the cloud to be pinched toward the symmetric axis. In contrast to the poloidal field, which plays a role in supporting the cloud, the toroidal field has the effect of shrinking the cloud. A cloud that is pinched by the toroidal field but has a low central density often shows a prolate spheroidal shape. With increasing central density the cloud becomes a concaved oblate spheroid. The maximum mass of the cloud supported by magnetic field and thermal pressure decreases with increasing toroidal field strength. Assuming that a cloud encounters a torsional Alfven wave, and the magnetic field begins to be wound up, the cloud begins dynamical collapse if the cloud mass exceeds the marginally supported maximum mass. This indicates a new mode triggering star formation: toroidal field-induced collapse.

Tomisaka, Kohji↗
NASA NTRS2003

Turbulent Mixing of Multiphase Flow

Thus we conduct numerical simulations of multiphase fluids stirred by two-dimensional turbulence to assess the possibility of self-similar drop size distribution in turbulence. In our turbulence simulations, we also explore the non-diffusive limit, where molecular mobility for the interface is vanishing. Special care is needed to transport the non-diffusive interface. Numerically, we use the particle level set method to evolve the interface. Instead of using the usual methods to calculate the surface tension force from the level set function, we reconstruct the interface based on phase- field modeling, and calculate the continuum surface tension forcing from the reconstructed interface.

Young, Y.-N.↗
NASA NTRS2009

Initial Results from the Vector Electric Field Investigation on the C/NOFS Satellite

Initial results are presented from the Vector Electric Field Investigation (VEFI) on the Air Force Communication/Navigation Outage Forecasting System (C/NOFS) satellite, a mission designed to understand, model, and forecast the presence of equatorial ionospheric irregularities. The VEFI instrument includes a vector DC electric field detector, a fixed-bias Langmuir probe operating in the ion saturation regime, a flux gate magnetometer, an optical lightning detector, and associated electronics including a burst memory. The DC electric field detector has revealed zonal and meridional electric fields that undergo a diurnal variation, typically displaying eastward and outward-directed fields during the day and westward and downward-directed fields at night. In general, the measured DC electric field amplitudes are in the 0.5-2 mV/m range, corresponding to I3 x B drifts of the order of 30-150 m/s. What is surprising is the high degree of large-scale (10's to 100's of km) structure in the DC electric field, particularly at night, regardless of whether well-defined spread-F plasma density depletions are present. The spread-F density depletions and corresponding electric fields that have been detected thus far have displayed a preponderance to appear between midnight and dawn. Associated with the narrow plasma depletions that are detected are broad spectra of electric field and plasma density irregularities for which a full vector set of measurements is available for detailed study. On some occasions, localized regions of low frequency (< 8 Hz) magnetic field broadband irregularities have been detected, suggestive of filamentary currents, although there is no one-to-one correspondence of these waves with the observed plasma density depletions, at least within the data examined thus far. Finally, the data set includes a wide range of ELF/VLF/HF waves corresponding to a variety of plasma waves, in particular banded ELF hiss, whistlers, and lower hybrid wave turbulence triggered by lightning-induced sferics. The VEFI data set represents a treasure trove of measurements that are germane to numerous fundamental aspects of the electrodynamics and irregularities inherent to the Earth's low latitude ionosphere.

Pfaff, R.↗
NASA NTRS2010

Initial Results of DC Electric Fields, Associated Plasma Drifts, Magnetic Fields, and Plasma Waves Observed on the C/NOFS Satellite

Initial results are presented from the Vector Electric Field Investigation (VEFI) on the Air Force Communication/Navigation Outage Forecasting System (C/NOFS) satellite, a mission designed to understand, model, and forecast the presence of equatorial ionospheric irregularities. The VEFI instrument includes a vector DC electric field detector, a fixed-bias Langmuir probe operating in the ion saturation regime, a flux gate magnetometer, an optical lightning detector, and associated electronics including a burst memory. Compared to data obtained during more active solar conditions, the ambient DC electric fields and their associated E x B drifts are variable and somewhat weak, typically < 1 mV/m. Although average drift directions show similarities to those previously reported, eastward/outward during day and westward/downward at night, this pattern varies significantly with longitude and is not always present. Daytime vertical drifts near the magnetic equator are largest after sunrise, with smaller average velocities after noon. Little or no pre-reversal enhancement in the vertical drift near sunset is observed, attributable to the solar minimum conditions creating a much reduced neutral dynamo at the satellite altitude. The nighttime ionosphere is characterized by larger amplitude, structured electric fields, even where the plasma density appears nearly quiescent. Data from successive orbits reveal that the vertical drifts and plasma density are both clearly organized with longitude. The spread-F density depletions and corresponding electric fields that have been detected thus far have displayed a preponderance to appear between midnight and dawn. Associated with the narrow plasma depletions that are detected are broad spectra of electric field and plasma density irregularities for which a full vector set of measurements is available for detailed study. Finally, the data set includes a wide range of ELF/VLF/HF oscillations corresponding to a variety of plasma waves, in particular banded ELF hiss, whistlers, and lower hybrid wave turbulence triggered by lightning-induced sferics. The VEFI data represents a new set of measurements that are germane to numerous fundamental aspects of the electrodynamics and irregularities inherent to the Earth's low latitude ionosphere.

Pfaff, R.↗
NASA NTRS2011

DC Electric Fields, Associated Plasma Drifts, and Irregularities Observed on the C/NOFS Satellite

Results are presented from the Vector Electric Field Investigation (VEFI) on the Air Force Communication/Navigation Outage Forecasting System (C/NOFS) satellite, a mission designed to understand, model, and forecast the presence of equatorial ionospheric irregularities. The VEFI instrument includes a vector DC electric field detector, a fixed-bias Langmuir probe operating in the ion saturation regime, a flux gate magnetometer, an optical lightning detector, and associated electronics including a burst memory. Compared to data obtained during more active solar conditions, the ambient DC electric fields and their associated E x B drifts are variable and somewhat weak, typically < 1 mV/m. Although average drift directions show similarities to those previously reported, eastward/outward during day and westward/downward at night, this pattern varies significantly with longitude and is not always present. Daytime vertical drifts near the magnetic equator are largest after sunrise, with smaller average velocities after noon. Little or no pre-reversal enhancement in the vertical drift near sunset is observed, attributable to the solar minimum conditions creating a much reduced neutral dynamo at the satellite altitude. The nighttime ionosphere is characterized by larger amplitude, structured electric fields, even where the plasma density appears nearly quiescent. Data from successive orbits reveal that the vertical drifts and plasma density are both clearly organized with longitude. The spread-F density depletions and corresponding electric fields that have been detected thus far have displayed a preponderance to appear between midnight and dawn. Associated with the narrow plasma depletions that are detected are broad spectra of electric field and plasma density irregularities for which a full vector set of measurements is available for detailed study. The VEFI data represents a new set of measurements that are germane to numerous fundamental aspects of the electrodynamics and irregularities inherent to the Earth s low latitude ionosphere.

Pfaff, R.↗
NASA NTRS1999

The Role of Self-Organized Criticality in the Substorm Phenomenon and its Relation to Localized Reconnection in the Magnetospheric Plasma Sheet

Evidence is presented that suggests there is a significant self-organized criticality (SOC) component in the dynamics of substorms in the magnetosphere. Observations of BBFs, fast flows, localized dipolarizations, plasma turbulence, etc. are taken to show that multiple localized reconnection sites provide the basic avalanche phenomenon in the establishment of SOC in the plasma sheet. First results are presented from a continuing plasma physical study of this avalanche process. A one-dimensional resistive MHD model of a magnetic field reversal is discussed. Resistivity, in this model, is self-consistently generated in response to the excitation of an idealized current-driven instability. When forced by convection of magnetic flux into the field reversal region, the model yields rapid magnetic field annihilation through a dynamic behavior that is shown to exhibit many of the characteristics of SOC. Over a large range of forcing strengths, the annihilation rate is shown to self-adjust to balance the rate at which flux is convected into the reversal region. Several analogies to magnetotail dynamics are discussed: (1) It is shown that the presence of a localized criticality in the model produces a remarkable stability in the global configuration of the field reversal while simultaneously exciting extraordinarily dynamic internal evolution. (2) Under steady forcing, it is shown that a loading-unloading cycle may arise that, as a consequence of the global stability, is quasi-periodic and, therefore, predictable despite the presence of internal turbulence in the field distribution. Indeed, it is shown that the global loading-unloading cycle is a consequence of the internal turbulence. (3) It is shown that, under steady, strong forcing the loading-unloading cycle vanishes. Instead, a recovery from a single unloading persists indefinitely. The field reversal is globally very steady while internally it is very dynamic as field annihilation goes on at the rate necessary to match the strong forcing. From this result we speculate that steady magnetospheric convection events result when the plasma sheet has been driven close to criticality over an extended spatial domain. During these events, we would expect to find localized reconnection sites distributed over the spatial domain of near criticality and we would expect to find plasma sheet transport in that domain to be closely related to that of BBF and fast flow events.

Klimas, Alex J.↗