Joseph E. Borovsky

The Space Science Institute, Boulder, Colorado, United States

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Publications (265)527.35 Total impact

  • John J. Podesta · Joseph E. Borovsky
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    ABSTRACT: Several physically motivated examples of stochastic processes that exhibit discontinuous jumps at random times are used to show that if the discontinuous jumps are replaced by continuous or smooth transitions with an average duration Δt, then the power spectral density of the process develops a high frequency spectral break at a frequency of order ωb = π/Δt. Conversely, if the spectrum of the original process is altered by imposing a high frequency spectral break, as may be accomplished by filtering with a low pass filter of some kind, then the discontinuous jumps in the original signal are replaced by continuous jumps having a duration of magnitude Δt = π/ωb, where ωb is the break-frequency of the altered spectrum. These results suggest that for any stochastic process containing randomly occurring jumps in the time domain and a high-frequency spectral break in the spectral domain with break-frequency ωb, the average durations of the jumps are of order Δt = π/ωb. This result is closely connected with the sampling theorem and the uncertainty principle for Fourier transform pairs and demonstrates that the physical processes responsible for the dissipation of solar wind turbulence also determine the thicknesses of the strongest current sheets in the solar wind.
    No preview · Article · Jan 2016 · Journal of Geophysical Research: Space Physics
  • Joseph E. Borovsky · John J. Podesta
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    ABSTRACT: The magnetic power spectrum of the solar wind at 1 AU exhibits a breakpoint at a frequency of about 0.1 - 1 Hz, with the spectrum being steeper above the breakpoint than below the breakpoint. Because magnetic discontinuities contain much of the Fourier power in the solar wind, it is suspected that current-sheet thicknesses (i.e. discontinuity thicknesses) may play a role in determining the frequency of this breakpoint. Using time-series measurements of the solar-wind magnetic field from the Wind spacecraft, the effect of current-sheet thicknesses on the breakpoint is investigated by time stretching the solar-wind time series at the locations of current sheets, effectively thickening the current sheets in the time series. This localized time stretching significantly affects the magnetic power spectral density of the solar wind in the vicinity of the high-frequency breakpoint: a substantial fraction of the Fourier power at the breakpoint frequency is contained in current sheets that occupy a small fraction of the spatial volume of the solar wind. It is concluded that current-sheet thickness appears to play a role in determining the frequency fB of the high-frequency breakpoint of the magnetic power spectrum of the solar wind. This analysis of solar-wind data is aided by comparisons with power spectra generated from artificial time series.
    No preview · Article · Oct 2015 · Journal of Geophysical Research: Space Physics
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    ABSTRACT: Knowledge of the plasma fluxes at geosynchronous orbit is important to both scientific and operational investigations. We present a new empirical model of the ion flux and the electron flux at geosynchronous orbit (GEO) in the energy range ~1 eV to ~40 keV. The model is based on a total of 82 satellite-years of observations from the Magnetospheric Plasma Analyzer instruments on Los Alamos National Laboratory satellites at GEO. These data are assigned to a fixed grid of 24 local-times and 40 energies, at all possible values of Kp. Bi-linear interpolation is used between grid points to provide the ion flux and the electron flux values at any energy and local-time, and for given values of geomagnetic activity (proxied by the 3-hour Kp index), and also for given values of solar activity (proxied by the daily F10.7 index). Initial comparison of the electron flux from the model with data from a Compact Environmental Anomaly Sensor II (CEASE-II), also located at geosynchronous orbit, indicate a good match during both quiet and disturbed periods. The model is available for distribution as a FORTRAN code that can be modified to suit user-requirements.
    No preview · Article · Mar 2015 · Space Weather
  • G. L. Delzanno · J. E. Borovsky · M. F. Thomsen · J. D. Moulton
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    ABSTRACT: Experiments where a high-voltage electron beam emitted by a spacecraft in the low-density magnetosphere is used to probe the magnetospheric configuration could greatly enhance our understanding of the near-Earth environment. Their challenge, however, resides in the fact that the background magnetospheric plasma cannot provide a return current that balances the electron beam current without charging the spacecraft to such high potential that in practice prevents beam emission. In order to overcome this problem, a possible solution is based on the emission of a high-density contactor plasma by the spacecraft prior to and after the beam.We perform Particle-In-Cell simulations to investigate the conditions under which a high-voltage electron beam can be emitted from a magnetospheric spacecraft, comparing two possible routes that rely on the high-density contactor plasma. The first is an ’electron collection’ route, where the contactor has lower current than the electron beam and is used with the goal of connecting to the background plasma and collecting magnetospheric electrons over a much larger area than that allowed by the spacecraft alone. The second is an ’ion emission’ route, where the contactor has higher current than the electron beam. Ion emission is then enabled over the large quasi-spherical area of the contactor cloud, thus overcoming the space charge limits typical of ion beam emission.Our results indicate that the ion emission route offers a credible pathway for performing beam experiments in the low-density magnetosphere, while the electron collection route is not viable because the contactor fails to draw a large neutralizing current from the background.
    No preview · Article · Mar 2015 · Journal of Geophysical Research: Space Physics
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    ABSTRACT: The idea of using a high-voltage electron beam with substantial current to actively probe magnetic field line connectivity in space has been discussed since the 1970's. However, its experimental realization onboard a magnetospheric spacecraft has never been accomplished because the tenuous magnetospheric plasma cannot provide the return current necessary to keep spacecraft charging under control. In this work, we perform Particle-In-Cell simulations to investigate the conditions under which a high-voltage electron beam can be emitted from a spacecraft and explore solutions that can mitigate spacecraft charging. The electron beam cannot simply be compensated for by an ion beam of equal current, because the Child-Langmuir space charge limit is violated under conditions of interest. On the other hand, releasing a high-density neutral contactor plasma prior and during beam emission is critical in aiding beam emission. We show that, after an initial transient controlled by the size of the contactor cloud where the spacecraft potential rises, the spacecraft potential can settle into conditions that allow for electron beam emission. A physical explanation of this result in terms of ion emission into spherical geometry from the surface of the plasma cloud is presented, together with scaling laws of the peak spacecraft potential varying the ion mass and beam current. These results suggest that a strategy where the contactor plasma and the electron beam operate simultaneously might offer a credible pathway to perform beam experiments in the magnetosphere.
    No preview · Article · Mar 2015 · Journal of Geophysical Research: Space Physics
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    Fei Xu · Joseph E. Borovsky
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    ABSTRACT: A 3-parameter algebraic scheme is developed to categorize the solar wind at 1 AU into 4 plasma types: coronal-hole-origin plasma, streamer-belt-origin plasma, sector-reversal-region plasma, and ejecta. The three parameters are the proton specific entropy Sp = Tp/np2/3, the proton Alfvén speed vA, and the proton temperature Tp compared with a velocity-dependent expected temperature. Four measurements are needed to apply the scheme: the proton number density np, the proton temperature Tp, the magnetic-field strength B, and the solar-wind speed vsw. The scheme is tested and is found to be more accurate than existing categorization schemes. The categorization scheme is applied to the 1963–2013 OMNI2 data set spanning 4 solar cycles and to the 1998–2008 ACE data set. The statistical properties of the 4 types of plasma are examined. The sector-reversal-region plasma is found to have statistically low alpha-to-proton density ratios and high Alfvén Mach numbers. The statistical relations between the proton and alpha-particle specific entropies and oxygen and carbon charge-state density ratios Sp, Sα, O7+/O6+, and C6+/C5+ from ACE are examined for the four types of plasma: the patterns observed imply a connection between sector-reversal-region plasma and ejecta and a connection between streamer-belt-origin plasma and coronal-hole-origin plasma. Plasma occurrence rates are examined and solar-cycle patterns are found for ejecta, for coronal-hole-origin plasma, and for sector-reversal-region plasma.
    Full-text · Article · Dec 2014 · Journal of Geophysical Research: Space Physics
  • M. H. Denton · J. E. Borovsky
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    ABSTRACT: The outer plasmasphere is eroded when the strength of the convection electric field increases. Following a return of lower levels of convection, the outer plasmasphere " refills" from the ionosphere. In-situ observations of the cold (~1 eV) ion number density from geosynchronous orbit indicate that within ~48 hours after plasmaspheric erosion events the number density may return to a level of ~100 cm-3, consistent with previously reported values. Current theoretical estimates of refilling rates at geosynchronous orbit are inconsistent with such rapid refilling. In order to shed light on this issue a theoretical investigation is carried out to determine the major factors governing the refilling process. While theoretical estimates of the refilling rate reported here still fall below observed levels by at least a factor of two, the results of this study indicate that the morphology of the neutral atmosphere, (particularly the neutral atmosphere number density), is critical in controlling the rate of refilling at geosynchronous orbit. The strength of vertical E × B drifts, and horizontal neutral winds are found to play only a minor role.
    No preview · Article · Nov 2014 · Journal of Geophysical Research: Space Physics
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    ABSTRACT: Long-lived (weeks) plasmaspheric drainage plumes are explored. The long-lived plumes occur during long-lived high-speed-stream-driven storms. Spacecraft in geosynchronous orbit see the plumes as dense plasmaspheric plasma advecting sunward toward the dayside magnetopause. The older plumes have the same densities and local-time widths as younger plumes, and like younger plumes they are lumpy in density and they reside in a spatial gap in the electron plasma sheet (in sort of a drainage corridor). Magnetospheric-convection simulations indicate that drainage from a filled outer plasmasphere can only supply a plume for 1.5 - 2 days. The question arises for long-lived plumes (and for any plume older than about 2 days): Where is the plasma coming from? Three candidate sources appear promising: (1) substorm disruption of the nightside plasmasphere which may transport plasmaspheric plasma outward onto open drift orbits, (2) radial transport of plasmaspheric plasma in velocity-shear-driven instabilities near the duskside plasmapause, and (3) an anomalously high upflux of cold ionospheric protons from the tongue of ionization in the dayside ionosphere, which may directly supply ionospheric plasma into the plume. In the first case the plume is drainage of plasma from the magnetosphere; in the second case it is not. Where the plasma in long-lived plumes is coming from is a quandary: to fix this dilemma further work, and probably full-scale simulations, are needed.
    No preview · Article · Aug 2014 · Journal of Geophysical Research: Space Physics
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    ABSTRACT: We investigated mass density ρm and O+ concentration ηO+≡nO+/ne (where nO+ and ne are the O+ and electron density, respectively) during two events, one active and one more quiet. We found ρm from observations of Alfvén wave frequencies measured by the GOES, and we investigated composition by combining measurements of ρm with measurements of ion density nMPA,i from the Magnetospheric Plasma Analyzer (MPA) instrument on Los Alamos National Laboratory spacecraft or ne from the Radio Plasma Imager instrument on the Imager for Magnetopause-to-Aurora Global Exploration spacecraft. Using a simple assumption for the He+ density at solar maximum based on a statistical study, we found ηO+ values ranging from near zero to close to unity. For geostationary spacecraft that corotate with the Earth, sudden changes in density for both ρm and ne often appear between dusk and midnight magnetic local time, especially when Kp is significantly above zero. This probably indicates that the bulk (total) ions have energy below a few keV and that the satellites are crossing from closed or previously closed to open drift paths. During long periods that are geomagnetically quiet, the mass density varies little, but ne gradually refills leading to a gradual change in composition from low-density plasma that is relatively cold and heavy (high-average ion mass M ≡ ρm/ne) to high-density plasma that is relatively cold and light (low M) plasmasphere-like plasma. During active periods we observe a similar daily oscillation in plasma properties from the dayside to the nightside, with cold and light high-density plasma (more plasmasphere-like) on the dayside and hotter and more heavy low-density plasma (more plasma sheet-like) on the nightside. The value of ne is very dependent on whether it is measured inside or outside a plasmaspheric plume, while ρm is not. All of our results were found at solar maximum; previous results suggest that there will be much less O+ at solar minimum under all conditions.
    No preview · Article · Aug 2014 · Journal of Geophysical Research: Space Physics
  • Joseph E. Borovsky · S. Peter Gary
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    ABSTRACT: This report explores the feasibility of explaining the observed proton heating in the inner heliosphere (1) by tapping the field-aligned relative drift between alpha particles and protons in the solar-wind plasma and (2) by tapping the strahl-electron heat flux from the Sun. The observed reduction of the alpha-proton drift kinetic energy from 0.3 AU to 1 AU and the observed reduction of electron heat flux from 0.3 AU to 1 AU are each about half of the energy needed to account for the observed heating of protons from 0.3 AU to 1 AU. A mechanism is identified to transfer the free energy of the alpha-proton relative drift into proton thermal energy: the alpha-proton magnetosonic instability. A mechanism is identified to transfer kinetic energy from the strahl-electron heat flux into proton thermal energy: weak double layers. At the current state of knowledge, the plausibility of heating the solar-wind protons via the alpha-proton magnetosonic instability is high. The properties of the weak double layers that have been observed in the solar wind are not well known; more data analysis and plasma simulations are needed before the plausibility of heating the solar-wind protons by the double-layer mechanism can be evaluated.
    No preview · Article · Jul 2014 · Journal of Geophysical Research: Space Physics
  • Joseph E. Borovsky
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    ABSTRACT: Canonical correlation analysis (CCA) will evaluate the degree of correlation between two multivariate data sets and will uncover patterns of correlation between the two data sets. Here CCA is applied to the multivariate solar-wind data set and the multivariate geomagnetic-index data set. CCA creates a new set of solar-wind variables and a new set of Earth variables. The first of the new solar-wind variables can be used as a solar-wind driver function for the magnetosphere; the conjugate Earth variable can be used as an Earth vector to describe global geomagnetic activity in the magnetosphere-ionosphere system. The CCA-generated driver functions are found to be superior in accuracy to other driver functions in the literature. CCA of the combined data sets provides information about: (1) differences in the solar-wind driving of high-latitude geomagnetic indices (AE, AU, AL, and PCI) versus magnetospheric-convection geomagnetic indices (Kp and MBI), (2) the properties of electric-field-based driver functions versus reconnection-based driver functions, and (3) improvements to solar-wind/magnetosphere correlations produced by time averaging the solar-wind clock angle. The CCA process tends to focus on the magnetospheric-convective indices over other indices: this may indicate that there is more predictable variance in the global-convective indices than in the others.
    No preview · Article · Jul 2014 · Journal of Geophysical Research: Space Physics
  • Joseph E. Borovsky · Michael H. Denton
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    ABSTRACT: The ULF magnetospheric indices Sgr, Sgeo, Tgr, and Tgeo are examined and correlated with solar-wind variables, geomagnetic indices, and the multispacecraft-averaged relativistic-electron flux F in the magnetosphere. The ULF indices are detrended by subtracting off sine waves with 24-hr periods to form Sgrd, Sgeod, Tgrd, and Tgeod. The detrending improves correlations. Autocorrelation-function analysis indicates that there are still strong 24-hr-period non-sinusoidal signals in the indices which should be removed in future. Indications are that the ground-based indices Sgrd and Tgrd are more predictable than the geosynchronous indices Sgeod and Tgeod. In the analysis a difference index ΔSmag ≈ Sgrd - 0.693 Sgeod is derived: the time integral of ΔSmag has the highest ULF-index correlation with the relativistic-electron flux F. In systems-science fashion, canonical correlation analysis (CCA) is used to correlate the relativistic-electron flux simultaneously with the time integrals of (a) the solar-wind velocity, (b) the solar-wind number density, (c) the level of geomagnetic activity, the (d) ULF indices, and (e) the type of solar-wind plasma (coronal-hole versus streamer belt): the time integrals of the solar-wind density and the type of plasma have the highest correlations with F. To create a solar-wind-Earth system of variables, the two indices Sgrd and Sgeod are combined with seven geomagnetic indices; from this CCA produces a canonical Earth variable that is matched with a canonical solar-wind variable. Very high correlations (rcorr = 0.926) between the two canonical variables are obtained.
    No preview · Article · Jun 2014 · Journal of Geophysical Research: Space Physics
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    ABSTRACT: A summary is presented of experimental optical observations at 4278 Å from close to a powerful (~150 kW) VLF transmitter (call-sign JXN) with a transmission frequency of 16.4 kHz. Approximately 2.5 seconds after transmitter turn-on, a sudden increase in optical emissions at 4278 Å was detected using a dedicated camera/CCD monitoring system recording at a frequency of 10 Hz. The optical signal is interpreted as a burst of electron precipitation lasting ~0.5 seconds, due to gyro-resonant wave-particle interactions between the transmitted wave and the magnetospheric electron population. The precipitation was centered on the zenith and had no detectable spatial structure. The timing of this sequence of events is in line with theoretical predictions and previous indirect observations of precipitation. This first direct measurement of VLF-induced precipitation at 4278 Å reveals the spatial and temporal extent of the resulting optical signal close to the transmitter.
    No preview · Article · Apr 2014
  • Joseph E Borovsky
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    ABSTRACT: A dense cold plasma from Earth's ionosphere can counter strong solar wind.
    No preview · Article · Mar 2014 · Science
  • Joseph E. Borovsky · Reiner H. W. Friedel · Michael H. Denton
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    ABSTRACT: five spacecraft in geosynchronous orbit, plasmaspheric drainage plumes are located in the dayside magnetosphere and the measured pitch angle anisotropies of radiation belt electrons are compared duskward and dawnward of the plumes. Two hundred twenty-six plume crossings are analyzed. It is found that the radiation belt anisotropy is systematically greater dawnward of plumes (before the electrons cross the plumes) than it is duskward of plumes (after the electrons have crossed the plumes). This change in anisotropy is attributed to pitch angle scattering of the radiation belt electrons during their passage through the plumes. A test database in the absence of plumes finds no equivalent change in the radiation belt anisotropy. The amount of pitch angle scattering by the plume is quantified, scattering times are estimated, and effective pitch angle diffusion coefficients within the plume are estimated. The pitch angle diffusion coefficients obtained from the scattering measurements are of the same magnitude as expected values for electromagnetic ion cyclotron (EMIC) waves at high electron energies (1.5 MeV); however, expected EMIC diffusion coefficients do not extend to pitch angles of 90° and would have difficulties explaining the observed isotropization of electrons. The pitch angle diffusion coefficients obtained from the scattering measurements are of the same magnitude as expected values for whistler mode hiss at lower electron energies (150 keV). Outward radial transport of the radiation belt caused by the pitch angle scattering in the plume is discussed.
    No preview · Article · Mar 2014 · Journal of Geophysical Research: Space Physics
  • Joseph E. Borovsky · John T. Steinberg
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    ABSTRACT: [1] Using measurements from the WIND spacecraft at 1 AU, the heating of protons in the solar wind at locations of intense velocity shear is examined. 4321 sites of intense shear in fast coronal-hole-origin plasma are analyzed. The proton temperature, the proton specific entropy, and the proton number density at the locations of the shears are compared with the same quantities in the plasmas adjacent to the shears. A very slight but statistically significant enhancement of the proton temperature is seen at the sites of the shears, but it is accompanied by a larger enhancement of the proton number density at the sites of the shears. Consequently there is no enhancement of the proton specific entropy at the shear sites, indicating no production of entropy; hence, no evidence for plasma heating is found at the sites of the velocity shears. Since the shearing velocities have appreciable Mach numbers, the authors suggest that there can be a slight adiabatic compression of the plasma at the shear zones.
    No preview · Article · Mar 2014 · Journal of Geophysical Research: Space Physics
  • Joseph E. Borovsky · Joachim Birn
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    ABSTRACT: [1] Working toward a physical understanding of how solar-wind/magnetosphere coupling works, four arguments are presented indicating that the solar-wind electric field v sw × B sw does not control the rate of reconnection between the solar wind and the magnetosphere. Those four arguments are (1) that the derived rate of dayside reconnection is not equal to solar-wind electric field, (2) that electric-field driver functions can be improved by a simple modification that disallows their interpretation as the solar-wind electric field, (3) that the electric field in the magnetosheath is not equal to the electric field in the solar wind, and (4) that the magnetosphere can mass load and reduce the dayside reconnection rate without regard for the solar-wind electric field. The data is more consistent with a coupling function based on local control of the reconnection rate than the Axford conjecture that reconnection is controlled by boundary conditions irrespective of local parameters. Physical arguments that the solar-wind electric field controls dayside reconnection are absent; it is speculated that it is a coincidence that the electric field does so well at correlations with geomagnetic indices.
    No preview · Article · Feb 2014 · Journal of Geophysical Research: Space Physics
  • Source
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    ABSTRACT: We describe a new electrostatic particle-in-cell (PIC) code in curvilinear geometry called curvilinear PIC (CPIC). The code models the microscopic (kinetic) evolution of a plasma with the PIC method, coupled with an adaptive computational grid that can conform to arbitrarily shaped domains. CPIC is particularly suited for multiscale problems associated with the interaction of complex objects with plasmas. A map is introduced between the physical space and the logical space, where the grid is uniform and Cartesian. In CPIC, most of the operations are performed in logical space. CPIC was designed following criteria of versatility, robustness, and performance. Its main features are the use of structured meshes, a scalable field solver based on the black box multigrid algorithm and a hybrid mover, where particles' position is in logical space while the velocity is in physical space. Test examples involving the interaction of a plasma with material boundaries are presented.
    Full-text · Article · Dec 2013 · IEEE Transactions on Plasma Science
  • Joseph E. Borovsky
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    ABSTRACT: [1] Driver functions for the Earth's magnetosphere-ionosphere system are derived from physical principles. Two processes act simultaneously: a reconnection-coupled MHD generator 𝒢 and a viscous interaction. 𝒢 accounts for the dayside reconnection rate, the length of the reconnection X line, and current saturation limits for the solar wind generator. Two viscous drivers are derived: Bohm viscosity ℬ and the freestream-turbulence effect ℱ. A problematic proxy effect is uncovered wherein the viscous driver functions also describe the strength of reconnection. Two magnetospheric-driver functions written in terms of upstream solar wind parameters are constructed: 𝒢 + ℬ and 𝒢 + ℱ. The driver functions are tested against seven geomagnetic indices. The reaction of the geomagnetic indices to 𝒢 + ℬ and 𝒢 + ℱ is nonlinear: Nonlinear versions of the driver functions are supplied. Applying the driver functions at multiple time steps yields correlation coefficients of ~85% with the AE and Kp indices; it is argued that multiple time stepping removes high-frequency uncorrelated signal from the drivers. Autocorrelation-function analysis shows strong 1 day and 1 year periodicities in the AE index, which are not in the solar wind driver functions; correspondingly, high-pass and low-pass filtering finds uncorrelated signal at 1 day and 1 year timescales. Residuals (unpredicted variance) between the geomagnetic indices and the driver functions are analyzed: The residuals are anticorrelated with the solar wind velocity, the solar F10.7 radio flux, and the solar wind current saturation parameter. Removing diurnal, semiannual, and annual trends from the indices improves their correlation with the solar wind driver functions. Simplified versions of the driver functions are constructed: The simplified drivers perform approximately as well as the full drivers.
    No preview · Article · Nov 2013 · Journal of Geophysical Research: Space Physics
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    ABSTRACT: Estimates are calculated for the storm time reduction of solar wind/magnetosphere coupling by the mass density ρm of the magnetospheric plasma. Based on the application of the Cassak‐Shay reconnection‐rate formula at the dayside magnetopause, a numerical factor M is developed to quantify the effect of ρm on the dayside reconnection rate. It is argued that the mass loading of dayside reconnection by ρm also makes reconnection more susceptible to shutoff by magnetosheath velocity shear: a formula is developed to estimate the shortening of the dayside reconnection X‐line by ρm. Surveys of plasmaspheric drainage plumes at geosynchronous orbit during high‐speed‐stream‐driven storms and coronal mass ejection (CME)‐driven storms are presented: in the surveys the CME‐driven storms are separated into sheath‐driven portions and magnetic‐cloud‐driven portions. The storm time mass density of the warm plasma cloak (ionospheric outflows into the electron plasma sheet) is obtained from Alfven‐wave analysis at geosynchronous orbit. A methodology is developed to extrapolate geosynchronous‐orbit plasma measurements to the dayside magnetopause. For each of the three plasmas, estimates of the fractional reduction of the total dayside reconnection rate vary, with typical values of tens of percent; i.e., solar wind/magnetosphere coupling is reduced by tens of percent during storms by oxygen in the ion plasma sheet, by the plasmaspheric drainage plume, and by the plasma cloak. Dependence of the reduction on the F 10.7 solar radio flux is anticipated. Via these ionospheric‐origin plasmas, the magnetosphere can exert some control over solar wind/magnetosphere coupling. Pathways to gain a fuller understanding of the physics of the solar wind‐driven magnetosphere‐ionosphere system are discussed.
    No preview · Article · Sep 2013 · Journal of Geophysical Research Atmospheres

Publication Stats

6k Citations
527.35 Total Impact Points


  • 2012-2015
    • The Space Science Institute
      Boulder, Colorado, United States
  • 2011-2015
    • University of Michigan
      Ann Arbor, Michigan, United States
    • University of New Hampshire
      • Space Science Center
      Durham, New Hampshire, United States
  • 2013-2014
    • Lancaster University
      • Department of Physics
      Lancaster, England, United Kingdom
  • 1029-2012
    • Los Alamos National Laboratory
      • • Theoretical Division
      • • Space Science and Applications Group
      • • Plasma Physics Group
      Лос-Аламос, California, United States
  • 1991
    • University of New Mexico
      • Department of Physics & Astronomy
      Albuquerque, New Mexico, United States
  • 1983-1989
    • University of Iowa
      • Department of Physics and Astronomy
      Iowa City, IA, United States