• A self-consistent time varying auroral model

      Min, Qilong; Rees, M. H.; Kan, J. R.; Lummerzheim, D.; Piacenza, R.; Stamnes, K. (1993)
      A time dependent model of auroral processes has been developed by self-consistently solving the electron transport equation, the ion continuity equations and the electron and ion energy equations. It is used to study the response of ionospheric and atmospheric properties in regions subjected to electron bombardment. The time history of precipitation events is computed for a variety of electron spectral energy distributions and flux magnitudes. Examples of daytime and night-time aurorae are presented. Precipitating energetic auroral electrons heat the ambient electrons and ions as well as enhancing the ionization rate which increases the ion concentration. The consequences of electric field acceleration and an inhomogeneous magnetic field in auroral electron transport in the topside ionosphere are investigated. Substantial perturbations of the low energy portion of the electron flux are produced: An upward directed electric field accelerates the downward directed flux of low energy secondary electrons and decelerates the upward directed component. Above about 400 km the inhomogeneous magnetic field produces anisotropies in the angular distribution of the electron flux. The effects of the perturbed energy distributions on auroral spectral emission features and on the electron temperature are noted. The response of the Hall and Pederson conductivities to auroral electron precipitation is discussed as a function of the characteristic energy of the spectral distribution.
    • A simulation study of three-dimensional magnetic reconnection

      Ma, Zhi-Wei; Lee, L. C.; Kan, J. R.; Shaw, G. E.; Smith, R. W.; Hawkins, J. G. (1994)
      The magnetic reconnection process plays an important role in the interaction between the solar wind and the magnetosphere. It leads to the transfer of energy from the solar wind into the magnetosphere. In this thesis, we study three-dimensional (3D) aspects of magnetic reconnection based on magnetohydrodynamic (MHD) simulations. First, we examine the magnetic field topology of magnetic flux ropes formed in multiple X line reconnection (MXR). It is found that the magnetic field topology depends on the relative extent and location of the two neighboring X lines. Magnetic flux ropes with either smooth or frayed ends are obtained in our simulations. For magnetic flux ropes with smooth ends, a major amount of magnetic flux is connected at each end to only one side of magnetopause. Second, the evolution of the core magnetic field in the magnetic flux tube is studied for various magnetic reconnection processes. We find that the 3D cases always lead to a larger enhancement of core field than the corresponding 2D cases since plasma can be squeezed out of the flux tube in the third direction. The MXR process gives rise to a larger increase of the core field than the single X line reconnection process. The core magnetic field can be enhanced to three times the ambient magnetic field strength in the 3D MXR process. Finally, we examine the generation and propagation of Alfven waves and field-aligned currents in the 3D reconnection process. For cases with a zero guide field, it is found that a large portion of the field-aligned currents ($\sim$40%) is located in the closed field line region. Both the pressure gradient term and inertia term contribute to the generation of field-aligned currents. For cases with nonzero guide field, one sense of field-aligned currents is dominant due to the presence of the initial field-aligned current. In these cases, the inertia term makes a major contribution to the redistribution of field-aligned currents. The influence of the initial guide field on the longitudinal shift of the current reversal site is found to be consistent with observations.
    • Dependence of the ionospheric convection pattern on the conductivity and the southward IMF

      Shue, Jih-Hong; Kan, J. R.; Akasofu, S.-I.; Biswas, N. N.; Rees, M. H.; Weimer, D. R. (1993)
      Electric field measurements from the DE-2 satellite were used to determine the location of the convection reversal boundary and the potential around this boundary under a combination of interplanetary magnetic field (IMF) and auroral electrojet conditions. The electric potential is obtained by the integration of the electric fields. The convection reversal boundary is defined in this study as where the potential has its absolute maximum and minimum values. The data were sorted into 18 categories according to two levels of the negative IMF $B\sb{z},$ three ranges of IMF $B\sb{y},$ and two substorm phases. The data were fit with both continuous and discontinuous boundaries to get a functional representation of boundary potentials and locations. A simple model is constructed by solving the Laplace's equation in order to illustrate the obtained boundary potentials and locations. The results show that the enhanced electric field in the midnight sector is associated with an intense westward electrojet current. It can also be seen that the convection reversal boundary is found to be discontinuous near midnight. The discontinuous convection reversal boundary on the dayside is related to the merging near dayside cusp region. The discontinuous convection reversal boundary on the nightside is related to the conductivity enhancement. The intrusion of the dawn cell into the dusk cell is due to nonuniformity of the Hall conductivity in the ionosphere. Another model is constructed by solving the current continuity equation with field-aligned current and nonuniform conductivity added. It can be found that a secondary convection reversal, which is detached from the dusk-cell convection reversal, appears in the evening-midnight sector within the polar cap when the IMF $B\sb{y}$ is positive and the conductivity is nonuniform. This convection reversal is attributed to be created by the B $\times$ V dynamo. Also, the inclusion of the region 2 field-aligned current leads to an enhancement of the electric field in the region between the region 1 and region 2 currents.
    • Electron transport and optical emissions in the aurora

      Lummerzheim, Dirk; Rees, M. H.; Lee, L. C.; Olson, J. V.; Royer, T. C.; Stamnes, K. (1987)
      A one-dimensional, steady state auroral model is developed based on a linear electron transport calculation. A set of cross sections for electron neutral collisions describing elastic scattering, energy loss, and photon emission is compiled and used in conjunction with a discrete ordinate transport code. Calculated electron intensities are compared with in situ rocket measurements. Auroral optical emissions that result from direct electron impact on neutrals are calculated for synthetic and observed electron spectra. A systematic dependence of the brightness of auroral features on energy flux, characteristic energy, and atmospheric composition is found and parameterized. A method for interpreting the brightness and the ratio of brightnesses of certain auroral emissions in terms of the energy flux, characteristic energy, and relative oxygen density is described. Application of this method to auroral images acquired by nadir viewing instruments aboard a satellite is discussed and the distribution of energy flux, characteristic energy, and ionospheric conductances over the auroral oval is determined. Emissions that are suitable for analysing auroral spectra in terms of the atomic oxygen abundance in the auroral zone are identified.
    • Formation of solar prominences and eruption of solar magnetic arcade systems

      Choe, Gwang-Son; Lee, Lou-Chuang; Akasofu, Syun-Ichi; Roederer, Juan G.; Swift, Daniel W.; Watkins, Brenton J. (1995)
      Formation and eruption of solar prominences, coronal mass ejections (CMEs) and solar flares are the most magnificent phenomena among solar activities. Observations show that there is an interrelationship among these events and that their manifestation is conditioned by certain common photospheric signatures. One of them is the increase in magnetic shear. In this thesis, the evolution of the solar atmosphere is studied by numerical simulations with photospheric motions as boundary conditions. Firstly, mechanisms of prominence formation are investigated. It is found that prominences can be formed by the development of a thermal instability (1) in a rapidly expanding magnetic arcade, (2) in a magnetic island created by magnetic reconnection or (3) in the current sheet between two bipolar arcades. Secondly, the quasi-static evolution of a magnetic arcade subject to footpoint shearing is studied under the ideal MHD condition. Three distinct evolutionary phases are found, in the last of which a current layer develops and grows indefinitely with the increasing shear. Force-free field solutions are also constructed and compared with dynamic solutions. Finally, resistive evolutions of magnetic arcades are investigated imposing resistivity on the pre-sheared magnetic fields. It is found that there is a critical amount of shear, over which magnetic reconnection can take place to create a magnetic island. The effects of different values and spatial patterns of resistivity are studied. With a localized resistivity, most of principal features in solar eruptive processes are reproduced. A comparative study is made between the numerical results and observations.
    • Observations and generation mechanisms of slow-mode waves in the magnetosheath

      Yan, Ming; Lee, Lou; Craven, John; Hawkins, Joseph; Sentman, Dave; Watkins, Brenton (1995)
      The interaction of solar wind with the geomagnetic field leads to the formation of the bow shock, magnetosheath, and magnetopause. Magnetohydrodynamic (MHD) slow-mode structures with a plasma density enhancement and magnetic field depression have been observed to appear frequently in the inner magnetosheath. In addition, the slow-mode structures usually consist of slow-mode waves with a smaller length scale. These slow-mode structures and waves are studied in this thesis through satellite observations and numerical simulations. We find, through satellite observations, that some of the slow-mode structures are associated with Alfven waves in the solar wind. On the other hand, simulations show that slow-mode waves are generated through the interactions between the bow shock and interplanetary shocks, magnetosonic waves, rotational discontinuities, or Alfven waves. The generated slow-mode waves stay in the inner magnetosheath for a long time (about 15 minutes) before the wave energy is convected away tailward. Of particular importance are the interactions between the bow shock and interplanetary rotational discontinuities or Alfven waves. These interactions generate a region with an enhanced plasma density and depressed magnetic field, which is very similar to the slow-mode structures observed in the inner magnetosheath. Based on observations and simulations, it is suggested that the interactions of various types of solar wind fluctuations with the bow shock may lead to the frequent appearance of slow-mode structures and waves in the inner magnetosheath. The generated slow-mode structures have strong pressure variations, and may impinge on the magnetopause as strong pressure pulses.
    • Particle simulations of magnetic field reconnection and applications to flux transfer events

      Ding, Da-Qing; Lee, L. C.; Akasofu, S-I; Hawkins, J. G.; Olson, J. V.; Swift, D. W. (1990)
      Basic plasma processes associated with driven collisionless magnetic reconnection at the Earth's dayside magnetopause are studied on the basis of particle simulations. A two-and-one-half-dimensional (2$1\over2$-D) electromagnetic particle simulation model with a driven inflow boundary and an open outflow boundary is developed for the present study. The driven inflow boundary is featured with a driving electric field for the vector potential, while the open outflow boundary is characterized by a vacuum force free condition for the electrostatic potential. The major findings are as follows. (1) The simulations exhibit both quasi-steady single X-line reconnection (SXR) and intermittent multiple X line reconnection (MXR). The MXR process is characterized by repeated formation and convection of magnetic islands (flux tubes or plasmoids). (2) Particle acceleration in the MXR process occurs mainly in O line regions as particles are trapped within magnetic islands, not in X line regions. The MXR process results in a power law particle energy spectrum of $f(E)\sim E\sp{-4}$. (3) Field-aligned particle heat fluxes and intense plasma waves associated with the collisionless magnetic reconnection process are also observed. (4) When applied to the dayside magnetopause, simulation results show that the MXR process tends to generate a simultaneous magnetic field perturbation on both sides of the dayside magnetopause, resembling the observed features of two-regime flux transfer events (FTEs). (5) An intrusion of magnetosheath plasma bulge into the magnetosphere due to the formation of magnetic islands may lead to the layered structures observed in magnetospheric FTEs. (6) In the current sheet, the enhanced tearing mode instability caused by the driving force applied at the driven inflow boundary creates an energy source at a specific wavenumber range with $k\sb{z}L\sim$ 0.3 in the modal spectrum of the magnetic field $B\sb{x}$ component. An inverse cascade of the modal spectrum of $B\sb{x}$ leads to the formation of the large-scale ordered magnetic island structures observed in the simulations. (7) In addition, the results of a theoretical study show that the tearing mode instability, and hence the magnetic reconnection at the dayside magnetopause, do not exhibit strong dependence on the magnetosheath $\beta$ values.
    • Structure of reconnection layers in the magnetosphere

      Lin, Yu; Lee, Lou-Chuang; Hawkins, J. G.; Sentman, D. D.; Smith, R. W.; Swift, D. W. (1993)
      Magnetic reconnection can lead to the formation of observed boundary layers at the dayside magnetopause and in the nightside plasma sheet of the magnetosphere. In this thesis, the structure of these reconnection layers is studied by solving the one-dimensional Riemann problem for the evolution of a current sheet. Analytical method, resistive MHD simulations, and hybrid simulations are used. Based on the ideal MHD formulation, rotational discontinuities, slow shocks, slow expansion waves, and contact discontinuity are present in the dayside reconnection layer. Fast expansion waves are also present in the solution of the Riemann problem, but they quickly propagate out of the reconnection layer. Our study provides a coherent picture for the transition from the reconnection layer with two slow shocks in Petschek's model to the reconnection layer with a rotational discontinuity and a slow expansion wave in Levy et al.'s model. In the resistive MHD simulations, the rotational discontinuities are replaced by intermediate shocks or time-dependent intermediate shocks. In the hybrid simulations, the time-dependent intermediate shock quickly evolves to a steady rotational discontinuity, and the contact discontinuity does not exist. The magnetotail reconnection layer consists of two slow shocks. Hybrid simulations of slow shocks indicate that there exists a critical number, $M\sb{c}$, such that for slow shocks with an intermediate Mach number $M\sb{I} \ge M\sb{c}$, a large-amplitude rotational wavetrain is present in the downstream region. For slow shocks with $M\sb{I} < M\sb{c}$, the downstream wavetrain does not exist. Chaotic ion orbits in the downstream wave provide an efficient mechanism for ion heating and wave damping and explain the existence of the critical number $M\sb{c}$ in slow shocks.
    • The quasiparallel collisionless shock wave: A simulation study

      Mandt, Mark Edward; Kan, J. R.; Das, D.; Lee, L. C.; Olson, J. V.; Swift, D. W. (1988)
      The structure of the quasi-parallel collisionless shock wave is studied via a numerical simulation model. The model is compared to observations and theoretical predictions and within its limitations appears to reproduce the true shock structure reasonably well. Three electron equations of state and their effects on the simulation are examined. It is found that only the isotropic-adiabatic electron equation of state yields acceptable results in the simulation at high Mach numbers. The scale lengths of the shock are measured, normalized by the natural scale lengths of the plasma, and plotted as a function of the Alfven Mach number. It is found that the wavelength of the upstream waves follows that predicted for a phase standing whistler quite well and the scalelength of the jump in the magnitude of the magnetic field is generally greater than, but approximately equal to this wavelength. For Alfven Mach numbers $M\sb{A} >$ 2.5, waves are generated in the downstream region. Their wavelength and the scale length of the plasma transition are larger than the natural scale lengths of the plasma. The ion heating is seen to occur in two stages. In the first stage which occurs upstream of the principal shock ramp, the heating can be characterized by a polytropic power law equation of state with an exponent much greater than the isentropic-adiabatic rate of $\gamma$ = 5/3. The second stage of heating which occurs from the principal shock ramp to the downstream region is characterized by an exponent on the order of the isentropic-adiabatic rate. The results show that the ion heating occurs mainly around the principle density jump near the center of the shock transition region, while the increase in entropy takes place mainly in the upstream side of the shock transition region. It is suggested that the ion heating is a consequence of the non-adiabatic scattering of the ions through the magnetic field of the shock and its upstream precursor wave.
    • Two- and three-dimensional study of the Kelvin-Helmholtz instability, magnetic reconnection and their mutual interaction at the magnetospheric boundary

      Chen, Qinxue; Otto, Antonius; Watkins, Brenton; Sentman, Davis; Smith, Roger (1997)
      Magnetic reconnection and the Kelvin-Helmholtz (KH) instability regulate the transport of magnetic flux, plasma, momentum and energy from the solar wind into the magnetosphere. In this thesis, I use two-dimensional and three-dimensional MHD simulations to investigate the KH instability, magnetic reconnection, and their relationship. Two basic flow and magnetic field configurations are distinguished at the Earth's magnetopause: (1) configurations where the difference in plasma velocity between the two sides of the boundary $\Delta$v (velocity shear) is parallel to the difference of the magnetic field $\Delta$b (magnetic shear), and (2) configurations where the velocity shear is perpendicular to the magnetic shear. For configuration (1), either magnetic reconnection is modified by the shear flow, or the KH instability is modified by the magnetic shear and resistivity. The evolution of the basic configuration (2) requires three dimensions. In this case, both processes can operate simultaneously in different planes. If the KH instability grows faster initially, it can wrap up the current layer and thereby initiate a very fast and turbulent reconnection process. The resulting magnetic turbulence can provide the first explanation of often very turbulent structures of the magnetopause current layer. For the first time, it is quantitatively confirmed that the KH instability operates at the magnetospheric boundary at low latitudes.