Electron Acceleration Modeling

FIGURE 1. 2-D plots of the northern hemisphere parallel electron current density (in curvilinear coordinates) for both the MHD (left) and hybrid (right) models at t=0.185 T_A. The left and right sides of each panel are the equator and northern ionospheric boundary respectively. The vertical lines in each panel indicate the noted distance from the equator [Damiano and Johnson, GRL 2012].
Some of the most intense electron precipitation and largest ion outflows are found in regions of intense, Alfvenic waves. Recent analysis of auroral turbulence [Chaston et al., Phys. Rev. Lett., 100, 175003, 2008] suggests that large-scale global waves couple energy to smaller scale lengths on the order of the electron inertial, ion-acoustic or ion-gyroradius. To address the physical processes responsible for the electron acceleration, we have performed the first two-dimensional, self-consistent study of electron acceleration in a field line resonance for realistic (keV) plasma sheet electron temperatures in a dipolar geometry [Damiano, P. A. and J. R. Johnson (2012), Electron acceleration in a geomagnetic Field Line Resonance, Geophys. Res. Lett., 39, L02102]. We found that mirror force effects are particularly important in the generation of the parallel electric field needed to accelerate these particles to keV energies in these global scale waves and that this acceleration can be a major sink of wave energy leading to significant wave damping on the order of the Alfven period. Cross-scale coupling associated with kinetic electron effects causes the fragmentation of the global current system into small-scale structure across the magnetic field as shown in Figure 1. In this figure, we contrast the parallel current density in the northern hemisphere of the simulation domain for the hybrid case with kinetic electrons (right panel) and the MHD case without kinetic electrons (left panel). At the ionospheric boundary (right side of each panel) in the hybrid case, the structuring of the current reaches the order of the electron inertial scale. 

In Figure 1, it is also apparent that the current layer has broadened in the hybrid case relative to the MHD. It was determined that the mirror force induced parallel electric field leads to a strong cross-field Poynting flux that disperses wave energy across field lines and broadens the current profile. These kinetic simulations were contrasted with a resistive MHD model that uses a parallel conductivity based on the linear Knight relation (that includes the effect of the magnetic mirror force). We found a good correspondence between the broadening seen in hybrid model simulations and those observed in the resistive MHD model for smaller values of the field-aligned current. This result confirms that the broadening that we are seeing in both simulations is due only to the mirror force induced parallel electric field (generated to maintain quasi-neutrality) and not other wave-particle interactions that are taking place within the hybrid model description [Damiano and Johnson, Mirror Force induced wave dispersion in Alfven waves, Physics of Plasmas, 20, 062901, 2013]. The model has recently been advanced to include ion Larmor radius effects (that are important in the equatorial region) and we are using it to study electron acceleration associated with dispersive scale Alfvenic wave pulses at the onset of substorms.

Self-consistent model for Regions of Downward Auroral Current

The FAST satellite provided the first small scale observations in the auroral current regions. In these regions, electron beams and heated ion populations that flow out of the ionosphere are commonly observed in association with broadband electromagnetic ion cyclotron (EMIC) wave activity near over the range 4Hz-20kHz. The outflows can be understood heuristically in terms of wave heating and conservation of magnetic moment, but have never been rigorously described using a self-consistent model. Our finite element wave model describes how the EMIC waves propagate along the magnetic field to low altitude where they are reflected and absorbed. The model gives an estimate of how much wave power goes into the ion cyclotron heating and Joule heating channels. Ion outflows in the presence of the waves can be modeled with a Monte Carlo simulation once the heating rate is specified. The heating rate may be computed from the wave solutions. Because the background profiles determine the wave propagation and absorption and the wave absorption determines the background profiles it is necessary to couple the wave propagation model with a Monte Carlo transport model. The coupling is performed in an iterative manner with the background profiles adjusting to the wave amplitudes and the wave propagation adjusting to the background profile until a convergent or limit cycle state is found. The waves and particle energies are consistent with satellite observations.  Future directions of research that may be useful to the space physics community would be to characterize wave sources based on parameters in global codes, and infer outflow rates using our model.


Gyrokinetic Model for the Inner Magnetosphere

FIGURE 2.  Solution of the compressional magnetic field component B|| for slow compressional modes excited by energetic particles in the inner magnetosphere Porazik and Lin [2011a].
Drs. Porazik and Johnson are currently working on advancement of a gyrokinetic model that he developed for dipole geometry.  The model has the potential to exploit the gyrosymmetry to provide a simplified kinetic description that essentially follows the self-consistent motion of charged rings in electromagnetic fields.  The model has been applied to study ULF waves that are generated through drift-bounce resonance with energetic particles as shown in Figure 2.  
The model that we are developing has advantages over current ring current models in that we do not employ a bounce averaged distribution and, rather than assuming a quasi-equilibrium, we allow for pressure imbalance, launching of MHD waves, and self-consistent evolution of the plasma population in the presence of MHD waves that cause radial transport.  The formalism that we use follows guiding centers that respond to the large-scale spatiotemporal fields and a transform that responds to small-scale spatio-temporal fields. The simplification is that the guiding center equations depend only on slowly varying quantities and the interaction of the waves with the particles is contained in a single scalar equation for the gauge (coordinate transformation).  This approach can potentially be coupled to our finite element wave model by separating the transport and wave timescales.  Moreover, the formalism also allows an extension to higher frequency, for a self-consistent description of EMIC and whistler waves as has currently been performed at PPPL [Kolesnikov, R. A., W. W. Lee, H. Qin, and E. Startsev, High frequency gyrokinetic particle simulation, Phys. Plasmas, 14, 072,506, 2007]. 


Multi-fluid Wave Modeling

ULF Waves in Mercury's Magnetospheres  The MESSENGER satellite has already provided a wealth of wave data from its two encounters with the planet Mercury and now that it is in orbit will allow detailed studies of its magnetosphere. The few measurements of Mercury’s magnetosphere already indicate that heavy exospheric ions such as sodium can play an important role in the magnetospheric dynamics. We  have been funded to explore the role of heavy ions on field-line resonances at Mercury and found that there are significant modifications to the field-line resonance due to ion cyclotron effects. We have also outlined a method to infer heavy ion densities from the wave spectrum, which would advance the MESSENGER science goal to understand the role of volatiles (such as exospheric sodium) at Mercury. Our recent paper [Kim, Johnson, and Lee, ULF wave absorption at Mercury, Geophys. Res. Lett., 2011] determines the effect of Sodium on the field line resonance and addresses the differences that might be expected at Mercury.

Radio emissions in the ionosphere, solar wind, and heliosphere
Radio emissions near the electron plasma or upper hybrid frequency region have been generated in various space plasmas, such as the solar corona and interplanetary medium (solar radio bursts), foreshock regions upstream of Earth’s bowshock, outer heliosphere, magnetospheres of Earth and other magnetized planets, and ionospheres. Because the radio emissions are a primary observable, understanding physical processes leading to wave emissions is fundamental to interpreting observations of the sun and the inner and outer heliosphere. At present, the role and importance of linear mode conversion (LMC) processes in producing such radio emissions is not well understood. Because early work on LMC suggested that its efficiency was inadequate to explain the emissions, subsequent research efforts primarily focused on nonlinear mechanisms due to the highly nonthermal levels of Langmuir waves. However, nonlinear processes could not explain the mixed polarizations of radio emissions. Moreover, other studies of LMC suggested a much higher efficiency than previously expected and that LMC would dominate over the efficiency of nonlinear processes. More recently, full-wave simulations found that LMC is not only efficient, but also leads immediately to linearly and partially polarized radiations consistent with observations, thereby resolving the mixed polarization issue. We are working on wave calculations to determine whether LMC is quantitatively important in producing solar radio bursts, magnetospheric continuum radiation, and ionospheric radio emissions, thereby resolving these longstanding controversies. To achieve this goal, we will use 1 and 2D time dependent simulations and full wave finite element calculations. The results will be compared with observed wave properties from satellites (e.g., WIND and STEREO), rockets, and nonlinear conversion efficiencies.

Finite Element Model of Magnetospheric Waves

FIGURE 3: Left: Alfven speed profile and finite element mesh using a plasma density model prescribed by Denton et al. [2004] with the addition of a plasmaspheric plume added at 5.5 RE. Right: full wave solutions for a 0.1 Hz magnetosonic wave launched at 8 RE showing wave trapping in the plume and associated ray paths.
We has developed a finite element 2D-full wave code in collaboration with the radio frequency heating group of PPPL.  This code solves the wave equation in arbitrary magnetic field geometry .  The code has been developed for magnetospheric geometry, but is also particularly suitable for the diverter region of fusion devices.  The current version of the code assumes a wave source and computes the wave fields given the plasma response, which can include kinetic effects such as Landau/cyclotron resonance and Larmor radius effects.  Sufficient resolution can be obtained to describe all wave frequencies up to and including whistler waves, so the code would be particularly useful to couple with a transport code in the inner magnetosphere.  Figure 3 shows an example of the finite element mesh for a situation where a compressional wave launched in the outer magnetosphere is trapped in a leaky eigenmode solution in the plasmaspheric plume.  The code is parallelized and fast (the solution shown in Figure 3 may be obtained in 12 seconds on a single processor).  We have also verified that the code appropriately resolves the field-line resonance and cyclotron resonance and describes mode conversion of those waves [Johnson, et al., A Full-Wave Model for Wave Propagation and Dissipation in the Inner Magnetosphere using the Finite Element Method, AGU, 2012].  This code should provide an improved description of waves in the inner magnetosphere, and we plan in the future to couple it with an inner magnetospheric transport model.   

Waves and Transport at the Magnetopause

Recent observations have brought attention to significant populations of cold, dense plasma in the boundary layers and plasma sheet of Earth’s magnetosphere.  This plasma can precondition the magnetospheric response to the solar wind such that storms could be more intense. The origin and physical processes that give rise to the cold plasma remains outstanding issue, but are believed to be related to either reconnection or wave turbulence. 
Recently, we have collaborated with Yu Lin examining the role of kinetic Alfven waves on magnetopause transport using a hybrid simulation code.  We have established the importance of nonlinear wave-wave coupling, which gives rise to large azimuthal modes on the gyroradius scale.  This finding is particularly important because the cross-field transport is directly related to the azimuthal mode number, while linear mode conversion mostly leads to short wavelength in the radial direction, which does not contribute to transport across the magnetic field.  A natural extension of this work is to incorporate such kinetic effects into a global model.  We have also begun to include the parallel electron dynamics with a modified version of Peter Damiano’s code, which will allow us to address Landau damping, which plays a particularly important role when there is shear. 
We are also funded to work on kinetic effects on Kelvin-Helmholtz instabilities at the magnetopause, which are excited by the velocity shear between the magnetosheath and magnetosphere.  In the nonlinear stage, the Kelvin-Helmholtz vortices twist up to kinetic scales and should be treated kinetically.  We are interested in understanding how kinetic effects affect the vortices and what transport results.  We are collaborating with Antonius Otto and with Peter Delamere (University of Colorado) to examine the effect of heavy ions on the K-H instability. 
We found that MHD simulations with higher mass density tended to have larger growth rates with a larger interchange of magnetic flux, which would suggest more mass transport.  However, the MHD approach does not include the ion inertial effects.  To study the effect of ion inertia, we performed a series of simulations (in collaboration with Peter Delamere). The hybrid simulations were strikingly different from the MHD results as shown in Figure 4.  In the hybrid simulations shown in Figure 4, we simulated an interface with equal mass density, but with different relative mass.  While the light ions were entrained in vortices, the heavy ions streamed through the vortex structures because of their larger inertia.  As a consequence, while the magnetic field and light ions formed the vortex, the heavy ions did not move in to the fill the part of the vortex in the light ion region, leading to significant mass density holes and enhancements. One important consequence is that there were significant increases in the local entropy, which could potentially lead to interchange motion in a more realistic interface and be an important effect on transport. 
The spectra of the ion density perturbations also revealed a markedly different behavior for the light and heavy ions.  For the case with only light ions, we found that the spectrum evolved from a broadband at early times to global scales at later times---the classical inverse cascade.  In contrast in the multi-ion case, we found that while the heavy ion density spectrum appears to follow the classical inverse cascade that the light ions appear to follow a forward cascade developing finer structures as the vortices are fragmented as the heavy ions stream through the vortices.  This different behavior in the power spectra suggests differences in the transport of the heavy versus light ions.  This should be explored as a possible explanation for observations of enhanced transport of light ions relative to heavy ions observed at the magnetopause [Fuselier et al., 1997].
FIGURE 4: Hybrid simulations of Kelvin-Helmholtz instability at a velocity shear boundary.  Heavy ions are on the lower half of of the simulation domain, while light ions are on the top.  The flow is in the x-direction with shear in the z direction.  While the protons organize into vortex motion following the field, the heavy ions stream through the vortex structures (breaking them up).  Heavy ions cannot follow the field lines as they wrap around leading the appearance of density holes where there are significant increases in the entropy. 


A problem of great practical importance in the area of space physics is that of understanding and predicting the magnetospheric response to solar wind input, and is a key element in understanding space weather. Building on earlier collaborations in this area of research described in section 1, Simon Wing and Jay Johnson have been funded to examine nonlinear dependencies between the solar wind variables and direct magnetospheric observations of energetic electron flux, tail stretching, and magnetospheric output to the ionosphere. We will consider multivariate output to determine the extent to which the coupling parameters drive different processes at different local time. We will identify a predictability horizon based on the cumulant-based measure of information flow. These results will be compared with entropy-based measures of information flow. We will identify combinations of solar wind variables that provide the most information about the future state of the ionosphere based on the information flow.
We have also recently been working on using information-theoretical techniques to explore issues of causality in nonlinear systems to be able to distinguish causal relationships form correlated relationships.  We have used transfer entropy, based on conditional probabilities, as a discriminating statistic to explore solar wind-magnetosphere coupling.  We are currently applying the method to substorms to explore whether external triggering is causal in nature (or whether the dynamics are determined internally).  The method can also be applied to auroral physics relation ion outflows to electrodynamics as well as coupling between plasma sheet pressures, Birkeland currents, and ion outflows.