Simulation of Plasma Dynamics in the Ionospheric Alfven Resonator (IAR)#

Shear Alfven waves (SAW) propagating along geomagnetic field lines give rise to an important range of magnetospheric pulsations. It is widely acknowledged that the precipitation of energetic electrons accelerated by SAWs provides energy transfer from the magnetosphere to the ionosphere. The structure of the SAW, which defines the electron acceleration, largely depends on the inertial or kinetic regime of SAW propagation along the geomagnetic field. In the vicinity of Earth, the Alfven speed rapidly decays towards the ionosphere and SAWs bounce between the highly conductive ionosphere and the Alfven speed gradient. This region bounded at one end by the top of the ionosphere and at the other end by the Alfven speed maximum, forms a weak resonator called the ionospheric Alfven resonator (IAR) [1].

The figure shows the IAR region relative to the surface of Earth. Waves propagate down geomagnetic field lines into the IAR, where they become trapped between the ionsophere and high-altitude peak in the Alfven speed gradient.

Motivation and objective#

Processes in IAR are crucial for the energy transfer between the magnetosphere and the ionosphere [2]. Small scale perturbations typical for the IAR may lead to the anomalous plasma resistivity and increase of the field-aligned electric field of SAW (here "field-aligned" means directed along the geomagnetic field line) [3]. The related electron acceleration [4] produces high energy electrons. Precipitation of these electrons in the ionosphere affects the reflection of SAW via the change of the ionospheric conductivity causing the feedback instability 5,6. This instability develops in IAR much faster (with time scales around 1 s) than the period of global magnetospheric oscillations (whose period is about 10^3-10^3 s). The fast feedback instability may excite intense Alfven waves itself, eventually leading to the aurora formation 7,8.

It is necessary to mention that the SAW field-aligned electric field predicted by MHD theory is too low to explain the appearance of electrons with energies of 1-10 keV. Therefore, the electron response to the wave must be described kinetically to obtain the correct magnitude of the parallel electric field 9,10.

The objective of the present project is the self-consistent study of kinetic effects of electron motion in IAR by means of numerical simulation. We expect to get insight into the physics of electron acceleration by SAW, which is an important part of space weather prediction. The numerical tool we are going to use is the hybrid code for plasma simulations with kinetic electrons and fluid ions, resolving two dimensions in configuration space (in the plane of a dipole geomagnetic field line), two dimensions in velocity space for electrons (parallel and perpendicular to the magnetic field), and all three velocity components for the ion fluid. The development of the code is a significant part of the project. The code will be a valuable outcome of the project, because it will be a universal and highly versatile tool for space plasma physics studies.

The two-dimensional (2D) kinetic plasma simulation is a formidable task even for modern supercomputers. In order to decrease the numerical cost, the area of simulation will be reduced to a narrow band stretched along the auroral geomagnetic field lines, as shown schematically in Fig.2. Note that the simulated area is terminated slightly above the Alfven speed maximum, which allows correct simulation of IAR eigenmodes with minimal cost provided the boundary conditions at the magnetospheric (top) boundary are properly selected.

Where does IAR Occur?#

Consider the formation of the Alfven speed gradient, constituting the upper IAR boundary. The speed of propagation of Alfven wave along the geomagnetic field line (the Alfven speed)

Fig.1. Nonuniformity of plasma density (a) and Earth magnetic field (b) along the geomagnetic field line produces non-monotonic Alfven velocity profile (c), forming the IAR. L is the distance along the field line, L=0 corresponds to the ionospheric boundary. Profiles are obtained for the field line with latitude 69 deg at the ionospheric boundary.

Preliminary simulation results#

Here we present some results of a test simulation, where the IAR is excited by a solitary Alfvenic pulse at the magnetospheric boundary. To achieve faster run times, the ionospheric boundary is positioned at 200km above the Earth surface (this reduced the length and increased the eigenfrequency of the IAR). The bounding geomagnetic field lines have latitudes 70 deg and 68 deg at the ionospheric boundary, the distance between the magnetospheric and ionospheric boundaries is about 6800 km along the geomagnetic field line.

The grid has 400 cells along the geomagnetic field and 30 cells in the perpendicular direction. The size of the computational grid is about 43.1 x 26.9 km2 at the magnetospheric boundary and 7.3 x 9.8 km2 at the ionospheric boundary.

The driving Alfvenic pulse has duration of 0.5s , it is symmetrical relative to the center of the magnetospheric boundary (along the mu direction, in dipole coordinates), as shown in Fig.4.

Fig.4. Profile (along the mu direction, across the geomagnetic field line) of the amplitude of transverse electric field of the driving Alfvenic pulse. Here x_mu is the distance along the magnetospheric boundary grid line.

At present time, the simulation code is implemented with cold fluid ions and electrons, in order to verify expected properties of the IAR when excited by a solitary Alfvenic pulse (see Fig.2). In future work, the code will combine fluid ions with the drift-kinetic Vlasov equation for electrons. However, the job done for the complete fluid simulations is not in vain - a significant part of the code related with ion dynamics, electromagnetic field solving, and diagnostics, will be ported to the kinetic version of the code in its present form.

Future work includes the following:

1. Implementation of the active ionosphere boundary conditions.
2. Implementation of kinetic electrons.
3. Parallelization of the code.
4. Study of kinetic effects and electron acceleration in the IAR.

References

1. S. V. Polyakov and V. O. Rapoport, "Ionospheric Alfven resonator", Geomagn. Aeron., 21, 816 (1981).
2. R. L. Lysak, "Magnetosphere-ionosphere coupling by Alfven waves at midlatitudes", J. Geophys. Res., 109, A07201 (2004).
3. V. Yu. Trakhtengertz and A. Ya. Feldstein, "Quiet auroral arcs: ionosphere effect of magnetospheric convection stratification", Planet. Space. Sci., 32, 127 (1984).
4. C. C. Chaston, J. W. Bonnell, C. W. Carlson, M. Berthomier, L. M. Peticolas, I. Roth, J. P. McFadden, R. E. Ergun, and R. J. Strangeway, "Electron acceleration in the ionospheric Alfven resonator", J. Geophys. Res., 107, 1413 (2002).
5. G. Atkinson, "Auroral arcs: Result of the interaction of a dynamic magnetosphere with the ionosphere", J. Geophys. Res., 75, 4746 (1970).
6. R. L. Lysak, "Feedback Instability of the Ionospheric Resonant Cavity", J. Geophys. Res., 96, 1553 (1991).
7. A. Miura and T. Sato, "Numerical simulation of global formation of auroral arcs", J. Geophys. Res., 85, 73 (1980).
8. D. Pokhotelov, W. Lotko, and A. V. Streltsov, "Harmonic structure of field line eigenmodes generated by ionospheric feedback instability",J. Geophys. Res., 107, 1363 (2002).
9. R. Rankin, J. C. Samson, and V. T. Tikhonchuk, "Parallel electric field in dispersive shear Alfven waves in the dipolar magnetosphere", Geophys. Res. Lett., 26, 3601 (1999).
10. C. E. J. Watt, R. Rankin,J. Rae, and D. M. Wright, “Inertial Alfven waves and acceleration of electrons in nonuniform magnetic fields", Geophys. Res. Lett., 33, L02106 (2006).
11. R. W. Hockney and J. W. Eastwood, "Computer simulation using particles", Bristol (England), Philadelphia: A. Hilger, 1988.
12. A. Staniforth and J. Cote, "Semi-Lagrangian Integration Schemes for Atmospheric Models - A Review", Mon. Weather Rev., 119, 2206 (1991).
13. E. L. Lindman, "Free-Space Boundary Conditions for the Time Dependent Wave Equation", J. Comput. Phys., 18, 66 (1975).

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