Three dimensional Simulations of Sprites and Elves

H. L. Rowland

Plasma Physics Division

Naval Research Laboratory

Washington, DC 20375-5000

Abstract

We present the first three dimensional simulations showing the formation of elves and sprites. Three different lightning discharges are considered. A vertical cloud-to-ground (cg), a horizontal cloud-to-cloud (cc) and a cg followed by a cc. The cg forms an elf and sprite directly above the discharge. The cc forms an elf displaced horizontally by up to 80 km and generates a pair of elves located above the end of the discharge. As the return stroke travels horizontally the sprite can also move providing a possible explanation for dancing sprites. The cg followed by a cc can act to move the sprite form above the cg to the end of the cc discharge. Thus the sprite seen to form following a cg could be located many km distant horizontally.

Introduction

Airglow has been observed above lightning storms from space , aircraft and the ground. The airglow has been divided into three groups- elves, sprites, and jets. The elves are occur between 80 and 90 km with horizontal widths of over a hundred km. Typical lifetimes are 0.1 ms. Sprites occur at between 60 to 80 km and have lifetimes of 10's ms. Filamentary structures termed tendrils can extend under the sprite to below 50 km. Jets are observed to emerge from the tops of lightning clouds and propagate upward to 40 km altitude. The theories and simulation models that have been developed to explain these observations have been recently reviewed [Rowland, 1998].

We present the first 3D simulations showing the formation of sprites and elves by a lightning discharge. By going to 3D it becomes possible to model more complex and realistic situations than is possible using a 2D code. In the case of a cloud-to-ground (cg) discharge, the axis of symmetry around z means that a 2D code in r,z coordinates can be accurate [Pasko et al., 1996]. For a cloud-to-cloud discharge there is not handy axis of symmetry. An r,z code would not work but a Cartesian x,z code could provide a reasonably accurate picture in the direction of the discharge [Fernsler and Rowland, 1996]. In the direction transverse to the discharge it would probably not be so accurate. There is also the problem that the focusing of the field by the sprites, which may be very important for the sprite to reach lower altitudes, would not be properly modelled. However, if one wants to look at the two classes of discharge together or if the cg is not perfectly vertical, it becomes necessary to use a 3D code. The obvious drawback is that 3D codes are slower which limits the how small the cell size is and the total time duration of the code. The simulations presented here have almost the same cell size and time extent as earlier 2D models. Work is underway to develop a finer-scale model that will act as a sub-grid to part of the existing code.

The 3D simulations show the formation of elves and sprites by a cg, a cc and a cg followed by a cc. For the cg the 3D simulations are seen to be in good agreement with (r,z) simulations [Pasko, 1996; Cho and Rycroft, 1998] and (x,z) [Rowland et al.1995; Rowland et al., 1996; Fernsler and Rowland, 1996]. For the cc the 3D simulations are seen to in reasonable agreement with earlier 2D simulations [Rowland et al. 1995,1996; Fernsler and Rowland, 1996] in the direction of the current flow. One can now see the development of the elves and sprites in the direction transverse to the current. The quasistatic field follows the horizontal motion of the current and causes the sprite to move with it. This could provide an explanation for the observed horizontal motion of sprites. The cg followed by a cc can act to move the sprite that forms directly above the cg to the end of the cc which can be displaced horizontally many km from the cg.

We present six animations showing the time development of the sprites and elves. For the three cases we show a view from above and below.

Simulation Model

The 3D simulation model is basically the same 2D model that has been used in previous studies of sprites and elves [Rowland et al., 1995; Rowland et al., 1996]. The main change is the addition of the third dimension, y.

The model now includes attachment for values of E/N (where E is the electric field and N is the neutral density). The attachment rate and the ionization rate are based upon swarm data [Raizer, 1991, p101]. These rates are also used to change the conductivities as in our 2D model.

The 1st and 2nd positive optical emissions of nitrogen are calculated using the same method as Cho and Rycroft [1998]. This is a rate equation for each band that includes decay and quenching. The 2nd positive band has a decay time of 38 ns. Since the timestep for the simulation is 1 s we do not solve a rate equation but simply balance the emission and loss. The emission rates for the two bands were calculated by Milkh et al. [1995].

The cell size is 4 km by 4 km by 2 km for dx, dy and dz. The number of cells is 120 by 120 by 60. The same low-density, nighttime ionospheric model and neutral density model is used as in earlier studies [Rowland et al., 1996]. The timestep is 1 s.

The lightning discharge is modelled as a moving line of current as used in Fernsler and Rowland [1996]. In the simulation reported here, the velocity is 0.35c. The current is 128 kA. For the vertical discharge between ground level and 10 km and is centered in the x-y plane. The horizontal discharge is at 10 km altitude and stretches from the from the midpoint of the xy plane to 40 km in the x direction.

Animations

In all the animations what is shown is an isosurface for the emission of the first positive (red) band of nitrogen. The surface shown has a value of 4E6 photons/cc-s. It takes approximately 270 ns for the pulse to travel to the bottom of the ionosphere. The animations do not show the first 200 ns after the start of the discharge because there is no significant airglow.

CGA shows a positive cloud-to-ground discharge from above. To provide a sense of how large these objects we show a map of the mid-west and assume the discharge occurs to the west of Chicago. Lake Michigan is roughly 120 -140 km wide. The circular ring is the elf and is formed by the emp of the lightning discharge causing breakdown in the lower D-region. Forming directly above the discharge is the sprite. The elf expands out radially with the emp. As the current continues to flow the electrostatic fields increase so that the sprite can form at lower altitudes where the neutral density is higher. CGB shows the same simulation but viewed from for a clearer view of the sprite.

CCA shows a cloud-to-cloud discharge. Relativistic effects shift the direction of the emp to the right so that the elf forms to the right of the discharge (Fernsler and Rowland, 1996). The emp also reflects from the ground so that the emp at the ionosphere is more spread out in time compared to the vertical discharge. Because of the ground plane the quasistatic field is a quadrupole. In the vertical discharge the quasistatic field is a dipole. In CCB one can see the sprite forms near the directly above the center of the xy plane where the discharge starts but then splits with a second sprite moving to the right with the current. This horizontal motion may explane the observed dancing sprites that are observed to move across the sky.

CGCCA combines the two discharges with the cg followed by the cc. In this simulation as soon as the current in the cg reaches the top of the discharge, the horizontal current begins to flow. The elf that is formed is a combination of the two emps. Because of interference between the pulses, the exact shape depends upon the timing between the discharges. The horizontal current transports the quasistatic dipole away from the cg to the opposite end of the cc discharge. One has a single sprite but located 40 km away from the associated cg discharge. Such displacements have been observed. CGCCB shows the elf and sprite from below.

Conclusions

We present the first three dimensional simulations showing the formation of sprites and elves. For the vertical discharge the results show good agreement with earlier simulations that used an r-z code. This is not surprising since a perfectly vertical discharge gives an obvious axis of symmetry. However, this is the only case that does provide such an axis of symmetry. For all other cases, because of the complicated reflection and interference patterns a three dimensional code is needed to provide an accurate picture of the sprites and elves. This is most evident for the cc discharge and the combined cg-cc discharge. The dynamics observed in these simulations can provide a straight forward explanation for the horizontal motion of sprites as well as their sometimes large horizontal separation from the associated cg discharge.

Acknowledgements

This work is supported by NASA under grant W-18324 and by the Office of Naval Research.

References

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