1. Modeling of Whistler Amplification Anatoly V. Streltsov Thayer School of Engineering, Dartmouth College, Hanover, NH 03755 Thayer School of Engineering, Dartmouth College, Hanover, NH 03755 MURI meeting March 3-6, 2008 Lake Arrowhead, CA

2. Our goal is to model and explain VLF triggering events measured on Siple (this example is courtesy of E. Mishin and A. Gibby)

3. Hybrid Fluid-Particle Model cold fluid electron momentum equation: Maxwell’s equations: hot electrons equations: ;

7. Siple Simulation GeometryBackground

9. 1D FDTD electron MHD model in Cartesian geometry z is pointing along B 0

10. 1D electron MHD model in Dipole geometry

11. 1 KHz and 3 KHz signals

12. Streltsov et al. [2007] 1 KHz, 1.5 KHz and 3 KHz signals

13. Dipole Magnetic Field

18. 1D Whistler Dispersion relation: Parallel group velocity: Traveling time:

23. VLF wave examples from Siple (courtesy E. Mishin and A. Gibby)

24. Fluid + PIC Code Before we run simulations on 512 grid cells with 500 particles per cell or 256,000 particles total. Simulations on the grid with 5000 cells and with 500 particles per cell (2,500,000 particles total) let us to resolve about 10% of L=4.2 magnetic field line.

25. Test of a new Fluid + PIC Code (time dynamic of E y )

26. Summary Our ResultsOur Goal