1. Kinetic based fluid model. J Egedal, W Fox, N Katz, A Le, A Vrublevskis, J Bonde, A Soane & M Porkolab MIT, PSFC, Cambridge, MA Thanks to: M Øieroset, R Lin, J Drake and W Daughton

2. Basic geometry and assumptions

3. Trapped electron in simulation by W Daughton

4. Electrostatic and Magnetic Trapping Combined magnetic and electrostatic trapping will ensure quasi neutrality Electrostatic & Magnetic Trapping: + + + + V || VV + + + + From Vlasov’s equation df/dt=0

5. Similar  trap observed with Open & closed BCs J Drake W Daughton

6. M. Øieroset et al. Nature 412, (2001) M. Øieroset et al. PRL 89, (2002) Wind spacecraft observations in distant magnetotail, 60R E Measurements within the ion diffusion region reveal: Strong anisotropy in f e. Log(f)  trap ~1kV J. Egedal et al., PRL (2005)

7. Model vs. Numerical Distributions

8. Kinetic Fluid Model    Likewise:

9. From code From (n,B) m i /m e =180 Kinetic Fluid Model

10. From code From (n,B) m i /m e =180 Kinetic Fluid Model

11. From code From (n,B) m i /m e =180 Kinetic Fluid Model

12. Converges with increasing mass ratio From code From (n,B) m i /m e =360

13. Up shot: New fluid model!  Ohm’s law:  Aydemir 1992 Compare to: