1. Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 11-dec-2008

2. Topics this week B&S Chapter 8 = Collisional Kinetic Theory Plasma transport coefficients Electrical conductivity Diffusion coefficient Heat conductivity Viscosity Ambipolar diffusion / ambipolar drift Two-fluid (ions & electrons) Three-fluid (neutral, ions & electrons)  Most astrophysics MHD-applications depend on this!!

3. Topic & tasks today Ambipolar diffusion Section 8.2.1 in B&S Solve and turn-in Exercise 8.2 in B&S Easy! Solve and turn-in one or more earlier assignments Ask for help & discussions

4. Ambipolar diffusion; ions and electrons Electrons and ions diffuse together Because they need to keep charge neutrality Since electrons otherwise are faster, they need to ”wait” for the ions Initial charge separation  electric field that accelerates the ions and decelerates the electrons Diffusion determined by the slower ions

5. Ambipolar drift; neutrals, ions & electrons Many astrophysical examples E.g. 10,000 times more neutrals than ions in the upper solar photosphere Electrons and ions still diffuse together Because they need to keep charge neutrality Almost all the pressure (gradient) from the neutral Collisions couple to the ions

6. Ambipolar drift Most of the electric current is carried by the electrons They have a higher mobility So, most of the Lorentz force acts on the electrons The drag the ions along via a charge separation electric field The ions drag the neutrals along – minus a drift – through ion-neutral collisions

7. Ambipolar drift speed How fast is that (ambi-polar) drift speed? We know the force per particle And the collision frequency Force  acceleration Stopped after a collision time Speed is (½) the acceleration times the acc. time

8. Ambipolar diffusion

9. .. continued

10. Exercises 5b = Exercise 8.2 in B&S Easy! 5c = Ambipolar drift in sunspot Also an illustration of scaling to/from physical units to/from non-dimensional units NOT a turn-in exercise! Catch up on earlier turn-in exercises!