1. Computational Astrophysics: Magnetic Fields and Plasma Astrophysics 10-nov-2008

2. Bookmark!

3. Topics this is crucial for in astrophysics Solar physics The Sun as an astrophysics laboratory The solar corona plasma heating particle acceleration Gamma Ray Bursts Collisionless shocks particle acceleration radiation diagnostics

4. Many other applications Magnetospheric physics Aurorae Fusions research Tokamaks (e.g. ITER)

5. Plans for today, and for the course Discuss what format / schedule to use Open to suggestions & changes!! Introduction to the general topics Basic plasma concepts Charged particle motion Today’s material; derivations etc. Today exercise

6. Format & schedule One topic per week 7 topics Illustrated by three exercises (IDL, Fortran,..) Monday 13-16 Thursday 9-12 Thursday 13-16

7. About programming: Tools and Languages This is NOT a programming course! nevertheless you may learn a thing or two we use IDL, C and Fortran, but … You do NOT need to know IDL, C or Fortran in advance much will be provided as “ready to run & modify” which is actually a very efficient way to learn!

8. Suggested format each ½-day Short introduction & discussion (20-40 min) Look for each time: What are the central points? Short reading break (~30 min) Sometimes Exercise (2-3 hours) Starting often with an example of a working tool Play with it, and change it Draw conclusions Sometimes: produce something to upload to the web

9. Suggested mode of working Instructions are often brief Questions should be asked, in class (loudly!) Answers should be questioned, if unclear! Consult the books during the exercises! Use pen and paper for derivations, sketches, …! turn off / turn away from the screen sometimes! Hints and partial solutions may be given Often on screen / blackboard Sometimes under “Discussions” on the web

10. We collaborate! Talking about methods and solutions everyone should have a good overview before we turn to the screens! Passing on hints possibly via the SIS “forum” – Q & A Helping out please talk to and help others on the way

11. Books: Get Boyd & Sanderson – you’re going to need it! Also, for complementary discussions: “Plasma Physics for Astrophysics”, Kulsrud (K) “Principles of Magnetohydrodynamics”, Goedbloed & Poedts (G&P) For computational procedures: “Plasma Physics via Computer Simulations”, Birdsall & Langdon (B&L) These (K+G&P+B&L) will be made available for circulation during the exercises

12. Central issues of the course Charged particle motion in given E & B.. including how to treat this numerically Plasma (collective) behavior Collisionless With collisions Magneto-hydrodynamics (MHD) Fluid description of plasma

13. This weeks topic: Single particle motion in electro-magnetic fields

14. What are the central points today? Basic concepts Debye length Plasma parameter, plasma oscillations Larmor radius & frequency (= gyro-frequency) Cyclotron motion gyro- (cyclotron-) frequency Ω = q B / m gyro- (cyclotron-) radius R = v / Ω E x B drift v d = E x B / B 2

15. Litterature Basic concepts: B&S; Chapter 1 Debye length Plasma parameter Larmor radius & frequency (= gyro-frequency) Cyclotron motion: B&S; Chapter 2 gyro- (cyclotron-) frequency Ω = q B / m gyro- (cyclotron-) radius R = v / Ω E x B drift v d = E x B / B 2 B&L; Chapter 4, especially Section 4.4

16. Basic Concepts Maxwell’s equation Continuum assumption Electric current density Electric charge density Equations of motion For individual particles For continua (sometimes) Velocity ”Temperature” and ”pressure”

17. Maxwell’s Equations

18. Today’s specific topic Motions in constant E & B fields circular (cyclotron) motion drift acceleration

19. [from “Principles of MHD”, lecture notes by Goedbloed, Poedts & Keppens]

22. About today’s tools: IDL widgets and 3-D graphics Widgets buttons, sliders, graphics windows application control event- (mouse-) driven programming Object graphics 3-D objects rotation zoom pan

23. Material that you may want to print experiment1a.pro IDL widget programming example to be re-used – slightly modified, also in 1b and 1c (Thursday) graphics.pro object graphics example to be re-used as is; but take a look at it (and be amazed!) controls.pro event handling; particle animation, etc. to be re-used as is, later possibly slightly enhanced

24. The main things to achieve from the exercise today motion_constant.pro implementing Eqs. (10)-(13) in B&L Section 4.4 Understanding! cyclotron motion (frequency depends only on B!) E x B drift (what causes it – how does it work?).. and a bit of IDL widgets and object graphics

25. Series of (magic) steps: Invented a long time ago! Very nice properties: conserves integrals of motion – radii of circular motions, etc. Particle motion procedure from Birdsall & Langdon

26. Central points today Fundamentals Maxwell’s equations Equations of motion Basic concepts Debye length Plasma parameter, plasma oscillations Larmor radius & frequency (= gyro-frequency) Cyclotron motion gyro- (cyclotron-) frequency Ω = q B / m gyro- (cyclotron-) radius R = v / Ω E x B drift v d = E x B / B 2

27. Over to the Exercise material!