Computational Astrophysics:Magnetic Fields and Plasma Astrophysics

10-nov-2008

Bookmark!

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

Many other applications

Magnetospheric physics Aurorae

Fusions research Tokamaks (e.g. ITER)

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

Format & schedule

One topic per week 7 topics

Illustrated by three exercises (IDL, Fortran, ..) Monday 13-16 Thursday 9-12 Thursday 13-16

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!

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

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

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

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

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

This weeks topic:

Single particle motion in electro-magnetic fields

Single particle motion in electro-magnetic fields

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 vd = E x B / B2

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 vd = E x B / B2

B&L; Chapter 4, especially Section 4.4

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”

Maxwell’s Equations

Today’s specific topic

Motions in constant E & B fields circular (cyclotron) motion drift acceleration

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

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

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

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

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

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

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

vvv

tvvv

tvvv

tt

Bt

vvv

Ev

d

ts

h

d

hd

dth

'

'

)1/(2

½

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 vd = E x B / B2

Over to the Exercise material!Over to the Exercise material!Over to the Exercise material!Over to the Exercise material!