Preparing for Plasma Physics (Jackson)

[dRic2]

Hi, I've posted here several time because you all gave me very helpful suggestions. Let me recap briefly my situation. I apologize for the very long post.

I have BS in chemical engineering but now I'm going through a MS degree in nuclear engineering. Although - given my background - I should have gone for nuclear plants management, I decided to switch to the "theoretical side" of nuclear engineering (reactor physics, plasma for fusion applications and so on...). Although I'm struggling a lot I managed to get very good grades (also thanks to you ) in mathematical methods and reactor physics courses.

My main problem is the lack of preparation in EM. When I started my MS degree (last September) the only EM I knew was "high-school" EM (I didn't even knew maxwell equations). I went through Griffiths' book during this seven month and I'm currently at chapter 9 (waves). I forced myself to do 10/15 exercises per chapter (I know the number is not much, but I'm self studying while attending other courses... time's limited ). I loved Griffiths' book, but now that I know something (not much, but I definitely feel more confident), Griffiths' book's starting to feel a bit "sloppy". My point is that, even though I do not know much of EM and I have little experience in solving EM boundary conditions problems, I know a little bit more of math: in my BS in chemE I've run into Navier-Stocks equations, conservation laws, and during last semester I ran into more advanced math like distributions, transforms, orthogonal expansions in Hilbert spaces, Green's functions ecc...

That's why I picked up Jackson. Next semester I'll attend a course in plasma physics and I know our professor will use Jackson's book a lot. I read a few random pages and I really enjoyed the insight he gives, but I also find some exercises very time consuming. I know exercises are very important, but I do not have the time to do 10/15 exercise per chapter as I did with Griffiths. I'd like to know if one can "go on" without doing a lot of exercises or not. One more thing: I suck at computing strange electric and magnetic fields, but I also hope to learn to do it during the course... I mean: to what extent do I have to know EM before takin the course?

All the topics are listed here (the evaluation is an oral exam at the end of the semester):

• Recalls of electromagnetism. Maxwell's equations. Lorentz force. Electrodynamic potentials. Gauge invariance. Lorenz and Coulomb gauges. Systems of Units in Electromagnetism: SI and gauss.
• Electrodynamics of continuous media. Poynting's theorem, conservation of energy in linear dispersive media. Anti-hermitian component of the dielectric tensor of a medium and its absorption properties of electromagnetic energy. Conservation of energy in the presence of spatial dispersion. Propagation of electromagnetic waves in uniform and dispersive media: linear theory.
• Fundamental plasma parameters. Shielding of the electric charge and the Debye length. Thermodynamic properties of a classical plasma. Plasma oscillations and plasma frequency. Electrical conductivity of a plasma. Conditions of "existence" of a plasma.
• Guiding center theory. Dynamics of charged particles in constant, uniform, external electric and magnetic fields. Motion in slowly varying fields: the guiding center approximation. Drift motions. Mirror effect.
• Methods for the description of a plasma. Microscopic description of a plasma: Klimontovich equation, kinetic theory, Vlasov equation. Macroscopic descriptions of a plasma: equations for the moments and multiple fluids model. Single fluid approach: Magnetohydrodynamics (MHD). Limits of validity.
• Waves in a plasma I. Macroscopic approach: waves in a cold plasma, waves in a hot plasma, waves in the presence of an external magnetic field. Kinetic approach: collisionless absorption of electrostatic waves, Landau damping. Physical interpretation of the resonant wave-plasma interaction.
• Emission of electromagnetic radiation in a plasma I. Results of the general theory of the radiation emission by moving charged particles. EM emission in a plasma: Cyclotron and Bremsstrahlung radiation.
• Controlled thermonuclear fusion. Introduction. Nuclear fusion reactions, thermonuclear plasmas.
• Waves in a Plasma II. General aspects of the kinetic study of collective modes in a plasma. Waves in the presence of an external magnetic field in the kinetic approach: Cyclotron resonances, their physical interpretation and main properties. Introduction to the study of collective modes in a nonlinear plasma: relativistic plasma models, wave propagation of arbitrary amplitude in the cold plasma approximation.
• Laser-plasma interaction. Introduction. Interaction between electromagnetic waves and underdense/overdense plasmas. Ponderomotive force, excitation of waves in plasmas, wave-breaking. Parametric instabilities. Applications of the superintense laser-plasma interaction.
• Physics of magnetically confined plasmas. Dynamics of charged particles in toroidal and “Tokamak” magnetic configurations: consequences on the system’s physical behavior. 1D MHD equilibrium and stability: theta-pinch, Z-pinch, screw-pinch. 2D MHD equilibria and stability: balance of toroidal forces, Grad-Shafranov equation, Solove'v equilibria, stability criteria. Fundamental properties of the plasma edge region in magnetically confined systems: limiters, divertor, scrape-off layer.
• Emission of electromagnetic radiation in a plasma II. General theory of the radiation emission by charged particles in motion and emission of EM radiation in a plasma: Cyclotron and Bremsstrahlung emission.
• Collisions in a plasma. General properties of the collisional term in the kinetic description. Coulomb collisions. Characteristic collision times. Collisional transmission of energy between electrons and ions. Descriptions of the collision integral: Balescu-Lenard, Landau and Fokker-Planck equations.
• Controlled thermonuclear fusion. Introduction. Lawson criteria and ignition conditions. Approaches to fusion: magnetic (MCF) and inertial (ICF) confinement. General scheme of a fusion power plant. Energy balances. Fundamental physical properties of magnetically/intertially confined thermonuclear plasmas. Main scientific and technological issues of fusion systems. Current state of research in MCF and ICF.

Really thanks in advanced for any suggestions.

 

[jasonRF]

I am an electrical engineer, but specialized in plasma physics in graduate school. Your upcoming plasma physics course should be fun, but a good background in EM will be essential.

By the way, what are the prerequisites for the course? For now my answer will assume that graduate EM is not a prerequisite, and that your class will not require special relativity.

My recommendation is to first make sure you really understand all of the sections of Griffith's book that cover waves and radiation. This would include solving problems. If you have a strong understanding of Griffiths then you are probably in pretty good shape to tackle a first course in plasma physics. Only after you have done this should you move on to Jackson.

In Jackson's book, I would not spend too much time on statics (deriving Greens functions, etc) but would focus more on the chapters on conservation theorems (energy, momentum), waves, and electrodynamics of continuous media. That should be plenty to keep you busy until your class starts. If you have more time, consider the plasma physics chapter, and perhaps the chapters on radiaition and dynamics of charges particles (but if I recall correctly those require you to know special relativity).

If you will be taking additional plasma physics courses, you may want to actually take a graduate EM course at the same time you are taking your first plasma physics class.

Have fun!

Jason

 

[dRic2]

Thanks for the help!

My recommendation is to first make sure you really understand all of the sections of Griffith's book that cover waves and radiation.

I thought to study them directly on Jackson... Do you think it is too hard?

If you will be taking additional plasma physics courses, you may want to actually take a graduate EM course at the same time you are taking your first plasma physics class.

I do not know jet. My university does not offer graduate EM course because only engineering disciplines are taught. But literally next to may university there is an other university where I could attend a very good graduate EM course (but I could only attend lessons and not enroll). Do you think it would be worth it ?

 

[jasonRF]

I thought to study them directly on Jackson... Do you think it is too hard?

For radiation? Absolutely! For waves and wave propagation? Maybe. My main concern is that if you jump to Jackson and find that you don't have time to do many problems, that you will not actually be learning much. If your choices are to study Griffiths and actually do a lot of problems, or to study Jackson and do very few problems, then you should chose Griffiths. If you have not solved problems at least at the level of Griffiths then you may have significant difficulties in your plasma physics class. I went to grad school with a fellow that had not learned waves and radiation at that level and the first plasma physics course was very rough for him.

I do not know jet. My university does not offer graduate EM course because only engineering disciplines are taught. But literally next to may university there is an other university where I could attend a very good graduate EM course (but I could only attend lessons and not enroll). Do you think it would be worth it ?

Since your school doesn't offer that class, you will not need to learn it. You may be better off concentrating on the courses you are taking for your program and do the best you can in those.

Once you are done with Griffiths, if you decide to go higher you may want to consider the book by Franklin since you are self-studying
https://www.amazon.com/dp/0486813711/?tag=pfamazon01-20
a book of solved problems is also available
https://www.amazon.com/dp/048681372X/?tag=pfamazon01-20
Franklin is at a similar level as Jackson, but to me seems better written and easier to learn from.

 

[dRic2]

Thank you very much for all the suggestions!