# Plasma Book recommendation for Introductory Plasma Physics?

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1. Dec 4, 2016

### TJGilb

Hello everybody. I'm interested in starting my learning about plasma physics (depending on how I like it I may choose something within it as my field), but unfortunately my university doesn't offer any undergrad courses in it. My current level includes all maths up to differential equations, vector calculus, and linear algebra. I'm also just finishing up my first quarter of Electrostatics and Magnestism at the Griffiths level and will be continuing that through the end of the academic year.

I'd appreciate any textbook recommendations for self teaching plasma physics (preferably w/solution manuals readily available). Basically, where do you recommend I start? If I'm not mistaken E+M is at least one of the foundations of plasma physics. Are there any others I need to look into? If so any book recommendations for those? Thank you in advance for any assistance.

2. Dec 4, 2016

### Staff: Mentor

Chen's books are pretty standard -- have you looked through them at your university's technical library?

https://www.amazon.com/Introduction...480882919&sr=1-1&keywords=chen+plasma+physics

Last edited by a moderator: May 8, 2017
3. Dec 4, 2016

### TJGilb

I'll take a look at that. Do you think Chen will be a good starting point for me then with my current level of education?

4. Dec 4, 2016

### Staff: Mentor

It may be a bit advanced, but you should be able to tell when you skim through it at your library.

5. Dec 4, 2016

### Staff: Mentor

BTW, you can use the Amazon feature "Look Inside" to look at the Table of Contents and a few pages. Just follow the link I posted and click on the "Look Inside" arrow above the book's picture...

6. Dec 4, 2016

I would recommend taking a look at the Plasma Physics book by Ichimaru. The version I have may be an older one=I googled it and he still has a plasma physics book that is currently in print. The book is somewhat advanced, but I particularly liked his first chapter or two where he explains the linear response theory for the dielectric response and the dielectric function which is the 4-D (3-D plus time) Fourier transform.

There are basically two ways to show linear response for a plasma which are equivalent. Let me summarize them here:

$J_p(x,t)=\iint \sigma(x-x',t-t') \cdot E(x',t') \, d^3x' \, dt'$ which with Fourier transforms becomes $\tilde{J}_p(k,\omega)=\tilde{\sigma}(k,\omega) \cdot \tilde{E}(k,\omega)$. $\\$

Alternatively one can write $P(x,t)=\iint \chi(x-x',t-t') \cdot E(x',t') \, d^3x' \, dt'$ and its F.T. $\tilde{P}(k,\omega)=\tilde{\chi}(k,\omega) \cdot \tilde{E}(k,\omega)$. $\\$

These two forms can be connected by the equation $J_p(x,t)=dP(x,t)/dt$ and/or the continuity equation $\nabla \cdot J_p(x,t)+\frac{\partial{\rho_p}}{\partial{t}}=0$.

Using also $-\nabla \cdot P=\rho_p$, the consistency can be shown. $\\$ I believe Ichimaru has one linear formalism where he uses $D(x,t)=\int \epsilon(x-x',t-t') \cdot E(x',t') \, d^3x' \, dt'$ and its Fourier transform $\tilde{D}(k,\omega)=\tilde{\epsilon}(k,\omega) \cdot \tilde{E}(k,\omega)$ which is also equivalent to the above with $\epsilon(x,t)=1+4 \pi \chi(x,t)$ in cg.s. units. $( D=E+4 \pi P )$. $\\$

The reason I'm showing you this is the dielectric function $\tilde{\epsilon}(k,\omega)$ gets used quite a lot in plasma physics, and Ichimaru is the best source I have run across that explains it in any detail. I've added a couple of details which also might be helpful in reading Ichimaru's first chapter or two.

7. Dec 4, 2016

### TJGilb

Just did that actually. It looks like it will be a challenge, but that's where the fun is. It'll be something to make my way through as I finish the E+M series. BTW, do you know anything regarding the solutions manual (for checking answers when problem solving since this will be self taught)? If I can't get a physical copy I suppose I can download a copy from scribd or someplace.

Edit: Just found they have some answers in the back.

8. Dec 4, 2016

### TJGilb

I'll give him a look too.

9. Dec 4, 2016

### Staff: Mentor

That I don't know. It looks like Appendix D does have answers to some questions, but maybe not to many of them (hard to tell with just the Look Inside feature). If there is an Instructor Solution Manual, that will be only for Instructors. Downloading a copy from some questionable website would be a copyright violation, which we do not support here at the PF.

10. Dec 4, 2016

### TJGilb

Fair enough.

11. Dec 4, 2016

I worked through much of Chen's book many years ago as a senior undergraduate. I think it is quite a good book for getting an introduction, but it is somewhat difficult keeping track of all the different types of plasma oscillations that can occur along with the derivations of each. The linear response and dielectric function of Ichimaru is actually a little easier to digest, but a combination of the two books along with Griffith's E&M should get you a good start on the subject.

12. Dec 4, 2016

### jasonRF

If you haven't learned electromagnetic waves at the level of Griffiths then I think you are not ready to learn plasma physics, in my opinion. Wait until you have worked through Griffiths, then Chen would be a great place to start.

Jason

13. Dec 4, 2016

### jasonRF

Charles LInk, which book by Ichimaru are you referring to? He has written a few: Basic principles of plasma physics, Statistical plasma physics volume 1, and plasma physics: an introduction to the statistical physics of charged particles. Surely it isn't Statistical plasma physics volume 2, as it is on strongly coupled plasmas? Or perhaps it is yet another book?

I did all my grad research in plasma physics and took a handful of grad plasma courses, and while I agree that the linear response formalism should be learned by a specialist in the field I don't believe it is necessary for a beginner at the undergrad level to worry about. This is a matter of taste - perhaps if you indicate exactly which book you mean it would help me understand the recommendation. I think the OPs time would be better spent understanding the basics.

By the way, I took a class partially based on volume 1 of statistical plasma physics (a significant number of our homework problems were from the book) and found it to be a very difficult book to learn from. The pre-requisites were a graduate class on plasma physics at a level significantly higher than Chen, as well as a strong working knowledge of complex analysis. Basic principles of plasma physics is a little better, but still well out of reach for someone who hasn't even learned electromagnetic waves at the level of Griffiths. I am less familiar with the last book I mentioned, as I have only spent an hour or so with it, but I didn't think it was particularly insightful either. If I recall correctly it was mostly a collection of "topics" chapters that would best be read after one already understands plasma physics.
Jason

14. Dec 4, 2016

### TJGilb

You're a plasma physics PhD? I don't suppose you have any good recommendations on grad schools for plasma physics study/research while we're at it?

15. Dec 4, 2016

### jasonRF

It really depends on what exactly you are interested in. For space plasmas (the field I was in), Berkely, University of Iowa, University of Illinois, Dartmouth, Stanford, UCLA, Colorado at Boulder, JUniversity of Washington, University of New Hampshire, Boston College, Boston University, Cornell, etc. all have had good programs in the past. Some schools, like Cornell and Stanford, seem to be letting their groups shrink as folks retire if I recall correctly.

I know little about laboratory and fusion work, but of course Princeton historically has had a very strong program. Wisconsin at Madison also has had a strong program, and I think MIT again has funding for their reactor.

I have been out of the field for 15+ years, and haven't really kept up to date as it doesn't pay my bills (one of the issues I found with plasma when looking for a job in the late 1990s ....). So I'm sure that I have left out many good schools, and possibly included schools that no longer matter.

jason

16. Dec 4, 2016

The book I have by Ichimaru is "Basic Principles of Plasma Physics-A Statistical Approach". And I wasn't suggesting the OP purchase this book=most of it is much too difficult. The first couple of chapters I think are very worthwhile and the 3-D F.T. is just a short extension from the 1-D F.T., but a necessary prerequisite to this is the linear response theory plus Fourier Transforms (using $e^{i \omega t}$) for the continuous case. Perhaps even a different approach for the OP would be recommended: To get a healthy background in linear response theory as well as a complete E&M background before attempting to jump into plasma physics studies. $\\$ To add more detail to this discussion, I found my studies of Chen's book (it was a special research project supervised by a professor when I was a senior and satisfied a course requirement) a very difficult intro to plasma physics. It wasn't until later (well into graduate work and later) that I discovered the first couple of chapters of Ichimaru that answered a couple of questions for me (regarding conductivity $\sigma$ and dielectric constant $\epsilon$ as shown in my above post) that surfaced in our graduate E&M textbook ( we used Classical Electrodynamics by J.D. Jackson). Ichimaru's textbook provides a couple very simple but detailed answers and explanations for the F.T. methodology that is used extensively in J.D. Jackson's textbook in his discussions of E&M wave propagation... $\\$ Eventually I wound up specializing in Optics and Spectroscopy and Infrared Physics, but if I were to do any major efforts with plasma physics, I do think I would review the first couple of chapters of Ichimaru's book and build upon it. Perhaps even the first couple of chapters of Ichimaru is a little too advanced for the level of the OP, but I do recommend the OP takes a good look at it. If nothing else, he might find it very worthwhile for future reference.

Last edited: Dec 4, 2016
17. Dec 5, 2016

### jasonRF

Your experience is enlightening. It sounds like the Fourier analysis and the electromagnetic modeling aspects (lumping effectsof charge into Polarization field, etc) was not sufficiently covered in Chen - I can see that when I leaf through the book now. I had a different background before taking plasma, and then the class didn't follow any book although Chen was one of the recommended books to read on the side.

So by linear response formalism you don't mean correlation functions, the fluctuation dissipation theorem, structure functions, etc. ? That is what I always include (Ichimaru seems to in his "statistical plasma physics" as well). Ichimaru also includes Kronig-Kramers relations as part of this, as do I. I don't think the OP needs any of this a first time through the material.

Perhaps the newer book by Gurnett and Bhattacharjee (I have the 1st edition) would be better for the OP than Chen. The first part of the waves chapter carefully covers Fourier analysis in 4D (3-space and time) and how the waves will be a sum over the roots of the dispersion relation, how we model the plasma with Polarization field, the polarization current, conductivity and dielectric tensors, etc. In general the text is very clear and the associated math is all explained throughout the book; the downside is that it has boring problems. It is a little higher level than Chen, but the first 6 or 7 chapters should be readable with a background of Griffiths. Some sections should be skipped by the OP, though (such as the section on Hamiltonians for single particle motion) but overall it is quite readable. It doesn't include the space-time domain relations of the form $P(x,t)=\iint \chi(x-x',t-t') \cdot E(x',t') \, d^3x' \, dt'$ but that is okay, in my opinion.

Jason

18. Dec 5, 2016

@jasonRF Your last paragraph sounds like a good approach, and I am glad to see you found another textbook for the OP that covers the linear response theory for plasma physics applications. And no, I don't mean correlation functions and fluctuation-dissipation theorem, etc. I have seen these topics in graduate school, but I don't have them at my fingertips, and they are certainly beyond the level of most undergraduates. As much as the 3-D linear response is often not covered in undergraduate coursework, I think that it is simple enough for an upper-level undergraduate to follow, and there is much to gain by the student seeing the details of the dielectric function $\tilde{\epsilon}(k, \omega)$.

Last edited: Dec 5, 2016
19. Dec 5, 2016

### jasonRF

TGJilb,

Sorry for the conversation Charles Link and I had on this thread. At the end of the day, Berkeman's advice really is the best:
So I will echo him: go to your library and look through books to find what is understandable to you. It may be Chen, or Gurnett, or something else entirely.

jason

20. Dec 5, 2016