[Plasma physcis] fluid equation

[good_phy]

Hi i just learned fluide equation form chen textbok

The equation is mn\left[ \frac{\partial u}{\partial t}+(u\cdot\nabla)u\right]=qn(E+u\times B)-\nabla\cdot P - \frac{mn(u-u_{o})}{\tau}. where P is pressure and last term is collision between charged particle and the nutral

I was confusing what is exactly \nabla\cdot P, force from pressure.

I think in strictly saying, in microsopic view, only electromagnetic force is imposing on each particle and pressure

is also E.M force. and E and B in this equation is Macroscopic field ( external field), not

microscopic field.

Is it right?

 

[Andy Resnick]

That equation looks analogous to ma=F, but written in terms of continuum mechanics. The LHS is ma, or m Dv/Dt, where the D/Dt is called the 'total', or 'material' derivative. The RHS is the force, broken down into electromagnetic (qn(E x uxB)), hydrostatic (divergence of the stress tensor) and some other term which I am unfamiliar with. Normally this is a vector equation, and the term 'P' is a stress tensor, not a (pressure) scalar.

The tensor 'P', based on what is written, is the total stress tensor which can usually be decomposed into an isotropic term (the pressure) and a term relating to the viscosity.

If the book insists that 'P' is the pressure, then it's a typo, and that term should be grad(P), not div(P). Also, the text assumes the fluid is inviscid, since there's no viscosity.

 

[jasonRF]

good_phy,

Yes, the E and B in the equation are macroscopic. The divergence of the pressure tensor represents the force associated with the gas pressure; usually in a plasma the pressure tensor is diagonal to a very good approximation (the off-diagonal terms represent viscosity). It is not a scalar since, in general, the temperatures can be different parallel and perpendicular to a magnetic field. Don't worry about these funny cases at first - get used to working with scalar pressure and you will get a good feel for the physics.

Jason

 

[good_phy]

Thank you for sharing me. Then i'll ask you what is the good plasma physics textbook

which is good combination with Chen book?

did you get any idea?

 

[Born2bwire]

Thank you for sharing me. Then i'll ask you what is the good plasma physics textbook

which is good combination with Chen book?

did you get any idea?

Ha, I always end up recommending Francis Chen's book in the first place.

 

[jasonRF]

Thank you for sharing me. Then i'll ask you what is the good plasma physics textbook

which is good combination with Chen book?

did you get any idea?

I will agree with Born2bwire: Chen's book is probably the best place to start. It is clearly written, avoids non-essential mathematics that would add no insight, and contains a ton of physics. If you really want another source, check out the e-book by Fitzpatrick:

http://farside.ph.utexas.edu/teaching/plasma/plasma.html

It is more advanced than Chen but is quite well written and is free! I also like his coverage of waves a little better than Chen's.

Good luck,

Jason

 

[Basu Dev]

Thanks