[Plasma physcis] fluid equation

In summary, the conversation discusses the fluid equation from the Chen textbook and its similarity to the equation ma=F. The equation is broken down into terms representing electromagnetic, hydrostatic, and other forces. The pressure tensor is also mentioned, with clarification that it is usually diagonal in a plasma. The conversation also touches on the topic of finding a good textbook on plasma physics, with Chen's book being highly recommended.
  • #1
good_phy
45
0
Hi i just learned fluide equation form chen textbok

The equation is [tex] 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}[/tex]. where P is pressure and last term is collision between charged particle and the nutral

I was confusing what is exactly [tex]\nabla\cdot P[/tex], 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?
 
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  • #2
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.
 
  • #3
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
 
  • #4
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?
 
  • #5
good_phy said:
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.
 
  • #6
good_phy said:
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
 
  • #7
Thanks
 

1. What is the fluid equation in plasma physics?

The fluid equation in plasma physics is a set of mathematical equations that describe the behavior and evolution of plasma, which is a state of matter consisting of charged particles. It takes into account various physical processes such as plasma motion, electromagnetic fields, and energy transfer.

2. What is the role of fluid equations in understanding plasma behavior?

The fluid equations play a crucial role in understanding the behavior of plasma, as they allow us to make predictions and simulations of how plasma will behave under different conditions. This is important for applications in fusion energy, space physics, and astrophysics.

3. Are the fluid equations accurate in describing plasma behavior?

The fluid equations are accurate in certain cases where the plasma is in a state of equilibrium or is not affected by strong electric and magnetic fields. However, in more complex and dynamic systems, such as in fusion plasmas or high-energy plasmas, the fluid equations may not fully capture the behavior and more advanced models are needed.

4. How are the fluid equations derived?

The fluid equations are derived from the fundamental principles of plasma physics, such as conservation of mass, momentum, and energy. They can also be derived from the kinetic theory of gases, which describes the behavior of individual particles in a plasma. The equations are then simplified and approximated to make them more manageable for practical use.

5. Can the fluid equations be solved analytically?

In most cases, the fluid equations cannot be solved analytically, meaning there is no exact mathematical solution. Instead, numerical methods and computer simulations are used to solve the equations and make predictions about plasma behavior. However, in some simplified cases, analytical solutions can be found, which can provide valuable insights into plasma behavior.

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