# Magnetic confinement and Alfven's theorem

1. Jul 19, 2012

### Boltzmann2012

Hi,

I was reading about Earnshaw's theorem and how it explains the non availability of electrostatic confinement of plasma, but does Alfven's theorem really prove the fact that magnetic confinement of hot plasma is achievable?

Regards,

Boltzmann

2. Jul 21, 2012

### sankalpmittal

3. Jul 21, 2012

### Boltzmann2012

Hey sankalpmittal,
I was actually reading Griffiths in which he states that electric confinement is not possible since a stable eq condition cannot be achieved by a space distribution of charges. According to alfven's theorem, the magnetic flux gets 'frozen' within the plasma/liquid and hence it acquires some magnetic character. Using this it can be confined.

Please tell me if im wrong. I am a beginner.

Thanks for your help and time,

Regards,

Boltzmann

4. Jul 22, 2012

### sankalpmittal

Yeah , you're right. Sorry about that huh. I kinda blundered it.

Ok , so Alfven's theorem states that in a perfectly conducting fluid , magnetic lines move within the fluids and at times (for example in sun which is but a very hot and churning ball of plasma) and when two bobs of plasma are connected by magnetic field at time , then they are also connected by it at all other times , for when fluid is very hot , the electrons from it are stripped off and hence its conducting , and thus the bobs of plasma are always being interacted by magnetic fields and at times , the magnetic fields are distorted and hence are frozen into the plasma. So its also known as "frozen flux theorem". But magnetic "topology" is always preserved.

So yes , the hot plasma can be confined and in other words magnetic confinement of hot plasma is achievable.

This takes place rarely (I think) when plasma isn't warm. (In my opinion its not possible in this case.)

But yes , you're right. Magnetic confinement of hot plasma is achievable by Alfven's theorem.

Hope this helps. :)

5. Jul 22, 2012

### Boltzmann2012

Thank you very much, sankalpmittal.

Best Wishes and Regards,

Boltzmann