Plasma in a Vacuum Reacting to Magnetic Field

[bueller11]

So, assume you have a plasma in a vacuum made of an even distribution of 50% electrons and 50% protons all flowing in one direction with low collision frequency. Then you suddenly turn on an external magnetic field and watch what happens. How will the plasma react?

Will the magnetic field lines cause currents that will cancel the magnetic field out within the plasma? Will the electrons and protons start going in circles in opposite directions? Will the plasma redistribute into currents that align with the magnetic field? Will something else happen?

 

[Chandra Prayaga]

Why do you feel that the field lines will cause currents that will cancel out the field within the plasma?

 

[bueller11]

Because it seems like the plasma might try to expel the external magnetic field from itself, causing currents to counter the external field and keep whatever field it initially had, internally.

Edit: I'm really confused on what will happen, because it seems like it could do so many things and none stick out in my mind as what will actually happen.

 

[Chandra Prayaga]

That is why we should attack the questions one after the other. First, what happens to a proton which is moving with some velocity, and you suddenly turn on a magnetic field?
If we answer this question clearly, the rest of the things will follow. How much have you learned about motion of a charged particle in a magnetic field?

 

[bueller11]

It could experience an additional Lorentz force, q*(v x B) (additional to the forces already experienced by particle-particle interactions)

Are you implying that the electrons and protons will start going in circles in opposite directions?

 

[Chandra Prayaga]

If you try to include particle - particle interactions, the problem becomes intractable by any elementary methods. Your assumption of low collision frequency also implies low density, and I would neglect the inter-particle interaction, at least until we understand the rest of it.

Circular motion in a magnetic field is a very special case, where the velocity is perpendicular to the field. In general, the motion is helical.

 

[bueller11]

Ok, so helical - specifically the axis of the helix (does that make sense?) would be in the direction of the magnetic field? Does that likewise mean the plasma would separate out (into an electron cloud and a proton cloud) or does the plasma try to maintain it's composition?

 

[Chandra Prayaga]

The magnetic field is indeed the axis of the helix. The radius of the orbit of a charge in a magnetic field is R = mv_⊥/qB, where v_⊥ is the component of the velocity perpendicular to the magnetic field. So a lot of the details you are asking for depends on the velocity distribution of the charges. It is certainly not true that all the particles have the same velocity.

 

[bueller11]

Thanks for answering my questions!

Ok, so particle velocity distributions I don't know a lot about either... Plasma follows a Maxwell distribution, though, right? Assuming that, would the plasma somehow stay a mass of protons and electrons or would it eventually split out into two separate groups, ignoring particle-particle interactions? In other words, is there anything happening in a plasma that would mean the particles would try to rearrange themselves and stay a unit or would the magnetic field ultimately rip the plasma apart?

 

[Chandra Prayaga]

I don't see the ripping apart happening. It is the electric field that tends to rip opposite charges apart.

 

[bueller11]

And in an evenly distributed plasma of an equal number of positive and negative charges, the E-field should essentially be 0 everywhere?

 

[Chandra Prayaga]

Well, the average E field, averaged over a reasonably large region, is zero. If you measure the E field close to any of the particles, certainly you will see a large field

 

[bueller11]

Got it. Thanks for your help!