Tokamak physics

[symplectic_manifold]

I've got an understanding problem. It's about the behaviour of charged particles in plasma inside of a tokamak.

 

It says that a particle in the non-homogeneous magnetic field (toroidal field), moving on the spiral trajectory all along the magnetic field lines, tends to drift downward (for ions) or upward (for electrons), together with the axis of the Larmor-spiral, which makes plasma highly unstable and damages the chamber walls. That's the reason why the second field (poloidal field) is necessary, which is provided by plasma current itself.

 

Which force is it, that causes the particles to drift (toroidal drift) downward/upward?

[UncleAl]

Consider stuff like the Hall effect. If there is an orbit and a field normal to its direction, there will be drift of opposite charges in opposite directions normal to both.

[symplectic_manifold]

The Hall effect is caused by the Lorentz force, but the Lorentz force is directed towards the axis, which is the magnetic field line, when the particle spirals all around it. The centrifugal force balances the Lorentz force out, so that the particle remains on its spiral trajectory with constant cross-section radius.

The force that causes the cross drift must be directed away from the axis.

 

In the source I read they say that it's exactly the force which causes charged particles in a winding conductor drift away from the axis of cylindrical surface (if you imagine the conductor winds around this surface; a solenoid). But I couldn't find anything about this force when I read some info about solenoids. The source doesn't name this force either.

 

In another source it reads that this force comes around because of a gradient of magnetic field intensity in plasma, which seems plausible. But why do the particles move upward/downward and not for example to the right or to the left? There is a gradient in these and other directions too!...because the strenght of magnetic field in a toroid depends on/is antiproportional to its radius from the big axis. (I've just noticed a mistake above...and will correct it; it's all about non-homogeneous magnetic field.)

 

You may also have a look at this: http://www-fusion-magnetique.cea.fr/gb/fusion/physique/trajectoire.htm

[Qfwfq]

After fixing the url I gave it a quick read, I think the key to answering your query is the sentence:

Unfortunately, on a simple circular trajectory of this type, the particle undergoes a slow cross drift, due to the drift gradient of the magnetic field and centrifugal force

which is followed by an explanation of how the solution to the problem works. The difference between vertical and horizontal in the plane perpendicular to the toroidal direction is quite obviously that horizontal is also radial to the torus' main axis, vertical clearly isn't.

 

I agree that Unc hadn't answered your question at all but it wasn't clear from the first post. The link helped more than the extensive use of bold. :doh:

[symplectic_manifold]

So you mean that a particle doesn't receive a pull in the horizontal plane.

 

I couldn't quite get why though. Could you please explane in more detail why it can't drift in the horizontal plane? Which properties of a toroid or magnetic field does it have to do with?

[Qfwfq]

So you mean that a particle doesn't receive a pull in the horizontal plane.

No, it does in the horizontal plane, by centrifugal force, and not in the vertical.

 

Perhaps I wrote a long winding sentence, I'll distill it: The difference is that horizontal is also radial to the torus' main axis, vertical clearly isn't. Centrifugal force is radial, of course.

[ixa]

I've got an understanding problem. It's about the behaviour of charged particles in plasma inside of a tokamak.

 

It says that a particle in the non-homogeneous magnetic field (toroidal field), moving on the spiral trajectory all along the magnetic field lines, tends to drift downward (for ions) or upward (for electrons), together with the axis of the Larmor-spiral, which makes plasma highly unstable and damages the chamber walls. That's the reason why the second field (poloidal field) is necessary, which is provided by plasma current itself.

 

Which force is it, that causes the particles to drift (toroidal drift) downward/upward?

 

 

The drift you mention is usually called the "gradient drift" because it is caused by the gradient of the B-field. In a magnetic field B with a gradient grad B the drift velocity has the form

 

v=(W/qB^3)B x grad B,

where W is the kinetic energy of the particle perpendicular to B, q is the charge of the particle and x denotes the cross product. Now if one has B in the toroidal direction and the gradient in the radial direction, then v is in the up/down direction.

 

The physical reason for the drift is that due to the gradient the magnetic field has a different strength on the different sides of the particle's Larmor circle. Therefore, for example, in the left part of the circle the (Larmor circle's) radius is smaller than on the right part, and over several Larmor periods this causes the gradient drift.