What prevents high Beta plasma confinement and how to overcome the problems....

[chandrahas]

In order to confine a plasma, the plasma pressure is supposed to be lower than the magnetic pressure. The ratio of the plasma pressure to the magnetic pressure is called beta . Theoretically, the value of beta is supposed to stay below one to confine a plasma, but can get close to it. But in tokamaks or other magnetic confinement devices, these devices can only operate at betas ranging between 1% to 40%.

Whenever I try to find out why, every single website ever points out to plasma instabilities. But that is obvious. I am interested in what causes those instabilities and how we can prevent them. How do we create high beta confinement devices? And thee Internet seems too offer no iinformation at all on this topic.

So, what kind of instabilities are preventing higher beta values? What causes them and how do we prevent them?

Any help would be VERY much appriciated. Thanks

 

[fresh_42]

First hit:
http://iopscience.iop.org/article/10.1088/0032-1028/24/3/002/pdf
And what's wrong with the Wikipedia explanation, which appears you got your figures from?
https://en.wikipedia.org/wiki/Beta_(plasma_physics)#Troyon_beta_limit

These low achievable betas are due to instabilities in the plasma generated through the interaction of the fields and the motion of the particles due to the induced current. As the amount of current is increased in relation to the external field, these instabilities become uncontrollable. In early pinch experiments the current dominated the field components and the kink and sausage instabilities were common, today collectively referred to as "low-n instabilities". As the relative strength of the external magnetic field is increased, these simple instabilities are damped out, but at a critical field other "high-n instabilities" will invariably appear, notably the ballooning mode. For any given reactor design, there is a limit to the beta it can sustain. As beta is a measure of economic merit, a practical reactor must be able to sustain a beta above some critical value, which is calculated to be around 5%.

http://www.sciencedirect.com/science/article/pii/S2468080X16300322

As eventual consequences of the MHD instability, the occurrence of plasma disruptions will determine the operational lifetime of machine components, especially those associated with plasma particle and energy exhaust.

So all in all it looks to me like the answers are:

So, what kind of instabilities are preventing higher beta values?

Statistical peaks and chaotic behavior.

What causes ...

Statistical peaks and chaotic behavior.

... them and how do we prevent them?

With low beta values.

 

[chandrahas]

But what causes these instabilities? Why does a plasma act the way it does? Can this be altered with changes in the configuration of magnetic fields? There seems to be a high beta nuclear reactor being built by Lockheed martin called the Lockheed Martin Compact Fusion Reactor . What reduces the instabilities in the plasma in this case?

 

[the_wolfman]

In order to confine a plasma, the plasma pressure is supposed to be lower than the magnetic pressure. The ratio of the plasma pressure to the magnetic pressure is called beta . Theoretically, the value of beta is supposed to stay below one to confine a plasma, but can get close to it. But in tokamaks or other magnetic confinement devices, these devices can only operate at betas ranging between 1% to 40%.

Whenever I try to find out why, every single website ever points out to plasma instabilities. But that is obvious. I am interested in what causes those instabilities and how we can prevent them. How do we create high beta confinement devices? And thee Internet seems too offer no iinformation at all on this topic.

So, what kind of instabilities are preventing higher beta values? What causes them and how do we prevent them?

Any help would be VERY much appriciated. Thanks

There are a slew of pressure driven instabilities that can limit beta: interchange modes, ballooning modes, infernal modes, etc.

The classic beta limit in tokamaks is called the Troyon limit. The limit is based on a comprehensive set of numerical simulations that considered multiple instabilities. In many cases the beta is limited by a Ballooning-Kink stability boundary. Ballooning modes are local pressure driven instability, but the can be stabilized by increasing the current. However external kink modes are current driven modes that go unstable at too high of a current.

One way to increase beta is to use a shaped plasma. We can usually increase the stability of a plasma by elongating it and adding triangularity. This is why most modern tokamaks have D-shaped cross sections instead of circular cross sections. Other options to increase beta include using active feedback to control these instabilities or applying 3-D fields magnetic fields to increase the threshold for instability.

 

[fresh_42]

But what causes these instabilities? Why does a plasma act the way it does? Can this be altered with changes in the configuration of magnetic fields? There seems to be a high beta nuclear reactor being built by Lockheed martin called the Lockheed Martin Compact Fusion Reactor . What reduces the instabilities in the plasma in this case?

Let's wait and see.

 

[chandrahas]

Can you explain what happens in each of these instabilities? That would be helpfful

 

[mfb]

Lockheed Martin: In early 2013 they announced a turnaround time (build, test, build an improved version) of a year, and a 100 MW prototype within 5 years.
Following that timeline, they should have the previous step now, a multi-MW machine (if operated with DT), at least running on DD fuel. I'm quite sure they would have announced that. The only numbers I see announced that don't refer to the future are those under "Projects" in the Wikipedia article: an electron temperature of 20 eV (not keV!), a tiny ionization fraction, and a tiny pressure (0.03 Pa - the big fusion experiments are at 10⁵ Pa).

They won't have a 100 MW prototype next year. It is not even clear if they will ever have one. No news for years usually means the project hit some obstacle they could not solve. My personal guess would be plasma instabilities.

 

[the_wolfman]

First hit:
http://iopscience.iop.org/article/10.1088/0032-1028/24/3/002/pdf
And what's wrong with the Wikipedia explanation, which appears you got your figures from?
https://en.wikipedia.org/wiki/Beta_(plasma_physics)#Troyon_beta_limit

http://www.sciencedirect.com/science/article/pii/S2468080X16300322So all in all it looks to me like the answers are:

Statistical peaks and chaotic behavior.

Statistical peaks and chaotic behavior.

With low beta values.

I like how you you give chandrahas a hard time for asking an informed and legitimate question regarding fusion research. You then do some quick research on your own and come to the conclusion that the operationally limits are set set by "statistical peaks and chaotic behavior." No only is the description cryptic and uninformative, it is also wrong.

 

[the_wolfman]

There seems to be a high beta nuclear reactor being built by Lockheed martin called the Lockheed Martin Compact Fusion Reactor . What reduces the instabilities in the plasma in this case?

You have to be a little careful when comparing beta values across different concepts. Lockheed Martin is proposing some sort of cusp confinement devices. The magnetic field at the center of a idealized cusp is 0. So here the local beta is infinity large. But really maters in terms of economics is the cost of creating the magnetic fields. Comparing a tokamak beta and a cusp beta is a an apples to oranges comparison.

That being said cusp devices stabilize pressure driven instabilities but having good magnetic curvature. Configurations where the magnetic field is concave towards regions of high pressure tend to be unstable to pressure driven interchange modes, and configurations where the magnetic field is convex towards regions of high pressure are interchange stable. However there are other trade offs. Cusp confinement devices have to deal with end losses. The weak magnetic fields in the core of a cusp means that the ions and electrons have large gyro-radii. This can result in poor confinement.

 

[berkeman]

Can you explain what happens in each of these instabilities? That would be helpfful

Do you have access to a university library? Or a library that could borrow the following book from a university library for you? (look inside at the Table of Contents)...

https://www.amazon.com/dp/3319223089/?tag=pfamazon01-20

Chen is one of the classic textbooks on plasma and controlled fusion. It provides the background to understanding plasma behavior, and has a chapter near the end on stability and the various common instabilities that arise in magnetic confinement. If you can borrow it or read through it at the library, I think you will enjoy it a lot.

 

[chandrahas]

" Configurations where the magnetic field is concave towards regions of high pressure tend to be unstable to pressure driven interchange modes, and configurations where the magnetic field is convex towards regions of high pressure are interchange stable."

When you said the magnetic field being convex towards areas of high pressures, does it mean Increasing the magnetic flux?, and how does it increase beta?

 

[chandrahas]

Can't the ratio still be pretty small? High pressure, even higher magnetic pressure and hence low beta? Low pressure, low magnetic pressure and the same beta?

 

[chandrahas]

I don't have access to any library, but I think I'll buy the book

 

[the_wolfman]

" Configurations where the magnetic field is concave towards regions of high pressure tend to be unstable to pressure driven interchange modes, and configurations where the magnetic field is convex towards regions of high pressure are interchange stable."

When you said the magnetic field being convex towards areas of high pressures, does it mean Increasing the magnetic flux?, and how does it increase beta?

No, I'm not talking about magnetic flux. The magnetic field is a vector field. That means at each point in space the magnetic field has a direction and a magnitude. You can picture a magnetic field by drawing arrows in space, much like a wind map. If you draw a line connection the head of one arrow to the tail of the next arrow you'll get a line that follows the magnetic field. The curvature of these field line partially determines the stability of magnetically confined plasma. If the field lines are concave towards regions of high pressure, then we say this system has bad "magnetic field line" curvature, and it will be more susceptible to interchange instabilities.

The curvature is a property of the shape of the magnetic field. The beta is related to the magnitude of the magnetic field. Therefore increasing or decreasing the curvature does not directly effect the beta. However, changing the curvature can be stabilizing or destabilizing, which would allow you to operate at higher pressures and therefore higher betas.