tokamak question

Discuss how polywell fusion works; share theoretical questions and answers.

Moderators: tonybarry, MSimon

ohiovr
Posts: 431
Joined: Mon Mar 02, 2009 6:36 pm
Contact:

tokamak question

Post by ohiovr »

Would tokamac be any more stable if it were an infinitely long solenoid? Meaning, is the tokamak unstable partially because

the magnetic field on the outer part of the torus is weaker than the inner part? Or this not matter at all? Sorry if this is a bit too absurd for now...

asdfuogh
Posts: 77
Joined: Wed Jan 23, 2013 6:58 am
Location: California

Re: tokamak question

Post by asdfuogh »

It's not the only instability, but as a practical matter, how much would it cost to produce such a magnetic field? Not worth considering if you are looking for an economically viable fusion reactor.

D Tibbets
Posts: 2775
Joined: Thu Jun 26, 2008 6:52 am

Re: tokamak question

Post by D Tibbets »

I think the length of travel of a fuel ion before it participates in a fusion reaction in a low Beta Tokamak is several hundred thousand miles. That would make for a fairly long cylinder 8) . Compare this to a Polywell, where the fuel ion needs to travel (be contained) for ~ 10 miles of travel. This back and forth and random motion is accomplished in perhaps ~ 10,000 passes across the Polywell space. The difference is due to the higher density achievable in a Polywell. Having a torus- circular race track has some consequences for cyclotron / mass spectroscopy effects where the faster / heavier ions tend to be thrown towards the outside of the torus. This has to be compensated for in some manner. I think a stellarator handles this with complex twisted magnetic fields. I don't know how Tokamaks handle this.

As for macro instabilities, edge instabilities, MHD instabilities, or what ever name is used, I think even a straight cylinder is susceptible to these effects. To avoid them complex interventions are needed, or more simply if the fields are at least mildly convex towards the plasma always. This is the case in the Polywell. And this also implies that there have to be cusps, which changes the priorities and dynamics considerably compared to a closed magnetic system like a Tokamak (there are no cusps in a torus). This would seem to have distinct confinement advantages, but oh :!: , those edge instabilities, not to mention ion ExB diffusion issues (both increase exponentially as the density is increased).

Dan Tibbets
To error is human... and I'm very human.

Ivy Matt
Posts: 711
Joined: Sat May 01, 2010 6:43 am

Re: tokamak question

Post by Ivy Matt »

I think a stellarator handles this with complex twisted magnetic fields. I don't know how Tokamaks handle this.
I thought tokamaks handled it by being made ever larger.
Temperature, density, confinement time: pick any two.

hanelyp
Posts: 2261
Joined: Fri Oct 26, 2007 8:50 pm

Re: tokamak question

Post by hanelyp »

D Tibbets wrote:I think a stellarator handles this with complex twisted magnetic fields. I don't know how Tokamaks handle this.
A stellarator twists the toroidal magnetic field using complex magnet shapes. A tokomak has a large toroidal current through the plasma producing a poloidal magnetic field, giving a twist to the net magnetic field. I understand the purpose of this twist is to deal with poleward cross field drift from the radial field gradient separating ions and electrons. A charged particle in a gradient magnetic field will have a larger cyclotron radius on one side and smaller on another.
The daylight is uncomfortably bright for eyes so long in the dark.

D Tibbets
Posts: 2775
Joined: Thu Jun 26, 2008 6:52 am

Re: tokamak question

Post by D Tibbets »

Ivy Matt wrote:
I think a stellarator handles this with complex twisted magnetic fields. I don't know how Tokamaks handle this.
I thought tokamaks handled it by being made ever larger.
I think the large size is mostly due to ion ExB drift issues. The ions will diffuse through the magnetic field at a certain rate given a certain temperature and pressure. For this diffusion to be slow enough for adequate containment time, the distance traveled perpendicular to the confining B fields needs to be
large enough. The Polywell mostly avoids this limitation due to the non neutral plasma- negative potential well, that actually confines the ions. There is no magnetic field within the Wiffleball borders, so no ExB diffusion of most of the ions (if not upscattered). The electrons do undergo expected ExB diffusion losses, but with a gyroradius ~ 60 times less than a Deuterium ion, the diffusion is ~ 60 times slower. Much smaller sizes can be used.

At the same temperature/ speed, as the radius of a torus is increased, the centrifugal force lessens, so larger size would seem to help in this regard also. I have not heard that this is the size limiting factor in a Tokamak though- ExB diffusion is. Unless I am miss informed (not impossible) the size may be a primary factor in controlling centrifugal forces, but the size necessary to limit ExB losses may already accommodate the centrifugal effect limits.

Or, as the intervening post states- huh?
Actually, it makes some tentative sense. Centrifugal force will throw heavier particles outward more, while a gradient B field might have an opposite effect on ExB diffusion, balancing out. Throw in different gyro radii for ions and electrons may add some mild charge separation effects. Combined this may be self stabilizing for centrifugal effects considerations.

Dan Tibbets
To error is human... and I'm very human.

ohiovr
Posts: 431
Joined: Mon Mar 02, 2009 6:36 pm
Contact:

Re: tokamak question

Post by ohiovr »

D Tibbets wrote:
Ivy Matt wrote:
I think a stellarator handles this with complex twisted magnetic fields. I don't know how Tokamaks handle this.
I thought tokamaks handled it by being made ever larger.
I think the large size is mostly due to ion ExB drift issues. The ions will diffuse through the magnetic field at a certain rate given a certain temperature and pressure. For this diffusion to be slow enough for adequate containment time, the distance traveled perpendicular to the confining B fields needs to be
large enough. The Polywell mostly avoids this limitation due to the non neutral plasma- negative potential well, that actually confines the ions. There is no magnetic field within the Wiffleball borders, so no ExB diffusion of most of the ions (if not upscattered). The electrons do undergo expected ExB diffusion losses, but with a gyroradius ~ 60 times less than a Deuterium ion, the diffusion is ~ 60 times slower. Much smaller sizes can be used.

At the same temperature/ speed, as the radius of a torus is increased, the centrifugal force lessens, so larger size would seem to help in this regard also. I have not heard that this is the size limiting factor in a Tokamak though- ExB diffusion is. Unless I am miss informed (not impossible) the size may be a primary factor in controlling centrifugal forces, but the size necessary to limit ExB losses may already accommodate the centrifugal effect limits.

Or, as the intervening post states- huh?
Actually, it makes some tentative sense. Centrifugal force will throw heavier particles outward more, while a gradient B field might have an opposite effect on ExB diffusion, balancing out. Throw in different gyro radii for ions and electrons may add some mild charge separation effects. Combined this may be self stabilizing for centrifugal effects considerations.

Dan Tibbets
I hadn't considered the Centrifugal force of the plasma.. essentially it pushes the plasma to the weakest parts of the field...

can we estimate how much centrifugal force there is in this case?

D Tibbets
Posts: 2775
Joined: Thu Jun 26, 2008 6:52 am

Re: tokamak question

Post by D Tibbets »

Centrifugal force is a consideration, but based on this abstract at least, it apparently is not a major concern in a typical tokamak.

http://link.springer.com/article/10.1134/1.1545585

Dan Tibbets
To error is human... and I'm very human.

ohiovr
Posts: 431
Joined: Mon Mar 02, 2009 6:36 pm
Contact:

Re: tokamak question

Post by ohiovr »

D Tibbets wrote:Centrifugal force is a consideration, but based on this abstract at least, it apparently is not a major concern in a typical tokamak.

http://link.springer.com/article/10.1134/1.1545585

Dan Tibbets
thanks Dan.

I still don't understand yet why the tokamak has to be so huge though. Could the size be decreased if the miracle 100 tesla magnet came along?

hanelyp
Posts: 2261
Joined: Fri Oct 26, 2007 8:50 pm

Re: tokamak question

Post by hanelyp »

ohiovr wrote:I still don't understand yet why the tokamak has to be so huge though. Could the size be decreased if the miracle 100 tesla magnet came along?
My understanding is it has to do with turbulence, related to unfavorable magnetic intensity profiles, and more severe as beta climbs. Without turbulence plasma leakage would be dominated by slower cross field diffusion.
The daylight is uncomfortably bright for eyes so long in the dark.

ohiovr
Posts: 431
Joined: Mon Mar 02, 2009 6:36 pm
Contact:

Re: tokamak question

Post by ohiovr »

hanelyp wrote:
ohiovr wrote:I still don't understand yet why the tokamak has to be so huge though. Could the size be decreased if the miracle 100 tesla magnet came along?
My understanding is it has to do with turbulence, related to unfavorable magnetic intensity profiles, and more severe as beta climbs. Without turbulence plasma leakage would be dominated by slower cross field diffusion.
Is there a plasma formation that exists in nature that is similar to a rotating tokamac plasma?

Or any gaseous motion I will add...

D Tibbets
Posts: 2775
Joined: Thu Jun 26, 2008 6:52 am

Re: tokamak question

Post by D Tibbets »

Natural torus shaped (and rotating?) plasma. Perhaps. Some ball lightning has appears as a torus. smoke rings in fires, and atom bombs. Some magnetic loops on the sun come close to a closed torus. I don't know how similar the magnetic fields would be.

Dan Tibbets
To error is human... and I'm very human.

D Tibbets
Posts: 2775
Joined: Thu Jun 26, 2008 6:52 am

Re: tokamak question

Post by D Tibbets »

hanelyp wrote:
ohiovr wrote:I still don't understand yet why the tokamak has to be so huge though. Could the size be decreased if the miracle 100 tesla magnet came along?
My understanding is it has to do with turbulence, related to unfavorable magnetic intensity profiles, and more severe as beta climbs. Without turbulence plasma leakage would be dominated by slower cross field diffusion.
Turbulence, especially turbueance on the plasma edge - edge instabilities, MHD instabilities, Macro instabilities are certainly a problem. A large size with a greater radius of curvature may not develope the turbulane as fast(?). I do not know if this is what limits the Tokamak to large sizes though. Bussard in his Google talk blamed the tokamak large size on ExB diffusion through the magnetic field. Specifically ion ExB diffusion/ cross field transport. At the same density and temperature and B field strength it takes the ions longer to reach the walls if there is a greater distance. Something like confinement time = 1/ion gyro radius * collision frequency. Both the size and density figure into the picture. In the polywell, only electrons are contained magnetically and their gyro radius is at least 60 times smaller, thus everything else being equal, the Polywell could be 60 times smaller in diameter- and have the same cross field ExB loss rates.

Increaseing the B field would shorten the gyro radius and lengthen the time for cross field transport.in the same diameter machine. But with increased B field strength coupled to smaller radii of curvature/ and or greater density the edge instabilities would worsen. If they are not alread dominate they will become so.

A tokamak could be made smaller with stronger B fields from a ExB loss standpoint, edge instabilities may be more problamatic. Keep in mind that if the volume of reactive plasma in a reactor is reduced the fusion rate will decrease proportionately, unless increased density is used to compensate. It is a vicious circle.

Dan Tibbets
To error is human... and I'm very human.

ohiovr
Posts: 431
Joined: Mon Mar 02, 2009 6:36 pm
Contact:

Re: tokamak question

Post by ohiovr »

D Tibbets wrote:Natural torus shaped (and rotating?) plasma. Perhaps. Some ball lightning has appears as a torus. smoke rings in fires, and atom bombs. Some magnetic loops on the sun come close to a closed torus. I don't know how similar the magnetic fields would be.

Dan Tibbets
Although if you notice, those examples all rotate around the cross section of the swept circle, not around the long way as with a tokamak.

choff
Posts: 2447
Joined: Thu Nov 08, 2007 5:02 am
Location: Vancouver, Canada

Re: tokamak question

Post by choff »

Bussard's Google talk had a good explanation of why Tokamak's had to be that big. He said they constrain the movement of hot plasma towards the walls but do not actually confine the plasma. He described it as a random walk process where each particle collision caused the particles to spiral away in the direction of the walls. Since the plasma has a Maxwellian energy distribution only a small portion is ever at fusion temperature. To get enough at the right temperature and pressure without having it all spiral out toward the wall from collision the machine has to be huge. The Stellarator cheats with geometry by sending the spiraling out plasma particles down a Mobius loop to keep them away from the walls much longer.
CHoff

Post Reply