Tokamak ELM Solution? Magnetohydrodynamic stability.

[MSimon]

ITER and large Tokamaks capable of fusion power production should avoid large Edge Localised Modes (ELMs), thought to be triggered by an ideal Magnetohydrodynamic instability due to current at the plasma's separatrix boundary. Unlike analytical work in a cylindrical approximation, numerical work finds the modes are stable. The plasma's separatrix might stabilise modes, but makes analytical and numerical work difficult. We generalise a cylindrical model to toroidal separatrix geometry, finding one parameter D determines stability. The conformal transformation method is generalised to allow non-zero derivatives of a function on a boundary, and calculation of the equilibrium vacuum field allows D to be found analytically. As a boundary more closely approximates a separatrix we find the energy principle indicates instability, but the growth rate asymptotes to zero.

Could one of our physics guys translate this into English and say if it has any application to BFRs?

http://prl.aps.org/accepted/L/1e07bYfdF ... 25d8f3c219

[scareduck]

The word "toroidal" appears in the title, so my inclination is to say "no". Bussard had a deathly fear of doughnuts!

[MSimon]

The word "toroidal" appears in the title, so my inclination is to say "no". Bussard had a deathly fear of doughnuts!

I wasn't thinking of direct application. Maybe the stability criteria would be useful though.

[Art Carlson]

Could one of our physics guys translate this into English and say if it has any application to BFRs?

I don't think I can translate that. I'm not even sure I understand it. I'd say it's another tiny step forward toward understanding tokamaks, that might or might not help us turn them into useful power plants.

Tokamaks, being axially symmetric, don't just have magnetic field lines, they have (until they start jittering) flux surfaces. Some of these flux surfaces are "closed" into a topological torus floating in the machine. Others are "open" in the sense that they penetrate a material wall somewhere. One surface, called the separatrix, is the boundary between these two types of flux surfaces. It looks like a loop that crosses itself (or, if you prefer, a lower case gamma). The point (actually a circle around the axis) where the separatrix crosses/touches itself is called the X-point. Turbulence near the X-point is surprisingly hard to model. These folks think they have found a way to do it a bit better.

[MSimon]

Art,

Thanks!

[chrismb]

As the newly declared "bonafide tokamak evangelist/troll" I guess I am duty-bound to explain this as I read it, as best I can.

In a tokamak there are two modes of operation 'H-mode' and 'L-mode'. L-mode is what conventional MHD/Vlasov/kinetic-theory/&c. ostensibly predicts and is a fairly gentle density gradient off to the 'edge' of the plasma.

Once they started pumping in seriously higher power into the tokamaks with RF and NBI (neutral beam injection) they found something else happened - it worked 'even better' than predicted!! The plasma density takes on an even steeper gradient at the edge.

This is good because it slows the plasma transport out to the edge, i.e. better confinement. But it comes with a heavy penalty - it's a bit like piling sand onto a little cone of sand, or snow on a mountain, you can get a steeper slope than might otherwise naturally occur, but it can all topple off the slope too quick and avalance, bringing the whole thing crashing down.

This is an ELM - plasma that has been too steeply stacked up on the edge of the plasma volume and crashes down, pulling the lot with it.

Why does it form H-modes in the first place? Good question - no real definite understanding of this yet, as far as I am aware. But the future of tokamak rests on it because otherwise the power densities will not stack up to a very useful machine.

That translates the first two and a half sentences for you, with some background.

Art has described the separatrix.

If you follow the 'edge' of the plasma down to the divertor (limiter) you'll find a separatrix there, where there is a convergence of magnetic surfaces around where the plasma comes into contact with the divertor.

What they appear to be saying after that is that they've started with a simple model which approximates this region of the plasma with a single parameter, then they slowly alter that parameter having derived a function of energy to this parameter. This function suggests instabilities that are not otherwise predicted by the usual treatments.

This is my understanding, and is worth what you've paid for it

Hope that helps!!

best regards,

Chris MB.

[The current favoured solution to ELMs is to install RF disruptors in the chamber. They pump some RF into the edge of the plasma, destablise it just a little, and 'ease off' the piled up plasma little by little so that it doesn't crash suddenly.

It's already an issue in JET and JT-60 because the total energy held within the plasmas is high enough that when suddenly dumped into the divertors it sputters huge quantities of materials. In ITER it is virtually a fatal flaw because the divertors will only be able to take this a couple of times before they are eroded. So sorting out 'ELMy' behaviour is a really big deal for the development of ITER - it's one of the potential show-stoppers.]

[Art Carlson]

It's already an issue in JET and JT-60 because the total energy held within the plasmas is high enough that when suddenly dumped into the divertors it sputters huge quantities of materials. In ITER it is virtually a fatal flaw because the divertors will only be able to take this a couple of times before they are eroded. So sorting out 'ELMy' behaviour is a really big deal for the development of ITER - it's one of the potential show-stoppers.

Chris might be confangeling ELMs and disruptions here.

In a disruption, the whole plasma goes south and deposits its energy on the wall in short order. Bad news, both in terms of ablation/melting of the surfaces and in terms of electromagnetic forces. I believe ITER is being designed to survive a handful of full scale disruptions.

In an ELM, only the energy in a layer on the outside of the plasma losses its shit and send its energy to the wall (in this case, mostly to the divertor). I believe a few percent of the total energy is involved, something like tens of times a second. The important point here is that a given amount of power does more damage if it comes in relatively infrequent but big packages. Most reactor scenarios try to live with ELMs, but limit the damage by making the frequency of these events faster.

[chrismb]

All agreed. I was trying to keep the flow of text as simple to be sufficient. ELM's are viewed as potentially seeding global disruptions, they are, themselves, not the disruptions.

Either way you swing it, ELM's need to be managed as they are an intrinsic consequence to the desired 'H-mode' for good confinement, but bad if they subsequently lead to divertor-damaging disruptions.

As far as I have been told, ITER will be built to tolerate very few disruptions due to the volume. Forseen power reactors will not be permitted to tolerate such disruptions, obviously because they will need to run for many years. Poisson will tell you that if there is one event over decades, there are almost equally likely to be several, so the target must be zero permitted disruptions.

[Skipjack]

Aaaaaargh! Please for the sake of those of us that are not worthy of participating in a discussion like this, but would really like to at least have the feeling they understand a fraction of what you are saying, could you guys please refrain from using abbreviations like that?
I think everyone here knows what ITER is and I got the ELM out of the other posts...kinda...
But what the heck is an H- mode? What does RF stand for? What is an RF disruptor (sounds like a sci fi weapon of sorts )
And this sentence almost made me loose my sanity:
"two modes of operation 'H-mode' and 'L-mode'. L-mode is what conventional MHD/Vlasov/kinetic-theory/&c"
Maybe I am the only one here, but when someone says something like that, I will put up a blank stare and nod quietly, then go down into the cellar and whine for a little bit...

[chrismb]

A dead fair comment.

Actually, I was secretly hoping someone would ask what H- and L- modes were, at least, because it proves to show how secretive and difficult people seem to like making modern science.

I was left wondering for some while and I asked straight away like you. I didn't get a straight answer at first. They mean;

H-more = High mode (!!)

L-mode = (you're ahead of me) Low mode

the other TLA's;

MHD = magneto hydrodynamics. This is 14 equations with 14 unknowns constructed to define how an electrically conductive fluid behaves. The others are other theories on how to define such behaviour.

RF = radio frequency. (disruptor - just that it disrupts these edge localised modes.)

best regards,

Chris MB.

PS. I say; always ask if you don't understand. Some folks seem to get annoyed by being asked lots of questions - well, many do when *I* ask!! But I am excessively persistent and I think I might touch on their ignorance sometime to which they do not wish to admit. I never let something go that I don't understand/know. This is the difference between recognising you are ignorant (nothing wrong with that and not backing away) or not knowing something you should know.

[Skipjack]

Thanks Chris!
Thats highly appreciated!
The MHD part I should have been able to guess, there is a hypthetical submarine propulsion system that works that way...
LOL