# Mechanical loads on ITER's magnetic coils

cmb
Is there a prediction/paper/etc. about the mechanical loads that will be reacted onto ITER's magnetic coils?

The reason I ask is a simple calculation. My understanding of the numerical figures on ITER are that it is intended to contain;
density ~10^20
temperature ~20keV

I think that means a specific energy density of; 2e4 * 1e20 * 1.6e-19 = 320kJ/m^3

So a pressure of 320kPa.

If there is 850m^2 surface area (from https://www.sciencedirect.com/science/article/pii/S0920379610004060) then that's a total mechanical load of 272MPa (~27 atmospheres of pressure).

That is an equivalent load of 27MN on the coils on 18 toroidal coils, or 1.5MN each. That's like a 150,000 tonne load inside each coil.

I am trying to visualise hanging one of these coils and putting 5,000 fully loaded trucks inside one!

What I am thinking wrongly? Or is this right and these are mechanically very strong coils?

jartsa
A small vertical segment of the coil provides some leftwards pointing centripetal force for those gyro-rotating particles that are accelerating to the left.

And also that same small vertical segment of the coil provides some rightwards pointing centripetal force for those gyro-rotating particles that are accelerating to the right.

The force on the coil segment is zero because current in the coil segment attracts parallel currents in the gas and repels anti-parallel currents in the gas.

(Well I guess even the horizontal parts of the coil are exerting horizontal forces on the particles - or maybe not, I don't know)

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cmb
I appreciate your reply and I can also appreciate the description of individual charges.

But I am thinking of the ensemble behaviour of those individual charges, the pressure caused by their movement, repulsion, collisions, radiative, etc..

A plasma obviously has a real internal pressure, else the Sun would collapse!

My question is about what is stopping the plasma from expanding from this mechanical pressure. Surely, at a 'system level', there must be a mechanical force pushing inwards to prevent the plasma expanding outwards?

jartsa
But I am thinking of the ensemble behaviour of those individual charges, the pressure caused by their movement, repulsion, collisions, radiative, etc..

So let's say that the radiation pressure is pushing charged particles radially outwards. Then the coil will absorb that radially outwards pointing momentum into itself. The coil does not feel any force or stress when doing that, because the sum of the absorbed momenta is zero, even if we consider just a small part of the coil.

Now the question is: Is it actually true that the sum of the absorbed momenta is zero if we consider a small part of the coil? Well at least there is some amount of cancellation of forces. My guess is that the cancellation is perfect.

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Mentor
My question is about what is stopping the plasma from expanding from this mechanical pressure. Surely, at a 'system level', there must be a mechanical force pushing inwards to prevent the plasma expanding outwards?
It sounds like you are thinking of the force on the magnetic coils as being a reaction force with the particles in the plasma. I'm no expert, but I think the main forces involved come from the coil currents being exposed to the very large magnetic fields generated by the coils:

https://indico.cern.ch/event/440690/contributions/1089756/attachments/1143849/1639302/U10_final.pdf

Mentor
The surface area is a torus, if you just multiply pressure by surface area you are double-counting forces that cancel each other.
Pressure is not the same as plasma energy per volume. ITER aims for 260 kPa pressure.

Even with your numbers: 1.5 MN corresponds to the gravitational force of 150 tonnes, not 150,000. As mentioned already forces on the magnets from the magnets are much more important.

cmb
The surface area is a torus, if you just multiply pressure by surface area you are double-counting forces that cancel each other.
Pressure is not the same as plasma energy per volume. ITER aims for 260 kPa pressure.
Forgive me, but surely that is exactly what pressure is, pressure is energy per unit volume. Hence I got that calculation roughly right, based on assumed density and energy.

J/m^3 = J/m / m^2 = N/m^2.

Could you clarify what forces you are describing as cancelling out, please? The way I am looking at it is that we have this very hot gas that wants to expand, and something has to stop it expanding, and naturally there has to be a mechanical reaction force to whatever is stopping it from expanding.

If you heat up a gas in a bottle, it puts more and more pressure on the inside of the bottle as the energy per unit volume (pressure) goes up. That puts an increasing strain on the bottle as it resists the expansion.

Even with your numbers: 1.5 MN corresponds to the gravitational force of 150 tonnes, not 150,000. As mentioned already forces on the magnets from the magnets are much more important.
Sorry, I got that calculation wrong there anyway. Taking that 260kPa figure, that is 260kN/m^2. There are 850m^2. So that should be 220MN on the equipment generating the forces to stop this gas expanding. Is this mistaken in some way?

essenmein
Forgive me, but surely that is exactly what pressure is, pressure is energy per unit volume. Hence I got that calculation roughly right, based on assumed density and energy.

J/m^3 = J/m / m^2 = N/m^2.

Could you clarify what forces you are describing as cancelling out, please? The way I am looking at it is that we have this very hot gas that wants to expand, and something has to stop it expanding, and naturally there has to be a mechanical reaction force to whatever is stopping it from expanding.

If you heat up a gas in a bottle, it puts more and more pressure on the inside of the bottle as the energy per unit volume (pressure) goes up. That puts an increasing strain on the bottle as it resists the expansion.

Sorry, I got that calculation wrong there anyway. Taking that 260kPa figure, that is 260kN/m^2. There are 850m^2. So that should be 220MN on the equipment generating the forces to stop this gas expanding. Is this mistaken in some way?

Interesting reduction of base SI units, I hadn't thought of pressure being energy density but cannot fault the units... Even thinking about it, pressure is acting like a compressed spring, who's energy at a give pressure/gas is proportional to volume, so it makes sense.

Regarding the stresses imposed on the coil, it'd be like pressure in a pipe, ie evenly imposed radially on the coil, ie the coil would have to hold this load in tension, which is not so bad. Making a pipe to hold a fluid at 2.6Bar is relatively trivial.

cmb
"Pressure = energy" is the basis of the Bernoulli principle

"static pressure + kinetic energy = constant", so as one goes up the other must come down.

Yes, I am not disputing it is engineer-able. Just wondered if the force did react directly on the magnetic coils, as if they were the sides of the 'pipe'.

The thing about a pipe, though, is that it is a continuous solid which can carry hoop stresses all along its length. There will be a likewise hoop stress on the magnetic coils, and to a much higher degree than for a pipe under similar pressure because it is not a continuous axial length of material, so each coil must take all the pressure for the length of the torus up to the next coil. If the coils occupy say 5% of the major azimuth of the torus then the forces will be 20 times higher than if it were a 'pipe'.

I don't know if those loop stresses are well within the limits of superconductors, which I thought were quite brittle, but one assumes they are engineered to cope with it. Is there a good engineering margin, or is it edge-case and 'just' enough? Do superconductors change their properties under a strain load?

Gold Member
essenmein
"Pressure = energy" is the basis of the Bernoulli principle

"static pressure + kinetic energy = constant", so as one goes up the other must come down.

Yes, I am not disputing it is engineer-able. Just wondered if the force did react directly on the magnetic coils, as if they were the sides of the 'pipe'.

The thing about a pipe, though, is that it is a continuous solid which can carry hoop stresses all along its length. There will be a likewise hoop stress on the magnetic coils, and to a much higher degree than for a pipe under similar pressure because it is not a continuous axial length of material, so each coil must take all the pressure for the length of the torus up to the next coil. If the coils occupy say 5% of the major azimuth of the torus then the forces will be 20 times higher than if it were a 'pipe'.

I don't know if those loop stresses are well within the limits of superconductors, which I thought were quite brittle, but one assumes they are engineered to cope with it. Is there a good engineering margin, or is it edge-case and 'just' enough? Do superconductors change their properties under a strain load?

Ahem electrical guy here!

Re forces, I would have to say they are imparted on the conductors themselves.

From ITER site:
"ITER uses high-performance, internally cooled superconductors called "cable-in-conduit conductors," in which bundled superconducting strands—mixed with copper—are cabled together and contained in a structural steel jacket."

The thing is an absolute monster! essenmein
Begs the question why so big, couldn't you prove the concept with something a 10th or even 100th the size?

Gold Member
Begs the question why so big, couldn't you prove the concept with something a 10th or even 100th the size?

The size is essential to allow a volume big enough for the fusion to proceed before the plasma gets cooled/poisoned/lost at the perimeter. ITER is sized to produce about 10x as much power as it uses.
The Wendelstein 7 stellarator design in Germany is a more compact and smaller unit, but there is less confidence that it will provide more power than is put in.

Mentor
It is known that Wendelstein 7-x is too small to produce a net power output (unless there are amazing revolutionary discoveries being made to change that). You need a large plasma for that, and the large size is the main point of ITER. We had 1/10 and 1/100 the size of ITER already. That's where the confidence comes from that ITER can produce a net power gain.

cmb
Begs the question why so big, couldn't you prove the concept with something a 10th or even 100th the size?
The size is essential to allow a volume big enough for the fusion to proceed before the plasma gets cooled/poisoned/lost at the perimeter. ITER is sized to produce about 10x as much power as it uses.
The Wendelstein 7 stellarator design in Germany is a more compact and smaller unit, but there is less confidence that it will provide more power than is put in.
I thought the 'concept' issue was confinement time. As the magnetic fields can never really 'confine' a thermal plasma (in a common meaning of 'confine' like a bottle that pushes back on the stuff inside it), because a magnetic field can't generate a net force on a group of particles with zero net motion, so it is more a case of 'how long before it all leaks out'.

This question of the direction of forces was really the basis of my question. A magnetic force is cross product and pushes charges sideways to their motion. There is a pinch current that pulls things inwards, but I understand that is dependent on the contraction of the magnetic fields which cannot go on indefinitely. So the concept to prove out is confining plasma with magnetic fields. I'd also have tended to think that could be proven on a smaller scale, but apparently not.

If a thermal plasma has, on average, motion in all directions, and a magnetic field acts based on the direction of particles, then the net force from a magnetic field must also be in all directions, surely?

If you add outward plasma pressure while it is inside a magnetic field that works in all directions, does that result in a net zero force on the coils?

essenmein
I thought the 'concept' issue was confinement time. As the magnetic fields can never really 'confine' a thermal plasma (in a common meaning of 'confine' like a bottle that pushes back on the stuff inside it), because a magnetic field can't generate a net force on a group of particles with zero net motion, so it is more a case of 'how long before it all leaks out'.

This question of the direction of forces was really the basis of my question. A magnetic force is cross product and pushes charges sideways to their motion. There is a pinch current that pulls things inwards, but I understand that is dependent on the contraction of the magnetic fields which cannot go on indefinitely. So the concept to prove out is confining plasma with magnetic fields. I'd also have tended to think that could be proven on a smaller scale, but apparently not.

If a thermal plasma has, on average, motion in all directions, and a magnetic field acts based on the direction of particles, then the net force from a magnetic field must also be in all directions, surely?

If you add outward plasma pressure while it is inside a magnetic field that works in all directions, does that result in a net zero force on the coils?

I always assumed, perhaps incorrectly, that the plasma is rotating around the toroid, other wise like you say there is no force on charged particles, basically I thought the plasma had current flowing in it, well, since current is rate of moving charge, current would simply be moving plasma in this case.

Re zero force, it depends on how you view "zero", there is no net force in any direction wrt to outside reference, since it equal in all directions from the center (ie vector sum = 0), both on the forces for each coil, and the torus itself, it doesn't get heavier or want to move sideways. However all the coils and the torus experience the tension from loop stress, this is tangential to surface the pressure is acting on.