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I understand that magnetic containment structures like tokamaks generate a toroidal magnetic field in which the plasma particles move in helices around the field lines, because of the Lorentz force. A single free particle would stay inside the torus for all time.

But how do such magnetic fields generate a force that generates a pressure from the torus walls to the inside of the torus? At the high plasma pressures, there must be a considerable force on the particles that moves them towards the magnets (or torus walls), so this force must be compensated somehow.

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    $\begingroup$ All magnetic confinement structures have diffusive loss terms. The particles that escape by diffusion are eventually going to collide with the walls of the machine and they will cause a classical pressure on these walls, it's just much smaller than the pressure on the magnets that cause the containment field. This classical pressure has to be eliminated with divertors and pumps that are removing this plasma to avoid damage to the walls. Is that your question? $\endgroup$ – CuriousOne Sep 6 '15 at 11:15
  • $\begingroup$ But if the plasma's temperature is 100 million degrees, surely there is a very high pressure. The plasma "wants" to explode and fill the whole space. How does the magnetic field hold it together? $\endgroup$ – Bass Sep 6 '15 at 11:49
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    $\begingroup$ Temperature and pressure are completely independent quantities. The plasma does try to fill the whole space and for a non-interacting plasma that space is defined by the magnetic field because of the circular trajectories of ions and electrons. For plasma with internal collisions we can still find magnetic field configurations that are efficiently holding the plasma for hundreds and even thousands of seconds. The internal pressure is acting on the magnetic field, which transfers it to the magnet rather than the walls of the vacuum vessel. $\endgroup$ – CuriousOne Sep 6 '15 at 11:56
  • $\begingroup$ "For plasma with internal collisions we can still find magnetic field configurations that are efficiently holding the plasma ..." That's what I'm asking, how can a magnetic field achieve that? Sorry if that wasn't clear. $\endgroup$ – Bass Sep 6 '15 at 12:08
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    $\begingroup$ The basic mechanism is that charged particles are confined to trajectories that are on average parallel to the magnetic field lines. In a configuration where the magnetic field lines are closed, i.e. in a toroidal field this is the volume of the torus. The details are anything but trivial, though. For a simple torus there is a radial drift term that has to be compensated with either a ring current (Tokamak) or by twisting the field lines (Stellarator). Then there is the thermodynamic collision drift term that can't be compensated other than by making the field strong and large. $\endgroup$ – CuriousOne Sep 6 '15 at 12:29
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The basic mechanism is that in a collision-less plasma charged particles are confined to trajectories that are on average parallel to magnetic field lines. In a toroidal configuration the magnetic field lines are closed, i.e. charged particles keep going around the torus and are confined to the volume of the torus. The details are anything but trivial, though. For a simple torus there is a radial drift term stemming from the fact that the field is stronger towards the center than the outside. This has to be compensated with either a ring current in the plasma (Tokamak configuration) or by twisting the field lines (Stellarator).

For plasma with internal collisions there is the thermodynamic collision drift/diffusion term which can't be compensated for. We simply have to make the field strong and large enough to have hundreds of seconds of confinement time. This has been essentially achieved at the cost of making machines with plasma diameters of several meters and $100m^3$ (JET) and $850m^3$ (ITER) of plasma volume.

The internal plasma pressure in these machines is acting on the magnetic field, which transfers it to the magnet rather than the walls of the vacuum vessel. I would venture to guess that the pressure of the magnetic field itself is many times greater than the pressure of the plasma on the field, i.e. the machine design has to accommodate forces from the machine itself more than it has to confine the plasma forces. In ITER this is done with up to 60mm thick structural steel ribs that stabilize the torus that weighs 23000 tons. I would expect potential commercial reactors to be somewhat stronger and more massive than ITER, still.

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  • $\begingroup$ are collision-less plasmas an idealization, or do they exist? Even though the collisions might be rare because of the sizes of the particles (compared to molecule sizes), they must happen, don't they? $\endgroup$ – Bass Sep 6 '15 at 18:56
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    $\begingroup$ @BastianTreichler: One can make low density near collision-less plasmas but without collisions there will be no fusion reactions. Having said that, the collision-less case is very important for an understanding of many plasma-effects. It's one of the toy scenarios (like the two-body problem in classical mechanics) that one has to understand before one can move on to the much more complicated case of high density plasmas. $\endgroup$ – CuriousOne Sep 6 '15 at 19:01
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The ions process along the magnetic field lines. The Lorentz force directs the plasma along the lines of the magnetic field. This is why neutral beam injection heating is used, since the neutral atoms can penetrate through the magnetic field lines, undergo charge exchange, and undergo fusion as ions, whereas injecting ions from an accelerator without neutralizing them is not effective, since they cannot penetrate into the center of the plasma due to the magnetic field. A minimum-B field configuration is need to ensure that the plasma stays confined, otherwise, as the plasma moves out of the center, it encounters decreasing magnetic field pressures, and can escape. With a minimum-B configuration, as the ions move outward toward the wall, they are met with an increasing magnetic field pressure, and are pushed back away from the wall.

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