# How can the magnetic field of a tokamak or stellatron hold against the outwards plasma pressure?

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.

• 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? – CuriousOne Sep 6 '15 at 11:15
• 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? – Bass Sep 6 '15 at 11:49
• 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. – CuriousOne Sep 6 '15 at 11:56
• "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. – Bass Sep 6 '15 at 12:08
• 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. – CuriousOne Sep 6 '15 at 12:29

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.