As can be seen in the attached picture, the toroidal coils produces a magnetic field parallel to the tokamak torus circular axis Bx. The poloidal coils produces vertical magnetic field By, then the composed magnetic field is drawn as Bxy.
Then theoretically the particles that goes parallel to the magnetic field escapes, so does the particles parallel to Bxy exits from the tokamak?
Hello Javier,
If your system is simple as the one depicted, not taking in consideration electric fields but only the magnetic field, then in theory yes, the charged particles following the field lines would have a tendency to go out. Nevertheless there might be electric fields due to plasma currents that will (most probably) make the particle rotate poloidally, as well as curvature issues that you might want to take care of, then theory does predict the confinement of the particles (or at least of most of them). Several books (Chen, Bellan and Friedberg among others) do describe with detail the dynamics of charged particles in magnetic fields and they analyze toroidal configurations as well, you might want to take a look at one of those books.
Cheers
Hello Hugo,
Electric fields follow equation F=Kq*q´/r^2 so it depends only of charges, independent of current generated by their movement. So movement of the particles in the poloidal trajectories will create a current loop that generates a circular magnetic field surrounding them that would help to compress them, but I have to see if the magnitude is enough (I read that plasma inducted current was about 1 mega amp)
Look at Rax or Wesson textbooks on Takamaks.
Presumably,in a very configuration,adequate electromagnetic systems prevent locally the particles escaping processes.
In a tokamak, a significant toroidal current is driven (often inductively) in the plasma. This produces poloidal fields, which, in combination with the toroidal field, creates close magnetic surfaces. In ideal theory, particles are confined on these surfaces - reality introduces additional effects that are still being addressed in current research.
Without the toroidal current, your picture is more of a stellarator, which would try and make the closed surfaces purely with external fields. The coils are not nearly as simple as your picture in that case.
>Without the toroidal current, your picture is more of a stellarator, which would try and make the closed surfaces purely with external fields.
I would use electrostatics and centrifugal force. Using plasma current radiates
>The coils are not nearly as simple as your picture in that case.
May be, It is not interesting copying a tokamak that is a well working and proven configuration, but just to reduce the number of coils
Escape along vertical field lines is precisely why large tokamaks like JET and (supposedly ) ITER are endowed with divertors, i.e. suitably manufactured plates on the top and/or the bottom of the vacuum vessel which aim at supporting the heat loss associated to such escape. Furthermore, particle recycling occurs at the divertor edge, allowing ionised particles to come back from the divertor to the plasma. Decades of Nuclear Fusion issues are dedicated to this problem.
Sure, but it would be faster working at 50 teslas. D+T fusion is easy: only it is needed 30keV and has lots of barns
Hello Javier, you are right about 50T, but there is no technology that can make such an amount of 50T coils suitable for tokamak's design. So we need to take a look somewhere else before 50T technology is available.
By the way, production of 50 T magnetic field is no easy task in any experimental lay-out whatsoever...
In a Tokamak, usually the poloidal coils produce a variation of By in the "hole" of the torus, hence, by induction, a toroidal current Itor (Ix in your coordinate system). This current produces a poloidal field, which runs parallel to the red rings of your picture. This combination of toroidal and poloidal magnetic fields prevents particles from escaping the plasma.
Look at some basic plasma physics textbook, for example Wesson, which was already mentioned, or Boyd and Sanderson, "The Physics of Plasmas" (2003), pp.85-100.
James Gilland has identified the key thing missing in your diagram. The toroidal field and the field due to the plasma current dominate the shape of the field lines, these remain on a closed surface for the majority of the plasma and those that are not on a closed surface are exhausted into a "divertor".
Incidentally, the plasma current is necessary exactly because in general the particles do not travel along field lines! http://en.wikipedia.org/wiki/Guiding_center The curvature of the toroidal field together with its variation in strength across the radius lead to a separation of ions and electrons towards the top and bottom of the machine. This in turn causes an electric field which causes the particles to be lost by polarisation drift http://en.wikipedia.org/wiki/Guiding_center#Polarization_drift. The plasma current short circuits the top and bottom of the tokamak plasma by causing the field lines to go in a spiral. It therefore prevents the build up of this particular electric field and prevents the particle loss from the drift behaviour of the particles. i.e. the current vastly improves the confinement!
The role of the poloidal field coils is for second order shaping and control. For example improvements in the degree of confinement can be seen if the plasma is not circular in cross-section, but slightly elliptical, or has an element of triangularity to it. The poloidal coils achieve this by producing a force on the current in the plasma http://en.wikipedia.org/wiki/Lorentz_force.
The role of plasma shaping in the confinement is far from a settled issue. Although it is agreed that the shaping affects the quality of confinement, exactly how much is difficult to predict and has been the subject of intense study for many decades.
>The curvature of the toroidal field together with its variation in strength across the radius lead to a separation of ions and electrons towards the top and bottom of the machine>
I do not understand well that issue, the logic said that the separation must be from the inner part to the outer part of the toroid due different mass of electrons and ions. This may be a problem due tritium would be separated from deuterium for the same reason.
The electric field could be cancelled using an external opposite electric field
How many teslas is achieved by the plasma current and how many due toroidal coils?
It is true that ITER will be working at 10.5T?
Hi Javier,
Please see the links that I posted along with the text. The main drift you need to consider is the Grad-B-drift. This depends on the charge of the particle. The Grad B drift is perpendicular to the field (mostly toroidal), the gradient in the field (mostly radial, due to the 1/r fall off of the toroidal field) and, importantly, the charge. I attach a picture from a particle tracing calculation which should clarify things for you. The field is in the z direction, and the gradient in the field is in the x direction, similar to a tokamak cross section. The drift speed is typically much less that the speed of the particles, I have exaggerated it here for clarity.
The current provides a poloidal field which when added to the existing toroidal field causes each field lines to visit both the top and bottom of the machine, providing a "short-circuit" for the build-up of charge. This is more robust than applying an external electric field as the electric field is likely to have a spatially dependent structure and will be dynamic.
Thank you Simon, I see the drift problem of the moving particles in the non uniform field. It is clear that as more uniform field we have less particle loss but less compression also so we must look for a compromise between both criteria
It exists shapes that reduces the non uniformity field in toroids, but it may be difficult to do it using superconducting wire at liquid helium temperatures.
The introduction of correction coils that smooth the field would cover the whole external surface making impossible to extract net power from the toroid
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