Discussion Forum

Hi all,

This discussion covers a number of related questions, hence the length of the post. I am a Ph.D student on a tokamak (experimental fusion reactor) project and I am using COMSOL Multiphysics 4.1 to test the survivability of a diagnostic system to large transient electromagnetic loads produced during so-called "disruptions" in which one component of the magnetic field disappears very quickly (e-folding time of about 1 ms).

Allow me to explain in more detail: a tokamak is a device that confines a hot plasma (kT ~ 5 keV) in a toroidal (donut) shape using a combination of toroidal (the *long* way around the donut) and poloidal (the *short* way around the donut) magnetic fields. The *toroidal* field is produced using external copper field coils (which run *poloidally* around the plasma), and the *poloidal* field is produced by a *toroidal* current actually flowing in the plasma itself. The resulting total field runs in a spiral around the plasma, like if you bent a barber-pole into a donut shape. There's a good image on Wikipedia here: en.wikipedia.org/wiki/File:Tokamak_fields_lg.png

The problem at hand is that sometimes a stability limit is crossed and confinement of the plasma is lost. This means that the energy in the hot plasma is lost to the wall (the "thermal quench") , and more importantly, the large toroidal current (about 10^6 amps in our device) decays on a very fast L/R timescale of about 1 ms, in what is known as the "current quench". As the toroidal plasma current decays, the poloidal field produced by that current also decays, producing eddy currents in all the stuff attached to the wall (chiefly various diagnostic systems). These eddy current loops then interact with the very strong *toroidal* field (which, you'll recall, is produced externally by copper coils, and does not change during a plasma disruption) to produce large torques on the wall components, wanting to align them with the toroidal field.

For a part on the device outer wall (which is where my device is located), the geometry works out so that there is an initial (poloidal) field of about 1.1 T in the +z direction, and a (toroidal) field of about 5 T in the +x direction. This field has completely penetrated my device (a 304L stainless steel device about 9 cm high (z), 4 cm wide (x) and 3.5 cm deep (y). The 1.1 T poloidal field then exponentially ramps down to 0 as Bz = Bz0 * exp(-t/tau) where Bz0 = 1.1 T and tau = 0.001 s. This induces eddy currents in the stainless steel box (in the x-y plane), which interact with the strong toroidal (Bx) field, to produce a torque vector in the +y direction (i.e. it wants to twist the box so the eddy current loop vector aligns with the strong toroidal magnetic field). The eddy current loops also produce a back emf which reduces the rate of change of the poloidal (Bz) field inside the material, reducing the torque in the initial phases of the current quench. (If the box were modelled zero-dimensionally as an ideal loop, this would correspond to taking into account the loop inductance in the time-dependent circuit equation.)

So I would like to use the AC/DC module to self-consistently calculate the current distribution vec(J)(x,y,z) inside the stainless steel device, and then use the structural mechanics module with a body force (vec(J) \times vec(B)) to calculate the transient stress distribution in the diagnostic box and its mounting bolts.

My difficulty in modelling the problem in COMSOL Multiphysics comes from the fact that the decaying poloidal field comes, from the point of view of the steel box, from infinity. I feel like this should be a very basic problem, but I am having a hard time setting up the appropriate combination of (a) geometry, (b) use of "infinite elements", and (c) boundary conditions in the AC/DC module to produce the time-dependent uniform poloidal field.

So to start, I'm trying a simpler problem: can I produce a uniform Bz field in the magnetic fields (mf) interface? I can do it in mfnc (magnetic fields, no currents) no problem (see attached) using a single cylinder as the geometry with Magnetic Insulation (MI) boundary conditions on the curved walls of the cylinder, and with Magnetic Potential (MP) and Zero Magnetic Scalar Potential (ZMSP) boundary conditions on the top and bottom cap. (See attached mfnc_cylinder_test.mph)

So a first question would be (since I need to not make this post any longer): how do I get the equivalent in the magnetic fields (mf) interface? I will make another post with my attempt to do so using surface currents and Magnetic Scalar Potential boundary conditions, so you can see how it isn't working.

What am I missing, where is my conceptual error? Or is this actually possible?

Thanks very much for any help you can provide.

Regards,

Geoff Olynyk