Page 91 - Fundamentals of Magnetic Thermonuclear Reactor Design

Simulation of Electromagnetic Fields Chapter | 4 75

into a system of magnetostatic field equations. Such problems include the
following:

l Distribution of the stray field of the PF magnet with allowance made for the
environments and steel rebars of the tokamak building structures. The stray
fields may affect the peripheral equipment and make the use of shielding
systems necessary.
l Analysis and formation of fields in high precision systems, such as particle
beam analysers and neutral atom injectors. These devices use mild steel for
passive magnetic shielding from the stray field that is highly prone to mag-
netic saturation.
l Assessment of the impact of magnet coil manufacturing/assembly toleranc-
es on field perturbations in the discharge chamber (vacuum vessel).
l Assessment of a toroidal field ripple and its reduction with ferromagnetic
inserts to the design level. To identify necessary parameters and design of
such inserts (which are virtually saturated), high-precision calculations of
their influence functions are necessary.
Quasi-stationary Problems: The EM processes associated with eddy cur-
rents that occur in conducting structures of tokamaks are approached in a quasi-
stationary approximation. Because the EM fields tend to change quite slowly,
polarisation events are able to keep pace with field variations and the relations
between vectors D, E, B, H and j are independent of their time derivatives.
At each instant, quasi-stationary alternating currents (AC), generating magnetic
field and the Lorentz forces resulting from their interaction have the same val-
ues as at direct currents of the same magnitude. The quasi-stationary ACs flow
in closed circuits and have the same intensity throughout the untapped parts of
the electric circuit. The EM field may only fit the quasi-stationarity criteria in
the immediate vicinity of those currents. As estimated, the displacement cur-
rents are negligibly small compared with the conduction currents for all fre-
quencies typical of the ITER machine. In this case, the first Maxwell equation
e
takes the form ∇ × H = j + j , and the second Maxwell equation can be written
as: ∇× E =−∂B / ∂t. ∇×E=−∂B/∂t
From now on, we shall consider static isotropic media, whose characteris-
tics are described by scalars. Using the Maxwell equations, one can obtain the
desired system of equations for a medium with electrophysical characteristics
variable in space. In a numerical context, it is easier, however, to consider a
set homogeneous media with contacting surfaces. Under these assumptions,
−7
ε = εε , and µ = µµ , where ε = 8.854·10 −12 F/m, and µ = 4π·10 H/m are
0
a
0
0
0
a
the electrical and magnetic vacuum permeability, respectively, and ε and µ are
relative quantities appropriate for a given medium.
The differential form of the Maxwell equations can be used for those points
where the field and medium characteristics are finite, continuous and have con-
tinuous derivatives. Discontinuities may occur due to interfaces of media with