Electromagnetic analysis for fusion reactors: status and needs Page: 3 of 6
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Status of Eddy Current Computer Codes
Computer codes capable of calculating these
electromagnetic effects are Just coming Into u*e.
Existing codes can handle no nore than: (l) several
Interacting systems, all with axlsymmetry; or (2) a
single system of thin, segmented pieces; or (3) a
single thick piece. None of the existing codes can
handle systems with narrow gaps.
Today's codes deal best with thin shells
carrying axlsymmetrlc currents, a somewhat adequate
characterization of the present generation of tokaaak
vacuum vessels. Only now are we beginning to develop
codes which are useful in modelling future tokaraaks
with thick, segmented FWBS systems and three-
dimensional eddy currents. Network codes can crudely
represent a single system, including Its segmenta-
tion. Codes with coupled coaxial current loops can
crudely represent the electromagnetic interactions of
several systems, but only under the assunptlon of axl-
symmetry. Codes which can Include both segmentation
and interaction between systems do not exist.
Following Is a description of the kinds of
eddy current codes which are of some use in electromag-
netic analysis of fusion reactors. References to some
codes are given In each section For a more complete
survey of codes, see reference [11.
No distinction is made here between finite-
element or integral-equation formulations or between
field or network conceptualizations since all have
achieved roughly the same level of development. Also,
It should be pointed out that after the problem Is
solved In terms of one variable (e.g., potential,
field, or current), the ether variables, including
forces and torques, are readily calculated.
Axlsymmetrlc Codes (2), , (4)
Many two-dimensional (2-D) codes can also
model axlsymmetrlc systems with toroidal current and
radial and pololdal fields. They can model some fusion
applications, but it is intrinsic in their 2-D nature
that they cannot handle breaks In the toroidal current
path. Hence they do not predict the large, complex
distribution of forces and torques that result from
interaction between eddy currents and the toroidal
Coupled Coaxial Current Loops (5)
An axlsymmetrlc system is modeled by up to a
hundred coaxial current loops. The resistance and
self- and mutual-inductances are assigned. The passive
loops respond to each other and to a number of loops
with specified currents as a function of time, repre-
senting the plasma and PF colls. Again by their 2-D
nature, these codes cannot handle segmentation or the
interaction between eddy currents and the toroidal
Coupled Coaxial Current Loops, Single Break 
If In one of the above codes one or more sub-
sets of the passive loops Is constrained to have zero
net current, that code can treat axlsymmetrlc systems
with a single current break. However, a single break
Is a poor model of segmentation, and these codes can
err by an order of magnitude in the size and time
variation of eddy current forces and torques.
Plates and Shells (7), , [9j, 
Some codes can model eddy currents in plates
and shells if the plate thickness la less than the skin
depth and the current density Is unlfoni across the
plate or shell, although there Is still some contro-
versy about the solution of what Is an Intrinsically 3-
D problem with 2-D codes. These codes can also model
systems of plates and shells. They cannot predict the
dependence of field penetration on the size of the gap
between plates. They require validation experiments to
determine the needed degree of time and space discreti-
Three-Dimensional Codes , , 
Three-dimensional (3-D) codes, allowing cur-
rent in all three dimensions, suffer from two problems,
one conceptual and the other practical. The conceptual
problem Is finding a formulation In which the variable
Is uniquely determined and the boundary conditions,
especially the boundary conditions between conducting
and non-conducting regions, are well defined in terms
of the variable. There has been much progress In solv-
ing this problem in recent years. The practical
problem is the choice of a mesh which Is sufficiently
fine to simulate the physical system yet coarse enough
that computation can be performed with existing compu-
ters. Some 3-D codes have reached the degree of devel-
opment that a simple 3-D geometry (brick, finite cylin-
der, sphere"' can be solved. But, systems of such
shapes, with narrow gaps between them, are still beyond
the capability of these codes and existing computers.
These codes require much development and testing.
Need for Experimental Code Validation
No eddy current computer code is based on
Maxwell's equations alone. Identifying a continuously
variable field with its values at a discrete nunber of
points and computing those values can only be carried
out after many assumptions are made. Some of these
assumptions can be checked by standard procedures em-
ploying the code itself or by comparing results with
another code with different assumptions. But other
assumptions are Intrinsic to all formulations, and
their consequences require verification against experi-
ment. Moreover, the more closely the verification
experiments resemble the systems to be analyzed, the
more confidence can be placed In the code's predic-
A good example of the requirements and
benefits of experimental verification occurs in
attempting to model 3-D geometries with 2-D codes.
Practical 3-D codes are at least five to ten years In
the future. Meanwhile 2-D codes are being used to
solve 3-D problems. We can Judge the limits of
validity of this procedure if we have results from
suitable 3-D experiments. A combined program of code
development and experiments will provide the capability
to solve design problems before 3-D codes become avail-
able, and screen a large number of design concepts,
choosing only a few for 3-D analysis. Among the 3-D
geometries which can to some degree be simulated with
2-D codes augmented by experiments are:
1. Thin plates. Except in the resistance-dominated
(low magnetic Reynolds number) limit, place problems
are 3-D problems; it Is an open question how well 2-
D codes model them. For example the sharp edges of
plates can create 3-D electric fields with large
gradients that pose an arcing problem.
2. Modelling a thick shell with a thin, hlgh-
3. Systems with 2x/n symmetry. In some cases these can
be modeled by axlsymmetrlc systems.
4. Misaligned axlsymmet-lc systems. Differences
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Turner, L.R. Electromagnetic analysis for fusion reactors: status and needs, article, January 1, 1983; Illinois. (digital.library.unt.edu/ark:/67531/metadc1067015/m1/3/: accessed August 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.