Page 394 - Fundamentals of Magnetic Thermonuclear Reactor Design

372 Fundamentals of Magnetic Thermonuclear Reactor Design

damage from the i-th type cycles, and [V ] = 1 is the ultimate cumulative fatigue
N
damage. Here, the term ‘type’ refers to all cycles that cause deformations of the
same amplitude.
Apart from the structural analysis, the design process should provide for the
capability to verify the VV components’ stability. This verification is usually
conducted by numerical methods due to the structure complexity and 3D stress
distribution. The structural materials behaviour is assessed using approximate
elastic–plastic analysis, with due consideration for the components’ potential
deviation from the ideal form.

12.7 STELLARATOR STRUCTURAL ANALYSIS

We start by pointing out that the structural analyses for tokamaks and stellara-
tors are conceptually, logically and algorithmically similar. This leads us to
further focus on specific issues related mostly to the W7-X stellarator design
experience.
Many characteristics needed for the strength and stiffness computations
are given approximately. Therefore, a parametric analysis is widely employed
in the design of an MFR, particularly its non-linear load-bearing and support
structures. The safety factors for nominal, anticipated and extreme individual
parameters are selected based on experience with similar structures, as well as
a comprehensive analysis of uncertainties. In the W7-X design, these safety
factors were taken to be 1.2, 1.1 and 1.0, respectively. Such a choice allowed
the variability of the materials’ structural and functional properties, the friction
coefficients, gaps fastener tightening degree, displacements of parts one relative
to another, and so on, to be accounted for.
In common with what we observe in tokamaks, the ponderomotive forces in
stellarators give rise to distributed loads acting on the coils. Toroidally directed
forces tend to flatten the coils and overturn them around the radial axis. These
forces are taken by the coils’ steel cases, the central load-bearing structure, and
supports in-between the coils.
For stellarators the magneto-elastic stability problem is not critical unlike
with tokamaks, as stellarators are exposed to much weaker ponderomotive forc-
es, and their 3D coils are not subject to potentially destabilising deformations.
Although the ponderomotive forces play the dominant role in developing the
stress state, other stress constituents, such as the weight and the coolant pres-
sure, are accounted for in the design. These factors have a fundamental impor-
tance for the strength analysis at the machine assembly and test stages. In stel-
larators, distributed mechanical loads are smaller than in tokamaks at the same
magnitude of magnetic field along the plasma column axis due to the greater
number of coils and, therefore, smaller winding cross-sections and coil currents.
An MS strength and stiffness analysis should be preceded by a physical–me-
chanical winding ‘homogenisation’, needed to determine their orthotropic ‘ef-
fective’ properties. The stellarator’s distinctive feature is that the highest stress