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Mechanics of Magnetic Fusion Reactors Chapter | 12 369

12.6 STRENGTH AND STIFFNESS ANALYSIS OF A VACUUM
VESSEL

12.6.1 Mechanical Loads
Mechanical loads on a VV may be grouped into the following:
l Inertial loads (the vessel dead weight, the coolant weight, seismic activity,
mechano-dynamical, or impact stresses);
l The coolant pressure in normal operating conditions and under heating or
hydraulic tests;
l Transient electromagnetic forces (associated with current disruptions,
plasma vertical displacements, fast current discharge from MS, etc.);
l Thermomechanical loads (plasma thermal radiation, neutron heating and
vessel heat conditioning); and
l Preloads during assembly operations, including the tightening of fasteners.

Electromagnetic loads (EMLs) dominate in an experimental tokamak reac-
tor. They have a diverse origin and different intensities and impact durations.
For example, plasma displacements and current disruptions give rise to more
than a dozen EMLs. The most significant EMLs have impact durations varying
from a few tens to a few hundred milliseconds. These times are comparable
with the lower harmonics of the characteristic oscillations of many chamber
structural components. Therefore, it is important to analyse the loading dynam-
ics when doing structural assessments, as a purely static approach may prove
dramatically inadequate [11].
An EML analysis is often divided into two separate problems. One is to cal-
culate EMLs developing due to changes in plasma current density, cross-section
shape and spatial position. The other is to estimate EMLs resulting from the
toroidal magnetic flux redistribution and/or halo currents development.
EMLs acting on the vacuum chamber may conventionally be divided into
symmetric and asymmetric loads. EMLs due to a plasma current central disrup-
tion, ‘fast’ vertical displacement of plasma or current discharge from the MS are
cyclically symmetric. Asymmetric EMLs result from a ‘slow’ vertical displace-
ment of plasma and asymmetric halo currents. The latter vary in the toroidal
direction following the cosine law and are measured using the toroidal peaking
factor, that is, the halo current’s peak-to-average linear density. The toroidal
peaking factor experimental value may reach 3 and more. Its theoretical value
for some of the ITER operating modes is greater than 2.
In some transient conditions, asymmetric EMLs tend to ‘rotate’ in the toroi-
dal direction about the tokamak’s vertical axis. In certain conditions, this can
cause resonance endangering the vessel’s constructional elements.
The EML magnitude is strongly dependent on the velocity of plasma vertical
displacement prior to the current disruption. It is determined by the machine’s
electrical engineering parameters and the features of the plasma automatic
control system.