Fusion Engineering and Design 88 (2013) 1848–1852

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Fusion Engineering and Design

journal homepage: www.elsevier.com/locate/fusengdes

Electromagnetic and structural analyses of the vacuum vessel and

plasma facing components for EAST
Weiwei Xu ∗ , Xufeng Liu, Yuntao Song, Jun Li, Mingxuan Lu
Institute of Plasma Physics, Chinese Academy of Science, Shushanhu Road 350, Hefei 230031, PR China

h i g h l i g h t s

• The electromagnetic and structural responses of VV and PFCs for EAST are analyzed.
• A detailed finite element model of the VV including PFCs is established.
• The two most dangerous scenarios, major disruptions and downward VDEs are considered.
• The distribution patterns of eddy currents, EMFs and torques on PFCs are analyzed.

a r t i c l e i n f o a b s t r a c t

Article history: During plasma disruptions, time-varying eddy currents are induced in the vacuum vessel (VV) and Plasma
Received 14 September 2012 Facing Components (PFCs) of EAST. Additionally, halo currents flow partly through these structures during
Received in revised form 4 March 2013 the vertical displacement events (VDEs). Under the high magnetic field circumstances, the resulting
Accepted 19 March 2013
electromagnetic forces (EMFs) and torques are large. In this paper, eddy currents and EMFs on EAST VV,
Available online 21 April 2013
PFCs and their supports are calculated by analytical and numerical methods. ANSYS software is employed
to evaluate eddy currents on VV, PFCs and their structural responses. To learn the electromagnetic and
Keywords:
structural response of the whole structure more accurately, a detailed finite element model is established.
Vacuum vessel
Plasma facing components
The two most dangerous scenarios, major disruptions and downward VDEs, are examined. It is found that
Plasma disruption distribution patterns of eddy currents for various PFCs differ greatly, therefore resulting in different EMFs
Eddy current and torques. It can be seen that for certain PFCs the transient reaction force are severe. Results obtained
Electromagnetic force here may set up a preliminary foundation for the future dynamic response research of EAST VV and PFCs
which will provide a theoretical basis for the future engineering design of tokamak devices.
© 2013 Elsevier B.V. All rights reserved.

1. Introduction During plasma disruptions, time-varying eddy currents are

induced on VV and PFCs. Additionally, halo currents will flow along
Experimental Advanced Superconducting Tokamak (EAST) is an the scrape layer to these structures and return to the scrape layer
advanced steady-state plasma physics experimental device which during the vertical displacement events (VDEs). Eddy currents and
has been built in ASIPP CAS. Its main objective is the wide investiga- halo currents interact with high toroidal magnetic field will cause
tion of both the physics and technology for state advance tokamak. large electromagnetic forces (EMFs) and torques on VV and PFCs. As
EAST has Plasma Facing Components (PFCs) mainly including inner these forces change drastically with time, the structural response
limiter, divertor, passive stabilizer and horizontal protective plate is dynamic [3]. This response determines important design drivers
to protect the vacuum vessel (VV), heating systems and diagnostic such as the reaction forces of supports, the displacements and stress
components from the plasma particles and heat loads. All PFCs are of the structure.
composed of graphite tiles, heat sink, support and cooling system. In this paper, analytical and numerical methods are used to cal-
Fig. 1 shows the elevation view of EAST PFCs. The PFCs are designed culate eddy currents and the resulting EMFs on EAST VV and PFCs
up-down symmetrical to the midplane, to meet the requirement of including the supports. A detailed finite element model of EAST VV
operation with single or double null plasma shape [1,2]. including double-walls, the ribs between the walls, all major PFCs
and their supports which allow the currents flow through them
between VV and PFCs is established. Two most dangerous situa-
∗ Corresponding author. Tel.: +86 551 5592013. tions: major disruptions (MD) and downward VDEs are examined
E-mail address: wwxu@ipp.ac.cn (W. Xu). in detail.

0920-3796/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.fusengdes.2013.03.067
 W. Xu et al. / Fusion Engineering and Design 88 (2013) 1848–1852 1849

Fig. 1. Elevation view of EAST PFCs.

2. Analytical analysis of eddy currents for VV during MD

Major disruption is a typical load case for the electromagnetic

analysis of Tokamak VV and PFCs. During MD, the plasma current
is modeled by one coil of which the current varies rapidly with
time but the position in space is constant. The sudden change of
plasma current will induce eddy currents and result in electromag-
netic forces on conducting structures around the plasma. According
to the principle of electromagnetic induction, by simplifying the
double-shell of VV to several dozens of circular coils, the distribu-
tion of eddy currents and their effects on the background magnetic
field can be simulated, and the resulting electromagnetic forces can
Fig. 2. (a) Total eddy current on VV and (b) eddy current density at different pos-
be calculated with Fortran software codes. Here, the vacuum vessel itions.
is divided into 120 conducting rings, and a current couple model
is established to calculate eddy currents for different conducting
When the large toroidal eddy currents interact with high
elements. The current couple model is given as:
poloidal magnetic field, large electromagnetic forces will emerge
dIi  dIj dIplasma on VV. Since the background magnetic field caused by plasma cur-
Li + Mij + Mi,plasma + Ri Ii = 0 (1) rent changes sharply as plasma current decay, the total magnetic
dt dt dt
j(j =
/ i) field’s direction may even reverse at some places [5], which result
in the electromagnetic force there reversing. Fig. 3 has shown how
where R, I, L and M represent the resistance, current, self-inductance the stress distribution changes gradually. The pressure at region A
and mutual inductance respectively. points inward at first and gradually turns outward, while the pres-
For EAST, the current decay of plasma during MD can be sup- sure at regions B and C points outward and inward respectively all
posed as below:

I = I0 e−t/ (2)

where I0 = 1 MA,  = 3 ms.

Eddy currents can be calculated from Eq. (1). The total eddy cur-
rent on VV and eddy current density at different positions of the
upper half vessel can be obtained, just shown in Fig. 2. Results show
that when plasma current decays exponentially, eddy currents
firstly grow rapidly and then decrease over time. The maximum
total eddy current on VV is 0.71 MA at about 7 ms. The maximum
current density occurs at the center of inner limiter at about 5 ms
and the value is 21 MA/m2 . The amplitude and response velocity of
eddy currents on every coil have an inverse relationship with its
distance to the plasma. At the same position, inner shell will reach
the peak current earlier than outer shell. Fig. 3. Force distribution on PFCs at different time during MD.
1850 W. Xu et al. / Fusion Engineering and Design 88 (2013) 1848–1852

Fig. 4. Finite element model of 1/16 EAST.

Fig. 6. Force and torque acting on PFCs during MD: (a) force acting on PFCs and (b)
radial torque.

the time. The maximum stress is 0.034 MPa, occurring at the center
of inner limiter at 3 ms.

3. Numerical analysis of eddy currents for VV and PFCs

3.1. Finite element model

EAST vacuum vessel is a D-shaped cross-section and double wall

torus assembled by 16 sections. Each section has an upper vertical
port, a lower vertical port, a horizontal port, a flexible support and
two middle poloidal ribs. As shown in Fig. 1, PFCs and other in-
vessel components are installed in VV. PFCs contain inner limiter,
divertor, passive stabilizer and horizontal protective plate. All PFCs
are composed of heat sinks including their supports, cooling system
and graphite tiles which are bolted to heat sinks. Since the mate-
rial electrical conductivity and geometric dimensioning of graphit
tile are both much smaller than heat sink, when calculating eddy
currents on PFCs, only heat sinks and their supports are considered.
The material of VV and heat sink are 316 L stainless steel and CuCrZr
respectively.
Simulations are performed with ANSYS software. The electro-
magnetic finite element model for subsequent analysis consist of
2 halves toroidal field (TF) coils, 14 poloidal field (PF) coils, a 22.5◦
VV sector, the nearby PFCs modules and their supports, as shown
Fig. 5. Eddy currents on VV and PFCs during MD: (a) eddy current loops and (b)
in Fig. 4.
eddy currents.
For the analyses presented in this paper, the two most dangerous
scenarios are considered: major disruptions and downward VDEs.
 W. Xu et al. / Fusion Engineering and Design 88 (2013) 1848–1852 1851

Fig. 8. Radial forces on VV and PFCs for the downward VDE.

3.3. Vertical displacement events

During VDEs, plasma current is modeled by one loop with

constant current while the position varies with time—drifting
downward at a velocity of 100 m/s [6]. The loading assumption is
rough, but it can reflect the effect of the vertical plasma movement
on eddy current distribution on PFCs and VV. Fig. 7 shows that the
maximum eddy current reaches the value 300 kA on VV and 230 kA
on PFCs (occurring on inner limiter).
Results show that the maximum force occurs at down divertor
outer plate in radial direction, as shown in Fig. 8. And the maxi-
mum torque occurs at the lower horizontal protective plate in axial
direction.
At the end of VDEs, plasma may touch the first wall, and the
currents will flow into PFCs and VV due to the lower electrical
resistivity. These currents are called halo currents, which are quite
harmful to the device due to the resulting huge dynamic EMFs.
According to EAST experiment datas, the path of halo currents
is assumed approximately as Fig. 9(a), flowing and exiting from
divertor inner plate and outer plate respectively, and the current
magnitude is about 50% of plasma current [6].
Fig. 7. Eddy currents on VV and PFCs during downward VDE: (a) eddy current loops
on PFCs and (b) eddy currents. In FEM model, the AMPS (indicating current in ANSYS) value is
applied to down divertor inner plate as halo currents’ entrance,
and the VOLT degrees of divertor outer plate are set to zero as
halo currents’ exit. And the flowing path, the distribution of halo
3.2. Major disruption currents and the resulting EMFs can be obtained. Results show that
halo currents will flow along two paths, as shown in Fig. 9(b), one
During MD, plasma current is modeled by one coil of which through VV and the other along divertor dome plate. Fig. 10 shows
the current varies rapidly with time but the position in space is that the maximum current density and stress are about 5.5 MA/m2
constant—equivalent to plasma current described in Eq. (2). and 19.9 MPa, occurring at the support of divertor inner plate.
Results show that for VV, eddy current loop is along the toroidal
direction, detouring around the ports; as for PFCs, independent
eddy current loops flow on them since these components are nor-
mally electrically isolated from one another, as shown in Fig. 5(a);
and along PFC supports, currents flow between VV and PFCs.
Fig. 5(b) shows that eddy currents on each PFC is much less than it
on VV. The maximum eddy current on VV is about 63% of the initial
plasma current, while the maximum eddy current on PFCs is only
about 24%, occurring on inner limiter.
Once eddy current distribution is obtained, the forces and
torques can be calculated. The distribution of the resulting Lorenz
forces is shown in Fig. 6. Results show that the maximum
stress is 106 MPa, occurring at the support of inner limiter at
about 7 ms. If PFCs are not considered, the maximum stress act-
ing upon VV is only about 30 MPa, which indicating that the
forces transferred to VV from PFCs are significant. The largest
torque is in the radial direction, and those results are shown in Fig. 9. Halo current loading and path: (a) assumed entrance and exit and (b) calcu-
Fig. 6(b). lated flowing path.
1852 W. Xu et al. / Fusion Engineering and Design 88 (2013) 1848–1852

Fig. 10. Halo current distribution and the stress distribution: (a) halo current distribution and (b) stress distribution.

4. Conclusion Science, CAS Innovation Foundation (Y15FZ10133). And the authors

would like to appreciate all the team members of the EAST design
The electromagnetic and structural responses of VV and PFCs and analysis team.
for EAST are analyzed by analytical and numerical methods. The
two most dangerous scenarios: major disruptions and downward References
VDEs are considered. Results show that the distribution pattern of
[1] Y.T. Song, X.B. Peng, H. Xie, Plasma facing components of EAST, Fusion Engineer-
eddy currents for different PFCs differ greatly, therefore the result- ing and Design 85 (2010) 2323–2327.
ing EMFs and torques cause different mechanical responses. It can [2] S.J. Du, L.H. Wang, X.F. Liu, Electromagnetic analysis of the passive stabilizers for
be also seen that for certain PFCs’ supports, the transient reaction EAST, Fusion Engineering and Design 81 (2006) 2267–2273.
[3] M. Ferrari, L. Anzidei, V. Cristini, Impact of the passive stabilization system on the
forces are severe. As these forces vary drastically with time, the dynamic loads of the ITER first wall/blanket during a plasma disruption event,
dynamic effects must be considered. Based on the results obtained Fusion Engineering and Design 27 (1995) 507–514.
here, the subsequent dynamic response of the structure need to be [5] W.W. Xu, X.F. Liu, Y.T. Song, Theoretical Analysis of the induced current for vac-
uum vessel of EAST Tokamak, Nuclear Fusion and Plasma Physics 33 (2013)
analysed in the future. 30–36.
[6] Y.H. Peng, Electromagnetic and structural analyses of EAST device under Halo
Acknowledgments current, Dissertation, Institute of Plasma Physics, Chinese Academy of Sciences
(2010).

This work was supported by National Natural Science Foun-

dation of China (No. 11202207), and Hefei Institute of Physical