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Thermo-mechanical analysis of the ICRH antenna for the ignitor experiment
Fusion Engineering and Design 73 (2005) 171–180
Thermo-mechanical analysis of the ICRH antenna for the ignitor experiment Part II: Antenna straps M.F. Salvetti a , T. Berruti b,∗ , M.M. Gola b b
a Department of Mechanical Engineering, MIT, 141 Pearl Street, Cambridge, MA 02139, USA Department of Mechanical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Received 7 January 2004; received in revised form 1 June 2005; accepted 22 June 2005 Available online 12 September 2005
Abstract This paper presents the design of the ion cyclotron resonance heating (ICRH) system of the ignitor machine. In addition, the paper presents relevant calculations and the design solutions adopted for the ICRH antenna straps. The thermal–mechanical analysis of the structure is illustrated. The displacements and stresses due to thermal loading and to dynamic loads induced during plasma vertical disruptions events (VDE) are calculated. The capability of carrying out both the assembly and maintenance of the antennas’ components in full remote handling (RH) conditions is one of the specifications to which the design has to comply. A mechanical design that guarantees ease of operation is discussed. The proposed solution minimizes the variety of movements required for the manipulator. © 2005 Elsevier B.V. All rights reserved. Keywords: Plasma; Ion cyclotron resonance heating (ICRH); Antenna straps; Design
1. Introduction In the ignitor [1] experiment the injection of additional radio frequency power at the ion cyclotron range of frequencies (about 100–140 MHz) is chosen to accelerate the phase of ␣-particle heating and to control the plasma current density profile. The most signifi∗ Corresponding author. Tel.: +39 011 5646935; fax: +39 011 5646999. E-mail address: [email protected] (T. Berruti).
0920-3796/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2005.06.337
cant effect is obtained with less than 5 MW. A number of ICRH antennas ranging from three to six will be installed to provide up to 24 MW of auxiliary heating power coupled to the plasma (about 4 MW provided by each antenna). The basic building block chosen is a poloidally-directed strap, fed at one end and shortcircuited to the vacuum vessel at the other extremity. Each antenna consists of four current straps grouped in poloidal pairs (2 + 2). During a reference plasma pulse, the strap experiences plasma heat fluxes up to about 0.5 MW/m2 and
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Nomenclature a B(t) Bp BT c d D Fpol Ftor I(t) Lcable N q qy qz qp qt r t T UX UY UZ W
distance between adjacent Faraday shield bars (mm) magnetic field (T) poloidal component of the magnetic field (T) toroidal component of the magnetic field (T) specific heat of Inconel 625 ((kg K)/m3 ) distance between upper and lower plates (mm) diameter of the Faraday shield bar (mm) Lorentz forces per unit of length in the poloidal direction (kN/m) Lorentz forces per unit of length in the toroidal direction (kN/m) current per turn driven in the toroidal field magnets (MA-turn) length of the coaxial cable (mm) number of toroidal field coils force per unit of length on the FS bar (kN/m) force per unit of length in the Y direction (kN/m) force per unit of length in the Z direction (kN/m) force per unit of length generated by the poloidal field on the FS bar (kN/m) force per unit of length generated by the toroidal field on the FS bar (kN/m) radial location of the strap relative to the machine axis (m) time (s) temperature (◦ C) displacement in the X direction (mm) displacement in the Y direction (mm) displacement in the Z direction (mm) nuclear deposition power per unit of volume (MW/m3 )
Greek symbols ρ density of Inconel 625 (kg/m3 ) ψ optical transparency
nuclear heat deposition up to 22 MW/m3 for an overall energy deposition of about 180 kJ. In case of vertical displacement events (VDE), Lorentz forces generated by the induced net and eddy currents strain the strap. In this framework, the main design requirements with which the straps have to comply are: - the capability to withstand the worst expected load conditions (thermal and mechanical); - the avoidance of excessive deformations on the structure, i.e., avoiding the possibility for the strap to reach other neighbouring components (the main design distances of straps from the other components are shown in Fig. 2); - the capability to carry out both mounting and maintenance operations in full remote handling (RH) conditions. Detailed non-linear 3D finite element (FE) analyses have been performed on a single antenna strap to predict the temperature and stress distributions within the structure and to verify the structural reliability of the chosen mechanical design. This paper presents the results and describes a mechanical solution that allows for simple RH operations. 2. Antenna straps geometry The strap array is one of the elements of crucial interest of the ignitor ICRH antenna because of its exposition to relevant thermal and electromagnetic (EM) loads. The strap framework has been chosen because is a well-established and tested configuration [2] that allows for a remotely installation through a vacuum vessel (VV) port. The basic building block is a poloidally directed strap, fed at one end and shortcircuited to the VV at the other extremity. Each antenna consists of two dipoles and each dipole consists of two current straps. The straps are aligned toroidally and inserted in recesses (ports) of the plasma chamber. Each strap is fed through a dedicated coaxial cable and a power amplifier and is properly phased to produce the required dipole array radiation pattern. The baseline EM design is a dipole mode with phase reversal between the feeding currents. When necessary, any phasing can be allowed, e.g., to compensate for plasma asymmetry.
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Fig. 2. Main distances (mm) of straps from the other components.
Fig. 1. Side view and front view of the Ignitor ICRH straps.
The geometry of the antenna is shown in Fig. 1. The two straps that constitute a dipole slightly differ in shape. In particular, the plasma facing plates are identical, but one of the straps (strap A in Fig. 1) has a longer lower plate to provide a proper connection to the coaxial cable, while the other (strap B in Fig. 1) has a shorter lower plate. Since the access port is narrower than the antenna itself, the feeders and the coaxial lines are grouped on the central part of the antenna and the RH assembly must be carried out from an adjacent port. Clearly, this solution excludes the presence of a septum between the dipoles. Each strap is fabricated with Inconel 625 alloy and is coated with a copper layer of 20–30 m, a thickness that exceeds the material skin depth at the relevant frequencies (100–140 MHz). The basic configuration of the straps has been chosen to produce the required EM high frequency behavior [3]. In particular, the length and width of the plasma facing plates are chosen taking into account only EM requirements. A subsequent structural optimization analysis allowed us to define the geometrical details of the strap, while satisfying all the relevant EM specifications. The final design complies with the relatively long length of the lower plate and the presence of the side arm (Fig. 1) that connects the lower strap plate to the coaxial cable. These elements enhance the bending and torque moments over the structure when exposed to thermal and mechanical loads. In order to
increase the rigidity of the structure and to optimize the limited space available, the two straps constituting a dipole are connected to each other at one extremity, sharing the central support that short-circuits them to the VV, to form a single mechanical structure. The main design distances of the straps from the other first wall (FW) elements are shown in Fig. 2 and the entire set of relevant geometrical parameters is listed in Table 1. The results presented in this article confirm the validity of the chosen design and the structural reliability of the straps.
3. Thermal loads The ICRH antenna straps are subjected to two types of thermal loads: plasma heat flux and nuclear energy deposition. The Joule dissipation produced by the curTable 1 Geometrical parameters of the ICRH strap Parameter
Value (mm)
Length of the plasma facing plate, L Length of the curved part of the lower plate, Li Width of the plates, Ws Thickness of the plates, Tp Radius of curvature of the plates, R Width of the side arm, Wcc Length of the side arm, Lcc Distance between upper and lower plates, d Length of the central support, Lpc Radius of curvature of fillets, Rf Length of the coaxial cable, Lcable
360 170 120 10 1818 72 134 44 88 22 200, 500, 1000
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rents flowing within the straps is estimated to be minimal and it is not modeled. In particular, during a VDE the Joule dissipation generated by the induced currents flowing on the strap is about 6–7 W/m3 and the overall energy deposition is very small (order of Joules) because of the short deposition time (about 5 ms). Plasma heat flux. Normally, the heat flux on the plasma facing components originates from both plasma radiation and charged particle transport. However, since the straps are recessed relative to the first wall and partially shielded by the Faraday shield (FS) rods and the surrounding tiles, the heat flux on the surfaces of the ICRH antennas straps is mainly ascribed to radiation. As a consequence, in the FE simulations no direct particle heat flux is modeled. The heat flux on the straps is evaluated by assuming that 70% of the total power of the ignitor machine (about 26 MW), operating at full parameters and at ignition conditions, radiates uniformly toward the FW. The overall surface of the FW is conservatively assumed to be identical to the plasma surface (36 m2 ) leading to a mean heat flux value on the straps of about 0.5 MW/m2 . The flux distribution over the straps is affected by the presence of the FS that acts as a material shield to the thermal loads. The expected heat flux distribution on the straps is characterized by a sequence of Gaussian-like shaped curves with peak values located in correspondence to the regions unshielded by the FS bars. In the FE simulations, the presence of the FS is considered in terms of the amount and distribution of the power that reaches the strap surfaces. The FS elements are designed to have an optical transparency factor ψ = 0.5, with ψ defined as the ratio of the distance between two adjacent FS bars (a) to the sum of the bar diameter (D) and the bar separation distance (ψ = a/(a + D)). Thus, it is assumed that the presence of the FS decreases the power that reaches the straps by a factor of about 2. Nuclear energy deposition. The nuclear energy deposition over the strap is guardedly estimated to be 22 MW/m3 . The value due to both neutron and gammas, averaged over the whole FW, is about 11 MW/m3 for an average shot, while it can reach a value of 22 MW/m3 in case of a peak neutron production [6]. During a reference plasma pulse, the strap is estimated to accumulate about 180 kJ of energy, of which
about 90 kJ are ascribed to nuclear energy deposition. Despite a similar contribution in terms of energy deposited over the strap, the plasma heat flux gives rise to high local temperatures while the nuclear heating deposition determines a uniform temperature increase over the structure. To quantify the order of magnitude of the thermal loads involved, the temperature of the strap would rise from 0 ◦ C to about 50 ◦ C, if the 180 kJ of energy were deposited uniformly.
4. Plasma vertical disruption event During a VDE the ICRH antenna straps are subjected to intense EM forces, which can be classified as two different kinds: (1) Lorentz forces originated by the interaction of the magnetic fields (toroidal and poloidal) and the induced net currents flowing within the straps. (2) Lorentz forces originated by the presence of eddy currents that flow in closed loops within the straps. Lorentz forces originated by the induced net currents. During a VDE the poloidal magnetic field Bp at the antenna location varies according to the following equation: Bp (t) = At2 + Bt + C, where A = 105 T/s2 , B = −103 T/s and C = 5 T. The electrical circuit constituted by the plasma chamber (ground), the strap, the coaxial cable and the coaxial cable’s connection to ground determines an area linked to the poloidal field Bp . As a consequence, a change in time of Bp determines a net induced current flowing within the circuit. Similarly to the case of the Faraday shield [4,5], the electrical circuit is modelled as a simple resistive lumped parameter circuit that takes into account the electrical resistance of the strap and of the coaxial cable. In this case, the inductance of the system has been neglected. The circuit equation is solved analytically and the peak value reached by the net induced current on the strap is about 3.7 kA. The directions of the currents flowing in the straps are imposed by the geometry of the straps and Lentz’s law. In particular, taking into account the geometry of the proposed ICRH antenna (Fig. 1), the currents flow from the plasma chamber to the coaxial cables in the two straps positioned on the left side of the strap array, and they flow
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VDE Lorentz forces due to the eddy currents. The eddy currents are circular currents induced by the variation of the magnetic field in the strap. The nodal values of the Lorentz forces due to the eddy currents are obtained from a numerical simulation of the strap EM behavior [3,4].
5. FE analysis
Fig. 3. Lorentz forces per unit length induced on the strap.
from the coaxial cable to the plasma chamber in the straps on the right side. At the antenna’s location, a conservative value of 9 T for the toroidal field is adopted. The value is computed by using the relation BT (r) =
µ0 NI 2πr
(1)
solution for the equation
· dl = H
J · n dS
(2)
integrated over a circular surface of radius r perpendicular to the machine axis, where N = 24 is the number of toroidal magnets of the ignitor machine, I = 85.7 MAturn the highest current driven in the magnets and r = 1.8 m the distance from the machine axis at which the straps are located. The interaction between the poloidal magnetic field, the toroidal magnetic field and the induced net currents, originates the Lorentz forces applied on the straps. In particular, the peak values of the toroidal and poloidal components of the forces (per unit length) are Ftor = 33.3 kN/m and Fpol = 18.5 kN/m. A sketch of the Lorentz forces behavior in time is shown in Fig. 3. Since the straps are joined two by two and share the central support, the intensity of the current flowing through the central support is the sum of the current intensities flowing on the plates of the joined straps. During a VDE, this configuration leads to Lorentz forces per unit of length of about 70 kN/m on the central support.
A 3D FE parametric model of a single strap was created (ANSYS code release 5.7). Since the lower plates of the straps are shielded from direct thermal loads, the length of the lower plate has a minimal influence on the thermal behavior of the strap. Thus, in order to limit computational time, only the strap characterized by the longer lower plate is modeled (strap A in Fig. 1). This is the strap subjected to the highest stresses in case of a VDE. Moreover, all the assumptions introduced to reduce the complexity of the FE model lead to results that are conservative when extended to the case of the complete structure. The FE model is used to run both thermal and structural non-linear analyses. The geometry of the model and a set of selected nodes are shown in Fig. 4. The dark stripes visible in the magnified window of Fig. 4 are representative of the regions to which the heat flux loads are applied. Nodes A, B, C, D, E and G are located on the surface of the model and on plane Z = 0. Node F is located at the connection to the coaxial cable. Structural constraints: All the nodes located at the end 1 (Fig. 4) are constrained along the three directions UX , UY and UZ to simulate a perfectly rigid constraint. This solution does not take into account the deformations of the plasma chamber during a VDE. Nevertheless, FE simulations [7] show that at the equatorial location, where the ICRH antennas will be installed, the chamber undergoes minimal deformations. Moreover, the assumption of perfectly rigid constraints leads to conservative results in terms of stress distributions. At the other end of the strap (end 2 in Fig. 4), part of the coaxial cable is modeled to take into account the flexibility of the connection. One side of the cable is constrained along the three directions UX , UY and UZ , while the opposite side is connected to the strap. The 65 mm Ø inner element of the coaxial cable is the only part of the cable that is modeled. In order to simplify
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Fig. 4. FE model of the strap and part of coaxial cable.
the model, a rectangular cross section is used instead of a circular one. The effect of a change in length of the coaxial cable over the structural behavior of the strap will be discussed in Section 6. At present, the reference length of the cable, i.e., the distance between the connection to the strap and that to the vacuum port, is 200 mm. Boundary conditions modeling symmetry are introduced on the central support to model the interface between two straps. Because of the non-symmetrical distribution of the Lorentz forces over the two straps, the symmetry boundary condition is not rigorously extendable to a structural analysis that takes into account the VDE dynamic loads. In this case, the symmetry constraints on the central support are removed, the thermal stress distribution is taken into account by modeling it as a pre-stressed initial condition, and the Lorentz forces are added. Since the full set of Lorentz forces is applied on the central support but only half
of the thickness of the support is modeled, the computed stress distribution over the central support and the related displacements are conservative compared to the real case. Moreover, the superimposition of the dynamic EM forces on an initial thermal stress distribution is justified by the considerable difference in the time scales of the two phenomena. In particular, in the ignitor machine a VDE is expected to occur in less than 10 ms, a time length during which the temperature distribution over the strap does not change significantly. Thermal constraints: The temperature of the strap at the beginning of the plasma pulse is about 20 ◦ C. Since the strap operates in nearly vacuum conditions, no radiation is modeled. In particular, the heat extraction mostly occurs by conduction through the connections to the plasma chamber and the coaxial cable. Nevertheless, the thermal conduction time scale is greater than that of the plasma pulse. Therefore, the strapcoaxial cable system is assumed to be adiabatic during the plasma pulse. During the entire plasma pulse, the near constancy of the temperatures in proximity to the connections of the strap and of the coaxial cable to the VV confirms the validity of the assumption. Material: In the FE simulations, the real non-linear elastic–plastic material properties of the Inconel 625 alloy, a nickel–chromium alloy, are used. This material has been chosen because of its high resistivity and high mechanical strength. In particular, a high electrical resistivity allows to limit the intensity of the currents induced on the straps during plasma disruption events and, therefore, to limit the induced Lorentz forces. Unfortunately, Inconel 625 is also characterized by a low thermal conductivity that makes heat extraction from the straps difficult and increases the required cooling time. Nevertheless, the time required to cool down the copper magnets of the machine, about 5 h, is long enough to allow for the cooling of the strap elements. All the structural analyses adopt temperature dependent material properties. The temperature dependent stress–strain curves implemented in the code are shown in [5]. 5.1. Thermal analysis A transient thermal analysis of the strap is initially performed. The nodal temperature values during the plasma pulse are obtained. The thermal stress distribu-
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the Inconel 625 coefficient of thermal conduction, the regions of the strap not directly loaded by the plasma heat flux remain rather cold during the plasma pulse. During the pulse flattop, the nuclear energy deposition is responsible for a nearly uniform temperature increase of about 25 ◦ C. This value is consistent to the one computed by means of the simple energy balance equation c¯ · ρ · T = W · t
(3)
where c¯ is the mean value of the Inconel 625 specific heat at 20 and 45 ◦ C, ρ the nearly constant material density, T the temperature increase in the period t, and W the nuclear deposition power per unit of volume. Fig. 5. Temperature during the reference plasma pulse at selected nodes.
tions during the plasma pulse are calculated by carrying out a second transient FE analysis in which the temperature distributions are used as inputs. Also, a third simulation is performed to compute the residual stresses on the structure. Note that the presence of residual stresses on the strap is possible only if during the plasma pulse the von Mises equivalent stresses exceed the plastic yield limit of the material in localized regions of the strap. Benchmarking of the results was done by solving similar thermal and elastic–plastic problems over simpler geometries and comparing results to the available analytical solutions [8]. 5.1.1. Results: temperature distribution Fig. 5 shows the temperature of relevant selected nodes of the FE model during the plasma pulse. The highest temperature value, 239 ◦ C, is experienced shortly after the end of the flattop (t = 8.3 s), while it will be shown that the highest thermal stresses are experienced at the end of the plasma pulse. In fact, despite the fact that the energy stored by the strap increases until the end of the plasma pulse, peak temperatures decrease after the end of the flattop because of the prevailing effect of thermal diffusion over energy deposition. Since the melting points of Inconel 625 and copper are about 1290 and 1083 ◦ C, respectively, the highest temperatures reached are not sufficient to cause localized melting on the structure. Given the low value of
5.1.2. Results: stresses induced by temperature As stated before, the highest thermal stresses are experienced at the end of the reference plasma pulse (t = 10 s), when the plasma column has deposited the highest amount of energy into the strap. Results show that no plastic yielding occurs on the strap, with the exception of one of the fingers connecting the strap to the coaxial cable, where about 3% of the cross section exceeds the plastic yield limit. Nevertheless, the yielding in the simulation has to be ascribed to the accuracy of the FE model. In fact, the model introduces stress concentration factors by approximating the fillet transitions between the surfaces of the real structure to sharp edges. Without taking into account the factitious yielding at the connection to the coaxial cable, the thermal loads applied on the strap are insufficient to cause plastic yielding and, therefore, no residual stresses are present on the strap after cooling. This statement is strictly accurate only in the case of complete absence of residual stresses generated by the manufacturing process of the strap. Nevertheless, this condition can be approached by exposing the structure to stress relieving processes before installing it inside the plasma chamber. The simulations show that the thermal loads expected on the strap neither generate permanent deformations on the structure nor undermine its reliability. The highest von Mises equivalent stresses and the total von Mises equivalent strains at the end of the plasma pulse are listed in Table 2; the highest nodal displacements in Table 3.
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Table 2 Highest von Mises equivalent stresses and total von Mises equivalent strains at the end of the plasma pulse
Table 4 Highest von Mises equivalent stresses and total strains during VDE and thermal loads
Location
Stress (MPa)
Strain
Location
Stress (MPa)
Strain
Plasma facing plate Lower plate Connection to the plasma chamber (central support) Connection to the coaxial cable
226 142 192
0.0015 0.0009 0.0012
367 317 367
0.0029 0.0021 0.0027
329
0.0023
Plasma facing plate Lower plate Interface between upper and lower plates Connection to the plasma chamber (central support) Connection to the coaxial cable
309
0.0018
405
0.0039
5.2. Combination of thermal loads and Lorentz forces during a VDE EM loads induced during a VDE are superimposed on thermal loads. A VDE can occur at any time during the flattop phase of the plasma pulse. In the simulation, the VDE is assumed to occur at the end of the flattop (t = 8 s), when the strap is characterized by its worst thermal stress configuration. Thus, the initial condition of the structure is assumed to be the stress distribution generated by the thermal loads at the end of the flattop. In addition to the thermal loads, the Lorentz forces generated by the induced net currents and those generated by the eddy currents are the external loads applied to the FE structural model. A transient analysis is performed by taking into account a load that increases linearly in time, from the initial condition (highest thermal stress distribution) to the highest forces applied during a VDE. In particular, the peak values of the Lorentz forces generated by the induced net currents and the eddy currents have been conservatively assumed to be simultaneous. 5.2.1. Results: stresses induced by thermal and EM loads The highest von Mises equivalent stresses and total von Mises equivalent strains are listed in Table 4; the highest displacements in Table 5.
Plastic yielding is experienced at localized regions of the plasma facing plate and at the connection to the coaxial cable. It is mainly due to equivalent bending moments along the X and Y directions (the reference triad is shown in Fig. 3) generated by the Lorentz forces applied on the strap. Conditions approaching the yielding limit are experienced at localized regions on the plasma facing plate surface. In particular, these conditions could be sufficiently severe to damage a ceramic coating applied on the strap to prevent it from possible electrical arching with the VV. In this regard, it is preferable not to employ a ceramic coating, normally Al2 O3 . Instead, by taking advantage of the modeling capabilities of the TOPICA code [3], an EM design of the straps that highly reduces the risk of breaking voltages is adopted. Like the case of the thermal stress analysis, yielding is experienced only at selected regions in proximity of sharp edges where stress concentration factors play an important role. Moreover, yielded regions on the plasma facing plate are confined to the surfaces of the plate and thus do not undermine the structural behavior of the strap. According to the simulation, the highest component of the strap displacement during a VDE is about 6 mm in the radial direction at the interface between the plasma facing plate and the lower plate of the strap (zone 3 in Fig. 4) and roughly 7% of the fingers cross section exceeds the plastic yield limit.
Table 3 Highest displacements of the strap at the end of the plasma pulse
Table 5 Highest displacements during VDE and thermal loads
Highest poloidal displacement, UX (mm) Highest radial displacement, UY (mm) Highest toroidal displacement, UZ (mm)
Highest poloidal displacement, UX (mm) Highest radial displacement, UY (mm) Highest toroidal displacement, UZ (mm)
0.6 −1.3 0.3
Zone 1 Zone 1 Zone 2
0.9 −5.7 2.6
Zone 1 Zone 3 Zone 2
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Table 6 Effects of the coaxial cable length on the strap structural behavior Parameter
UX (mm) UY (mm) UZ (mm) Highest von Mises stress (MPa) Highest von Mises strain
Lcable
Zone
200 mm (reference configuration)
500 mm
1000 mm
0.9 −5.7 2.6 405 0.0039
1.0 −5.5 2.7 408 0.0039
1.0 −5.4 2.7 399 0.0042
6. Influence of the coaxial cable length A parametric structural analysis is performed varying the length of the coaxial cable (Lcable in Fig. 4). Three different lengths are considered: 200, 500 and 1000 mm. All the results presented previously refer to a 200 mm long coaxial cable that is constrained at the beginning of the port, shortly outside the plasma chamber. Table 6 lists few parameters that are indicators of the structural behavior of the strap when the length of the coaxial cable is changed. Results show that the length of the coaxial cable does not affect the stress and strain distributions on the strap significantly. In the range of the coaxial cable lengths considered, it can be deduced that the choice of the length will be driven only by electrical, vacuum related and convenience factors.
Zone 1 Zone 3 Zone 2
devices of the straps and the FS elements must guarantee ease of operation, a sufficient degree of reliability and an acceptable rapidity in performing maintenance operations. The suggested solution uniforms the movements required by the assembly of all the antenna components and, therefore, requires the RH system to perform a minimal variety of movements. The clamping systems are welded to the straps. The straps-coaxial cables and straps-central support use the same principle for their connections. The architecture of the suggested clamp is shown in Fig. 6. In particular, the clamping system has been designed with the following features: - Presence of wedge systems to fasten the strap to the coaxial cable. - Use of a locking ring to secure the bolt to the clamp during RH movements and to keep the wedge in position.
7. Design details Taking into account the difficulties in bending a relatively long plate by an angle of 180◦ while providing a small radius of curvature (d/2 = 22 mm), the suggested solution is to manufacture the plasma facing plate and the lower plate of the strap as two different pieces. The two plates are subsequently welded together by means of an interface element (welding details in Fig. 1). The use of welding is proposed as a possible solution. The ultimate choice will be in charge of the vendor who owns the technology: in case of availability of a technology capable of bending the plates without failure, each strap can be machined as a single piece without welding. The capability of operating the assembly and maintenance of the ignitor’s ICRH antennas in full RH conditions is one of the tightest specifications to which the design has to comply. In particular, the clamping
Fig. 6. Clamp system of the strap to the coaxial cable.
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- Presence of a machined shaping (1) on the coaxial cable (and on the central support) to avoid possible separation between the clamp and the coaxial cable (Fig. 6). - Presence of a machined shaping (2) on the coaxial cable (and on the central support) to locate the clamp during RH assembly (Fig. 6). - Ability to carry out easy maintenance operations in case of damage of the internal threads. As a consequence, only the strap module has to be substituted. Both the bolt and the internal threads of the clamp are subcomponents of the removable strap. Since no threads are present on the coaxial cable and on the central support, the need for maintenance of these components is minimized.
no impact over the structural behavior of the strap. The simulations show that the structural response of the strap is not particularly sensitive to the length of the coaxial cable. Thus, from a mechanical point of view, there are no limiting factors relative to the location of the coaxial cables connection to the VV port. Taking into account the need of operating the assembly and maintenance of the ignitor’s ICRH antennas in full RH, a possible technical solution is suggested. The straps carry the clamps for the attachment to the coaxial cables and to the central support. This solution allows uniforming and minimizing the movements required to the RH manipulator. Moreover, in this solution bolts and internal threads are in the clamps (removable with the strap) and can be easily substituted in case of damage.
8. Conclusions Acknowledgements The longer straps (strap A) of the ICRH antenna array are those subjected to the highest loads. FE simulations show that the structure is able to withstand the applied thermal and EM loads. Conservative assumptions about the applied loads have been introduced to obtain a reliable mechanical design and account for possible unexpected load conditions. Thermal loads produce no plastic yielding on any region of the strap but some at the connection to the coaxial cable. Nevertheless, at this location, plasticization can be avoided by adopting geometrical configurations that reduce the presence of stress concentration factors, such as the clamping solution presented in this work. The highest temperatures reached are well below the Inconel 625 melting point and the energy stored during a plasma pulse is exhausted mainly via thermal conduction through the VV and the coaxial cable. During a VDE, peak dynamic displacements in the radial direction of about 6 mm (zone 3 in Fig. 4) are expected. The highest displacements in the poloidal and toroidal directions are within 3 mm. On the surface of the plasma facing plate, the combination of thermal and EM loads produces conditions approximating plastic yield limit. In particular, limited surface plasticization is experienced at the interface between the plasma facing plate and the lower plate but it has
Many thanks are due to B. Coppi and F. Bombarda for their useful suggestions and stimulating discussions on this subject.
References [1] B. Coppi, A. Airoldi, F. Bombarda, Optimal regimes for ignitor and the ignitor experiment, Nucl. Fusion 41 (9) (2001) 1253. [2] T. Fujii, M. Saigusa, Mechanical Design and Analysis of JT-60U ICRF Launcher, 91CH3035-3S03.00 IEEE, 1992, pp. 107–110. [3] G. Vecchi, Third and Final Technical Report: Analysis and Design of the ICRH system for the IGNITOR machine, Politecnico di Torino, contract no. 97/58/50/88, 2003. [4] M. Riccitelli, G. Vecchi, R. Maggiora, C.K. Phillips, ICRF heating scenarios for the IGNITOR machine, Fusion Eng. Des. 45 (1999) 1–13. [5] T. Berruti, M.M. Gola, M.F. Salvetti, Thermo-mechanical analysis of the ICRH antenna for the ignitor experiment. Part I: Faraday shield, Fusion Eng, Des. 73 (2005) 155–169. [6] S. Rollet, P. Batistoni, R. Forrest, Activation analysis for the ignitor tokamak, Fusion Eng. Des. 51 (2000) 599. [7] G. Mazzone, A. Pizzuto, Transient behavior of the ignitor plasma chamber under vertical displacement and halo current event, in: Proceedings of the 17th IEEE/NPSS Symposium on Fusion Engineering, San Diego, CA, October 6–10, 1997. [8] M. Salvetti, Thermo-mechanical analysis of the ICRH antenna’s Faraday shield in the ignitor machine, Master Thesis, University of Illinois, Chicago, 2001.
Thermo-mechanical analysis of the ICRH antenna for the ignitor experiment Part II: Antenna straps M.F. Salvetti a , T. Berruti b,∗ , M.M. Gola b b
a Department of Mechanical Engineering, MIT, 141 Pearl Street, Cambridge, MA 02139, USA Department of Mechanical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Received 7 January 2004; received in revised form 1 June 2005; accepted 22 June 2005 Available online 12 September 2005
Abstract This paper presents the design of the ion cyclotron resonance heating (ICRH) system of the ignitor machine. In addition, the paper presents relevant calculations and the design solutions adopted for the ICRH antenna straps. The thermal–mechanical analysis of the structure is illustrated. The displacements and stresses due to thermal loading and to dynamic loads induced during plasma vertical disruptions events (VDE) are calculated. The capability of carrying out both the assembly and maintenance of the antennas’ components in full remote handling (RH) conditions is one of the specifications to which the design has to comply. A mechanical design that guarantees ease of operation is discussed. The proposed solution minimizes the variety of movements required for the manipulator. © 2005 Elsevier B.V. All rights reserved. Keywords: Plasma; Ion cyclotron resonance heating (ICRH); Antenna straps; Design
1. Introduction In the ignitor [1] experiment the injection of additional radio frequency power at the ion cyclotron range of frequencies (about 100–140 MHz) is chosen to accelerate the phase of ␣-particle heating and to control the plasma current density profile. The most signifi∗ Corresponding author. Tel.: +39 011 5646935; fax: +39 011 5646999. E-mail address: [email protected] (T. Berruti).
0920-3796/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2005.06.337
cant effect is obtained with less than 5 MW. A number of ICRH antennas ranging from three to six will be installed to provide up to 24 MW of auxiliary heating power coupled to the plasma (about 4 MW provided by each antenna). The basic building block chosen is a poloidally-directed strap, fed at one end and shortcircuited to the vacuum vessel at the other extremity. Each antenna consists of four current straps grouped in poloidal pairs (2 + 2). During a reference plasma pulse, the strap experiences plasma heat fluxes up to about 0.5 MW/m2 and
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Nomenclature a B(t) Bp BT c d D Fpol Ftor I(t) Lcable N q qy qz qp qt r t T UX UY UZ W
distance between adjacent Faraday shield bars (mm) magnetic field (T) poloidal component of the magnetic field (T) toroidal component of the magnetic field (T) specific heat of Inconel 625 ((kg K)/m3 ) distance between upper and lower plates (mm) diameter of the Faraday shield bar (mm) Lorentz forces per unit of length in the poloidal direction (kN/m) Lorentz forces per unit of length in the toroidal direction (kN/m) current per turn driven in the toroidal field magnets (MA-turn) length of the coaxial cable (mm) number of toroidal field coils force per unit of length on the FS bar (kN/m) force per unit of length in the Y direction (kN/m) force per unit of length in the Z direction (kN/m) force per unit of length generated by the poloidal field on the FS bar (kN/m) force per unit of length generated by the toroidal field on the FS bar (kN/m) radial location of the strap relative to the machine axis (m) time (s) temperature (◦ C) displacement in the X direction (mm) displacement in the Y direction (mm) displacement in the Z direction (mm) nuclear deposition power per unit of volume (MW/m3 )
Greek symbols ρ density of Inconel 625 (kg/m3 ) ψ optical transparency
nuclear heat deposition up to 22 MW/m3 for an overall energy deposition of about 180 kJ. In case of vertical displacement events (VDE), Lorentz forces generated by the induced net and eddy currents strain the strap. In this framework, the main design requirements with which the straps have to comply are: - the capability to withstand the worst expected load conditions (thermal and mechanical); - the avoidance of excessive deformations on the structure, i.e., avoiding the possibility for the strap to reach other neighbouring components (the main design distances of straps from the other components are shown in Fig. 2); - the capability to carry out both mounting and maintenance operations in full remote handling (RH) conditions. Detailed non-linear 3D finite element (FE) analyses have been performed on a single antenna strap to predict the temperature and stress distributions within the structure and to verify the structural reliability of the chosen mechanical design. This paper presents the results and describes a mechanical solution that allows for simple RH operations. 2. Antenna straps geometry The strap array is one of the elements of crucial interest of the ignitor ICRH antenna because of its exposition to relevant thermal and electromagnetic (EM) loads. The strap framework has been chosen because is a well-established and tested configuration [2] that allows for a remotely installation through a vacuum vessel (VV) port. The basic building block is a poloidally directed strap, fed at one end and shortcircuited to the VV at the other extremity. Each antenna consists of two dipoles and each dipole consists of two current straps. The straps are aligned toroidally and inserted in recesses (ports) of the plasma chamber. Each strap is fed through a dedicated coaxial cable and a power amplifier and is properly phased to produce the required dipole array radiation pattern. The baseline EM design is a dipole mode with phase reversal between the feeding currents. When necessary, any phasing can be allowed, e.g., to compensate for plasma asymmetry.
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Fig. 2. Main distances (mm) of straps from the other components.
Fig. 1. Side view and front view of the Ignitor ICRH straps.
The geometry of the antenna is shown in Fig. 1. The two straps that constitute a dipole slightly differ in shape. In particular, the plasma facing plates are identical, but one of the straps (strap A in Fig. 1) has a longer lower plate to provide a proper connection to the coaxial cable, while the other (strap B in Fig. 1) has a shorter lower plate. Since the access port is narrower than the antenna itself, the feeders and the coaxial lines are grouped on the central part of the antenna and the RH assembly must be carried out from an adjacent port. Clearly, this solution excludes the presence of a septum between the dipoles. Each strap is fabricated with Inconel 625 alloy and is coated with a copper layer of 20–30 m, a thickness that exceeds the material skin depth at the relevant frequencies (100–140 MHz). The basic configuration of the straps has been chosen to produce the required EM high frequency behavior [3]. In particular, the length and width of the plasma facing plates are chosen taking into account only EM requirements. A subsequent structural optimization analysis allowed us to define the geometrical details of the strap, while satisfying all the relevant EM specifications. The final design complies with the relatively long length of the lower plate and the presence of the side arm (Fig. 1) that connects the lower strap plate to the coaxial cable. These elements enhance the bending and torque moments over the structure when exposed to thermal and mechanical loads. In order to
increase the rigidity of the structure and to optimize the limited space available, the two straps constituting a dipole are connected to each other at one extremity, sharing the central support that short-circuits them to the VV, to form a single mechanical structure. The main design distances of the straps from the other first wall (FW) elements are shown in Fig. 2 and the entire set of relevant geometrical parameters is listed in Table 1. The results presented in this article confirm the validity of the chosen design and the structural reliability of the straps.
3. Thermal loads The ICRH antenna straps are subjected to two types of thermal loads: plasma heat flux and nuclear energy deposition. The Joule dissipation produced by the curTable 1 Geometrical parameters of the ICRH strap Parameter
Value (mm)
Length of the plasma facing plate, L Length of the curved part of the lower plate, Li Width of the plates, Ws Thickness of the plates, Tp Radius of curvature of the plates, R Width of the side arm, Wcc Length of the side arm, Lcc Distance between upper and lower plates, d Length of the central support, Lpc Radius of curvature of fillets, Rf Length of the coaxial cable, Lcable
360 170 120 10 1818 72 134 44 88 22 200, 500, 1000
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rents flowing within the straps is estimated to be minimal and it is not modeled. In particular, during a VDE the Joule dissipation generated by the induced currents flowing on the strap is about 6–7 W/m3 and the overall energy deposition is very small (order of Joules) because of the short deposition time (about 5 ms). Plasma heat flux. Normally, the heat flux on the plasma facing components originates from both plasma radiation and charged particle transport. However, since the straps are recessed relative to the first wall and partially shielded by the Faraday shield (FS) rods and the surrounding tiles, the heat flux on the surfaces of the ICRH antennas straps is mainly ascribed to radiation. As a consequence, in the FE simulations no direct particle heat flux is modeled. The heat flux on the straps is evaluated by assuming that 70% of the total power of the ignitor machine (about 26 MW), operating at full parameters and at ignition conditions, radiates uniformly toward the FW. The overall surface of the FW is conservatively assumed to be identical to the plasma surface (36 m2 ) leading to a mean heat flux value on the straps of about 0.5 MW/m2 . The flux distribution over the straps is affected by the presence of the FS that acts as a material shield to the thermal loads. The expected heat flux distribution on the straps is characterized by a sequence of Gaussian-like shaped curves with peak values located in correspondence to the regions unshielded by the FS bars. In the FE simulations, the presence of the FS is considered in terms of the amount and distribution of the power that reaches the strap surfaces. The FS elements are designed to have an optical transparency factor ψ = 0.5, with ψ defined as the ratio of the distance between two adjacent FS bars (a) to the sum of the bar diameter (D) and the bar separation distance (ψ = a/(a + D)). Thus, it is assumed that the presence of the FS decreases the power that reaches the straps by a factor of about 2. Nuclear energy deposition. The nuclear energy deposition over the strap is guardedly estimated to be 22 MW/m3 . The value due to both neutron and gammas, averaged over the whole FW, is about 11 MW/m3 for an average shot, while it can reach a value of 22 MW/m3 in case of a peak neutron production [6]. During a reference plasma pulse, the strap is estimated to accumulate about 180 kJ of energy, of which
about 90 kJ are ascribed to nuclear energy deposition. Despite a similar contribution in terms of energy deposited over the strap, the plasma heat flux gives rise to high local temperatures while the nuclear heating deposition determines a uniform temperature increase over the structure. To quantify the order of magnitude of the thermal loads involved, the temperature of the strap would rise from 0 ◦ C to about 50 ◦ C, if the 180 kJ of energy were deposited uniformly.
4. Plasma vertical disruption event During a VDE the ICRH antenna straps are subjected to intense EM forces, which can be classified as two different kinds: (1) Lorentz forces originated by the interaction of the magnetic fields (toroidal and poloidal) and the induced net currents flowing within the straps. (2) Lorentz forces originated by the presence of eddy currents that flow in closed loops within the straps. Lorentz forces originated by the induced net currents. During a VDE the poloidal magnetic field Bp at the antenna location varies according to the following equation: Bp (t) = At2 + Bt + C, where A = 105 T/s2 , B = −103 T/s and C = 5 T. The electrical circuit constituted by the plasma chamber (ground), the strap, the coaxial cable and the coaxial cable’s connection to ground determines an area linked to the poloidal field Bp . As a consequence, a change in time of Bp determines a net induced current flowing within the circuit. Similarly to the case of the Faraday shield [4,5], the electrical circuit is modelled as a simple resistive lumped parameter circuit that takes into account the electrical resistance of the strap and of the coaxial cable. In this case, the inductance of the system has been neglected. The circuit equation is solved analytically and the peak value reached by the net induced current on the strap is about 3.7 kA. The directions of the currents flowing in the straps are imposed by the geometry of the straps and Lentz’s law. In particular, taking into account the geometry of the proposed ICRH antenna (Fig. 1), the currents flow from the plasma chamber to the coaxial cables in the two straps positioned on the left side of the strap array, and they flow
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VDE Lorentz forces due to the eddy currents. The eddy currents are circular currents induced by the variation of the magnetic field in the strap. The nodal values of the Lorentz forces due to the eddy currents are obtained from a numerical simulation of the strap EM behavior [3,4].
5. FE analysis
Fig. 3. Lorentz forces per unit length induced on the strap.
from the coaxial cable to the plasma chamber in the straps on the right side. At the antenna’s location, a conservative value of 9 T for the toroidal field is adopted. The value is computed by using the relation BT (r) =
µ0 NI 2πr
(1)
solution for the equation
· dl = H
J · n dS
(2)
integrated over a circular surface of radius r perpendicular to the machine axis, where N = 24 is the number of toroidal magnets of the ignitor machine, I = 85.7 MAturn the highest current driven in the magnets and r = 1.8 m the distance from the machine axis at which the straps are located. The interaction between the poloidal magnetic field, the toroidal magnetic field and the induced net currents, originates the Lorentz forces applied on the straps. In particular, the peak values of the toroidal and poloidal components of the forces (per unit length) are Ftor = 33.3 kN/m and Fpol = 18.5 kN/m. A sketch of the Lorentz forces behavior in time is shown in Fig. 3. Since the straps are joined two by two and share the central support, the intensity of the current flowing through the central support is the sum of the current intensities flowing on the plates of the joined straps. During a VDE, this configuration leads to Lorentz forces per unit of length of about 70 kN/m on the central support.
A 3D FE parametric model of a single strap was created (ANSYS code release 5.7). Since the lower plates of the straps are shielded from direct thermal loads, the length of the lower plate has a minimal influence on the thermal behavior of the strap. Thus, in order to limit computational time, only the strap characterized by the longer lower plate is modeled (strap A in Fig. 1). This is the strap subjected to the highest stresses in case of a VDE. Moreover, all the assumptions introduced to reduce the complexity of the FE model lead to results that are conservative when extended to the case of the complete structure. The FE model is used to run both thermal and structural non-linear analyses. The geometry of the model and a set of selected nodes are shown in Fig. 4. The dark stripes visible in the magnified window of Fig. 4 are representative of the regions to which the heat flux loads are applied. Nodes A, B, C, D, E and G are located on the surface of the model and on plane Z = 0. Node F is located at the connection to the coaxial cable. Structural constraints: All the nodes located at the end 1 (Fig. 4) are constrained along the three directions UX , UY and UZ to simulate a perfectly rigid constraint. This solution does not take into account the deformations of the plasma chamber during a VDE. Nevertheless, FE simulations [7] show that at the equatorial location, where the ICRH antennas will be installed, the chamber undergoes minimal deformations. Moreover, the assumption of perfectly rigid constraints leads to conservative results in terms of stress distributions. At the other end of the strap (end 2 in Fig. 4), part of the coaxial cable is modeled to take into account the flexibility of the connection. One side of the cable is constrained along the three directions UX , UY and UZ , while the opposite side is connected to the strap. The 65 mm Ø inner element of the coaxial cable is the only part of the cable that is modeled. In order to simplify
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Fig. 4. FE model of the strap and part of coaxial cable.
the model, a rectangular cross section is used instead of a circular one. The effect of a change in length of the coaxial cable over the structural behavior of the strap will be discussed in Section 6. At present, the reference length of the cable, i.e., the distance between the connection to the strap and that to the vacuum port, is 200 mm. Boundary conditions modeling symmetry are introduced on the central support to model the interface between two straps. Because of the non-symmetrical distribution of the Lorentz forces over the two straps, the symmetry boundary condition is not rigorously extendable to a structural analysis that takes into account the VDE dynamic loads. In this case, the symmetry constraints on the central support are removed, the thermal stress distribution is taken into account by modeling it as a pre-stressed initial condition, and the Lorentz forces are added. Since the full set of Lorentz forces is applied on the central support but only half
of the thickness of the support is modeled, the computed stress distribution over the central support and the related displacements are conservative compared to the real case. Moreover, the superimposition of the dynamic EM forces on an initial thermal stress distribution is justified by the considerable difference in the time scales of the two phenomena. In particular, in the ignitor machine a VDE is expected to occur in less than 10 ms, a time length during which the temperature distribution over the strap does not change significantly. Thermal constraints: The temperature of the strap at the beginning of the plasma pulse is about 20 ◦ C. Since the strap operates in nearly vacuum conditions, no radiation is modeled. In particular, the heat extraction mostly occurs by conduction through the connections to the plasma chamber and the coaxial cable. Nevertheless, the thermal conduction time scale is greater than that of the plasma pulse. Therefore, the strapcoaxial cable system is assumed to be adiabatic during the plasma pulse. During the entire plasma pulse, the near constancy of the temperatures in proximity to the connections of the strap and of the coaxial cable to the VV confirms the validity of the assumption. Material: In the FE simulations, the real non-linear elastic–plastic material properties of the Inconel 625 alloy, a nickel–chromium alloy, are used. This material has been chosen because of its high resistivity and high mechanical strength. In particular, a high electrical resistivity allows to limit the intensity of the currents induced on the straps during plasma disruption events and, therefore, to limit the induced Lorentz forces. Unfortunately, Inconel 625 is also characterized by a low thermal conductivity that makes heat extraction from the straps difficult and increases the required cooling time. Nevertheless, the time required to cool down the copper magnets of the machine, about 5 h, is long enough to allow for the cooling of the strap elements. All the structural analyses adopt temperature dependent material properties. The temperature dependent stress–strain curves implemented in the code are shown in [5]. 5.1. Thermal analysis A transient thermal analysis of the strap is initially performed. The nodal temperature values during the plasma pulse are obtained. The thermal stress distribu-
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the Inconel 625 coefficient of thermal conduction, the regions of the strap not directly loaded by the plasma heat flux remain rather cold during the plasma pulse. During the pulse flattop, the nuclear energy deposition is responsible for a nearly uniform temperature increase of about 25 ◦ C. This value is consistent to the one computed by means of the simple energy balance equation c¯ · ρ · T = W · t
(3)
where c¯ is the mean value of the Inconel 625 specific heat at 20 and 45 ◦ C, ρ the nearly constant material density, T the temperature increase in the period t, and W the nuclear deposition power per unit of volume. Fig. 5. Temperature during the reference plasma pulse at selected nodes.
tions during the plasma pulse are calculated by carrying out a second transient FE analysis in which the temperature distributions are used as inputs. Also, a third simulation is performed to compute the residual stresses on the structure. Note that the presence of residual stresses on the strap is possible only if during the plasma pulse the von Mises equivalent stresses exceed the plastic yield limit of the material in localized regions of the strap. Benchmarking of the results was done by solving similar thermal and elastic–plastic problems over simpler geometries and comparing results to the available analytical solutions [8]. 5.1.1. Results: temperature distribution Fig. 5 shows the temperature of relevant selected nodes of the FE model during the plasma pulse. The highest temperature value, 239 ◦ C, is experienced shortly after the end of the flattop (t = 8.3 s), while it will be shown that the highest thermal stresses are experienced at the end of the plasma pulse. In fact, despite the fact that the energy stored by the strap increases until the end of the plasma pulse, peak temperatures decrease after the end of the flattop because of the prevailing effect of thermal diffusion over energy deposition. Since the melting points of Inconel 625 and copper are about 1290 and 1083 ◦ C, respectively, the highest temperatures reached are not sufficient to cause localized melting on the structure. Given the low value of
5.1.2. Results: stresses induced by temperature As stated before, the highest thermal stresses are experienced at the end of the reference plasma pulse (t = 10 s), when the plasma column has deposited the highest amount of energy into the strap. Results show that no plastic yielding occurs on the strap, with the exception of one of the fingers connecting the strap to the coaxial cable, where about 3% of the cross section exceeds the plastic yield limit. Nevertheless, the yielding in the simulation has to be ascribed to the accuracy of the FE model. In fact, the model introduces stress concentration factors by approximating the fillet transitions between the surfaces of the real structure to sharp edges. Without taking into account the factitious yielding at the connection to the coaxial cable, the thermal loads applied on the strap are insufficient to cause plastic yielding and, therefore, no residual stresses are present on the strap after cooling. This statement is strictly accurate only in the case of complete absence of residual stresses generated by the manufacturing process of the strap. Nevertheless, this condition can be approached by exposing the structure to stress relieving processes before installing it inside the plasma chamber. The simulations show that the thermal loads expected on the strap neither generate permanent deformations on the structure nor undermine its reliability. The highest von Mises equivalent stresses and the total von Mises equivalent strains at the end of the plasma pulse are listed in Table 2; the highest nodal displacements in Table 3.
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Table 2 Highest von Mises equivalent stresses and total von Mises equivalent strains at the end of the plasma pulse
Table 4 Highest von Mises equivalent stresses and total strains during VDE and thermal loads
Location
Stress (MPa)
Strain
Location
Stress (MPa)
Strain
Plasma facing plate Lower plate Connection to the plasma chamber (central support) Connection to the coaxial cable
226 142 192
0.0015 0.0009 0.0012
367 317 367
0.0029 0.0021 0.0027
329
0.0023
Plasma facing plate Lower plate Interface between upper and lower plates Connection to the plasma chamber (central support) Connection to the coaxial cable
309
0.0018
405
0.0039
5.2. Combination of thermal loads and Lorentz forces during a VDE EM loads induced during a VDE are superimposed on thermal loads. A VDE can occur at any time during the flattop phase of the plasma pulse. In the simulation, the VDE is assumed to occur at the end of the flattop (t = 8 s), when the strap is characterized by its worst thermal stress configuration. Thus, the initial condition of the structure is assumed to be the stress distribution generated by the thermal loads at the end of the flattop. In addition to the thermal loads, the Lorentz forces generated by the induced net currents and those generated by the eddy currents are the external loads applied to the FE structural model. A transient analysis is performed by taking into account a load that increases linearly in time, from the initial condition (highest thermal stress distribution) to the highest forces applied during a VDE. In particular, the peak values of the Lorentz forces generated by the induced net currents and the eddy currents have been conservatively assumed to be simultaneous. 5.2.1. Results: stresses induced by thermal and EM loads The highest von Mises equivalent stresses and total von Mises equivalent strains are listed in Table 4; the highest displacements in Table 5.
Plastic yielding is experienced at localized regions of the plasma facing plate and at the connection to the coaxial cable. It is mainly due to equivalent bending moments along the X and Y directions (the reference triad is shown in Fig. 3) generated by the Lorentz forces applied on the strap. Conditions approaching the yielding limit are experienced at localized regions on the plasma facing plate surface. In particular, these conditions could be sufficiently severe to damage a ceramic coating applied on the strap to prevent it from possible electrical arching with the VV. In this regard, it is preferable not to employ a ceramic coating, normally Al2 O3 . Instead, by taking advantage of the modeling capabilities of the TOPICA code [3], an EM design of the straps that highly reduces the risk of breaking voltages is adopted. Like the case of the thermal stress analysis, yielding is experienced only at selected regions in proximity of sharp edges where stress concentration factors play an important role. Moreover, yielded regions on the plasma facing plate are confined to the surfaces of the plate and thus do not undermine the structural behavior of the strap. According to the simulation, the highest component of the strap displacement during a VDE is about 6 mm in the radial direction at the interface between the plasma facing plate and the lower plate of the strap (zone 3 in Fig. 4) and roughly 7% of the fingers cross section exceeds the plastic yield limit.
Table 3 Highest displacements of the strap at the end of the plasma pulse
Table 5 Highest displacements during VDE and thermal loads
Highest poloidal displacement, UX (mm) Highest radial displacement, UY (mm) Highest toroidal displacement, UZ (mm)
Highest poloidal displacement, UX (mm) Highest radial displacement, UY (mm) Highest toroidal displacement, UZ (mm)
0.6 −1.3 0.3
Zone 1 Zone 1 Zone 2
0.9 −5.7 2.6
Zone 1 Zone 3 Zone 2
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Table 6 Effects of the coaxial cable length on the strap structural behavior Parameter
UX (mm) UY (mm) UZ (mm) Highest von Mises stress (MPa) Highest von Mises strain
Lcable
Zone
200 mm (reference configuration)
500 mm
1000 mm
0.9 −5.7 2.6 405 0.0039
1.0 −5.5 2.7 408 0.0039
1.0 −5.4 2.7 399 0.0042
6. Influence of the coaxial cable length A parametric structural analysis is performed varying the length of the coaxial cable (Lcable in Fig. 4). Three different lengths are considered: 200, 500 and 1000 mm. All the results presented previously refer to a 200 mm long coaxial cable that is constrained at the beginning of the port, shortly outside the plasma chamber. Table 6 lists few parameters that are indicators of the structural behavior of the strap when the length of the coaxial cable is changed. Results show that the length of the coaxial cable does not affect the stress and strain distributions on the strap significantly. In the range of the coaxial cable lengths considered, it can be deduced that the choice of the length will be driven only by electrical, vacuum related and convenience factors.
Zone 1 Zone 3 Zone 2
devices of the straps and the FS elements must guarantee ease of operation, a sufficient degree of reliability and an acceptable rapidity in performing maintenance operations. The suggested solution uniforms the movements required by the assembly of all the antenna components and, therefore, requires the RH system to perform a minimal variety of movements. The clamping systems are welded to the straps. The straps-coaxial cables and straps-central support use the same principle for their connections. The architecture of the suggested clamp is shown in Fig. 6. In particular, the clamping system has been designed with the following features: - Presence of wedge systems to fasten the strap to the coaxial cable. - Use of a locking ring to secure the bolt to the clamp during RH movements and to keep the wedge in position.
7. Design details Taking into account the difficulties in bending a relatively long plate by an angle of 180◦ while providing a small radius of curvature (d/2 = 22 mm), the suggested solution is to manufacture the plasma facing plate and the lower plate of the strap as two different pieces. The two plates are subsequently welded together by means of an interface element (welding details in Fig. 1). The use of welding is proposed as a possible solution. The ultimate choice will be in charge of the vendor who owns the technology: in case of availability of a technology capable of bending the plates without failure, each strap can be machined as a single piece without welding. The capability of operating the assembly and maintenance of the ignitor’s ICRH antennas in full RH conditions is one of the tightest specifications to which the design has to comply. In particular, the clamping
Fig. 6. Clamp system of the strap to the coaxial cable.
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- Presence of a machined shaping (1) on the coaxial cable (and on the central support) to avoid possible separation between the clamp and the coaxial cable (Fig. 6). - Presence of a machined shaping (2) on the coaxial cable (and on the central support) to locate the clamp during RH assembly (Fig. 6). - Ability to carry out easy maintenance operations in case of damage of the internal threads. As a consequence, only the strap module has to be substituted. Both the bolt and the internal threads of the clamp are subcomponents of the removable strap. Since no threads are present on the coaxial cable and on the central support, the need for maintenance of these components is minimized.
no impact over the structural behavior of the strap. The simulations show that the structural response of the strap is not particularly sensitive to the length of the coaxial cable. Thus, from a mechanical point of view, there are no limiting factors relative to the location of the coaxial cables connection to the VV port. Taking into account the need of operating the assembly and maintenance of the ignitor’s ICRH antennas in full RH, a possible technical solution is suggested. The straps carry the clamps for the attachment to the coaxial cables and to the central support. This solution allows uniforming and minimizing the movements required to the RH manipulator. Moreover, in this solution bolts and internal threads are in the clamps (removable with the strap) and can be easily substituted in case of damage.
8. Conclusions Acknowledgements The longer straps (strap A) of the ICRH antenna array are those subjected to the highest loads. FE simulations show that the structure is able to withstand the applied thermal and EM loads. Conservative assumptions about the applied loads have been introduced to obtain a reliable mechanical design and account for possible unexpected load conditions. Thermal loads produce no plastic yielding on any region of the strap but some at the connection to the coaxial cable. Nevertheless, at this location, plasticization can be avoided by adopting geometrical configurations that reduce the presence of stress concentration factors, such as the clamping solution presented in this work. The highest temperatures reached are well below the Inconel 625 melting point and the energy stored during a plasma pulse is exhausted mainly via thermal conduction through the VV and the coaxial cable. During a VDE, peak dynamic displacements in the radial direction of about 6 mm (zone 3 in Fig. 4) are expected. The highest displacements in the poloidal and toroidal directions are within 3 mm. On the surface of the plasma facing plate, the combination of thermal and EM loads produces conditions approximating plastic yield limit. In particular, limited surface plasticization is experienced at the interface between the plasma facing plate and the lower plate but it has
Many thanks are due to B. Coppi and F. Bombarda for their useful suggestions and stimulating discussions on this subject.
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