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Three-dimensional modelling and numerical optimisation of the W7-X ICRH antenna
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Three-dimensional modelling and numerical optimisation of the W7-X ICRH antenna F. Louche a,∗ , A. Kˇrivská a , A. Messiaen a , J. Ongena a , V. Borsuk b , F. Durodié a , B. Schweer a a Laboratoire de physique des plasmas de l’ERM, Laboratorium voor plasmafysica van de KMS (LPP-ERM/KMS), Ecole Royale Militaire, Koninklijke Militaire School, Brussels, Belgium1 b Institute of Energy and Climate Research – Plasma Physics, Forschungszentrum Juelich, Germany1
h i g h l i g h t s • A simplified version of the ICRF antenna for the stellarator W7-X has been modelled with the 3D electromagnetic software Microwave Studio. This antenna can be tuned between 25 and 38 MHz with the help of adjustable capacitors.
• In previous modellings the front of the antenna was modelled with the help of 3D codes, while the capacitors were modelled as lumped elements with a given DC capacitance. As this approach does not take into account the effect of the internal inductance, a MWS model of these capacitors has been developed. • The initial geometry does not permit the operation at 38 MHz. By modifying some geometrical parameters of the front face, it was possible to increase the frequency band of the antenna, and to increase (up to 25%) the maximum coupled power accounting for the technical constraints on the capacitors. • The W7-X ICRH antenna must be operated at 25 and 38 MHz, and for various toroidal phasings of the strap RF currents. Due to the considered duty cycle it is shown that thanks to a special procedure based on minimisation techniques, it is possible to define a satisfactory optimum geometry in agreement with the specifications of the capacitors. • The various steps of the optimisation are validated with TOPICA simulations. For a given density profile the RF power coupling expectancy can be precisely computed.
a r t i c l e
i n f o
Article history: Received 2 October 2014 Received in revised form 19 December 2014 Accepted 27 January 2015 Available online xxx Keywords: Antennas Capacitors W7-X ICRH Simulations
a b s t r a c t Ion Cyclotron Resonance Heating (ICRH) is a promising heating and wall conditioning method considered for the W7-X stellarator and a dedicated ICRH antenna has been designed. This antenna must perform several tasks in a long term physics programme: fast particles generation, heating at high densities, current drive and ICRH physics studies. Various minority heating scenarios are considered and two frequency bands will be used. In the present work a design for the low frequency range (25–38 MHz) only is developed. The antenna is made of 2 straps with tap feeds and tuning capacitors with DC capacitance in the range 15–200 pF. These capacitors introduce additional constraints on the optimisation and on the maximum amount of power that can be coupled to the plasma: not only the capacitor voltages cannot exceed a certain value (42 kV) but also the currents are limited to approximately 740 A rms to ensure sufficient heat dissipation for the considered duty cycle. Starting from an initial geometry we used the tridimensional electromagnetic software CST MicroWave Studio (MWS) to assess and optimise its coupling properties. By modifying some geometrical parameters of the front face (strap width, antenna box depth, strap length, strap feeders shape), we show that a substantial increase in maximum coupled power can be obtained accounting for the technical constraints on the capacitors. The various steps of the optimisation are validated with TOPICA simulations. For a given density profile the RF power coupling expectancy can be precisely computed. © 2015 Published by Elsevier B.V.
∗ Corresponding author. Tel.: +32 27426590. E-mail address: [email protected] (F. Louche). 1 TEC Partner. http://dx.doi.org/10.1016/j.fusengdes.2015.01.039 0920-3796/© 2015 Published by Elsevier B.V.
Please cite this article in press as: F. Louche, et al., Three-dimensional modelling and numerical optimisation of the W7-X ICRH antenna, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.01.039
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Fig. 1. Conceptual design of ICRH antenna; from left to right: MWS model of the front face with port numbering, circuit model and strap circuit.
1. Conceptual design of an ICRH antenna for W7-X Ion Cyclotron Resonance Heating (ICRH) is a promising heating and wall conditioning method considered for the W7-X stellarator. For a magnetic field of approximately 2.5 T various minority heating scenarios are being considered: fundamental He3 minority heating in H or in He4 at 25 MHz, fundamental H minority heating in D or He4 at 38 MHz [1]. Harmonic heating of H in D or He4 at 76 MHz is also considered. Therefore two frequency ranges (25–38 and 76 MHz respectively) are necessary to cover all the heating scenarios and a satisfactory conceptual antenna design should in theory be able to couple power in a very broad frequency range (see [8] for a description of the principles of the antenna operation based on circuit and semi-analytical modelling). An initial conceptual design for the low-frequency range was previously proposed [2,1]. This design is based on two short-circuited long straps with a coaxial line at the top and one approximately central tap feed. The top coaxial lines are connected to a capacitor needed for tuning at 25 or 38 MHz. Fig. 1 shows a simplified (flat) model of the front face of the antenna, the conceptual circuit model, and the strap circuit. The latter is a resonator tuned by the adjustable capacitance Cadj in such a way to have its reactance XC (given by −(ωCadj )−1 ) matching the total strap inductive reactance XL . The electrical properties of the antenna were validated by measurements on a reduced-scale mock-up [3]. A preliminary optimisation with the three-dimensional electromagnetic software CST Microwave Studio [4] (MWS) was presented in [2], demonstrating that a substantial increase in coupled power could be obtained by changing the geometry and dimensions of some parts of the antenna while keeping up with the limitations on the capacitors. It should be noted that the current design of the antenna does not include a Faraday screen. The main motivation of this choice is the similarity of the heating performance of the unshielded TEXTOR ICRH antenna to that of a shielded antenna, with no impurity problems encountered. Furthermore it was proven that sheath effects are not expected to be worse than in the shielded case [9]. Recent results on LHD have confirmed this result. 2. Modelling of capacitors and pre-matching with MWS Nevertheless the previously used approach did not consider the internal inductance of the capacitor Lcapa , the length ladj and the Z0 of the piece of transmission line connecting the capacitor to the port, which are likely to significantly reduce the value of Cadj,DC needed for tuning at a given frequency ω and phasing, according to Cadj (ω) = (ladj /Z0 c) + (Cadj,DC /1 − ω2 Lcapa Cadj,DC ) for ladj /4 (Z0 = 50 ). This is crucial to take these quantities into account, as the DC capacitance must stay within specified values, and using lumped elements (with series inductances as provided by manufacturer) could lead to frequency range deficiency in the matching of the antenna [5]. The capacitors foreseen for the present antenna were previously used for TEXTOR ICRF antenna
Fig. 2. Left: Cut views of the MWS model of the capacitor for minimal and maximal possible values of Cadj ; right: DC capacitance needed to match the needed Cadj at a given frequency.
(CV5W 15-200 PR200121 capacitors manufactured by COMET) and have the operation range 15 pF < Cadj,DC < 200 pF. From a technical drawing of these capacitors we have developed a 3D model which features most of the relevant geometrical details of the capacitor. Only the thin concentrical cylinders which mostly determines the DC capacitance (they barely contribute to the internal inductance) are replaced by a slab of uniform dielectric medium between two metallic conductors of area S. For a slab thickness d we get the value of dielectric relative permittivity equivalent to a given Cadj,DC from r = (Cadj,DC * d/0 S). It should be noted that a detailed modelling of the thin cups with a finite-element code would lead to huge number of mesh cells and accordingly large CPU and memory resources for the simulations. Therefore, as we are only interested in the relation between the capacitance at the outer port (connected to the coaxial lines) for a given frequency and the DC capacitance Cadj,DC , any local model equivalent to a given Cadj,DC (like the slab capacitor model) will provide the necessary information with a rather fast and accurate 3D model. On the contrary the displacement of the bellow is included into the model. Fig. 2 shows cut views of the model for the two extreme values Cadj , and the value of the capacitance at the connection as a function of Cadj,DC : we see that the inclusion of the real geometry substantially increases the capacitance at the port, which could compromise proper tuning of the antenna. Before describing the model in details and its optimisation, let us briefly remind the methodology. For a given geometry and given generator frequency we compute the 4 × 4 scattering matrix S4×4 which is afterwards inserted into a circuit model where we connected ports 1 and 3 to the tuning capacitors and imposed |I1 | = |I3 |. From a scan in Cadj,DC (the same value for both capacitors) we can deduce the tuning capacitance Cadj for which the averaged minimum conductance Gmin in the feeding lines connected to port 2 and 4 is maximum, with Gmin = 2P/|Vmax |2 , at a given frequency (Vmax is the antinode voltage) and for a given toroidal current phasing. This value Cadj allows to compute the 2 × 2 scattering matrix of the resulting 2port network, and the various voltages, currents at each port, as well as the maximum power which can be coupled to the plasma accounting for the various operational limitations specified by the manufacturer, i.e. a maximum voltage: |VC,max | = 42 kV (peak) and a maximum current: |IC,max | = 1045 A (peak) = 740 A (rms). This later value is determined to ensure sufficient heat dissipation for the considered duty cycle (10 s pulse every 5 min). The details on S4X4 matrices, for various load-antenna distances, as well for various types of loading conditions, can be obtained from [3]. In particular a comparison between modeling and measurements with a scaled mock-up of the initial geometry of the antenna (labeled “Geo#0”
Please cite this article in press as: F. Louche, et al., Three-dimensional modelling and numerical optimisation of the W7-X ICRH antenna, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.01.039
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in the following) for various types of dielectrics (salted water and BaTiO3 ) are showing satisfactory agreement. Also the dependency of the power coupled on load-strap distance compared nicely with modelling results and is similar to the one presented in [10] for the TORE-SUPRA antenna. 3. 3D modelling of front face and optimisation options Fig. 3 reminds the shape and dimensions of the front face of the initial 2-strap antenna considered for W7-X [1]. We label this geometry “Geo#0”. One can see that this model is flat and that the curvature is neglected. As long as the antenna curvature follows the plasma curvature and that the discrepancy to this parallelism stays minimal, the predictions of the flat model with constant antennaload distance should agree with the ones for a curved model. The maximum power than can be coupled at a given frequency and the DC capacitance needed to achieve it are given in Fig. 4. An inflection point is clearly visible where the transition between the regime dominated by |I1,3 | = |IC,max | to the regime where |V1,3 | = |VC,max | occurs. While working at 25 MHz is not a problem, it is clear that the value of Cadj,DC needed to maximise power at 38 MHz is lower than 15 pF hence out of range of capacitance, due to a too long transmission line connecting the strap to the capacitors (ladj ≈ 460 mm). If we take instead 50 mm between the capacitor and the strap front, we obtain the results of geometry “Geo#1”, and we see on the straight curves of Fig. 4 that Cadj,DC is now significantly increased, making the tuning at 38 MHz now possible. We know from previous work performed on the ITER array antenna that increasing the strap width (strapw ) can substantially increase the power coupling [6]. Nevertheless the increase is here limited by the restrictions on currents and voltages on the capacitors. The main problem comes from the location of the inflection point, between 25 and 38 MHz. As the increase in strap width decreases both the strap input resistance RF and reactance XF , it will decrease the power coupled in the region defined by |IC | = cst (left from the inflection point) as Pmax = 1/2RF |IC |2 while Pmax will increase in the region defined by |VC | = cst as in this region Pmax = 1/2GF |VC |2 (Gmin ∼ GF = RF /XF 2 [6]). Due to this combination of effects the inflection point is moved towards larger frequencies (to the right). This is illustrated for current drive operation in Fig. 5(a) and (b) where the strap width is increased from 68 mm to 90 mm: Cadj,DC increases uniformly but the impact on coupling is significantly different at 25 and 38 MHz. Furthermore enlarging the straps will reduce the gap between the strap edge and the box hence
Fig. 4. Results for initial geometry (“Geo#0”) and first optimised geometry (reduced length of connection line between strap and capacitor, “Geo#1”) in function of frequency of maximum coupling. Top: maximum power; bottom: adjustable DC capacitance.
Fig. 5. Effect of the variation of two parameters of the antenna geometry on operation in current drive; (a) maximum power and (b) adjustable DC capacitance for two values of the strap width; (c) maximum power and (d) adjustable DC capacitance for two values of the strap height. The performance of the optimal geometry “Geo#2” (strapw = 90 mm, straph = 820 mm, boxd = 110 mm) has been added.
Fig. 3. 3D MWS model of the initial geometry (strapw = 68 mm, boxh = 740 mm, straph = 710 mm). Left: front view; right: cut view. All lengths are given in mm.
have an impact on the local electric fields. We make here the conservative assumption that with |E,max |=1.5 kV/mm (ITER reference values) and |Vmax | = 42 kV, the gap cannot be smaller than 28 mm. Therefore decreasing the inter-straps distance is necessary when the strap width becomes larger than 90 mm to keep the gap at its minimum value of 40 mm. The simulations show that this transformation has a negligible impact on coupling. The reduction of the box depth boxd was also tested. As expected this transformation has a qualitatively similar impact on antenna properties, but with lower values. A further possibility of optimising the geometry is to exploit the fact that some space was still available around the plug to increase the size of the antenna box boxh by a maximum of 140 mm (to 880 mm) and the length of the strap straph to at most 866 mm.
Please cite this article in press as: F. Louche, et al., Three-dimensional modelling and numerical optimisation of the W7-X ICRH antenna, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.01.039
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Table 1 Summary of optimisation by MWS (dielectric loading). f (MHz)
Geo
0/2
0
Pmax (MW) 25 25 25 38 38 38 25 25 38
#0 #1 #2 #0 #1 #2 P(0 → 2) P(1 → 2) P(1 → 2)
0.53 0.74 0.86 – 0.90 1.00
Cadj,DC (pF)
74 115 100.3 – 33.3 24.7 +61% +16% +11%
Pmax (MW) 0.12 0.15 0.18 – 0.31 0.38
Cadj,DC (pF) 85 131 124 – 41 36.1 +53% +21% +22%
The larger plasma facing area leads to an increase in RF , but the longer strap reduces Cadj for a given frequency. Therefore the strap inductance XF is also increased, the input conductance GF is lower, and we can apply the same reasoning as for the strap enlargement, but in the opposite way: the inflection point is moved towards the lower frequencies, coupling increases at 25 MHz but decreases at 38 MHz: see Fig. 5(c) and (d). 4. Definition of an optimum and impact on coupling performances The difference in behaviour of the coupled power under the effect of the various geometry transformations for various frequencies discussed in the previous section makes the selection of an unique optimum impossible and requires a statistic treatment (maximising gains while minimising losses). We can nevertheless understand the final result from a simple analysis. We know from previous section that increasing the strap width substantially enhances coupling at 38 MHz but reduces it at 25 MHz due to the presence of the inflection point between the two relevant frequencies. We have also shown that increasing boxh reduces frequency where inflection occurs, but at the expense of the coupling efficiency. If we could reduce the box height in such a way to displace the inflection point below 25 MHz, we could synergistically increase the coupling at both frequencies by then enlarging the width of the strap. Of course the price to pay is a slight loss of coupling with respect to the absolute optimum for the given scenario, due to the longer strap. A broad scan in parameters has been performed and statistical analysis has lead to an acceptable candidate for an “optimal” geometry “Geo#2”: strapw =90 mm, boxd =110 mm, and straph =820 mm (corresponding to boxh =834 mm). The gains in power and DC capacitances required to achieve it are given in Table 1: at 25 MHz this new geometry increases the power level by respectively 16 and 21% in 0/2 and 0 as compared with “Geo#1” (61 and 53% with respect to “Geo#0”), while the enhancement reaches respectively 11 and 22% at 38 MHz. The lowest DC
Fig. 6. TOPICA results for the optimised geometry “Geo#2” (strapw = 90 mm, straph = 820 mm, boxd = 110 mm) with a D plasma. Left: maximum power; right: adjustable capacitance.
capacitance needed would be 24.67 pF at 38 MHz in current drive. The values of maximum power and adjustable capacitance in the whole frequency range for this geometry can be seen in Fig. 5. 5. Conclusion The front face of the W7-X ICRH antenna has been simulated and optimised with CST MWS. The model includes self-consistent modelling of the TEXTOR adjustable capacitors which will allow operation at both 25 and 38 MHz. The optimisation was achieved for a pulse time of 10 s every 5 min. The increase of coupled power was comprised between 10 and 60% depending on frequency and poloidal phasing of the straps. The new geometry was also simulated with the TOPICA code [7], for a realistic W7-X density and temperature profile (see [1]), and a pure Deuterium plasma. The coupling code predicts a power level comprised between 0.9 MW and 1.65 MW (see Fig. 6). References [1] J. Ongena, A. Messiaen, D. Van Eester, B. Schweer, P. Dumortier, F. Durodie, et al., Phys. Plasmas 21 (2014) 061514. [2] F. Louche, A. Krivská, A.M. Messiaen, J. Ongena, P. Dumortier, F. Durodie, et al., Europhysics Conference Abstracts, in: 40th EPS Conference on Plasma Phys., vol. 37D, 1–5 July 2013, Helsinki, Finland, 2013, P4.181. [3] P. Dumortier, A. Krivská, A.M. Messiaen, M. Vervier, F. Louche, J. Ongena, et al., Validation of the Electrical Design of the W7-X ICRF Antenna on a ReducedScale Mock-up, 2014 (in this conference). [4] CST GmbH, CST Microwave Studio® User Manual, 2008. [5] F. Durodié, M. Nightingale, A. Argouarch, G. Berger-By, T. Blackman, J. Caughman, et al., Fusion Eng. Design 84 (2009) 279–283. [6] F. Louche, P. Dumortier, A. Messiaen, F. Durodie, Nucl. Fusion (2011) 103002. [7] V. Lancellotti, D. Milanesio, R. Maggiora, G. Vecchi, V. Kyrytsya, Nucl. Fusion (2006) S476–S499. [8] A. Messiaen, A. Krivska, F. Louche, J. Ongena, P. Dumortier, F. Durodie, Fusion Eng. Design 1580 (2014) 354. [9] R. Van Nieuwenhove, R. Koch, G. Van Oost, J.A. Boedo, P. Dumortier, F. Durodie, Nucl. Fusion 32 (1992) 1913. [10] F. Clairet, L. Colas, S. Heuraux, G. Lombard, Plasma Phys. Control. Fusion 46 (2004) 1567.
Please cite this article in press as: F. Louche, et al., Three-dimensional modelling and numerical optimisation of the W7-X ICRH antenna, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.01.039
ARTICLE IN PRESS
FUSION-7733; No. of Pages 4
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Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Three-dimensional modelling and numerical optimisation of the W7-X ICRH antenna F. Louche a,∗ , A. Kˇrivská a , A. Messiaen a , J. Ongena a , V. Borsuk b , F. Durodié a , B. Schweer a a Laboratoire de physique des plasmas de l’ERM, Laboratorium voor plasmafysica van de KMS (LPP-ERM/KMS), Ecole Royale Militaire, Koninklijke Militaire School, Brussels, Belgium1 b Institute of Energy and Climate Research – Plasma Physics, Forschungszentrum Juelich, Germany1
h i g h l i g h t s • A simplified version of the ICRF antenna for the stellarator W7-X has been modelled with the 3D electromagnetic software Microwave Studio. This antenna can be tuned between 25 and 38 MHz with the help of adjustable capacitors.
• In previous modellings the front of the antenna was modelled with the help of 3D codes, while the capacitors were modelled as lumped elements with a given DC capacitance. As this approach does not take into account the effect of the internal inductance, a MWS model of these capacitors has been developed. • The initial geometry does not permit the operation at 38 MHz. By modifying some geometrical parameters of the front face, it was possible to increase the frequency band of the antenna, and to increase (up to 25%) the maximum coupled power accounting for the technical constraints on the capacitors. • The W7-X ICRH antenna must be operated at 25 and 38 MHz, and for various toroidal phasings of the strap RF currents. Due to the considered duty cycle it is shown that thanks to a special procedure based on minimisation techniques, it is possible to define a satisfactory optimum geometry in agreement with the specifications of the capacitors. • The various steps of the optimisation are validated with TOPICA simulations. For a given density profile the RF power coupling expectancy can be precisely computed.
a r t i c l e
i n f o
Article history: Received 2 October 2014 Received in revised form 19 December 2014 Accepted 27 January 2015 Available online xxx Keywords: Antennas Capacitors W7-X ICRH Simulations
a b s t r a c t Ion Cyclotron Resonance Heating (ICRH) is a promising heating and wall conditioning method considered for the W7-X stellarator and a dedicated ICRH antenna has been designed. This antenna must perform several tasks in a long term physics programme: fast particles generation, heating at high densities, current drive and ICRH physics studies. Various minority heating scenarios are considered and two frequency bands will be used. In the present work a design for the low frequency range (25–38 MHz) only is developed. The antenna is made of 2 straps with tap feeds and tuning capacitors with DC capacitance in the range 15–200 pF. These capacitors introduce additional constraints on the optimisation and on the maximum amount of power that can be coupled to the plasma: not only the capacitor voltages cannot exceed a certain value (42 kV) but also the currents are limited to approximately 740 A rms to ensure sufficient heat dissipation for the considered duty cycle. Starting from an initial geometry we used the tridimensional electromagnetic software CST MicroWave Studio (MWS) to assess and optimise its coupling properties. By modifying some geometrical parameters of the front face (strap width, antenna box depth, strap length, strap feeders shape), we show that a substantial increase in maximum coupled power can be obtained accounting for the technical constraints on the capacitors. The various steps of the optimisation are validated with TOPICA simulations. For a given density profile the RF power coupling expectancy can be precisely computed. © 2015 Published by Elsevier B.V.
∗ Corresponding author. Tel.: +32 27426590. E-mail address: [email protected] (F. Louche). 1 TEC Partner. http://dx.doi.org/10.1016/j.fusengdes.2015.01.039 0920-3796/© 2015 Published by Elsevier B.V.
Please cite this article in press as: F. Louche, et al., Three-dimensional modelling and numerical optimisation of the W7-X ICRH antenna, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.01.039
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Fig. 1. Conceptual design of ICRH antenna; from left to right: MWS model of the front face with port numbering, circuit model and strap circuit.
1. Conceptual design of an ICRH antenna for W7-X Ion Cyclotron Resonance Heating (ICRH) is a promising heating and wall conditioning method considered for the W7-X stellarator. For a magnetic field of approximately 2.5 T various minority heating scenarios are being considered: fundamental He3 minority heating in H or in He4 at 25 MHz, fundamental H minority heating in D or He4 at 38 MHz [1]. Harmonic heating of H in D or He4 at 76 MHz is also considered. Therefore two frequency ranges (25–38 and 76 MHz respectively) are necessary to cover all the heating scenarios and a satisfactory conceptual antenna design should in theory be able to couple power in a very broad frequency range (see [8] for a description of the principles of the antenna operation based on circuit and semi-analytical modelling). An initial conceptual design for the low-frequency range was previously proposed [2,1]. This design is based on two short-circuited long straps with a coaxial line at the top and one approximately central tap feed. The top coaxial lines are connected to a capacitor needed for tuning at 25 or 38 MHz. Fig. 1 shows a simplified (flat) model of the front face of the antenna, the conceptual circuit model, and the strap circuit. The latter is a resonator tuned by the adjustable capacitance Cadj in such a way to have its reactance XC (given by −(ωCadj )−1 ) matching the total strap inductive reactance XL . The electrical properties of the antenna were validated by measurements on a reduced-scale mock-up [3]. A preliminary optimisation with the three-dimensional electromagnetic software CST Microwave Studio [4] (MWS) was presented in [2], demonstrating that a substantial increase in coupled power could be obtained by changing the geometry and dimensions of some parts of the antenna while keeping up with the limitations on the capacitors. It should be noted that the current design of the antenna does not include a Faraday screen. The main motivation of this choice is the similarity of the heating performance of the unshielded TEXTOR ICRH antenna to that of a shielded antenna, with no impurity problems encountered. Furthermore it was proven that sheath effects are not expected to be worse than in the shielded case [9]. Recent results on LHD have confirmed this result. 2. Modelling of capacitors and pre-matching with MWS Nevertheless the previously used approach did not consider the internal inductance of the capacitor Lcapa , the length ladj and the Z0 of the piece of transmission line connecting the capacitor to the port, which are likely to significantly reduce the value of Cadj,DC needed for tuning at a given frequency ω and phasing, according to Cadj (ω) = (ladj /Z0 c) + (Cadj,DC /1 − ω2 Lcapa Cadj,DC ) for ladj /4 (Z0 = 50 ). This is crucial to take these quantities into account, as the DC capacitance must stay within specified values, and using lumped elements (with series inductances as provided by manufacturer) could lead to frequency range deficiency in the matching of the antenna [5]. The capacitors foreseen for the present antenna were previously used for TEXTOR ICRF antenna
Fig. 2. Left: Cut views of the MWS model of the capacitor for minimal and maximal possible values of Cadj ; right: DC capacitance needed to match the needed Cadj at a given frequency.
(CV5W 15-200 PR200121 capacitors manufactured by COMET) and have the operation range 15 pF < Cadj,DC < 200 pF. From a technical drawing of these capacitors we have developed a 3D model which features most of the relevant geometrical details of the capacitor. Only the thin concentrical cylinders which mostly determines the DC capacitance (they barely contribute to the internal inductance) are replaced by a slab of uniform dielectric medium between two metallic conductors of area S. For a slab thickness d we get the value of dielectric relative permittivity equivalent to a given Cadj,DC from r = (Cadj,DC * d/0 S). It should be noted that a detailed modelling of the thin cups with a finite-element code would lead to huge number of mesh cells and accordingly large CPU and memory resources for the simulations. Therefore, as we are only interested in the relation between the capacitance at the outer port (connected to the coaxial lines) for a given frequency and the DC capacitance Cadj,DC , any local model equivalent to a given Cadj,DC (like the slab capacitor model) will provide the necessary information with a rather fast and accurate 3D model. On the contrary the displacement of the bellow is included into the model. Fig. 2 shows cut views of the model for the two extreme values Cadj , and the value of the capacitance at the connection as a function of Cadj,DC : we see that the inclusion of the real geometry substantially increases the capacitance at the port, which could compromise proper tuning of the antenna. Before describing the model in details and its optimisation, let us briefly remind the methodology. For a given geometry and given generator frequency we compute the 4 × 4 scattering matrix S4×4 which is afterwards inserted into a circuit model where we connected ports 1 and 3 to the tuning capacitors and imposed |I1 | = |I3 |. From a scan in Cadj,DC (the same value for both capacitors) we can deduce the tuning capacitance Cadj for which the averaged minimum conductance Gmin in the feeding lines connected to port 2 and 4 is maximum, with Gmin = 2P/|Vmax |2 , at a given frequency (Vmax is the antinode voltage) and for a given toroidal current phasing. This value Cadj allows to compute the 2 × 2 scattering matrix of the resulting 2port network, and the various voltages, currents at each port, as well as the maximum power which can be coupled to the plasma accounting for the various operational limitations specified by the manufacturer, i.e. a maximum voltage: |VC,max | = 42 kV (peak) and a maximum current: |IC,max | = 1045 A (peak) = 740 A (rms). This later value is determined to ensure sufficient heat dissipation for the considered duty cycle (10 s pulse every 5 min). The details on S4X4 matrices, for various load-antenna distances, as well for various types of loading conditions, can be obtained from [3]. In particular a comparison between modeling and measurements with a scaled mock-up of the initial geometry of the antenna (labeled “Geo#0”
Please cite this article in press as: F. Louche, et al., Three-dimensional modelling and numerical optimisation of the W7-X ICRH antenna, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.01.039
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in the following) for various types of dielectrics (salted water and BaTiO3 ) are showing satisfactory agreement. Also the dependency of the power coupled on load-strap distance compared nicely with modelling results and is similar to the one presented in [10] for the TORE-SUPRA antenna. 3. 3D modelling of front face and optimisation options Fig. 3 reminds the shape and dimensions of the front face of the initial 2-strap antenna considered for W7-X [1]. We label this geometry “Geo#0”. One can see that this model is flat and that the curvature is neglected. As long as the antenna curvature follows the plasma curvature and that the discrepancy to this parallelism stays minimal, the predictions of the flat model with constant antennaload distance should agree with the ones for a curved model. The maximum power than can be coupled at a given frequency and the DC capacitance needed to achieve it are given in Fig. 4. An inflection point is clearly visible where the transition between the regime dominated by |I1,3 | = |IC,max | to the regime where |V1,3 | = |VC,max | occurs. While working at 25 MHz is not a problem, it is clear that the value of Cadj,DC needed to maximise power at 38 MHz is lower than 15 pF hence out of range of capacitance, due to a too long transmission line connecting the strap to the capacitors (ladj ≈ 460 mm). If we take instead 50 mm between the capacitor and the strap front, we obtain the results of geometry “Geo#1”, and we see on the straight curves of Fig. 4 that Cadj,DC is now significantly increased, making the tuning at 38 MHz now possible. We know from previous work performed on the ITER array antenna that increasing the strap width (strapw ) can substantially increase the power coupling [6]. Nevertheless the increase is here limited by the restrictions on currents and voltages on the capacitors. The main problem comes from the location of the inflection point, between 25 and 38 MHz. As the increase in strap width decreases both the strap input resistance RF and reactance XF , it will decrease the power coupled in the region defined by |IC | = cst (left from the inflection point) as Pmax = 1/2RF |IC |2 while Pmax will increase in the region defined by |VC | = cst as in this region Pmax = 1/2GF |VC |2 (Gmin ∼ GF = RF /XF 2 [6]). Due to this combination of effects the inflection point is moved towards larger frequencies (to the right). This is illustrated for current drive operation in Fig. 5(a) and (b) where the strap width is increased from 68 mm to 90 mm: Cadj,DC increases uniformly but the impact on coupling is significantly different at 25 and 38 MHz. Furthermore enlarging the straps will reduce the gap between the strap edge and the box hence
Fig. 4. Results for initial geometry (“Geo#0”) and first optimised geometry (reduced length of connection line between strap and capacitor, “Geo#1”) in function of frequency of maximum coupling. Top: maximum power; bottom: adjustable DC capacitance.
Fig. 5. Effect of the variation of two parameters of the antenna geometry on operation in current drive; (a) maximum power and (b) adjustable DC capacitance for two values of the strap width; (c) maximum power and (d) adjustable DC capacitance for two values of the strap height. The performance of the optimal geometry “Geo#2” (strapw = 90 mm, straph = 820 mm, boxd = 110 mm) has been added.
Fig. 3. 3D MWS model of the initial geometry (strapw = 68 mm, boxh = 740 mm, straph = 710 mm). Left: front view; right: cut view. All lengths are given in mm.
have an impact on the local electric fields. We make here the conservative assumption that with |E,max |=1.5 kV/mm (ITER reference values) and |Vmax | = 42 kV, the gap cannot be smaller than 28 mm. Therefore decreasing the inter-straps distance is necessary when the strap width becomes larger than 90 mm to keep the gap at its minimum value of 40 mm. The simulations show that this transformation has a negligible impact on coupling. The reduction of the box depth boxd was also tested. As expected this transformation has a qualitatively similar impact on antenna properties, but with lower values. A further possibility of optimising the geometry is to exploit the fact that some space was still available around the plug to increase the size of the antenna box boxh by a maximum of 140 mm (to 880 mm) and the length of the strap straph to at most 866 mm.
Please cite this article in press as: F. Louche, et al., Three-dimensional modelling and numerical optimisation of the W7-X ICRH antenna, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.01.039
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Table 1 Summary of optimisation by MWS (dielectric loading). f (MHz)
Geo
0/2
0
Pmax (MW) 25 25 25 38 38 38 25 25 38
#0 #1 #2 #0 #1 #2 P(0 → 2) P(1 → 2) P(1 → 2)
0.53 0.74 0.86 – 0.90 1.00
Cadj,DC (pF)
74 115 100.3 – 33.3 24.7 +61% +16% +11%
Pmax (MW) 0.12 0.15 0.18 – 0.31 0.38
Cadj,DC (pF) 85 131 124 – 41 36.1 +53% +21% +22%
The larger plasma facing area leads to an increase in RF , but the longer strap reduces Cadj for a given frequency. Therefore the strap inductance XF is also increased, the input conductance GF is lower, and we can apply the same reasoning as for the strap enlargement, but in the opposite way: the inflection point is moved towards the lower frequencies, coupling increases at 25 MHz but decreases at 38 MHz: see Fig. 5(c) and (d). 4. Definition of an optimum and impact on coupling performances The difference in behaviour of the coupled power under the effect of the various geometry transformations for various frequencies discussed in the previous section makes the selection of an unique optimum impossible and requires a statistic treatment (maximising gains while minimising losses). We can nevertheless understand the final result from a simple analysis. We know from previous section that increasing the strap width substantially enhances coupling at 38 MHz but reduces it at 25 MHz due to the presence of the inflection point between the two relevant frequencies. We have also shown that increasing boxh reduces frequency where inflection occurs, but at the expense of the coupling efficiency. If we could reduce the box height in such a way to displace the inflection point below 25 MHz, we could synergistically increase the coupling at both frequencies by then enlarging the width of the strap. Of course the price to pay is a slight loss of coupling with respect to the absolute optimum for the given scenario, due to the longer strap. A broad scan in parameters has been performed and statistical analysis has lead to an acceptable candidate for an “optimal” geometry “Geo#2”: strapw =90 mm, boxd =110 mm, and straph =820 mm (corresponding to boxh =834 mm). The gains in power and DC capacitances required to achieve it are given in Table 1: at 25 MHz this new geometry increases the power level by respectively 16 and 21% in 0/2 and 0 as compared with “Geo#1” (61 and 53% with respect to “Geo#0”), while the enhancement reaches respectively 11 and 22% at 38 MHz. The lowest DC
Fig. 6. TOPICA results for the optimised geometry “Geo#2” (strapw = 90 mm, straph = 820 mm, boxd = 110 mm) with a D plasma. Left: maximum power; right: adjustable capacitance.
capacitance needed would be 24.67 pF at 38 MHz in current drive. The values of maximum power and adjustable capacitance in the whole frequency range for this geometry can be seen in Fig. 5. 5. Conclusion The front face of the W7-X ICRH antenna has been simulated and optimised with CST MWS. The model includes self-consistent modelling of the TEXTOR adjustable capacitors which will allow operation at both 25 and 38 MHz. The optimisation was achieved for a pulse time of 10 s every 5 min. The increase of coupled power was comprised between 10 and 60% depending on frequency and poloidal phasing of the straps. The new geometry was also simulated with the TOPICA code [7], for a realistic W7-X density and temperature profile (see [1]), and a pure Deuterium plasma. The coupling code predicts a power level comprised between 0.9 MW and 1.65 MW (see Fig. 6). References [1] J. Ongena, A. Messiaen, D. Van Eester, B. Schweer, P. Dumortier, F. Durodie, et al., Phys. Plasmas 21 (2014) 061514. [2] F. Louche, A. Krivská, A.M. Messiaen, J. Ongena, P. Dumortier, F. Durodie, et al., Europhysics Conference Abstracts, in: 40th EPS Conference on Plasma Phys., vol. 37D, 1–5 July 2013, Helsinki, Finland, 2013, P4.181. [3] P. Dumortier, A. Krivská, A.M. Messiaen, M. Vervier, F. Louche, J. Ongena, et al., Validation of the Electrical Design of the W7-X ICRF Antenna on a ReducedScale Mock-up, 2014 (in this conference). [4] CST GmbH, CST Microwave Studio® User Manual, 2008. [5] F. Durodié, M. Nightingale, A. Argouarch, G. Berger-By, T. Blackman, J. Caughman, et al., Fusion Eng. Design 84 (2009) 279–283. [6] F. Louche, P. Dumortier, A. Messiaen, F. Durodie, Nucl. Fusion (2011) 103002. [7] V. Lancellotti, D. Milanesio, R. Maggiora, G. Vecchi, V. Kyrytsya, Nucl. Fusion (2006) S476–S499. [8] A. Messiaen, A. Krivska, F. Louche, J. Ongena, P. Dumortier, F. Durodie, Fusion Eng. Design 1580 (2014) 354. [9] R. Van Nieuwenhove, R. Koch, G. Van Oost, J.A. Boedo, P. Dumortier, F. Durodie, Nucl. Fusion 32 (1992) 1913. [10] F. Clairet, L. Colas, S. Heuraux, G. Lombard, Plasma Phys. Control. Fusion 46 (2004) 1567.
Please cite this article in press as: F. Louche, et al., Three-dimensional modelling and numerical optimisation of the W7-X ICRH antenna, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.01.039