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Investigations of energy penetration for the 2003 design of the target cell at the Hermes experiment
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 558 (2006) 214–219 www.elsevier.com/locate/nima
Investigations of energy penetration for the 2003 design of the target cell at the Hermes experiment Susan Wipf Deutsches Elektronen Synchrotron, DESY, Hoelderlinstrasse 22, D22607 Hamburg, Germany Available online 28 December 2005
Abstract Calculations have been made to investigate the energy penetration through the pumping holes of the beam tube at the interaction point of the HERMES experiment at HERA. A shielding screen made from etched nickel foil, pressed into the aluminium of the target cell, was proposed. Several different models were studied. Calculations for the new design of the spring fingers were also made, and the results for the 2000 design are included for comparison. As there have been no measurements as yet, the 2000 values are the only indication of an upper limit of radio frequency interference which is not tolerable for the detector electronics. The effect of discretisation on the results was also analysed. r 2005 Elsevier B.V. All rights reserved. PACS: 07.05.Tp; 03.50.De; 41.20.–q Keywords: Field computation and analysis; Design of accelerators and components
1. Introduction The 2003 design of the target cell requires six pumping holes on either side of the elliptical beam tube at the interaction point of the HERMES experiment. Fig. 1 shows the present installation. These holes would be stamped out of the sides of the beam tube, 4 mm high, 10 mm long, with a separation of 2.5 mm, see the insert in Fig. 1. The radii of the elliptical beam pipe of the target cell are 4.45 10.5 mm. Previous experience with insufficiently shielded gaps in the beam tube at other positions of the target cell, i.e. the spring fingers which connect the target cell to the wakefield suppressor on the one side, at 0.347 m, and the C2 collimator, at 0.24 m, on the other, has shown that high-frequency electro-magnetic fields from the beam can saturate the detector electronics so that data cannot be taken.
Corresponding author. Tel.: +49 40 827139, +49 899 82466; fax: +49 899 42466. E-mail address: [email protected].
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.11.187
A fine screen pressed into the aluminium of the target cell has been proposed for shielding the sensitive detector electronics. The screen would be formed by etching nickel foil, 20 mm thick, leaving 12 line/cm with 90% transparency. The width of the metal separating the square cells would be 40 mm and the thickness 20 mm. The cells are 0.4 mm square. Preliminary calculations were first carried out to evaluate possible models for the shielding. Then a simpler model was used to examine the mechanism of coupling through a fine screen. Two other simplified models were used to investigate the effect of discretisation on the results directly and also on the inductance, as a qualitative measure of the coupling. After that, a detailed model was constructed. The calculation used an excitation which allowed a variable mesh in the beam direction. All calculations were carried out with the MAFIA [1] programs. Calculations for the new design of the spring fingers, using much shorter and narrower gaps are also presented here. This provides a comparison between a model with elliptical beam cross-section and the rectangular approximation, which is used in the other calculations. The previous design had also been calculated and is included
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Fig. 1. Hermes 2000 target cell, with beam tube in place (no pumping holes). Inset shows the type of pumping holes used at the target cell.
Fig. 2. Elliptical calculation model with a view of new spring fingers.
for comparison, as this is the only available indication of the level of RF power which is not tolerable. 2. Spring fingers—comparison with previous calculations So far there have been no measurements which can be correlated to the amount of RF noise tolerable for the diagnostic equipment. However, in 2000 the level was so high that data could not be taken. Spring fingers are used in the first place to provide RF shielding and to facilitate the removal of the target cell when necessary, but also as pumping slits. Naturally, pumping power is only achieved at the expense of the shielding. The gaps in the beam tube have been reduced in the 2003 design, reducing the calculated energy penetration by five orders of magnitude, from 183 mW to 1.3 mW.
2003 Design: fingers 2 mm wide, 5 mm long, with a spacing of 0.8 mm. 2000 Design: fingers 2 mm wide, 35.5 mm long, with a spacing of 5 mm.
that the model must include at least 10 mm empty space for the case of a 3 mm sigma bunch and then 40 mm for a 12 mm sigma bunch. It was also shown that using a rectangular instead of an elliptical model for the beam tube underestimated the energy penetration by less than a factor of 2. Fig. 2 shows the elliptical calculation model and the 2003 design for the spring fingers. 3. Preliminary calculations For the preliminary calculations the screen was modelled with a coarser mesh, 12 2 wires instead of 23 5, a rectangular beam tube was used and 14 of the geometry was modelled. Sheets, elements with zero thickness available in the MAFIA [1] programs, were used to model the wires of the screen. The following assumptions were made:
The equipment around the beam tube could not be modelled accurately, thus multiple reflections in that area were neglected. For a good approximation of the actual energy transfer, a half wavelength of empty space round the beam tube was modelled, with sufficiently fine discretisation to allow EM waves to propagate. This means
Shielding is effective: after bunch passage, no coupling between beam tube and outer volume; field energy in outer volume is a measure of the coupling; energy loss for all bunches adds up incoherently and is absorbed in the outer volume.
Five models were compared. (1) Screen over the holes, surrounded by a cage; (2) cage surrounding open holes;
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Fig. 3. Geometry of models 4 and 5.
Fig. 4. Left hand side: calculation model. Right hand side: model with boundary conditions.
(3) two horizontal wires; (4) screen over the holes; (5) open holes. Models 4 and 5, shown in Fig. 3, were chosen for further investigation. Model 3 shields better than Model 4, but the wires cannot be attached firmly. Model 1 provides better shielding but would only be considered if Model 4 proves insufficient, as it is mechanically less stable. 4. Simplified models 4.1. Transmission line In order to gain insight into these results, a much simplified calculation model was designed, see Fig. 4; a transmission line consisting of three electric plates with two waveguide ports at each end was used, as shown in Fig. 5. The model represented the six holes in the beam pipe, each 10 mm long with a 2 mm separation bar; the holes in the screen were 400 400 mm, with 40 mm for the width of the wire. Periodic boundary conditions were applied transversally producing an infinitely wide model. The reflection, (r), and transmission, (t), together with the coupling, (c) and the isolation, (i), were calculated (see Fig. 5). The excitation is a Gaussian pulse which travels from the bottom left at the speed of light. As the main scattering effect seemed to come from the edges of the pumping holes and to a lesser extent from the edge of each of the holes in the screen (see Fig. 6), the shape of the screen holes was varied, using rectangular holes two and four times as long. A tapering of the ends of the holes was also tried.
Fig. 5. Four ports are monitored to calculate the transmission (t), reflection (r), coupling (c) and isolation (i).
The energy transfer calculated for each port was for sigma ¼ 3 mm
for sigma ¼ 12 mm
ðrÞ ¼ 1:5%; ðiÞ ¼ 0:18%, ðtÞ ¼ 95:2%; ðcÞ ¼ 3:1%,
ðrÞ ¼ 0:32%; ðiÞ ¼ 0:025%, ðtÞ ¼ 99:4%; ðcÞ ¼ 0:2%.
For a 12 mm bunch the energy penetration was 0.11 mW. Using rectangular holes, with a 2:1 ratio, this could be reduced to 0.051 mW and with 4:1, to 0.038 mW.
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4.2. Discretisation test—TEM conductors
4.3. Discretisation test—inductance of wires in screen
In so fine a structure as the shielding screen, it was important to establish to what degree the discretisation affected the results obtained. Outside the beam tube there is a large area where waves can propagate. In order to investigate the effect of varying the mesh density within and either side of the screen, a waveguiding structure was introduced; a model with TEM conductor plates, see Fig. 7, guides and reflects the electromagnetic waves, representing a similar physical situation in a smaller volume with better discretisation. As expected, the actual size of the holes in the screen plays a large role, so that the coarser screen used in Section 3 overestimates the power transmission by two orders of magnitude. However, the fineness of the discretisation within these holes also affects the results, making the screen more transparent. This is not in contradiction to the results in Section 4.1, as there the holes were changed from square to rectangular. It was seen in Model 3 of Section 3 that the wires parallel to the beam direction have a screening effect, while those perpendicular to the beam cause reflections.
The inductance of wires in a screen was investigated with an even simpler model. The screen consists of many individual wires. Current flowing through the wires causes magnetic fields round each wire. This magnetic field is responsible for the coupling and, as the inductance describes the relation of the current to the field energy, the inductance is a good measure of the coupling strength. Thus, the inductance is used to investigate the effect of discretisation on the results. A very simple model can be used to consider the effect of varied discretisations on the calculated coupling. A twoplate resonator with periodic structure was chosen, that of a metal post between two metal plates, top and bottom, with periodic boundaries on the other two sides, left and right (see Fig. 8). This represents the resonant conditions for one wire of the screen. The height of the post must be small with respect to the length of the resonator. The frequency shift caused by the presence of the wire is calculated in the frequency domain. The effect of the use of sheets on the calculated field penetration through the shielding screen was also investigated. In Fig. 9 the lower curves (yellow and blue) represent the solid post, (almost coincident) and the upper curves show the sheet model with different orientations L/Z0 was normalised to the best discretisation of the solid post, and plotted versus the mesh density. The curves rise steeply initially and then flatten out. Each wire acts as a very small magnetic filter, thus the thickness of the wire would also affect the coupling. As the calculated fields are constant in each mesh cell, a coarse mesh simulates a thicker wire even when the dimensions of the wire remain constant. Sheets increase transmission through the screen by a factor of almost two. 5. Full model In the time domain, when wakefields are not required, it is no longer necessary to maintain an equidistant mesh. A model with solid wires in the screen was generated, shown
Fig. 6. Energy transfer to the four ports is plotted against time, showing the reflections from the edges of the six holes.
Fig. 7. Model with TEM capacitor plates.
Fig. 8. Simplified model for inductance calculations of wires in a screen as a metal post between two metal plates.
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SHEETS : RED Y-Z / GREEN X-Y,
SOLID : YELLOW / BLUE
L/Z0 [NORMALISED TO BEST DISRETISATION, SOLID POST]
2.00 1.80
Sheets Y-Z Sheets X-Z
1.60 1.40 1.20
Solid. extra mesh line in post
1.00 Solid, no mesh line in post
0.800 0.600 0.0
2.0E + 04 4.0E + 04 6.0E + 04 8.0E + 04 1.0E + 05 1.2E + 05 1.4E + 05 1.6E + 05 MESH DENSITY, MESH CELLS/MM**3
Fig. 9. L/Z0 (normalised to best discretisation of solid post) vs. mesh density. The lower curves (yellow and blue) represent the solid post, (almost coincident). The upper curves show the sheet model with different orientations.
Fig. 10. Full model, a detail of the mesh of the screen is shown in the inset.
in Fig. 10. For comparison, models were also calculated with wires as sheets and without screening. Using sheets also allows more energy to reach the outer area and the higher resolution, i.e. more mesh lines between the wires of the screen is also necessary to obtain the correct energy penetration. Table 1 shows the results. Although the differences between the solid and the sheet model are small when sigma ¼ 12 mm, it is interesting to note that increasing the discretisation makes the screen more transparent to higher frequency components. In Section 4.3, L/Z0 was plotted against the mesh density.
The differences found there between the solid and the sheet model are also apparent in these calculations.
6. Conclusions A calculation model was found which gave reliable results within the given restrictions. The factors which affected the results were the use of sheets, discretisation, and the coarseness of the screen. The initial results were a factor of 10 too high.
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Table 1 Energy penetration through the pumping holes of the full model for two bunch lengths Screen model
Resolution
Sigma ¼ 3 mm Energy outsidea ( 106 V A s/m3)
Solid Solid Sheets Sheets Open Open holes
Low High Low High Low
0.3549 0.3944 0.8490 0.9215 834.4
Sigma ¼ 12 mm Power lossb (mW)
0.1278 0.1420 0.3056 0.3317 300.4
Energy outsidea (( 103 V A s/m3) 0.2693 0.2951 0.5711 0.6136 32.13
Power lossb (mW) o o o o
1 1 1 1
11.57
The screen wires were modelled as either sheets or solid, with 6 6 mesh lines per screen hole (high-resolution), or 4 4 (low-resolution). a Energy calculated for a bunch with 1 C charge. b Energy scaled to the HERA design current, 60 mA.
The screening reduces the energy penetration by at least two orders of magnitude for a 12 mm beam. This should be sufficient to reduce the radio frequency interference to a tolerable level. Measurements are in progress. To be effective the screening must be firmly attached.
References [1] MAFIA, CST GmbH, Bad Nauheimer Str. 19 D-64289, Darmstadt, Germany.
Nuclear Instruments and Methods in Physics Research A 558 (2006) 214–219 www.elsevier.com/locate/nima
Investigations of energy penetration for the 2003 design of the target cell at the Hermes experiment Susan Wipf Deutsches Elektronen Synchrotron, DESY, Hoelderlinstrasse 22, D22607 Hamburg, Germany Available online 28 December 2005
Abstract Calculations have been made to investigate the energy penetration through the pumping holes of the beam tube at the interaction point of the HERMES experiment at HERA. A shielding screen made from etched nickel foil, pressed into the aluminium of the target cell, was proposed. Several different models were studied. Calculations for the new design of the spring fingers were also made, and the results for the 2000 design are included for comparison. As there have been no measurements as yet, the 2000 values are the only indication of an upper limit of radio frequency interference which is not tolerable for the detector electronics. The effect of discretisation on the results was also analysed. r 2005 Elsevier B.V. All rights reserved. PACS: 07.05.Tp; 03.50.De; 41.20.–q Keywords: Field computation and analysis; Design of accelerators and components
1. Introduction The 2003 design of the target cell requires six pumping holes on either side of the elliptical beam tube at the interaction point of the HERMES experiment. Fig. 1 shows the present installation. These holes would be stamped out of the sides of the beam tube, 4 mm high, 10 mm long, with a separation of 2.5 mm, see the insert in Fig. 1. The radii of the elliptical beam pipe of the target cell are 4.45 10.5 mm. Previous experience with insufficiently shielded gaps in the beam tube at other positions of the target cell, i.e. the spring fingers which connect the target cell to the wakefield suppressor on the one side, at 0.347 m, and the C2 collimator, at 0.24 m, on the other, has shown that high-frequency electro-magnetic fields from the beam can saturate the detector electronics so that data cannot be taken.
Corresponding author. Tel.: +49 40 827139, +49 899 82466; fax: +49 899 42466. E-mail address: [email protected].
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.11.187
A fine screen pressed into the aluminium of the target cell has been proposed for shielding the sensitive detector electronics. The screen would be formed by etching nickel foil, 20 mm thick, leaving 12 line/cm with 90% transparency. The width of the metal separating the square cells would be 40 mm and the thickness 20 mm. The cells are 0.4 mm square. Preliminary calculations were first carried out to evaluate possible models for the shielding. Then a simpler model was used to examine the mechanism of coupling through a fine screen. Two other simplified models were used to investigate the effect of discretisation on the results directly and also on the inductance, as a qualitative measure of the coupling. After that, a detailed model was constructed. The calculation used an excitation which allowed a variable mesh in the beam direction. All calculations were carried out with the MAFIA [1] programs. Calculations for the new design of the spring fingers, using much shorter and narrower gaps are also presented here. This provides a comparison between a model with elliptical beam cross-section and the rectangular approximation, which is used in the other calculations. The previous design had also been calculated and is included
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Fig. 1. Hermes 2000 target cell, with beam tube in place (no pumping holes). Inset shows the type of pumping holes used at the target cell.
Fig. 2. Elliptical calculation model with a view of new spring fingers.
for comparison, as this is the only available indication of the level of RF power which is not tolerable. 2. Spring fingers—comparison with previous calculations So far there have been no measurements which can be correlated to the amount of RF noise tolerable for the diagnostic equipment. However, in 2000 the level was so high that data could not be taken. Spring fingers are used in the first place to provide RF shielding and to facilitate the removal of the target cell when necessary, but also as pumping slits. Naturally, pumping power is only achieved at the expense of the shielding. The gaps in the beam tube have been reduced in the 2003 design, reducing the calculated energy penetration by five orders of magnitude, from 183 mW to 1.3 mW.
2003 Design: fingers 2 mm wide, 5 mm long, with a spacing of 0.8 mm. 2000 Design: fingers 2 mm wide, 35.5 mm long, with a spacing of 5 mm.
that the model must include at least 10 mm empty space for the case of a 3 mm sigma bunch and then 40 mm for a 12 mm sigma bunch. It was also shown that using a rectangular instead of an elliptical model for the beam tube underestimated the energy penetration by less than a factor of 2. Fig. 2 shows the elliptical calculation model and the 2003 design for the spring fingers. 3. Preliminary calculations For the preliminary calculations the screen was modelled with a coarser mesh, 12 2 wires instead of 23 5, a rectangular beam tube was used and 14 of the geometry was modelled. Sheets, elements with zero thickness available in the MAFIA [1] programs, were used to model the wires of the screen. The following assumptions were made:
The equipment around the beam tube could not be modelled accurately, thus multiple reflections in that area were neglected. For a good approximation of the actual energy transfer, a half wavelength of empty space round the beam tube was modelled, with sufficiently fine discretisation to allow EM waves to propagate. This means
Shielding is effective: after bunch passage, no coupling between beam tube and outer volume; field energy in outer volume is a measure of the coupling; energy loss for all bunches adds up incoherently and is absorbed in the outer volume.
Five models were compared. (1) Screen over the holes, surrounded by a cage; (2) cage surrounding open holes;
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Fig. 3. Geometry of models 4 and 5.
Fig. 4. Left hand side: calculation model. Right hand side: model with boundary conditions.
(3) two horizontal wires; (4) screen over the holes; (5) open holes. Models 4 and 5, shown in Fig. 3, were chosen for further investigation. Model 3 shields better than Model 4, but the wires cannot be attached firmly. Model 1 provides better shielding but would only be considered if Model 4 proves insufficient, as it is mechanically less stable. 4. Simplified models 4.1. Transmission line In order to gain insight into these results, a much simplified calculation model was designed, see Fig. 4; a transmission line consisting of three electric plates with two waveguide ports at each end was used, as shown in Fig. 5. The model represented the six holes in the beam pipe, each 10 mm long with a 2 mm separation bar; the holes in the screen were 400 400 mm, with 40 mm for the width of the wire. Periodic boundary conditions were applied transversally producing an infinitely wide model. The reflection, (r), and transmission, (t), together with the coupling, (c) and the isolation, (i), were calculated (see Fig. 5). The excitation is a Gaussian pulse which travels from the bottom left at the speed of light. As the main scattering effect seemed to come from the edges of the pumping holes and to a lesser extent from the edge of each of the holes in the screen (see Fig. 6), the shape of the screen holes was varied, using rectangular holes two and four times as long. A tapering of the ends of the holes was also tried.
Fig. 5. Four ports are monitored to calculate the transmission (t), reflection (r), coupling (c) and isolation (i).
The energy transfer calculated for each port was for sigma ¼ 3 mm
for sigma ¼ 12 mm
ðrÞ ¼ 1:5%; ðiÞ ¼ 0:18%, ðtÞ ¼ 95:2%; ðcÞ ¼ 3:1%,
ðrÞ ¼ 0:32%; ðiÞ ¼ 0:025%, ðtÞ ¼ 99:4%; ðcÞ ¼ 0:2%.
For a 12 mm bunch the energy penetration was 0.11 mW. Using rectangular holes, with a 2:1 ratio, this could be reduced to 0.051 mW and with 4:1, to 0.038 mW.
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4.2. Discretisation test—TEM conductors
4.3. Discretisation test—inductance of wires in screen
In so fine a structure as the shielding screen, it was important to establish to what degree the discretisation affected the results obtained. Outside the beam tube there is a large area where waves can propagate. In order to investigate the effect of varying the mesh density within and either side of the screen, a waveguiding structure was introduced; a model with TEM conductor plates, see Fig. 7, guides and reflects the electromagnetic waves, representing a similar physical situation in a smaller volume with better discretisation. As expected, the actual size of the holes in the screen plays a large role, so that the coarser screen used in Section 3 overestimates the power transmission by two orders of magnitude. However, the fineness of the discretisation within these holes also affects the results, making the screen more transparent. This is not in contradiction to the results in Section 4.1, as there the holes were changed from square to rectangular. It was seen in Model 3 of Section 3 that the wires parallel to the beam direction have a screening effect, while those perpendicular to the beam cause reflections.
The inductance of wires in a screen was investigated with an even simpler model. The screen consists of many individual wires. Current flowing through the wires causes magnetic fields round each wire. This magnetic field is responsible for the coupling and, as the inductance describes the relation of the current to the field energy, the inductance is a good measure of the coupling strength. Thus, the inductance is used to investigate the effect of discretisation on the results. A very simple model can be used to consider the effect of varied discretisations on the calculated coupling. A twoplate resonator with periodic structure was chosen, that of a metal post between two metal plates, top and bottom, with periodic boundaries on the other two sides, left and right (see Fig. 8). This represents the resonant conditions for one wire of the screen. The height of the post must be small with respect to the length of the resonator. The frequency shift caused by the presence of the wire is calculated in the frequency domain. The effect of the use of sheets on the calculated field penetration through the shielding screen was also investigated. In Fig. 9 the lower curves (yellow and blue) represent the solid post, (almost coincident) and the upper curves show the sheet model with different orientations L/Z0 was normalised to the best discretisation of the solid post, and plotted versus the mesh density. The curves rise steeply initially and then flatten out. Each wire acts as a very small magnetic filter, thus the thickness of the wire would also affect the coupling. As the calculated fields are constant in each mesh cell, a coarse mesh simulates a thicker wire even when the dimensions of the wire remain constant. Sheets increase transmission through the screen by a factor of almost two. 5. Full model In the time domain, when wakefields are not required, it is no longer necessary to maintain an equidistant mesh. A model with solid wires in the screen was generated, shown
Fig. 6. Energy transfer to the four ports is plotted against time, showing the reflections from the edges of the six holes.
Fig. 7. Model with TEM capacitor plates.
Fig. 8. Simplified model for inductance calculations of wires in a screen as a metal post between two metal plates.
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SHEETS : RED Y-Z / GREEN X-Y,
SOLID : YELLOW / BLUE
L/Z0 [NORMALISED TO BEST DISRETISATION, SOLID POST]
2.00 1.80
Sheets Y-Z Sheets X-Z
1.60 1.40 1.20
Solid. extra mesh line in post
1.00 Solid, no mesh line in post
0.800 0.600 0.0
2.0E + 04 4.0E + 04 6.0E + 04 8.0E + 04 1.0E + 05 1.2E + 05 1.4E + 05 1.6E + 05 MESH DENSITY, MESH CELLS/MM**3
Fig. 9. L/Z0 (normalised to best discretisation of solid post) vs. mesh density. The lower curves (yellow and blue) represent the solid post, (almost coincident). The upper curves show the sheet model with different orientations.
Fig. 10. Full model, a detail of the mesh of the screen is shown in the inset.
in Fig. 10. For comparison, models were also calculated with wires as sheets and without screening. Using sheets also allows more energy to reach the outer area and the higher resolution, i.e. more mesh lines between the wires of the screen is also necessary to obtain the correct energy penetration. Table 1 shows the results. Although the differences between the solid and the sheet model are small when sigma ¼ 12 mm, it is interesting to note that increasing the discretisation makes the screen more transparent to higher frequency components. In Section 4.3, L/Z0 was plotted against the mesh density.
The differences found there between the solid and the sheet model are also apparent in these calculations.
6. Conclusions A calculation model was found which gave reliable results within the given restrictions. The factors which affected the results were the use of sheets, discretisation, and the coarseness of the screen. The initial results were a factor of 10 too high.
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Table 1 Energy penetration through the pumping holes of the full model for two bunch lengths Screen model
Resolution
Sigma ¼ 3 mm Energy outsidea ( 106 V A s/m3)
Solid Solid Sheets Sheets Open Open holes
Low High Low High Low
0.3549 0.3944 0.8490 0.9215 834.4
Sigma ¼ 12 mm Power lossb (mW)
0.1278 0.1420 0.3056 0.3317 300.4
Energy outsidea (( 103 V A s/m3) 0.2693 0.2951 0.5711 0.6136 32.13
Power lossb (mW) o o o o
1 1 1 1
11.57
The screen wires were modelled as either sheets or solid, with 6 6 mesh lines per screen hole (high-resolution), or 4 4 (low-resolution). a Energy calculated for a bunch with 1 C charge. b Energy scaled to the HERA design current, 60 mA.
The screening reduces the energy penetration by at least two orders of magnitude for a 12 mm beam. This should be sufficient to reduce the radio frequency interference to a tolerable level. Measurements are in progress. To be effective the screening must be firmly attached.
References [1] MAFIA, CST GmbH, Bad Nauheimer Str. 19 D-64289, Darmstadt, Germany.