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RF tests of the electrical insulations for the toroidal structures of RFX
Fusion Engineering and Design 75–79 (2005) 525–530
RF tests of the electrical insulations for the toroidal structures of RFX A. Masiello, G. Mella, P. Sonato ∗ , C. Taccon Consorzio RFX, Associazione EURATOM-ENEA sulla Fusione, Corso Stati Uniti 4, I-35127 Padova, Italy Available online 19 September 2005
Abstract Modified conducting structures of the RFX machine have been designed to intentionally reduce electrical discontinuities, thus error fields due to eddy currents have been substantially reduced also. For this reason, for example, the stabilizing shell features a single poloidal and a single equatorial gap. Electrical insulations of those gaps shall be verified before and during the assembly phase of the various components. On the other hand, an applied voltage test can not be carried out in the quasi-static regime, so a radio frequency (RF) method has been used. This paper deals with description of the test bed, set up to verify the feasibility of the RF test and to set up the necessary equipments. Moreover, all the tests carried out are described in details together with the actions taken to overcome some of the problems which arise with radiated electromagnetic power. © 2005 Elsevier B.V. All rights reserved. Keywords: Radio frequency (RF); Toroidal structures; Electrical insulations
1. Introduction The new load assembly of RFX, almost completed and restored, is characterized by an Inconel® vacuum vessel, a copper shell and a stainless steel toroidal supporting structure [1]. The copper shell is composed of two halves joined on the outer equatorial plane by copper plates which short-circuit the gap on the outer side, whereas the inner remains open. In the region of the single poloidal gap, two copper layers overlap each other for about 23 toroidal degrees and the ∗ Corresponding author. Tel.: +39 049 8295037/5000; fax: +39 049 8700718. E-mail address: [email protected] (P. Sonato).
0920-3796/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2005.06.318
electrical insulation between them is guaranteed by a 2 mm PTFE layer (see Fig. 1). This particular arrangement for the poloidal gap of the shell has been found to be effective for the reduction of the error fields [2]. The maximum toroidal loop voltage attainable with the magnetizing winding of RFX is 700 V, whereas in the case of fast plasma current termination the observed peak reaches roughly the same value (duration <1 ms), at least for plasma current up to 1.1 MA. The maximum poloidal loop voltage is instead about one order of magnitude lower than the toroidal one. All the insulating gaps need to be tested during the assembly phases, to verify the good conditions of the electrical insulation. In particular, the poloidal gap on
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Fig. 2. Priciple scheme for the capacitor bank discharge test.
Fig. 1. Exploded CAD view of the new RFX shell.
the shell shall be tested at least at 1 kV, which cannot be applied using a conventional scheme. Simulations of a first method based on a capacitor bank discharge, have been carried out, but the duration of the voltage applied at the gap was very short (fractions of milliseconds) and, moreover, the circuit design to reach such high voltages was rather complex. A different approach was then studied: the principle of this second method is to exploit the overvoltage on a capacitance, the shell poloidal gap in our system, at the resonant frequency of the circuit on which it is connected. Since the calculated resonant frequency of the new RFX shell was in the range of radio frequency (RF), also the electromagnetic radiated power had to be taken into account. Considering that the new copper shell was under construction, it was necessary to develop in advance a reliable system to perform the electrical tests on the vertical insulated gap. For this reason, some preliminary tests have been carried out. In particular, the RF system was previously set up on the old RFX shell, to select the best matching equipment for the RF amplifier and to verify both the maximum attainable voltage and the ground effect. Then the RF system was efficiently used to apply 1 kV to each halves of the shell as acceptance test. 2. Equivalent circuit of the shell The equivalent electric circuit of the shell, in terms of lumped parameters, consists in an RLC series cir-
cuit (see Fig. 2). Calculations of their values in steady state yield Ls = 3.6 H, Cs = 22 nF and Rs = 2.5 . Unavoidable mechanical tolerances on the two halves of the shell, which generate two air gaps between the PTFE insulation layer and the copper sheets, suggest to consider for Cs roughly half of the theoretical value. On the other hand, the value of Rs shall account for the penetration thickness according to the formula: s Rs ∼ = R0s δ where R0s is the steady state value, s the shell thickness and λ is the penetration thickness. With the above mentioned values, the natural frequency of the shell results 735 kHz.
3. First method A principle scheme for a capacitor bank discharge test is reported in Fig. 2, where C1 is the capacitor bank, whose value has been chosen equal to that of an available equipment, Lp is the sum of the connections inductance and capacitor bank inductance, T1 is a solid state switch (e.g. a thyristor) which includes also the 10 m connections resistance. For t > 0, C1 will charge Cs with a fast time constant then the capacitor equivalent to the parallel of C1 and Cs will run down oscillating with a frequency of about 7 kHz. If C1 is charged with 1 V the resulting potential on Cs is reported in Fig. 3, whereas the current in C1 is reported in Fig. 4. Fig. 3 shows that the applied voltage to Cs is halved in 0.5 ms and is practically extinguished after 2 ms. This type of test to verify the electrical insulation of the vertical joint of the shell, involves substantially different types of drawbacks:
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Fig. 3. Voltage on Cs for t > 0.
Fig. 4. Current on C1 for t > 0.
• the current supplied by the capacitor bank and its time derivative are rather high (6 A and 100 A/s, respectively, for each volt at which C1 is charged). This implies the use of a high performance switch (e.g. thyristor) and of a suitable controller; • the voltage attainable on the joint decreases rapidly, so the test would not be an applied voltage test and it should be carried out at more than 1 kV; • to verify the electrical insulation is necessary to test it in more than one voltage step and comparing the voltage waveform, even if this is a standard proce-
dure for high voltage testing, it introduces uncertainties on the test results, at least compared to the method reported in the next section.
4. Second method A different way to test the electrical insulation of the shell overlapped gap, which is equivalent to a shortcircuited capacitance, is to exploit the overvoltage generated by feeding the shell at its resonant frequency.
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The maximum applied voltage on the capacitance is: VC max =
√ 2XC I
where XC is the reactance of the capacitor at the given frequency. Accordingly, it yields: √ P = KA P 0.5 VC max = 2XC RR
Fig. 5. Principle scheme of the shell gap RF test.
The equivalent electrical circuit is reported in Fig. 5; the voltage attainable on the capacitance is related to the applied voltage by the well known Q factor. Since the resonant frequency of the shell is expected to be in the range of RF, the shell itself will behave like a radiating magnetic dipole, that is a loop antenna. For this reason, some preliminary tests have been carried out to verify both an equivalent circuit model of the antenna and to select the best matching equipment. 4.1. Test on a model A circular loop with radius a = 0.5 m has been built with a copper tube whose diameter was 18 mm and its thickness 1 mm. Measured inductance of the loop was L = 2.8 H. On the loop terminals, an in-vacuum capacitance of 50 pF was connected, thus the natural frequency of the loop was about 13.4 MHz. The RF generator used in the tests consisted in a waveform generator connected to wideband linear amplifier (0.5–90 MHz, gain 48 db, 50 , 100 W); also a standing wave ratio meter was used to verify the matching between amplifier and antenna. The radiation resistance of this loop antenna at 13.4 MHz (function of circumference of the loop in wavelengths Cλ = 2πa/λ = 0.14), is expected to be RR = 74 m [3]. In the hypothesis that RF input power P is totally radiated, the RMS value of the current in the loop results into: P I= RR
which directly correlates the voltage with the power of the RF amplifier needed for the tests. For the loop antenna, it results: VC max = KA P 0.5 = 1217P 0.5 which means that to obtain 1 kV on the capacitance the power amplifier shall theoretically supply about 1 W. On the other hand, the unavoidable effect of the soil shall also be taken into account [4,5], which results in a large increase of the radiation resistance. In fact, the intrinsic impedance of a dissipative media is lower than the vacuum one, so the radiation resistance in presence of the ground is increased, typically by a few Ohms depending on the distance between soil and antenna and on the soil conductivity. For this reason, with the same RF power, the overvoltage on the capacitance will result, lowered by a factor whose value implies the knowledge of the ground resistivity and relative permittivity. During tests it was measured KA = 240, which correspond to RR = 1.95 ; thus, 20 W were necessary to obtain 1 kV on the capacitance. Finally, some different matching equipments have been used, however, it resulted that the lowest reflected power and the simplest arrangement was obtained with the so called “gamma-match” [6], which consists of a wire placed inside or outside the loop spanning roughly 90◦ (see Fig. 5). 4.2. Test on a reduced scale model In order to have a more realistic approach, the invacuum capacitance was replaced by a plane capacitance similar to that generated by the shell overlapped gap and consisting of two copper plates, 0.5 m2 each, separated by a 0.2 mm PTFE sheet, which exhibited a 20 nF capacitance. The experimental relation between voltage on the capacitance and the power supplied by
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the amplifier was VC max ∼ = 80(P)0.5 at the frequency of 680 kHz. The measured radiation resistance in this case was 44 m and comparing these results with the one reported in the previous paragraph: √ √ KA RR2 f2 C2 ∼ 2 2RR2 2πf2 C2 = √ = √ =3 KA2 RR1 f1 C1 2 2RR1 2πf1 C1 thus, the attainable voltage on the capacitance was reduced by a factor three, since even if the radiation resistance decreases, which results in increase of the antenna current, the capacitive reactance was 20 times lower. 4.3. Test on the old RFX shell The last preliminary test was carried out on the old aluminium RFX shell, whose dimensions are about the same of the new copper one [7]. One of the two vertical butt joint of the old shell was short-circuited, whereas on the other the plane capacitance described in Section 4.2 was connected. Also the external equatorial gap was short-circuited. The measured resonant frequency was 670 kHz and the voltage on the capacitance was given by: VC max ∼ = 40(P)0.5 that is half of the one obtained in the previous test. It is believed that the main reason of the reduced performance in terms of attainable voltage was due to the proximity of the ground to the shell (20 mm). It should be also noted that at the resonant frequency of 670 kHz, since RR = 0.19 Rs = 85 , the hypothesis of P totally radiated still holds.
Fig. 6. The new RFX copper shell.
respectively, and εPTFE = 2.1 is the relative permittivity of PTFE, the electric field in the air gap is given by: Eair =
VC max + 2air
PTFE εPTFE
In the hypothesis of air → 0 and VC max = 1 kV, it results Eair = 10.5 kV/cm, which is well within the dielectric strength of dry air. Tests on the new copper shell were firstly carried out on each single half, upper and lower. The lower half was in the assembling room at about 4 m from the soil (see Figs. 6 and 7), laid on a reinforced concrete floor 0.5 m thick. At the resonant frequency of 1.78 MHz, experimental value of KA was about 100, whereas RR was
5. Applied voltage tests on the copper shell A preliminary evaluation of the maximum electric field strength in the unavoidable air gaps between PTFE insulating sheet and copper have been carried out to avoid discharges and thus, damages in the insulation. Considering two equal small air gaps, on both surfaces of the PTFE layer, an equivalent model can be represented by three capacitance in series. Thus, if PTFE and air are the insulation and one air gap thickness,
Fig. 7. Half of the copper shell connected to the wire used as “gamma-match”.
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0.23 , then to apply 1 kV, it was necessary to increase the power up to 100 W. The voltage was applied during 1 min without noticing any changes on the acquired measurements. An additional check has been carried out increasing the power up to 110 W, until a discharge occurred on the ∼0.2 mm spark gap, installed to preserve insulation integrity. The upper half of the shell was instead at ground floor, that is close to soil. At the resonant frequency of 1.56 MHz, measurements gave KA = 43 and RR = 1.5 . With those values, it was not possible to apply 1 kV to the gap, since a 540 W power amplifier would have had to be available. So it was decided to lift the shell at about 3 m from the ground obtaining KA = 165 and RR = 0.09 at 1.29 MHz. Thus, it was applied 1 kV to the gap supplying only 40 W RF power.
6. Test on the shell assembled on the vacuum vessel Once the copper shell has been assembled onto the vacuum vessel, the RF insulation has been repeated. After various attempts to match the impedance of the shell varying the “gamma-match” position and length, it was decided to measure the impedance of the shell at the resonant frequency from two connections close to vertical gap. The impedance was very close to 50 , so the Q factor was unitary and the maximum attainable voltage on the gap was the output voltage of the RF amplifier. For this reason, it was possible to apply only 100 V with the allowable generator (100 W on a 50 resistor), whereas the presence of the vacuum vessel inside the shell would have required 10 kW RF power to obtain 1 kV on the shell gap. On the other hand, considering the successful pre-test at 1 kV, it was retained
that 100 V were enough to prevent mistakes during the assembly phase. 7. Conclusions The proposed RF method to generate high electric voltage at the shell gap allowed to overcome difficulties of both a steady state and a capacitor bank discharge method. Moreover, all tests that have been carried out have shown that the RF method use relatively small power and it can be applied on close structure with a single insulating gap, providing that there are no inductively coupled resistive structures.
Acknowledgments Authors are grateful to M. Moresco for the fruitful discussions and suggestions and G. Marchiori for his precious help.
References [1] P. Sonato, G. Chitarin, P. Zaccaria, F. Gnesotto, S. Ortolani, A. Buffa, et al., Machine modification for active MHD control in RFX, Fusion Eng. Des. 66–68 (September) (2003) 161–168. [2] R. Piovan, F. Gnesotto, S. Ortolani, W.R. Baker, O. Barana, P. Bettini, et al., RFX machine and power supply improvements for RFP advanced studies, Fusion Eng. Des. 56–57 (2001) 819–824. [3] J.D. Kraus, Antennas, McGraw-Hill, New York, 2002. [4] A. Paraboni, Antenna, McGraw-Hill, New York, 1999. [5] J.D. Jackson, Classical Electrodynamics, J. Wiley & Sons, New York, 1999. [6] R.C. Johnson, H. Jasik, Antenna Engineering Handbook, McGraw-Hill, New York, 1988. [7] F. Gnesotto, P. Sonato, W.R. Baker, A. Doria, F. Elio, M. Fauri, et al., The plasma system of RFX, Fusion Eng. Des. 25 (4 January 1995) 316–335.
RF tests of the electrical insulations for the toroidal structures of RFX A. Masiello, G. Mella, P. Sonato ∗ , C. Taccon Consorzio RFX, Associazione EURATOM-ENEA sulla Fusione, Corso Stati Uniti 4, I-35127 Padova, Italy Available online 19 September 2005
Abstract Modified conducting structures of the RFX machine have been designed to intentionally reduce electrical discontinuities, thus error fields due to eddy currents have been substantially reduced also. For this reason, for example, the stabilizing shell features a single poloidal and a single equatorial gap. Electrical insulations of those gaps shall be verified before and during the assembly phase of the various components. On the other hand, an applied voltage test can not be carried out in the quasi-static regime, so a radio frequency (RF) method has been used. This paper deals with description of the test bed, set up to verify the feasibility of the RF test and to set up the necessary equipments. Moreover, all the tests carried out are described in details together with the actions taken to overcome some of the problems which arise with radiated electromagnetic power. © 2005 Elsevier B.V. All rights reserved. Keywords: Radio frequency (RF); Toroidal structures; Electrical insulations
1. Introduction The new load assembly of RFX, almost completed and restored, is characterized by an Inconel® vacuum vessel, a copper shell and a stainless steel toroidal supporting structure [1]. The copper shell is composed of two halves joined on the outer equatorial plane by copper plates which short-circuit the gap on the outer side, whereas the inner remains open. In the region of the single poloidal gap, two copper layers overlap each other for about 23 toroidal degrees and the ∗ Corresponding author. Tel.: +39 049 8295037/5000; fax: +39 049 8700718. E-mail address: [email protected] (P. Sonato).
0920-3796/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2005.06.318
electrical insulation between them is guaranteed by a 2 mm PTFE layer (see Fig. 1). This particular arrangement for the poloidal gap of the shell has been found to be effective for the reduction of the error fields [2]. The maximum toroidal loop voltage attainable with the magnetizing winding of RFX is 700 V, whereas in the case of fast plasma current termination the observed peak reaches roughly the same value (duration <1 ms), at least for plasma current up to 1.1 MA. The maximum poloidal loop voltage is instead about one order of magnitude lower than the toroidal one. All the insulating gaps need to be tested during the assembly phases, to verify the good conditions of the electrical insulation. In particular, the poloidal gap on
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Fig. 2. Priciple scheme for the capacitor bank discharge test.
Fig. 1. Exploded CAD view of the new RFX shell.
the shell shall be tested at least at 1 kV, which cannot be applied using a conventional scheme. Simulations of a first method based on a capacitor bank discharge, have been carried out, but the duration of the voltage applied at the gap was very short (fractions of milliseconds) and, moreover, the circuit design to reach such high voltages was rather complex. A different approach was then studied: the principle of this second method is to exploit the overvoltage on a capacitance, the shell poloidal gap in our system, at the resonant frequency of the circuit on which it is connected. Since the calculated resonant frequency of the new RFX shell was in the range of radio frequency (RF), also the electromagnetic radiated power had to be taken into account. Considering that the new copper shell was under construction, it was necessary to develop in advance a reliable system to perform the electrical tests on the vertical insulated gap. For this reason, some preliminary tests have been carried out. In particular, the RF system was previously set up on the old RFX shell, to select the best matching equipment for the RF amplifier and to verify both the maximum attainable voltage and the ground effect. Then the RF system was efficiently used to apply 1 kV to each halves of the shell as acceptance test. 2. Equivalent circuit of the shell The equivalent electric circuit of the shell, in terms of lumped parameters, consists in an RLC series cir-
cuit (see Fig. 2). Calculations of their values in steady state yield Ls = 3.6 H, Cs = 22 nF and Rs = 2.5 . Unavoidable mechanical tolerances on the two halves of the shell, which generate two air gaps between the PTFE insulation layer and the copper sheets, suggest to consider for Cs roughly half of the theoretical value. On the other hand, the value of Rs shall account for the penetration thickness according to the formula: s Rs ∼ = R0s δ where R0s is the steady state value, s the shell thickness and λ is the penetration thickness. With the above mentioned values, the natural frequency of the shell results 735 kHz.
3. First method A principle scheme for a capacitor bank discharge test is reported in Fig. 2, where C1 is the capacitor bank, whose value has been chosen equal to that of an available equipment, Lp is the sum of the connections inductance and capacitor bank inductance, T1 is a solid state switch (e.g. a thyristor) which includes also the 10 m connections resistance. For t > 0, C1 will charge Cs with a fast time constant then the capacitor equivalent to the parallel of C1 and Cs will run down oscillating with a frequency of about 7 kHz. If C1 is charged with 1 V the resulting potential on Cs is reported in Fig. 3, whereas the current in C1 is reported in Fig. 4. Fig. 3 shows that the applied voltage to Cs is halved in 0.5 ms and is practically extinguished after 2 ms. This type of test to verify the electrical insulation of the vertical joint of the shell, involves substantially different types of drawbacks:
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Fig. 3. Voltage on Cs for t > 0.
Fig. 4. Current on C1 for t > 0.
• the current supplied by the capacitor bank and its time derivative are rather high (6 A and 100 A/s, respectively, for each volt at which C1 is charged). This implies the use of a high performance switch (e.g. thyristor) and of a suitable controller; • the voltage attainable on the joint decreases rapidly, so the test would not be an applied voltage test and it should be carried out at more than 1 kV; • to verify the electrical insulation is necessary to test it in more than one voltage step and comparing the voltage waveform, even if this is a standard proce-
dure for high voltage testing, it introduces uncertainties on the test results, at least compared to the method reported in the next section.
4. Second method A different way to test the electrical insulation of the shell overlapped gap, which is equivalent to a shortcircuited capacitance, is to exploit the overvoltage generated by feeding the shell at its resonant frequency.
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The maximum applied voltage on the capacitance is: VC max =
√ 2XC I
where XC is the reactance of the capacitor at the given frequency. Accordingly, it yields: √ P = KA P 0.5 VC max = 2XC RR
Fig. 5. Principle scheme of the shell gap RF test.
The equivalent electrical circuit is reported in Fig. 5; the voltage attainable on the capacitance is related to the applied voltage by the well known Q factor. Since the resonant frequency of the shell is expected to be in the range of RF, the shell itself will behave like a radiating magnetic dipole, that is a loop antenna. For this reason, some preliminary tests have been carried out to verify both an equivalent circuit model of the antenna and to select the best matching equipment. 4.1. Test on a model A circular loop with radius a = 0.5 m has been built with a copper tube whose diameter was 18 mm and its thickness 1 mm. Measured inductance of the loop was L = 2.8 H. On the loop terminals, an in-vacuum capacitance of 50 pF was connected, thus the natural frequency of the loop was about 13.4 MHz. The RF generator used in the tests consisted in a waveform generator connected to wideband linear amplifier (0.5–90 MHz, gain 48 db, 50 , 100 W); also a standing wave ratio meter was used to verify the matching between amplifier and antenna. The radiation resistance of this loop antenna at 13.4 MHz (function of circumference of the loop in wavelengths Cλ = 2πa/λ = 0.14), is expected to be RR = 74 m [3]. In the hypothesis that RF input power P is totally radiated, the RMS value of the current in the loop results into: P I= RR
which directly correlates the voltage with the power of the RF amplifier needed for the tests. For the loop antenna, it results: VC max = KA P 0.5 = 1217P 0.5 which means that to obtain 1 kV on the capacitance the power amplifier shall theoretically supply about 1 W. On the other hand, the unavoidable effect of the soil shall also be taken into account [4,5], which results in a large increase of the radiation resistance. In fact, the intrinsic impedance of a dissipative media is lower than the vacuum one, so the radiation resistance in presence of the ground is increased, typically by a few Ohms depending on the distance between soil and antenna and on the soil conductivity. For this reason, with the same RF power, the overvoltage on the capacitance will result, lowered by a factor whose value implies the knowledge of the ground resistivity and relative permittivity. During tests it was measured KA = 240, which correspond to RR = 1.95 ; thus, 20 W were necessary to obtain 1 kV on the capacitance. Finally, some different matching equipments have been used, however, it resulted that the lowest reflected power and the simplest arrangement was obtained with the so called “gamma-match” [6], which consists of a wire placed inside or outside the loop spanning roughly 90◦ (see Fig. 5). 4.2. Test on a reduced scale model In order to have a more realistic approach, the invacuum capacitance was replaced by a plane capacitance similar to that generated by the shell overlapped gap and consisting of two copper plates, 0.5 m2 each, separated by a 0.2 mm PTFE sheet, which exhibited a 20 nF capacitance. The experimental relation between voltage on the capacitance and the power supplied by
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the amplifier was VC max ∼ = 80(P)0.5 at the frequency of 680 kHz. The measured radiation resistance in this case was 44 m and comparing these results with the one reported in the previous paragraph: √ √ KA RR2 f2 C2 ∼ 2 2RR2 2πf2 C2 = √ = √ =3 KA2 RR1 f1 C1 2 2RR1 2πf1 C1 thus, the attainable voltage on the capacitance was reduced by a factor three, since even if the radiation resistance decreases, which results in increase of the antenna current, the capacitive reactance was 20 times lower. 4.3. Test on the old RFX shell The last preliminary test was carried out on the old aluminium RFX shell, whose dimensions are about the same of the new copper one [7]. One of the two vertical butt joint of the old shell was short-circuited, whereas on the other the plane capacitance described in Section 4.2 was connected. Also the external equatorial gap was short-circuited. The measured resonant frequency was 670 kHz and the voltage on the capacitance was given by: VC max ∼ = 40(P)0.5 that is half of the one obtained in the previous test. It is believed that the main reason of the reduced performance in terms of attainable voltage was due to the proximity of the ground to the shell (20 mm). It should be also noted that at the resonant frequency of 670 kHz, since RR = 0.19 Rs = 85 , the hypothesis of P totally radiated still holds.
Fig. 6. The new RFX copper shell.
respectively, and εPTFE = 2.1 is the relative permittivity of PTFE, the electric field in the air gap is given by: Eair =
VC max + 2air
PTFE εPTFE
In the hypothesis of air → 0 and VC max = 1 kV, it results Eair = 10.5 kV/cm, which is well within the dielectric strength of dry air. Tests on the new copper shell were firstly carried out on each single half, upper and lower. The lower half was in the assembling room at about 4 m from the soil (see Figs. 6 and 7), laid on a reinforced concrete floor 0.5 m thick. At the resonant frequency of 1.78 MHz, experimental value of KA was about 100, whereas RR was
5. Applied voltage tests on the copper shell A preliminary evaluation of the maximum electric field strength in the unavoidable air gaps between PTFE insulating sheet and copper have been carried out to avoid discharges and thus, damages in the insulation. Considering two equal small air gaps, on both surfaces of the PTFE layer, an equivalent model can be represented by three capacitance in series. Thus, if PTFE and air are the insulation and one air gap thickness,
Fig. 7. Half of the copper shell connected to the wire used as “gamma-match”.
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0.23 , then to apply 1 kV, it was necessary to increase the power up to 100 W. The voltage was applied during 1 min without noticing any changes on the acquired measurements. An additional check has been carried out increasing the power up to 110 W, until a discharge occurred on the ∼0.2 mm spark gap, installed to preserve insulation integrity. The upper half of the shell was instead at ground floor, that is close to soil. At the resonant frequency of 1.56 MHz, measurements gave KA = 43 and RR = 1.5 . With those values, it was not possible to apply 1 kV to the gap, since a 540 W power amplifier would have had to be available. So it was decided to lift the shell at about 3 m from the ground obtaining KA = 165 and RR = 0.09 at 1.29 MHz. Thus, it was applied 1 kV to the gap supplying only 40 W RF power.
6. Test on the shell assembled on the vacuum vessel Once the copper shell has been assembled onto the vacuum vessel, the RF insulation has been repeated. After various attempts to match the impedance of the shell varying the “gamma-match” position and length, it was decided to measure the impedance of the shell at the resonant frequency from two connections close to vertical gap. The impedance was very close to 50 , so the Q factor was unitary and the maximum attainable voltage on the gap was the output voltage of the RF amplifier. For this reason, it was possible to apply only 100 V with the allowable generator (100 W on a 50 resistor), whereas the presence of the vacuum vessel inside the shell would have required 10 kW RF power to obtain 1 kV on the shell gap. On the other hand, considering the successful pre-test at 1 kV, it was retained
that 100 V were enough to prevent mistakes during the assembly phase. 7. Conclusions The proposed RF method to generate high electric voltage at the shell gap allowed to overcome difficulties of both a steady state and a capacitor bank discharge method. Moreover, all tests that have been carried out have shown that the RF method use relatively small power and it can be applied on close structure with a single insulating gap, providing that there are no inductively coupled resistive structures.
Acknowledgments Authors are grateful to M. Moresco for the fruitful discussions and suggestions and G. Marchiori for his precious help.
References [1] P. Sonato, G. Chitarin, P. Zaccaria, F. Gnesotto, S. Ortolani, A. Buffa, et al., Machine modification for active MHD control in RFX, Fusion Eng. Des. 66–68 (September) (2003) 161–168. [2] R. Piovan, F. Gnesotto, S. Ortolani, W.R. Baker, O. Barana, P. Bettini, et al., RFX machine and power supply improvements for RFP advanced studies, Fusion Eng. Des. 56–57 (2001) 819–824. [3] J.D. Kraus, Antennas, McGraw-Hill, New York, 2002. [4] A. Paraboni, Antenna, McGraw-Hill, New York, 1999. [5] J.D. Jackson, Classical Electrodynamics, J. Wiley & Sons, New York, 1999. [6] R.C. Johnson, H. Jasik, Antenna Engineering Handbook, McGraw-Hill, New York, 1988. [7] F. Gnesotto, P. Sonato, W.R. Baker, A. Doria, F. Elio, M. Fauri, et al., The plasma system of RFX, Fusion Eng. Des. 25 (4 January 1995) 316–335.