Numerical simulation of electromagnetic fields and impedance of CERN LINAC4 H− source taking into account the effect of the plasmaa) A. Grudiev, J. Lettry, S. Mattei, M. Paoluzzi, and R. Scrivens Citation: Review of Scientific Instruments 85, 02B134 (2014); doi: 10.1063/1.4842317 View online: http://dx.doi.org/10.1063/1.4842317 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Status and operation of the Linac4 ion source prototypesa) Rev. Sci. Instrum. 85, 02B122 (2014); 10.1063/1.4848975 Numerical study of the inductive plasma coupling to ramp up the plasma density for the Linac4 H− ion sourcea) Rev. Sci. Instrum. 85, 02B113 (2014); 10.1063/1.4833920 Modeling of neutrals in the Linac4 H− ion source plasma: Hydrogen atom production density profile and Hα intensity by collisional radiative modela) Rev. Sci. Instrum. 85, 02B118 (2014); 10.1063/1.4833016 A new extraction system for the Linac4 H−ion sourcea) Rev. Sci. Instrum. 83, 02B710 (2012); 10.1063/1.3670344 Finite element thermal study of the Linac4 plasma generatora) Rev. Sci. Instrum. 81, 02A722 (2010); 10.1063/1.3277144
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 02B134 (2014)
Numerical simulation of electromagnetic fields and impedance of CERN LINAC4 H− source taking into account the effect of the plasmaa) A. Grudiev,b) J. Lettry, S. Mattei, M. Paoluzzi, and R. Scrivens CERN, Geneva, Switzerland
(Presented 10 September 2013; received 7 September 2013; accepted 22 October 2013; published online 21 January 2014) Numerical simulation of the CERN LINAC4 H− source 2 MHz RF system has been performed taking into account a realistic geometry from 3D Computer Aided Design model using commercial FEM high frequency simulation code. The effect of the plasma has been added to the model by the approximation of a homogenous electrically conducting medium. Electric and magnetic fields, RF power losses, and impedance of the circuit have been calculated for different values of the plasma conductivity. Three different regimes have been found depending on the plasma conductivity: (1) Zero or low plasma conductivity results in RF electric field induced by the RF antenna being mainly capacitive and has axial direction; (2) Intermediate conductivity results in the expulsion of capacitive electric field from plasma and the RF power coupling, which is increasing linearly with the plasma conductivity, is mainly dominated by the inductive azimuthal electric field; (3) High conductivity results in the shielding of both the electric and magnetic fields from plasma due to the skin effect, which reduces RF power coupling to plasma. From these simulations and measurements of the RF power coupling on the CERN source, a value of the plasma conductivity has been derived. It agrees well with an analytical estimate calculated from the measured plasma parameters. In addition, the simulated and measured impedances with and without plasma show very good agreement as well demonstrating validity of the plasma model used in the RF simulations. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4842317] I. ELECTROMAGNETIC SIMULATIONS OF THE ION SOURCE WITHOUT PLASMA
The H− source is one of the key components of the LINAC4 which is under construction at CERN.1 In Fig. 1, a cross-section of the ion source is presented. The 3D Computer Aided Design model of the ion source has been imported into commercial code for high frequency electromagnetic simulations ANSYS HFSS2 including all parts and realistic material properties relevant for the electromagnetic field configuration. The plasma in the ion source is ignited and heated by means of a RF antenna in the form of a 6-turn coil driven by the external power source at 2 MHz. This configuration has been implemented in HFSS code by connecting the 6-turn coil to an input coaxial port and using a driven modal solution to calculate the impedance of the coil in the realistic ion source environment. The cross section of the HFSS model is presented in Fig. 1. As a result of the simulation the impedance is calculated together with the electric-magnetic EM fields driven from the input port. Since the matching circuit3 between the RF power source connected with the circuit via 50 cable and the ion source was not included in the simulations the normalization of the EM fields is done by calculating the RF current flowing in the coil and scaling it to the operating value. Good agreement of the antenna resistance Rant and antenna inductance Lant calculated from the impedance has been found between
simulated (Rant = 0.26 , Lant = 3.0 μH) and measured (Rant = 0.4 , Lant = 3.2 μH) values. The measured values have been calculated from the forward and reflected waves measured using directional couplers at the final stage of the high power amplifier.3 The distributions of the RF magnetic and electric fields are presented in Figs. 2 and 3, respectively.
a) Contributed paper, published as part of the Proceedings of the 15th
International Conference on Ion Sources, Chiba, Japan, September 2013. b) Author to whom correspondence should be addressed. Electronic mail:
[email protected]. 0034-6748/2014/85(2)/02B134/3/$30.00
FIG. 1. The HFSS model of the ion source. 85, 02B134-1
© 2014 AIP Publishing LLC
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02B134-2
Grudiev et al.
Rev. Sci. Instrum. 85, 02B134 (2014)
II. MODELLING PLASMA IN THE EM SIMULATIONS
6
1
4
0.5
R
plasma
[Ω ]
Only the 6-turn coil is visualized in order not to overload images with the details of the ion source model shown in Fig. 1. Fields are normalized to 0.22 A RF coil current amplitude. Whereas magnetic field configuration is to be expected in the case of a solenoid showing mainly axial component inside of the plasma chamber, the electric field configuration is very different from the one created by the RF coil current flowing in azimuthal direction. The presence of the coil conductor carrying the current completely changes the distribution of the electric field. The direction of the electric field is mainly axial with its direction changing near the highest RF potential point in the middle of the plasma chamber. The calculated EM field distribution is exported to the plasma PIC code.4
0
2
R
-Lplasma [μ H]
FIG. 2. The distribution of the magnetic field is shown for the ion source cross section shown in Fig. 1.
Since no plasma can be simulated in the HFSS code, a plasma model has to be introduced in order to describe the ion source impedance and EM fields in the presence of plasma. Modeling plasma as a homogeneous conducting medium of a conductivity σ is possible in the HFSS code. In the following simulations the volume of the plasma chamber shown in violet in Fig. 1 has been filled with a conductor which conductivity has been varied in the range from 0 for the case of vacuum presented in the previous section up to the 10 000 S/m. For higher values the skin depth at 2 MHz becomes smaller than 1 mm and the simulations require very fine mesh. The results of the simulations are presented below. In Fig. 4, resistance and inductance of plasma as it was defined in Ref. 3 (Rplasma = Rant+plasma – Rant ; Lplasma = Lant+plasma – Lant ) are plotted as a function of conductivity of the plasma conductor used in the simulations. The maximum Rplasma = 5 is obtained for conductivity value near 1000 S/m. This point corresponds to the optimum coupling of the power from the source to the plasma. Lplasma is negative and its absolute value ranges from 0 to 0.6 μH. The simulated values of the plasma resistivity and inductance are in a very good agreement with the measured values of plasma resistivity (4.3 ) and inductance (−0.1 μH) if the conductivity is assumed to be in the range of 300– 500 S/m which is not so far from the maximum Rplasma point. The value of the plasma conductivity of 500 S/m which results in the best agreement between simulated and measured plasma impedance can be compared with the plasma conductivity values estimated using the standard equation for the plasma conductivity. The plasma will mostly behave like a conductor (i.e., the conductivity has a mostly real value) when the sum of the electron-neutral and electron-ion collision frequencies, as given by the Spitzer equations,5 is higher than the RF drive frequency. In this case the plasma conductivity (σ ) is given by Eq. (1) where ne is the electron density, m is the electron mass, P is the vacuum pressure in Torr, and Te is
plasma
-Lplasma 0
0
200
400
600
800
1000
1200
1400
1600
-0.5 1800
σ [S/m]
FIG. 3. The distribution of the electric field is shown for the ion source cross section shown in Fig. 1.
FIG. 4. The dependence of the plasma resistivity and inductance on the plasma conductivity used in the simulations is presented.
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02B134-3
Grudiev et al.
Rev. Sci. Instrum. 85, 02B134 (2014)
the electron temperature in eV. σ =
ne e2 ne e2 ≈ . m (γ0 + j ω) m(1.9 × 109 P + 1.5 × 10−11 ne Te−3/2 ) (1)
Measurements of CERN’s RF ion source types6 have shown that at the H2 pressure is approximately 20 mTorr, the plasma density is of the order of 1018 –1019 m−3 and the electron temperature inside the RF coil should be approximately 10 eV (in order to produce sufficient excited H2 molecules for associative detachment). Using these values to calculate the collision rate, leads to an estimate of the conductivity of 730–6600 S/m for the above given density range, slightly higher than value required by the electromagnetic model of the source to explain the measured plasma resistance. The electric field distribution in the plasma chamber region for the conductivity σ = 1000 S/m is presented in Fig. 5. It is very different from the one presented in Fig. 3. The electric field is much lower and the direction is mainly azimuthal as one would expect from an azimuthal current loop. The so-called capacitive electric field dominating at σ = 0 is completely suppressed in the plasma volume by the plasma surface currents for σ = 1000 S/m. The capacitive field still dominates the volume outside the plasma region. In the plasma volume, however, only the azimuthal inductive electric field is still present providing coupling of RF power to the plasma. The small negative Lplasma , whose absolute value starts to grow at σ > 200 S/m, corresponds to the reduction of the
total inductance of the ion source due to skin-effect taking place on the plasma conductor surface pushing both magnetic and electric fields outside of the plasma volume. For higher σ > 10 000 S/m, practically no EM field is present inside of the plasma conductor volume and consequently no power is coupled to the plasma. In summary, three different regimes can be identified depending on the plasma conductivity: (1) Zero or low plasma conductivity < 100 S/m results in the electric field induced by the RF antenna being mainly capacitive and has mainly axial direction; (2) Intermediate conductivity 100–10 000 results in the expulsion of capacitive electric field from plasma. At the same time, the RF power coupling, which is dominated by the inductive azimuthal electric field not affected by the expulsion, increases linearly with the plasma conductivity; (3) High conductivity > 10 000 S/m results in the shielding of EM fields from plasma due to the skin effect, which reduces RF power coupling to plasma. III. CONCLUSIONS
EM simulations of the full 3D model of the CERN Linac4 ion source have been performed providing important insight into the 2 MHz RF electric field distribution inside of the plasma chamber. It has been observed that at very lower plasma density or no plasma capacitive electric field dominates the electric field distribution. From the simulations and measurements of the RF power coupling to plasma in the CERN ion source, a value of the plasma conductivity has been derived. Although slightly lower, it agrees with an analytical estimate calculated from the measured plasma parameters. In addition, the simulated and measured impedances with and without plasma show very good agreement as well demonstrating validity of the plasma model used in the RF simulations and giving confidence that such simulation tools can be used in the design of ion sources and in providing EM field distribution for plasma simulations. 1 J.
FIG. 5. Electric field distribution for plasma conductivity σ = 1000 S/m.
Lettry, D. Aguglia, Y. Coutron, E. Chaudet, A. Dallocchio, J. Gil Flores, J. Hansen, E. Mahner, S. Mathot, S. Mattei, O. Midttun, P. Moyret, D. Nisbet, M. O’Neil, M. Paoluzzi, C. Pasquino, H. Pereira, J. Sanchez Arias, C. Schmitzer, R. Scrivens, and D. Steyaert, “H− ion sources for CERN’s Linac4,’’ AIP Conf. Proc. 1515, 302–311 (2013). 2 See http://www.ansys.com for information about HFSS code. 3 M. M. Paoluzzi, M. Haase, J. Marques Balula, and D. Nisbet, AIP Conf. Proc. 1390, 265 (2011). 4 S. Mattei, M. Ohta, M. Yasumoto, A. Hatayama, J. Lettry, and A. Grudiev, “Plasma ignition and steady state simulations of the Linac4 H− Ion Source,” Rev. Sci. Instrum. 85, 02B115 (2014). 5 Y. P. Raizer, Gas Discharge Physics (Springer, Berlin, 1991), p. 11. 6 C. Schmitzer, M. Kronberger, J. Lettry, J. Sanchez-Arias, and H. Störi, Rev. Sci. Instrum. 83, 02A715 (2012).
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 136.165.238.131 On: Fri, 19 Dec 2014 11:53:27
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 136.165.238.131 On: Fri, 19 Dec 2014 11:53:27
REVIEW OF SCIENTIFIC INSTRUMENTS 85, 02B134 (2014)
Numerical simulation of electromagnetic fields and impedance of CERN LINAC4 H− source taking into account the effect of the plasmaa) A. Grudiev,b) J. Lettry, S. Mattei, M. Paoluzzi, and R. Scrivens CERN, Geneva, Switzerland
(Presented 10 September 2013; received 7 September 2013; accepted 22 October 2013; published online 21 January 2014) Numerical simulation of the CERN LINAC4 H− source 2 MHz RF system has been performed taking into account a realistic geometry from 3D Computer Aided Design model using commercial FEM high frequency simulation code. The effect of the plasma has been added to the model by the approximation of a homogenous electrically conducting medium. Electric and magnetic fields, RF power losses, and impedance of the circuit have been calculated for different values of the plasma conductivity. Three different regimes have been found depending on the plasma conductivity: (1) Zero or low plasma conductivity results in RF electric field induced by the RF antenna being mainly capacitive and has axial direction; (2) Intermediate conductivity results in the expulsion of capacitive electric field from plasma and the RF power coupling, which is increasing linearly with the plasma conductivity, is mainly dominated by the inductive azimuthal electric field; (3) High conductivity results in the shielding of both the electric and magnetic fields from plasma due to the skin effect, which reduces RF power coupling to plasma. From these simulations and measurements of the RF power coupling on the CERN source, a value of the plasma conductivity has been derived. It agrees well with an analytical estimate calculated from the measured plasma parameters. In addition, the simulated and measured impedances with and without plasma show very good agreement as well demonstrating validity of the plasma model used in the RF simulations. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4842317] I. ELECTROMAGNETIC SIMULATIONS OF THE ION SOURCE WITHOUT PLASMA
The H− source is one of the key components of the LINAC4 which is under construction at CERN.1 In Fig. 1, a cross-section of the ion source is presented. The 3D Computer Aided Design model of the ion source has been imported into commercial code for high frequency electromagnetic simulations ANSYS HFSS2 including all parts and realistic material properties relevant for the electromagnetic field configuration. The plasma in the ion source is ignited and heated by means of a RF antenna in the form of a 6-turn coil driven by the external power source at 2 MHz. This configuration has been implemented in HFSS code by connecting the 6-turn coil to an input coaxial port and using a driven modal solution to calculate the impedance of the coil in the realistic ion source environment. The cross section of the HFSS model is presented in Fig. 1. As a result of the simulation the impedance is calculated together with the electric-magnetic EM fields driven from the input port. Since the matching circuit3 between the RF power source connected with the circuit via 50 cable and the ion source was not included in the simulations the normalization of the EM fields is done by calculating the RF current flowing in the coil and scaling it to the operating value. Good agreement of the antenna resistance Rant and antenna inductance Lant calculated from the impedance has been found between
simulated (Rant = 0.26 , Lant = 3.0 μH) and measured (Rant = 0.4 , Lant = 3.2 μH) values. The measured values have been calculated from the forward and reflected waves measured using directional couplers at the final stage of the high power amplifier.3 The distributions of the RF magnetic and electric fields are presented in Figs. 2 and 3, respectively.
a) Contributed paper, published as part of the Proceedings of the 15th
International Conference on Ion Sources, Chiba, Japan, September 2013. b) Author to whom correspondence should be addressed. Electronic mail:
[email protected]. 0034-6748/2014/85(2)/02B134/3/$30.00
FIG. 1. The HFSS model of the ion source. 85, 02B134-1
© 2014 AIP Publishing LLC
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02B134-2
Grudiev et al.
Rev. Sci. Instrum. 85, 02B134 (2014)
II. MODELLING PLASMA IN THE EM SIMULATIONS
6
1
4
0.5
R
plasma
[Ω ]
Only the 6-turn coil is visualized in order not to overload images with the details of the ion source model shown in Fig. 1. Fields are normalized to 0.22 A RF coil current amplitude. Whereas magnetic field configuration is to be expected in the case of a solenoid showing mainly axial component inside of the plasma chamber, the electric field configuration is very different from the one created by the RF coil current flowing in azimuthal direction. The presence of the coil conductor carrying the current completely changes the distribution of the electric field. The direction of the electric field is mainly axial with its direction changing near the highest RF potential point in the middle of the plasma chamber. The calculated EM field distribution is exported to the plasma PIC code.4
0
2
R
-Lplasma [μ H]
FIG. 2. The distribution of the magnetic field is shown for the ion source cross section shown in Fig. 1.
Since no plasma can be simulated in the HFSS code, a plasma model has to be introduced in order to describe the ion source impedance and EM fields in the presence of plasma. Modeling plasma as a homogeneous conducting medium of a conductivity σ is possible in the HFSS code. In the following simulations the volume of the plasma chamber shown in violet in Fig. 1 has been filled with a conductor which conductivity has been varied in the range from 0 for the case of vacuum presented in the previous section up to the 10 000 S/m. For higher values the skin depth at 2 MHz becomes smaller than 1 mm and the simulations require very fine mesh. The results of the simulations are presented below. In Fig. 4, resistance and inductance of plasma as it was defined in Ref. 3 (Rplasma = Rant+plasma – Rant ; Lplasma = Lant+plasma – Lant ) are plotted as a function of conductivity of the plasma conductor used in the simulations. The maximum Rplasma = 5 is obtained for conductivity value near 1000 S/m. This point corresponds to the optimum coupling of the power from the source to the plasma. Lplasma is negative and its absolute value ranges from 0 to 0.6 μH. The simulated values of the plasma resistivity and inductance are in a very good agreement with the measured values of plasma resistivity (4.3 ) and inductance (−0.1 μH) if the conductivity is assumed to be in the range of 300– 500 S/m which is not so far from the maximum Rplasma point. The value of the plasma conductivity of 500 S/m which results in the best agreement between simulated and measured plasma impedance can be compared with the plasma conductivity values estimated using the standard equation for the plasma conductivity. The plasma will mostly behave like a conductor (i.e., the conductivity has a mostly real value) when the sum of the electron-neutral and electron-ion collision frequencies, as given by the Spitzer equations,5 is higher than the RF drive frequency. In this case the plasma conductivity (σ ) is given by Eq. (1) where ne is the electron density, m is the electron mass, P is the vacuum pressure in Torr, and Te is
plasma
-Lplasma 0
0
200
400
600
800
1000
1200
1400
1600
-0.5 1800
σ [S/m]
FIG. 3. The distribution of the electric field is shown for the ion source cross section shown in Fig. 1.
FIG. 4. The dependence of the plasma resistivity and inductance on the plasma conductivity used in the simulations is presented.
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02B134-3
Grudiev et al.
Rev. Sci. Instrum. 85, 02B134 (2014)
the electron temperature in eV. σ =
ne e2 ne e2 ≈ . m (γ0 + j ω) m(1.9 × 109 P + 1.5 × 10−11 ne Te−3/2 ) (1)
Measurements of CERN’s RF ion source types6 have shown that at the H2 pressure is approximately 20 mTorr, the plasma density is of the order of 1018 –1019 m−3 and the electron temperature inside the RF coil should be approximately 10 eV (in order to produce sufficient excited H2 molecules for associative detachment). Using these values to calculate the collision rate, leads to an estimate of the conductivity of 730–6600 S/m for the above given density range, slightly higher than value required by the electromagnetic model of the source to explain the measured plasma resistance. The electric field distribution in the plasma chamber region for the conductivity σ = 1000 S/m is presented in Fig. 5. It is very different from the one presented in Fig. 3. The electric field is much lower and the direction is mainly azimuthal as one would expect from an azimuthal current loop. The so-called capacitive electric field dominating at σ = 0 is completely suppressed in the plasma volume by the plasma surface currents for σ = 1000 S/m. The capacitive field still dominates the volume outside the plasma region. In the plasma volume, however, only the azimuthal inductive electric field is still present providing coupling of RF power to the plasma. The small negative Lplasma , whose absolute value starts to grow at σ > 200 S/m, corresponds to the reduction of the
total inductance of the ion source due to skin-effect taking place on the plasma conductor surface pushing both magnetic and electric fields outside of the plasma volume. For higher σ > 10 000 S/m, practically no EM field is present inside of the plasma conductor volume and consequently no power is coupled to the plasma. In summary, three different regimes can be identified depending on the plasma conductivity: (1) Zero or low plasma conductivity < 100 S/m results in the electric field induced by the RF antenna being mainly capacitive and has mainly axial direction; (2) Intermediate conductivity 100–10 000 results in the expulsion of capacitive electric field from plasma. At the same time, the RF power coupling, which is dominated by the inductive azimuthal electric field not affected by the expulsion, increases linearly with the plasma conductivity; (3) High conductivity > 10 000 S/m results in the shielding of EM fields from plasma due to the skin effect, which reduces RF power coupling to plasma. III. CONCLUSIONS
EM simulations of the full 3D model of the CERN Linac4 ion source have been performed providing important insight into the 2 MHz RF electric field distribution inside of the plasma chamber. It has been observed that at very lower plasma density or no plasma capacitive electric field dominates the electric field distribution. From the simulations and measurements of the RF power coupling to plasma in the CERN ion source, a value of the plasma conductivity has been derived. Although slightly lower, it agrees with an analytical estimate calculated from the measured plasma parameters. In addition, the simulated and measured impedances with and without plasma show very good agreement as well demonstrating validity of the plasma model used in the RF simulations and giving confidence that such simulation tools can be used in the design of ion sources and in providing EM field distribution for plasma simulations. 1 J.
FIG. 5. Electric field distribution for plasma conductivity σ = 1000 S/m.
Lettry, D. Aguglia, Y. Coutron, E. Chaudet, A. Dallocchio, J. Gil Flores, J. Hansen, E. Mahner, S. Mathot, S. Mattei, O. Midttun, P. Moyret, D. Nisbet, M. O’Neil, M. Paoluzzi, C. Pasquino, H. Pereira, J. Sanchez Arias, C. Schmitzer, R. Scrivens, and D. Steyaert, “H− ion sources for CERN’s Linac4,’’ AIP Conf. Proc. 1515, 302–311 (2013). 2 See http://www.ansys.com for information about HFSS code. 3 M. M. Paoluzzi, M. Haase, J. Marques Balula, and D. Nisbet, AIP Conf. Proc. 1390, 265 (2011). 4 S. Mattei, M. Ohta, M. Yasumoto, A. Hatayama, J. Lettry, and A. Grudiev, “Plasma ignition and steady state simulations of the Linac4 H− Ion Source,” Rev. Sci. Instrum. 85, 02B115 (2014). 5 Y. P. Raizer, Gas Discharge Physics (Springer, Berlin, 1991), p. 11. 6 C. Schmitzer, M. Kronberger, J. Lettry, J. Sanchez-Arias, and H. Störi, Rev. Sci. Instrum. 83, 02A715 (2012).
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