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Study on the influence of the magnetic field geometry on the power deposition in a helicon plasma source

Published online by Cambridge University Press:  15 July 2019

M. Magarotto*
Affiliation:
Centro di Ateneo di Studi e Attività Spaziali ‘Giuseppe Colombo’ – CISAS, University of Padova, Via Venezia 15, 35131 Padova, Italy
D. Melazzi
Affiliation:
Technology for Propulsion and Innovation S.r.l., Via della Croce Rossa 112, 35129 Padova, Italy
D. Pavarin
Affiliation:
Department of Industrial Engineering, University of Padova, Via Gradenigo 6/a, 35131 Padova, Italy
*
Email address for correspondence: [email protected]

Abstract

We have numerically studied how an actual confinement magnetostatic field affects power deposition in a helicon source. We have solved the wave propagation by means of two electromagnetic solvers, namely: (i) plaSma Padova Inhomogeneous Radial Electromagnetic solver (SPIREs), a mono-dimensional finite-difference frequency-domain code, and (ii) Advanced coDe for Anisotropic Media and ANTennas (ADAMANT), a full-wave three-dimensional tool based on the method of moments. We have computed the deposited power spectrum with SPIREs, power deposition profile with ADAMANT and the antenna impedance with both codes. First we have verified the numerical accuracy of both SPIREs and ADAMNT. Then, we have analysed two configurations of magnetostatic field, namely produced by Maxwell coils, and Helmholtz coils. For each configuration we have studied three cases: (i) low density $n=10^{17}~\text{m}^{-3}$ and low magnetic field $B_{0}=250$ G; (ii) medium density $n=10^{18}~\text{m}^{-3}$ and medium magnetic field $B_{0}=500$ G; (iii) high density $n=10^{19}~\text{m}^{-3}$ and high magnetic field $B_{0}=1000$ G. We have found that the Maxwell coil configuration does not produces significant changes in the deposited power phenomenon with respect to a perfectly uniform and axial magnetostatic field. While the Helmholtz coil configuration can lead to a power spectrum peaked near the axis of the discharge.

Type
Research Article
Copyright
© Cambridge University Press 2019 

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References

Ahedo, E. & Merino, M. 2010 Two-dimensional supersonic plasma acceleration in a magnetic nozzle. Phys. Plasmas 17 (7), 073501.Google Scholar
Amestoy, P., Duff, I., LExcellent, J. & Koster, J.2007. Multifrontal massively parallel solver (mumps version 4.6): Users guide http://enseeiht. fr/apo/mumps/ and http://graal.enslyon.fr.Google Scholar
Balanis, C. A. 2016 Antenna Theory: Analysis and Design. Wiley.Google Scholar
Batishchev, O. V. 2009 Minihelicon plasma thruster. IEEE Trans. Plasma Sci. 37 (8), 15631571.Google Scholar
Bose, D., Govindan, T. & Meyyappan, M. 2003 Modeling of a helicon plasma source. IEEE Trans. Plasma Sci. 31 (4), 464470.Google Scholar
Braginskii, O., Vasileva, A. & Kovalev, A. 2001 Helicon plasma in a nonuniform magnetic field. Phys. Rep. 27 (8), 699707.Google Scholar
Breizman, B. N. & Arefiev, A. V. 2000 Radially localized helicon modes in nonuniform plasma. Phys. Rev. Lett. 84 (17), 3863.Google Scholar
Cardinali, A., Melazzi, D., Manente, M. & Pavarin, D. 2014 Ray-tracing WKB analysis of whistler waves in non-uniform magnetic fields applied to space thrusters. Plasma Sources Sci. Technol. 23 (1), 015013.Google Scholar
Chang, L., Hole, M., Caneses, J., Chen, G., Blackwell, B. & Corr, C. 2012 Wave modeling in a cylindrical non-uniform helicon discharge. Phys. Plasmas 19 (8), 083511.Google Scholar
Chen, F. F. 2015 Helicon discharges and sources: a review. Plasma Sources Sci. Technol. 24 (1), 014001.Google Scholar
Chen, F. F. & Arnush, D. 1997 Generalized theory of helicon waves. I. Normal modes. Phys. Plasmas 4 (9), 34113421.Google Scholar
Chen, F. F. & Blackwell, D. D. 1999 Upper limit to Landau damping in helicon discharges. Phys. Rev. Lett. 82 (13), 2677.Google Scholar
Chen, G., Arefiev, A. V., Bengtson, R. D., Breizman, B. N., Lee, C. A. & Raja, L. L. 2006 Resonant power absorption in helicon plasma sources. Phys. Plasmas 13 (12), 123507.Google Scholar
Diaz, F. R. C. 2000 The VASIMR rocket. Sci. Am. 283 (5), 9097.Google Scholar
Goebel, D. M. & Katz, I. 2008 Fundamentals of Electric Propulsion: Ion and Hall Thrusters. JPL Space Science and Technology Series.Google Scholar
Guo, X. M., Scharer, J., Mouzouris, Y. & Louis, L. 1999 Helicon experiments and simulations in nonuniform magnetic field configurations. Phys. Plasmas 6 (8), 34003407.Google Scholar
Jackson, J. D. 1999 Classical Electrodynamics. John Wiley & Sons Inc.Google Scholar
Kinder, R. L. & Kushner, M. J. 2001 Wave propagation and power deposition in magnetically enhanced inductively coupled and helicon plasma sources. J. Vacuum Sci. Technol. A 19 (1), 7686.Google Scholar
Krämer, M. 1999 Propagation and damping of $m=+1$ and $m=-1$ helicon modes in an inhomogeneous plasma column. Phys. Plasmas 6 (4), 10521058.Google Scholar
Kuwahara, D., Koyama, Y., Otsuka, S., Ishii, T., Ishii, H., Fujitsuka, H., Waseda, S. & Shinohara, S. 2014 Development of direct thrust measurement system for the completely electrodeless helicon plasma thruster. Plasma Fusion Res. 9, 3406025.Google Scholar
Lafleur, T., Charles, C. & Boswell, R. 2010 Plasma control by modification of helicon wave propagation in low magnetic fields. Phys. Plasmas 17 (7), 073508.Google Scholar
Lafleur, T., Charles, C. & Boswell, R. 2011 Characterization of a helicon plasma source in low diverging magnetic fields. J. Phys. D: Appl. Phys. 44 (5), 055202.Google Scholar
Manente, M., Trezzolani, F., Magarotto, M., Fantino, E., Selmo, A., Bellomo, N., Toson, E. & Pavarin, D. 2019 REGULUS: A propulsion platform to boost small satellite missions. Acta Astron. 157, 241249.Google Scholar
Melazzi, D., Curreli, D., Manente, M., Carlsson, J. & Pavarin, D. 2012 SPIREs: A finite-difference frequency-domain electromagnetic solver for inhomogeneous magnetized plasma cylinders. Comput. Phys. Commun. 183 (6), 11821191.Google Scholar
Melazzi, D. & Lancellotti, V. 2014 ADAMANT: A surface and volume integral-equation solver for the analysis and design of helicon plasma sources. Comput. Phys. Commun. 185 (7), 19141925.Google Scholar
Merino, M., Navarro, J., Casado, S., Ahedo, E., Gómez, V., Ruiz, M., Bosch, E. & del Amo, J. G. 2015 Design and development of a 1 kW-class helicon antenna thruster. In 34th International Electric Propulsion Conference.Google Scholar
Mouzouris, Y. & Scharer, J. E. 1996 Modeling of profile effects for inductive helicon plasma sources. IEEE Trans. Plasma Sci. 24 (1), 152160.Google Scholar
Pavarin, D., Ferri, F., Manente, M., Lucca Fabris, A., Trezzolani, F., Faenza, M., Tasinato, L., Rondini, D., Curreli, D., Melazzi, D. et al. 2012 Characterization of the Helicon Plasma Thruster of the EU FP7 HPH.com program. In Proceedings of the 3rd Space Propulsion Conference.Google Scholar
Peterson, A. F., Ray, S. L. & Mittra, R. 1998 Computational Methods for Electromagnetics, vol. 2. IEEE Press.Google Scholar
Pottinger, S., Lappas, V., Charles, C. & Boswell, R. 2011 Performance characterization of a helicon double layer thruster using direct thrust measurements. J. Phys. D: Appl. Phys. 44 (23), 235201.Google Scholar
Rothwell, E. J. & Cloud, M. J. 2018 Electromagnetics. CRC press.Google Scholar
Sheehan, J. P., Collard, T. A., Ebersohn, F. H. & Longmier, B. W. 2015 Initial operation of the cubesat ambipolar thruster. In 34th International Electric Propulsion Conference.Google Scholar
Shinohara, S., Nishida, H., Tanikawa, T., Hada, T., Funaki, I. & Shamrai, K. P. 2014 Development of electrodeless plasma thrusters with high-density helicon plasma sources. IEEE Trans. Plasma Sci. 42 (5), 12451254.Google Scholar
Stix, T. H. 1962 The theory of plasma waves. In The Theory of Plasma Waves. McGraw-Hill.Google Scholar
Swanson, D. G. 2012 Plasma Waves. Elsevier.Google Scholar
Takahashi, K., Komuro, A. & Ando, A. 2015 Effect of source diameter on helicon plasma thruster performance and its high power operation. Plasma Sources Sci. Technol. 24 (5), 055004.Google Scholar
Takahashi, K., Lafleur, T., Charles, C., Alexander, P., Boswell, R., Perren, M., Laine, R., Pottinger, S., Lappas, V., Harle, T. et al. 2011 Direct thrust measurement of a permanent magnet helicon double layer thruster. Appl. Phys. Lett. 98 (14), 141503.Google Scholar
Trezzolani, F., Manente, M., Selmo, A., Melazzi, D., Magarotto, M., Moretto, D., De Carlo, P., Pessana, M. & Pavarin, D. 2017 Development and test of an high power RF plasma thruster in project SAPERE-STRONG. In Proceedings of the 35th International Electric Propulsion Conference (IEPC), IEPC-2017-462, Atlanta, GA, USA.Google Scholar
Tysk, S. M., Denning, C. M., Scharer, J. E. & Akhtar, K. 2004 Optical, wave measurements, and modeling of helicon plasmas for a wide range of magnetic fields. Phys. Plasmas 11 (3), 878887.Google Scholar
Virko, V., Shamrai, K., Virko, Y. V. & Kirichenko, G. 2004 Wave phenomena, hot electrons, and enhanced plasma production in a helicon discharge in a converging magnetic field. Phys. Plasmas 11 (8), 38883897.Google Scholar
Ziemba, T., Carscadden, J., Slough, J., Prager, J. & Winglee, R. 2005 High power helicon thruster. In 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Tucson AZ, USA.Google Scholar