1. Charles C. Plasmas for Spacecraft Propulsion. J Phys D: Appl Phys (2009) 42:
163001. doi:10.1088/0022-3727/42/16/163001
2. Merino M, Ahedo E. Effect of the Plasma-Induced Magnetic Field on a
Magnetic Nozzle. Plasma Sourc Sci. Technol. (2016) 25:045012. doi:10.1088/
0963-0252/25/4/045012
3. Little JM, Choueiri EY. Electron Demagnetization in a Magnetically
Expanding Plasma. Phys Rev Lett (2019) 123:145001. doi:10.1103/
PhysRevLett.123.145001
4. Takahashi K. Helicon-Type Radiofrequency Plasma Thrusters and Magnetic Plasma
Nozzles. Rev Mod Plasma Phys (2019) 3:3. doi:10.1007/S41614-019-0024-2
5. Chen Z, Wang Y, Tang H, Ren J, Li M, Zhang Z, et al. Electric Potential
Barriers in the Magnetic Nozzle. Phys Rev E (2020) 101:053208. doi:10.1103/
PhysRevE.101.053208
6. Doyle SJ, Bennet A, Tsifakis D, Dedrick JP, Boswell RW, Charles C.
Characterization and Control of an Ion-Acoustic Plasma Instability
Downstream of a Diverging Magnetic Nozzle. Front Phys (2020) 8:24.
doi:10.3389/fphy.2020.00024
Frontiers in Physics | www.frontiersin.org
11
December 2021 | Volume 9 | Article 779204
Emoto et al.
Energy Loss in Magnetic Nozzle
14. Virko VF, Virko YV, Slobodyan VM, Shamrai KP. The Effect of Magnetic
Configuration on Ion Acceleration From a Compact Helicon Source With
Permanent Magnets. Plasma Sourc Sci. Technol. (2010) 19:015004.
doi:10.1088/0963-0252/19/1/015004
15. Ahedo E, Merino M. Two-dimensional Supersonic Plasma Acceleration in a
Magnetic Nozzle. Phys Plasmas (2010) 17:073501. doi:10.1063/1.3442736
16. Fruchtman A, Takahashi K, Charles C, Boswell RW. A Magnetic Nozzle
Calculation of the Force on a Plasma. Phys Plasmas (2012) 19:033507.
doi:10.1063/1.3691650
17. Takahashi K, Charles C, Boswell RW. Approaching the Theoretical
Limit of Diamagnetic-Induced Momentum in a Rapidly Diverging
Magnetic Nozzle. Phys Rev Lett (2013) 110:195003. doi:10.1103/
PhysRevLett.110.195003
18. Takahashi K, Chiba A, Komuro A, Ando A. Experimental Identification of an
Azimuthal Current in a Magnetic Nozzle of a Radiofrequency Plasma
Thruster. Plasma Sourc Sci. Technol. (2016) 25:055011. doi:10.1088/09630252/25/5/055011
19. Emoto K, Takahashi K, Takao Y. Numerical Investigation of Internal Plasma
Currents in a Magnetic Nozzle. Phys Plasmas (2021) 28:093506. doi:10.1063/
5.0053336
20. Takahashi K. Magnetic Nozzle Radiofrequency Plasma Thruster Approaching
Twenty Percent Thruster Efficiency. Sci Rep (2021) 11:2768. doi:10.1038/
s41598-021-82471-2
21. Goebel DM, Katz I. Fundamentals of Electric Propulsion: Ion and Hall
Thrusters. Hoboken: John Wiley & Sons (2008).
22. Di Cara DM, Estublier D. Smart-1: An Analysis of Flight Data. Acta
Astronautica (2005) 57:250–6. doi:10.1016/J.ACTAASTRO.2005.03.036
23. Pidgeon D, Corey R, Sauer B, Day M. Two Years of On-Orbit Performance
of Spt-100 Electric Propulsion. In: 24th AIAA International
Communications Satellite Systems Conference (2006). p. 5353.
doi:10.2514/6.2006-5353
24. Scime EE, Keiter PA, Balkey MM, Boivin RF, Kline JL, Blackburn M, et al. Ion
Temperature Anisotropy Limitation in High Beta Plasmas. Phys Plasmas
(2000) 7:2157–65. doi:10.1063/1.874036
25. Takahashi K, Lafleur T, Charles C, Alexander P, Boswell RW. Electron Diamagnetic
Effect on Axial Force in an Expanding Plasma: Experiments and Theory. Phys Rev
Lett (2011) 107:235001. doi:10.1103/PhysRevLett.107.235001
26. Aguirre EM, Bodin R, Yin N, Good TN, Scime EE. Evidence for Electron
Energization Accompanying Spontaneous Formation of Ion Acceleration
Regions in Expanding Plasmas. Phys Plasmas (2020) 27:123501.
doi:10.1063/5.0025523
27. Lafleur T. Helicon Plasma Thruster Discharge Model. Phys Plasmas (2014) 21:
043507. doi:10.1063/1.4871727
28. Takahashi K, Chiba A, Komuro A, Ando A. Axial Momentum Lost to a Lateral
Wall of a Helicon Plasma Source. Phys Rev Lett (2015) 114:195001.
doi:10.1103/PhysRevLett.114.195001
29. Takahashi K, Sugawara T, Ando A. Spatially- and Vector-Resolved
Momentum Flux Lost to a Wall in a Magnetic Nozzle Rf Plasma Thruster.
Sci Rep (2020) 10:1061. doi:10.1038/s41598-020-58022-6
30. Emoto K, Takahashi K, Takao Y. Axial Momentum Gains of Ions and
Electrons in Magnetic Nozzle Acceleration. Plasma Sources Sci. Technol.
(2021) 30:115016. doi:10.1088/1361-6595/ac33ee
31. Takahashi K, Charles C, Boswell RW, Ando A. Demonstrating a New
Technology for Space Debris Removal Using a Bi-directional Plasma
Thruster. Sci Rep (2018) 8:14417. doi:10.1038/s41598-018-32697-4
32. Takao Y, Takahashi K. Numerical Validation of Axial Plasma Momentum Lost
to a Lateral Wall Induced by Neutral Depletion. Phys Plasmas (2015) 22:
113509. doi:10.1063/1.4935903
33. Takase K, Takahashi K, Takao Y. Effects of Neutral Distribution and External
Magnetic Field on Plasma Momentum in Electrodeless Plasma Thrusters. Phys
Plasmas (2018) 25:023507. doi:10.1063/1.5015937
34. Birdsall C, Langdon A. Plasma Physics via Computer Simulation. Boca Raton:
CRC Press (1991).
35. Vahedi V, Surendra M. A Monte Carlo Collision Model for the Particle-In-Cell
Method: Applications to Argon and Oxygen Discharges. Computer Phys
Commun (1995) 87:179–98. doi:10.1016/0010-4655(94)00171-W
Frontiers in Physics | www.frontiersin.org
36. Rapp D, Englander-Golden P. Total Cross Sections for Ionization and
Attachment in Gases by Electron Impact. I. Positive Ionization. J Chem
Phys (1965) 43:1464–79. doi:10.1063/1.1696957
37. Heer FJd., Jansen RHJ, Kaay Wv. d.. Total Cross Sections for Electron
Scattering by Ne, Ar, Kr and Xe. J Phys B: Mol Phys (1979) 12:979–1002.
doi:10.1088/0022-3700/12/6/016
38. Hayashi M. Determination of Electron-Xenon Total Excitation CrossSections, from Threshold to 100 eV, from Experimental Values of
Townsend’s α. J Phys D: Appl Phys (1983) 16:581–9. doi:10.1088/00223727/16/4/018
39. Takao Y, Kusaba N, Eriguchi K, Ono K. Two-dimensional Particle-In-Cell
Monte Carlo Simulation of a Miniature Inductively Coupled Plasma Source.
J Appl Phys (2010) 108:093309. doi:10.1063/1.3506536
40. Takao Y, Eriguchi K, Ono K. Effect of Capacitive Coupling in a Miniature
Inductively Coupled Plasma Source. J Appl Phys (2012) 112:093306.
doi:10.1063/1.4764333
41. Takahashi K, Charles C, Boswell R, Cox W, Hatakeyama R. Transport of
Energetic Electrons in a Magnetically Expanding Helicon Double Layer
Plasma. Appl Phys Lett (2009) 94:191503. doi:10.1063/1.3136721
42. Charles C. High Density Conics in a Magnetically Expanding Helicon Plasma.
Appl Phys Lett (2010) 96:051502. doi:10.1063/1.3309668
43. Ghosh S, Yadav S, Barada KK, Chattopadhyay PK, Ghosh J, Pal R,
et al..Formation of Annular Plasma Downstream by Magnetic Aperture in
the Helicon Experimental Device. Phys Plasmas (2017) 24:020703.
doi:10.1063/1.4975665
44. Gulbrandsen N, Fredriksen Å. Rfea Measurements of High-Energy Electrons
in a Helicon Plasma Device With Expanding Magnetic Field. Front Phys (2017)
5:2. doi:10.3389/fphy.2017.00002
45. Takahashi K, Akahoshi H, Charles C, Boswell RW, Ando A. High Temperature
Electrons Exhausted From Rf Plasma Sources along a Magnetic Nozzle. Phys
Plasmas (2017) 24:084503. doi:10.1063/1.4990110
46. Magarotto M, Pavarin D. Parametric Study of a Cathode-Less Radio Frequency
Thruster. IEEE Trans Plasma Sci (2020) 48:2723–35. doi:10.1109/
tps.2020.3006257
47. Chen FF, Sudit ID, Light M. Downstream Physics of the Helicon
Discharge. Plasma Sourc Sci. Technol. (1996) 5:173–80. doi:10.1088/
0963-0252/5/2/009
48. Cox W, Charles C, Boswell RW, Hawkins R. Spatial Retarding Field Energy
Analyzer Measurements Downstream of a Helicon Double Layer Plasma. Appl
Phys Lett (2008) 93:071505. doi:10.1063/1.2965866
49. Takahashi K, Fujiwara T. Observation of Weakly and Strongly Diverging Ion
Beams in a Magnetically Expanding Plasma. Appl Phys Lett (2009) 94:061502.
doi:10.1063/1.3080205
50. Zhang Y, Charles C, Boswell R. Effect of Radial Plasma Transport at the
Magnetic Throat on Axial Ion Beam Formation. Phys Plasmas (2016) 23:
083515. doi:10.1063/1.4960828
51. Bennet A, Charles C, Boswell R. Non-local Plasma Generation in a Magnetic
Nozzle. Phys Plasmas (2019) 26:072107. doi:10.1063/1.5098484
52. Martinez-Sanchez M, Navarro-Cavallé J, Ahedo E. Electron Cooling and Finite
Potential Drop in a Magnetized Plasma Expansion. Phys Plasmas (2015) 22:
053501. doi:10.1063/1.4919627
53. Ahedo E, Correyero S, Navarro-Cavallé J, Merino M. Macroscopic and
Parametric Study of a Kinetic Plasma Expansion in a Paraxial Magnetic
Nozzle. Plasma Sourc Sci. Technol. (2020) 29:045017. doi:10.1088/13616595/ab7855
54. Pottinger S, Lappas V, Charles C, Boswell R. Performance Characterization
of a Helicon Double Layer Thruster Using Direct Thrust Measurements.
J Phys D: Appl Phys (2011) 44:235201. doi:10.1088/0022-3727/44/23/
235201
55. Takahashi K, Lafleur T, Charles C, Alexander P, Boswell RW, Perren M,
et al. Direct Thrust Measurement of a Permanent Magnet Helicon
Double Layer Thruster. Appl Phys Lett (2011) 98:141503. doi:10.1063/
1.3577608
56. Charles C, Takahashi K, Boswell RW. Axial Force Imparted by a Conical
Radiofrequency Magneto-Plasma Thruster. Appl Phys Lett (2012) 100:113504.
doi:10.1063/1.3694281
12
December 2021 | Volume 9 | Article 779204
Emoto et al.
Energy Loss in Magnetic Nozzle
Publisher’s Note: All claims expressed in this article are solely those of the authors
and do not necessarily represent those of their affiliated organizations, or those of
the publisher, the editors, and the reviewers. Any product that may be evaluated in
this article, or claim that may be made by its manufacturer, is not guaranteed or
endorsed by the publisher.
57. Charles C, Boswell R, Takahashi K. Boltzmann Expansion in a Radiofrequency
Conical Helicon Thruster Operating in Xenon and Argon. Appl Phys Lett
(2013) 102:223510. doi:10.1063/1.4810001
58. Williams LT, Walker MLR. Thrust Measurements of a Radio Frequency
Plasma Source. J Propulsion Power (2013) 29:520–7. doi:10.2514/
1.B34574
59. Takahashi K, Komuro A, Ando A. Operating a Magnetic Nozzle Helicon
Thruster With strong Magnetic Field. Phys Plasmas (2016) 23:033505.
doi:10.1063/1.4943406
Copyright © 2021 Emoto, Takahashi and Takao. This is an open-access article
distributed under the terms of the Creative Commons Attribution License (CC BY).
The use, distribution or reproduction in other forums is permitted, provided the
original author(s) and the copyright owner(s) are credited and that the original
publication in this journal is cited, in accordance with accepted academic practice.
No use, distribution or reproduction is permitted which does not comply with
these terms.
Conflict of Interest: The authors declare that the research was conducted in the
absence of any commercial or financial relationships that could be construed as a
potential conflict of interest.
Frontiers in Physics | www.frontiersin.org
13
December 2021 | Volume 9 | Article 779204
...