7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Demonstrating a thrust generation by electrons
in a magnetic nozzle rf plasma thruster

Soya Sumikawa1 and Kazunori Takahashi1,21Department of Electrical Engineering, Tohoku University, Sendai 980-8579, Japan
2
National Institute for Fusion Science, Toki 509-5292, Japane-mail (speaker): sumikawa.soya.t6@dc.tohoku.ac.jp
In the last few decades, electric propulsion systems
such as a gridded-ion thruster, an electron cyclotron
resonance thruster, and a Hall thruster [1-3], which
generate thrust by ions, have been vigorouslyinvestigated. Especially in recent years, a magnetic
nozzle (MN) radiofrequency (rf) plasma thruster [4,5](called a helicon thruster) is often the subject of studies.
The MN rf plasma thruster typically consists of an rf
antenna, an insulated glass tube, and a solenoid; it has anelectrodeless structure that allows a long lifetime even ina high-power operation. The processes of thrustgeneration have been investigated [6-8] in detail, andnow the thruster efficiency approaching thirty percent
has been obtained [9], while further clarification of themechanism is required yet.
The total thrust imparted by the MN rf plasma thruster
can be given by [10]𝑇total = 𝑇𝑠 + 𝑇𝑤 + 𝑇𝐵 ,(1)where 𝑇𝑠 , 𝑇𝑤 , and 𝑇𝐵 is the static electron pressure
force onto the back wall of the plasma source, the axial
momentum lost to the radial source wall, and the Lorentz
force exerted to the MN, respectively. The terms on theRHS in Eq. (1) can be measured individually [10] byattaching the back wall, the source tube, and the solenoid
to the thrust balance, respectively. The previous study
shows that the Lorentz force 𝑇𝐵 arising from theazimuthal internal current 𝑗𝜃 and the radial magnetic
field 𝐵𝑧 is the major contributor to the thrust; 𝑇𝐵 and𝑗𝜃 are given by [10]𝑗𝜃 =1 𝜕𝑝𝑒
𝐸𝑟 1 𝜕𝑝𝑖
𝐸𝑟 1+ 𝑒𝑛𝑒 +− 𝑒𝑛𝑖 + [∇ ⋅ (𝑚𝑖 𝑛𝑖 𝒗2𝑖 )]𝑟 (2)𝐵𝑧 𝜕𝑟𝐵𝑧 𝐵𝑧 𝜕𝑟
𝐵𝑧 𝐵𝑧𝑧𝑟𝑝

𝑇𝐵 = ∫ 𝑗𝜃 × 𝐵𝑟 𝑑𝑉 ≈ −2𝜋 ∫ ∫ 𝑟00𝐵𝑟 𝜕𝑝𝑒𝑑𝑟𝑑𝑧,𝐵𝑧 𝜕𝑟(3)

where, 𝑟𝑝 , 𝐵𝑧 , 𝑝𝑒 , 𝑝𝑖 , 𝑛𝑒 , 𝑛𝑖 , 𝒗𝑖 , 𝐸𝑟 , and 𝑒 are theplasma radius, axial magnetic field, electron and ionpressure, density, ion velocity, radial electric field, andelementary charge, respectively. In previous studies[7,10,11], only the first term of the RHS in Eq. (2), i.e.,
the electron diamagnetic current, was considered,assuming that an axisymmetric plasma with cold ionsand electron and radial ion inertia is negligible. As aresult, the form of the RHS in Eq. (3) can be derived,
which indicates that even though the mass of an ion ismuch heavier than the mass of an electron, most of thethrust imparted to the MN rf plasma thruster iscontributed from the electrons. Textbooks on the electric
propulsion, e.g., [12], said that the major contributor forthe thrust is the ions due to their significant momentum;
deep understanding on the thrust generation by theelectrons will be useful to improve the thrusterperformance. Especially, it is challenging and interesting
to demonstrate the thrust generation by the electrons in
the MN.

In this study, an electron beam plasma source that canprovide a plasma potential 𝑉𝑝 close to zero [13] is used
to demonstrate the above-mentioned electron-oriented
thrust generation, where only the solenoid is attached tothe thrust balance to measure 𝑇𝐵 solely as shown in Fig.
1. The results show that the electrons generate the thrustwith a 1.2 cm diameter plasma source (diameter of thefilament).
References[1] J. R. Brophy, Rev. Sci. Instrum. 73, 1071-1078(2002)[2] A. Sánchez-Villar et al, Plasma Sources Sci. Technol.
30, 045005 (2021)[3] J. P. Boeuf, J. Appl. Phys. 121, 011101 (2017)[4] C. Charles, J. Phys. D: Appl. Phys. 42, 163001(2009)[5] K. Takahashi, Rev. Mod. Plasma Phys. 3, 3 (2019)[6] A. Fruchtman, Phys. Rev. Lett. 96, 065002 (2006)[7] K. Takahashi et al, Phys. Rev. Lett. 107, 235001(2011)[8] M. Merino and E. Ahedo, Phys. Plasmas 23, 023506(2016)[9] K. Takahashi, Sci. Rep. 12, 18618 (2022)[10] K. Takahashi et al, Phys. Rev. Lett. 110, 195003(2013)[11] K. Takahashi et al, Plasma Source Sci. Technol. 25,055011 (2016)[12] D. M. Goebel and I. Katz, “Fundamentals ofElectric Propulsion: Ion and Hall Thrusters” (John Wiley& Sons, NJ, USA, 2008)[13] K. Takahashi et al, Phys. Rev. Lett. 120, 045001(2018)

Figure 1. (a)Schematic diagram of the experimental
setup. (b)The axial profile of the magnetic field on theaxis.