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Ionization instability and turbulence in the plume of sub-ampere hollow cathodes depending on an applied magnetic field

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Abstract

When operated with a Hall effect thruster, either centrally or externally mounted, the hollow cathode discharge occurs in a magnetic field environment. Therefore, it is important to assess the influence of the magnetic field on the standalone operation of a hollow cathode to better predict device behavior when coupled with a Hall effect thruster. This study focuses on the influence of an applied axial magnetic field on the main oscillatory phenomena in the plume of a Kr-fed sub-ampere hollow cathode operated with an external disk anode. A probe array consisting of two cylindrical Langmuir probes and an emissive probe is used to assess changes in plasma parameters and collected ion saturation current as the magnetic field strength is varied up to 3 mT at the cathode’s location. The electron transport along the cathode–anode space is analyzed in terms of total electron collision frequency. It is shown that a higher magnetic field strength induces larger plasma densities and lower electron temperatures. Applying a magnetic field to the discharge of a cathode operating in plume mode causes a reduction in both the ionization instability and ion acoustic turbulence (IAT) energies. This suggests a dampening of the main oscillatory phenomena in the plume of the hollow cathode. Furthermore, the total electron collision frequency and its main contributor, the anomalous collision frequency due to high-frequency IAT, decrease at higher field strengths. The results included in this communication are, to the best of the authors’ knowledge, the first characterization of the response in low- and high-frequency wave content depending on a magnetic field in low-current hollow cathodes operating in standalone mode at \(<1\) A.

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Data availability statement

The data that support the findings of this study are available upon reasonable request from the authors.

Abbreviations

\(A_p\) :

Probe collection area, m\(^{2}\)

\(A_z\) :

Plume cross-sectional area, m\(^{2}\)

B :

Magnetic field strength,  T

CEVAC:

Cathode Experiments Vacuum Chamber

e :

Elementary charge, 1.602\(\times\)10\(^{-19}\) C

E :

Electric field strength,  V cm\(^{-1}\)

f :

Frequency,  Hz

IAT:

Ion acoustic turbulence

\(I_a\) :

Anode current, A

\(I_{a,std}\) :

Standard deviation of the anode current, A

\(I_k\) :

Keeper current, A

\(I_{sat}\) :

ion saturation current, A

\(J_e\) :

current density,  A

\(k_{B}\) :

Boltzmann’s constant, 1.38\(\times\)10\(^{-23}\) J K\(^{-1}\)

KE:

Knife-edge

\(L_{ca}\) :

Cathode–anode distance, m

\(\dot{m}\) :

Mass flow rate, kg s\(^{-1}\)

m :

Electron mass, 9.1\(\times\)10\(^{-31}\) kg

M :

Ion mass, kg

\(n_e\) :

Plasma (electron) density, m\(^{-3}\)

\(n_n\) :

Neutral density, m\(^{-3}\)

p :

Plasma pressure, N m\(^{-2}\)

PSAC:

Plasma Sources and Applications Centre

\(r_{ko}\) :

Keeper orifice radius,  m

\(T_e\) :

Electron temperature,  eV

\(T_i\) :

Ion temperature,  eV

\(T_g\) :

Neutral gas temperature,  eV

\(u_e\) :

Electron drift velocity,  m s\(^{-1}\)

\(U_{iz}\) :

Ionization reaction rate,  m\(^{3}\) s\(^{-1}\)

\(v_n\) :

Neutral thermal velocity,  m s\(^{-1}\)

z :

Axial distance,  m

\(\alpha\) :

Correction parameter

\(\phi _{em}\) :

Floating potential of the hot emissive probe, V

\(\phi _f\) :

Floating potential, V

\(\phi _p\) :

Plasma potential, V

\(\varphi\) :

Phase angle,  degrees

\(\eta\) :

Total plasma resistivity, \(\Omega \cdot {m}\)

\(\nu _{an}^{IAT}\) :

Anomalous collision frequency due to IAT,  Hz

\(\nu _{e}\) :

Total electron collision frequency,  Hz

\(\nu _{ei}\) :

Electron–ion collision frequency,  Hz

\(\nu _{en}\) :

Electron–neutral collision frequency,  Hz

\(\nu _{iz}\) :

Ionization collision frequency,  Hz

\(\theta\) :

Plume half-angle,  degrees

\(\sigma _{en}\) :

Electron–neutral scattering cross section, m\(^{2}\)

\(\sigma _{iz}\) :

Ionization cross section, m\(^{2}\)

\(\omega\) :

Oscillation frequency,  Hz

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Acknowledgements

The authors would like to thank Dr Sedina Tsikata for her valuable insights into plasma instabilities and turbulence.

Funding

This work was supported by OSTIn-SRP/EDB through the National Research Foundation and in part by the Ministry of Education Singapore through MOE AcRF (RP6/16XS). George-Cristian Potrivitu acknowledges the support from the National Institute of Education Singapore through the NIE PhD Scholarship.

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  1. Shuyan Xu has contributed equally to this work.

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  1. Plasma Sources and Applications Centre/Space Propulsion Centre, National Institute of Education, Nanyang Technological University, Singapore, 637616, Singapore

    George-Cristian Potrivitu & Shuyan Xu

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  1. George-Cristian Potrivitu
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Potrivitu, GC., Xu, S. Ionization instability and turbulence in the plume of sub-ampere hollow cathodes depending on an applied magnetic field. CEAS Space J 15, 729–749 (2023). https://doi.org/10.1007/s12567-022-00478-5

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