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First Application of a Ball-Pen Probe for Direct Measurements of Plasma Potential and Nonlinear Fluctuations Dynamics in a Linear Helicon Plasma

This paper reports the first successful application of a ball-pen probe on a linear helicon plasma device to directly measure plasma potential and electron temperature, revealing low-frequency instabilities and nonlinear dynamics that are inaccessible via traditional Langmuir probes.

Original authors: Donato Di Matteo, Jiri Adamek, Jordan Cavalier, Yoshihiko Nagashima, Takuma Yamada, Ren Namimatsu, Huiwon Chung, Chanho Moon

Published 2026-08-20

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CC BY 4.0

Original authors: Donato Di Matteo, Jiri Adamek, Jordan Cavalier, Yoshihiko Nagashima, Takuma Yamada, Ren Namimatsu, Huiwon Chung, Chanho Moon

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the invisible world of magnetized plasmas, where superheated gas swirls under the influence of powerful magnetic fields, understanding the behavior of charged particles is essential. Scientists study these environments to improve how we generate energy in fusion reactors and to make spacecraft propulsion systems more efficient. A key challenge in this field is measuring the electric potential, or voltage, within the plasma itself. While researchers have long relied on indirect methods to guess this value, direct measurement has remained difficult because the tools used to probe the plasma often disturb the very thing they are trying to observe. Without a clear picture of the electric potential and how it fluctuates, it is hard to understand the turbulent movements that can cause heat and particles to escape, undermining the stability of the system.

To solve this, a team of researchers at Kyushu University and the Czech Academy of Sciences recently installed a specialized diagnostic tool called a ball-pen probe into a linear plasma device known as PANTA. This device generates a steady stream of high-density plasma using a helicon antenna, creating conditions similar to those found in advanced thrusters and fusion experiments. The researchers wanted to see if the ball-pen probe could directly measure the plasma's electric potential and electron temperature without the need for complex calculations or assumptions. By comparing this new tool against a standard probe, they aimed to reveal the true nature of the plasma's fluctuations and the hidden dynamics that drive turbulence.

The ball-pen probe works on a clever principle involving the different sizes of the paths electrons and ions take as they spiral around magnetic field lines. Electrons are light and hug the magnetic lines tightly, while heavier ions follow wider paths. The probe consists of a metal tip hidden inside a non-conductive ceramic tube. By adjusting how far the metal tip sticks out of the tube, the researchers can block most of the tiny, tight-spiraling electrons while still allowing the larger, wider-spiraling ions to reach the tip. When the probe collects roughly equal numbers of electrons and ions, its electrical potential naturally settles to match the surrounding plasma potential. This allows for a direct reading of the voltage within the plasma, a feat that was previously difficult to achieve with such precision in this type of high-density environment.

In their experiments, the team carefully adjusted the depth of the probe's tip for different locations across the plasma's width. They found that the optimal position for the tip changed depending on where they were measuring, largely because the density of the plasma varied from the center to the edge. In the dense core of the plasma, collisions between particles became frequent enough to disrupt the ideal behavior of the probe, requiring a specific mathematical adjustment to get an accurate reading. However, in the outer regions where the plasma was less dense, the probe worked perfectly without any correction. The results showed that the ball-pen probe could successfully map the electric potential and electron temperature across the entire plasma, matching the data from standard probes in the outer regions while providing new, direct insights in the core.

Beyond just mapping the steady state of the plasma, the researchers used the ball-pen probe to listen to the rapid fluctuations of the electric potential. Standard probes often confuse changes in temperature with changes in voltage, making it hard to tell what is driving the turbulence. The ball-pen probe, however, could distinguish between the two. The team observed distinct waves of instability, including a type of drift instability that is common in plasma thrusters. By analyzing how different frequencies of these waves interacted, they discovered that low-frequency instabilities were coupling with high-frequency turbulence in a non-linear way. This kind of complex interaction was invisible to the standard probes, which saw only a blurred mix of signals.

The study demonstrates that the ball-pen probe is a powerful new tool for investigating the hidden dynamics of linear helicon plasmas. It proved capable of providing direct measurements of the plasma potential and electron temperature, revealing details about turbulence and instability that were previously inaccessible. While the probe required careful tuning to handle the dense conditions in the center of the plasma, its success in the outer regions and its ability to uncover non-linear wave interactions suggest it will be invaluable for future research. These findings offer a clearer path toward understanding the turbulent transport of heat and particles, which is a critical step in improving the performance of plasma-based technologies.

Technical Summary: First Application of a Ball-Pen Probe for Direct Measurements of Plasma Potential and Nonlinear Fluctuations Dynamics in a Linear Helicon Plasma

Problem Statement
Understanding anomalous turbulent transport in magnetized plasmas is critical for improving confinement in fusion devices and the efficiency of plasma propulsion systems. Accurate characterization of these phenomena requires direct measurements of the plasma space potential ( $\phi_s$ ) and electron temperature ( $T_e$ ). However, $\phi_s$ remains a difficult quantity to measure directly. In many experiments, floating potential fluctuations measured by standard Langmuir probes (LP) are used as a proxy for plasma potential fluctuations. This approach is limited because finite temperature fluctuations introduce spurious contributions to the LP signal, particularly in regimes where temperature fluctuations are non-negligible. While diagnostics like heavy ion beam probes and emissive probes exist, the ball-pen probe (BPP) offers a robust, minimally perturbing alternative that has been successfully utilized in various high- and low-temperature devices but had not yet been applied to high-density linear helicon plasmas.

Methodology
The study was conducted using the PANTA (Plasma Assembly for Non-linear Turbulence Analysis) device at Kyushu University, a linear helicon plasma source operating with Argon gas at 7 MHz and 3 kW input power. The device generates steady-state plasmas with electron densities of $10^{18}–10^{19} \text{ m}^{-3}$ and electron temperatures of 1–3 eV under a 100 mT axial magnetic field.

A custom-built BPP was installed in a radially movable probe array alongside two Langmuir probes. The BPP consists of a stainless-steel collector shielded by an alumina tube. The core operating principle relies on the difference in Larmor radii between electrons and ions; by retracting the collector into the shielding tube, electron collection is preferentially reduced until the electron and ion saturation currents become comparable ( $R = I_{sat}^- / I_{sat}^+ \approx 1$ ), causing the BPP floating potential ( $\phi_f$ ) to approach the plasma space potential ( $\phi_s$ ).

Key experimental steps included:

Optimization: A systematic scan of the collector depth ( $h_d$ ) was performed to find the optimal retraction where the current ratio $R$ is minimized and the I-V curve is symmetric.
Calibration: The Hall parameter ( $\beta_i$ ) was analyzed to understand the impact of ion magnetization and collisionality on the probe's operation, particularly in the high-density core.
Measurement: The BPP was used to measure $\phi_s$ and, in combination with an LP, $T_e$ (using the relation $T_e = (\phi_{f,BPP} - \phi_{f,LP}) / (\alpha_{LP} - \alpha_{BPP})$ ).
Fluctuation Analysis: High-speed sampling (1 MHz) was used to analyze temporal fluctuations, power spectral densities, and nonlinear coupling via bicoherence analysis.

Key Results

Optimization and Core Limitations: In the PANTA helicon plasma, the optimal collector depth varied radially due to changes in plasma density and collisionality. Unlike in some other devices, no broad plateau of optimal operation was found; the BPP required precise depth adjustment. In the plasma core, where ion magnetization is weak ( $\beta_i \ll 1$ ) and collisions dominate, the BPP floating potential deviated from the true plasma potential. However, applying a correction based on the measured coefficient $\alpha_{BPP}$ ( $\phi_s = \phi_f + \alpha_{BPP}T_e$ ) successfully reconciled BPP measurements with Langmuir probe data across the entire radius.
Direct Profiles: The study successfully obtained the first direct radial profiles of both plasma potential and electron temperature in a linear helicon plasma. In the edge region (where $\beta_i > 0.1$ ), the BPP provided reliable direct measurements without correction.
Fluctuation Dynamics: Time-resolved measurements revealed that LP floating potential fluctuations generally exhibited higher amplitudes than BPP measurements, confirming that LP signals are contaminated by temperature fluctuations. The BPP directly captured plasma potential fluctuations, identifying low-frequency modes at 1–3 kHz (attributed to Simon-Hoh type drift instabilities) and 4–5 kHz (drift-wave modes).
Nonlinear Interactions: Bicoherence analysis of the BPP data revealed nonlinear phase coupling between low-frequency instabilities and broadband turbulence. These nonlinear structures were not observable in the LP data, highlighting the unique capability of the BPP to resolve true potential dynamics.

Significance and Claims
The paper claims to present the first application of a ball-pen probe in a linear helicon plasma device. The primary significance of this work is the demonstration that BPPs can provide direct, fast measurements of plasma space potential and electron temperature in high-density helicon plasmas, a regime where ion magnetization is often insufficient for ideal BPP operation.

The authors assert that the BPP is a powerful diagnostic tool for investigating nonlinear dynamics and turbulence. By providing direct access to plasma potential, the BPP allows for the accurate characterization of fluctuation-driven phenomena, such as the Simon-Hoh instability and drift-wave modes, which are critical for understanding anomalous transport in plasma thrusters and fusion devices. The study concludes that while corrections are necessary in the high-collisionality core, the BPP offers a superior method for resolving plasma potential fluctuations compared to conventional Langmuir probes, particularly for studying nonlinear coupling and transport mechanisms.

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