Discharge parameters of PlasmaKristall-4BU: A modifiable dusty plasma experiment

Since 2014, the dusty plasma experiment “Plasmakristall-4” (PK-4) has been on board the International Space Station (ISS)^1,2 and employed for various experimental campaigns. As part of the PK-4 program, identical devices exist on the ground³ to allow final preparation and testing of experiments for the ISS. The PK-4BU experiment described here offers the advantage of preliminary campaign planning and testing under as close to identical circumstances as possible before proposing new campaigns and final ground testing for these campaigns using a PK-4 device. However, there are additional (and possibly) more important strengths of the PK-4BU. By default, all official devices used for final experimental scripting before flight on the PK-4 ISS are sealed with no modification to their experimental hardware allowed. This requirement, although obviously essential, makes it difficult if not impossible to gain insight into the unusual properties of the discharge (i.e., the “leak” manifested during campaigns 1–4) or behavior of the dust outside the well-defined parameter spaces. Furthermore, the data collected on the PK-4 ISS is by de facto limited to onboard diagnostics, making observations of effects outside these diagnostic capabilities impossible. The PK-4BU experiment allows modification of all aspects of the experiment, providing the ability to collect data that can then be compared to data collected on orbit, which can help resolve these issues. One recent example of this is the data collected by the PK-4BU device, which was used to establish a relationship between plasma ionization waves,⁴ dust chain formation, the dispersion relation, and overall cloud behavior. Given these data required video of the plasma at 50 000 fps, it was only possible due to the ability for modification (in this case, adding a photo multiplier tube to the system) allowed by the PK-4BU. Since the cameras within the sealed devices are only capable of frame rates up to 100 fps, these results would not have been possible to be achieved in any other device. In addition, the PK4 BU facility is not limited in size and materials of dust in comparison to the sealed devices; therefore, the behavior of these dust variations in the same discharge conditions can be tested. Within this work, the discharge properties of the PK-4BU are reported. A brief description of the facility is provided to allow comparison to the properties of similar facilities currently on the ISS or to other ground experiments. The discharge properties discussed here were primarily measured using an electrostatic probe. The results from the electrostatic probe measurements were then compared to results from similar devices used at the Institute for High Energy Density (IHED), Moscow,³ and the PK-4 facility that is now installed on the ISS.² In addition, the discharge spectrum was measured using optical emission spectroscopy (OES) in order to identify impurities within the plasma and allow comparisons to spectroscopic measurements conducted at these facilities.

The design of the PK-4BU is based on the facility used on the International Space Station and its associated ground facilities; therefore, the hardware used has chosen to be as similar as possible to the hardware used within those. In general, the facility consists of a π shaped cylindrical quartz-glass tube with an inner diameter of d_tube = 30 mm. A schematic of the facility and an image are shown in Figs. 1 and 2, respectively. A DC discharge is driven by a hivolt.de HA51U programmable high voltage power supply connected to the active electrode. This power supply is capable of operating in a DC-switching mode, allowing the applied voltage to be switched at frequencies up to f_DC,switch = 1000 Hz. In addition to the DC discharge, a radio-frequency (RF) coil operating at a frequency of f_RF = 80.56 MHz at a maximum power of P_RF = 10 W can also be used to manipulate the plasma. The coil consists of a single wire device and is movable along the horizontal axis. The RF signal is generated by a Rohde & Schwarz SMC100A high-frequency signal generator and amplified by an ENI 411LA linear RF power amplifier. The RF signal is coupled to the coil by a MFJ Versa Tuner II roller inductor antenna tuner. Usually, the facility is operated using neon. Vacuum is provided by a Edwards E2M8 dual stage rotary vane roughing pump and a Pfeiffer Vacuum TPH 062 turbo-molecular pump achieving a base pressure of p = 10⁻³ Pa. The quartz-glass tube is mounted on a movable, air-suspended table and can be turned by 90° to operate the discharge tube in either the vertical or the horizontal position. The quartz-glass tube has multiple access ports with DN25 vacuum flanges. Two of these are used for gas inflow and outflow and for insertion of the active and ground electrodes. Two additional ports provide windows for illumination, diagnostic access (e.g., electrostatic probes), and manipulation laser access. Finally, two ports on top of the tube are used to insert dust into the discharge. Dust within the tube and the discharge itself are observed using two Photron Fastcam Mini UX 50 high-speed cameras with tele-microscopy lenses. For low-speed imaging, a Basler pilot piA1600-35gc camera is used. The low- and high-speed cameras can be used simultaneously using a beam splitter; a comparison of imaging at 50 fps and 500 fps is shown in Fig. 10. As shown in Fig. 1, one camera is positioned at the side of the discharge tube, within the plane of the experiment, allowing the possibility to view both the discharge and the dust along the plane spanned by the horizontal z and vertical axis r in the direction of gravity. The second camera is positioned above the discharge, providing observation of the plane rectangular to the field of view of the first camera. This combination allows observation of the motion of the dust within the discharge tube in three dimensions. Additionally, a spectroscope can be connected to either of these lenses using a beam splitter. In the majority of cases, the dust inside the discharge tube is illuminated by a Coherent Optics Verdi G8 laser at a wavelength of λ = 532 nm ± 2 nm with a maximal output power of 8 W, as shown in Figs. 2 and 9.

Knowledge of the operational parameters of the facility, such as the electron temperature T_e, electron density n_e, plasma potential ϕ and electric field E, is essential for the planning and design of facility experiments as well as for comparisons to other facilities. Each of these, in addition to the current–voltage relationship of the discharge itself, was measured for various pressures, which are shown in Fig. 3.

An electrostatic probe system was designed for use within the facility and was employed to measure the electron temperature T_e, electron density n_e, and plasma potential φ_s. (The plasma potential can be used to calculate the electric field using E = −∇φ_s.) The electrostatic probe itself consists of a tungsten electrode with radius r_probe = 0.3810 mm and length l_probe = 7.5 mm contained within an alumina rod isolating the probe from the plasma. The probe can be turned radially within an angle of ±180° and moved axially (±100 mm) through a vacuum flange in a similar manner to the probe described in the work Fortov et al.³ In order to achieve measurements along the complete volume of the discharge tube, probe measurements were taken from both ends. Outside the vacuum tube, the (active) electrode was connected to a signal generator and amplifier as well as a Tektronix MDO3024 digital 4-channel oscilloscope in a similar manner, as described in the work of Schmidt et al.⁵ For the single probe setup, only one electrode was used and connected, as shown in Fig. 4. A potential was applied to electrode 1 using a Kepco BOP 200-1M bipolar operational power amplifier fed using an Agilent 33120A signal generator and directly measured at the oscilloscope. Using the signal generator and amplifier, a signal with a frequency of f_P = 50 Hz across a range of V_p = ±30 V was applied to the electrode. The resulting current I_p = I_e + I_i was measured with reference to the ground potential. It should be noted that despite the relatively large diameter of the probe electrodes, the probe can still be assumed to be operating in a collisionless regime due to the high electron temperature. The electron energy distribution function (EEDF) was assumed to be close to a Maxwell–Boltzmann distribution function, as shown in  Appendix B. The electron temperature T_e was calculated directly from

where I_e is the electron current, V_p is the probe voltage, e is the electron charge, and k_b is the Boltzmann constant.⁶ The ion density n_i was then determined from the ion saturation current I_i,s using

where A describes the probe surface area in the plasma and i_i ≈ 2–3 is the Laframboise correction factor depending on the ratio r/λ_D and the normalized probe potential. The electron density n_e was then calculated as n_e ≈ ni under the assumption of quasi-neutrality. Probe measurements were carried out along both the axial and radial directions to calculate the electric field E and gain detailed spatial information about the discharge. In Fig. 5, the electron density n_e, electron temperature T_e, and (axial) electric field E are shown as a function of the DC current I_DC for operation of the facility with neon. As shown in Fig. 5, for increasing current, the electron temperature drops significantly from around 8 eV–10 eV to 4 eV–7 eV depending on the pressure, while the axial electric field decreases from around 2 V cm⁻¹ to less than 1 V cm⁻¹. In contrast, a significant increase in the electron density by an order of magnitude can be observed, rising from n_e = 2 × 10⁸/cm³ to n_e = 12 × 10⁸/cm³. Comparison of the measurement results against two other facilities is shown in Fig. 5. For a pressure of p = 30 Pa, the results from measurements conducted at the facility at the IHED3 and the results for a pressure of p = 100 Pa measurements made at the facility, which is now installed on the ISS², are shown. At low pressures, there is good agreement between measurement results for these facilities where a similar trend for the electron temperature and density can be observed. However, for higher pressures, the measured electron density at the PK-4BU facility is significantly higher than that measured at either facility. Additionally, the PK-4BU facility exhibited a decrease in the electric field with increasing current, while the values at the other facilities remained constant at a value of E ≈ 2 V cm⁻¹. Both the axial and radial profiles of the plasma parameters were measured without an active RF coil and with the axis system defined as in Fig. 1. With the electrostatic probe inserted, the most stable discharge parameters were achieved for a DC current of I_DC = 2 mA. The axial profiles of the electron temperature, electron density, and plasma potential for a discharge with a pure DC current at a pressure of p = 50 Pa are shown in Fig. 6. As also shown in Fig. 6, the electron temperature and the electron density along the axial direction remained relatively constant, despite minor fluctuations. This could be a result of the disturbance of the plasma due to the relatively large probe electrode. The plasma potential Φ drops linearly along the axis, maintaining a positive potential at z = 100 mm closer to the active electrode and a negative potential at z = 0 mm. In addition to the axial change in plasma parameters, the radial distribution of the electron temperature, density, and plasma potential were also measured in the middle of the discharge tube. As shown in Fig. 7, while the electron temperature T_e is relatively constant along the discharge channel, the electron density n_e and plasma potential both drop significantly at the channel wall.

Using an Oceanview FLMS15048 spectroscope, the emission spectra of the PK-4BU discharge were measured both to gain information on plasma composition and to identify possible impurities in the system. The Oceanview FLMS15048 spectroscope is able to measure between wavelengths of λ = 334 nm and 1023 nm with a resolution of λ ≈ 0.5 nm. A representative spectrum of the PK-4BU discharge is shown in Fig. 8. In addition to the very strong lines of neon, particularly for the 1s → 1p transition at λ = 565.6 nm, several other components of the plasma can easily be identified. These impurities are assumed to be caused by remainders of the melamine–formaldehyde dust used in experiments. Melamine–formaldehyde has the chemical composition of C₃H₆N₆ (melamine) and CH₂O (formaldehyde), and therefore, the decomposition of these particles by energetic electrons of the plasma is assumed to be the reason for the spectral lines of CO, O, H, and N observed within the discharge. This theory is bolstered by the fact that the intensity of these spectral lines decreases after long episodes of pumping the system to its lowest achievable vacuum pressure. Despite these impurities, strong emission lines of neon can still be easily observed. This shows that even though impurities exist, a stable neon discharge is established. In comparison to the facility used on the ISS, cleaning of the discharge tube using an argon–oxygen plasma is not possible due to the operational limit of the vacuum pumps, which do not allow operation with oxygen. In Fig. 9, a dust cloud of 1.3 μm MF dust is shown for the same discharge parameters before and after pumping down for an extended period of time. This shows that even though cleaning of the discharge tube using an argon–oxygen plasma is not possible, the effect of lowering impurities by extended periods of pumping down can be seen within an experiment. After a long-phase of pumping down and removing impurities, the dust cloud is much further extended and stable.

The essential discharge parameters of the PK-4BU facility have been determined, and comparison with similar facilities shows good agreement with electron temperature T_e, electron density n_e, and plasma potential φ. The axial distribution of the electron temperature and density is similar to other facilities, although higher fluctuations in the discharge parameters along the horizontal axis are observed. This may be caused by the disturbance of the plasma due to the electrostatic probe. The radial distribution of the potential is parabolic while the potential is highly negative at the wall, while the electron temperature exhibits a more logarithmic profile. Measurements of electron temperature T_e, plasma potential ϕ, and electric field E provide comparable results to other facilities,^2,3 although there is slight disagreement that falls within the range of the measurement error. In addition, the plasma composition for complex plasma experiments have been determined employing spectroscopy, revealing impurities that partially influence the discharge and dust behavior. It has also been shown that a stable discharge at various pressures can be established for discharge currents between 1 mA and 3 mA over extended periods of time. Thus, the PK-4BU device can be used for various dusty plasma experiments, and for known discharge parameters, experimental results of the facility can be compared to the existing data. Furthermore, it was shown that the new facility has unique qualities due to the possibility of modification and the employment of additional and more sophisticated diagnostics such as high-speed cameras or photomultipliers, allowing it to exceed the capabilities of similar devices. In Fig. 10, a comparison between an image series taken with a low speed camera at 50 fps and a high-speed camera at 500 fps is shown. It can clearly be seen that information is lost in the low speed image series, as only streaks of the particles are visible. The position and velocity of the particles, especially the frequency at which they follow the electric field during the DC switching, cannot be resolved from the low-speed images. Comparison of the data gained from low- and high-speed imaging can also give information and further insights into phenomena observed in other devices at low frame rates. Finally, future (dusty) plasma experiments can be explored using this experimental device.

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

This work was funded under Grant Nos. NASA JPL 1571701 and NSF 1740203.

The relative error Δf for an measurement f is given by

which applied to Eq. (1) and dln(I_e) = ln(J) − ln(K) = ln(J/K) and dV_p = U − V, neglecting the errors in accuracy of e and k_b, and division by Eq. (1) gives for the error ΔT_e/T_e,

Consequently, for the ion density n_i as given by Eq. (2), we yield

Evaluation of Eqs. (A2) and (A3) using the parameters given in Table I results in an estimated error of ΔT_e = 30%–90% for the electron temperature T_e, an error Δn_i ≈ 46% for the ion and electron density n_i ≈ n_e, and an error of δE = 1%–29% for the electric field E for the measurement results shown in Figs. 5–7.

For selected measurements, the electron energy distribution f(ε = −eV) was evaluated⁷ from the second derivative probe current density $∂2je∂V2$ as

with the current density being $je=eneTe/(2πme)exp(−eV/Te)$⁠. As shown in Fig. 11, for low electron energies ε ≤ 8 eV, the behavior of the EEDF is similar to a Maxwell–Boltzmann distribution. For higher energies, measurement was not possible due to the limit of the applied probe potential of V_p = ±30 V.