Sheared E × B flow encountered in space plasma excited from two controllable methods

With the electric field varying along the radial position, the corresponding E × B flow in different strengths yield sheared E × B flow.


Introduction
Ionospheric irregularities can cause severe problems, such as ionospheric scintillation [1] , that impacts radio communication and remote sensing. Thus, an in-depth study on the characteristics and the mechanisms by which these irregularities are generated is crucial [2][3][4] . The generation of the ionosphere irregularities can be attributed to various factors, such as altitudinal variations in ionospheric conductivity, neutral wind, and plasma instabilities [5] . Among these, plasma instabilities are widely considered to play an essential role in generating ionospheric irregularities [6,7] . The mechanisms of many ionospheric physical processes can be linked to plasma instabilities, which may alter the equilibrium state of space. However, the details of the mechanisms by which these are generated, and their processes, remain ambiguous.
In a controlled laboratory experiment, plasma instabilities can be artificially excited by various methods, such as an inhomogeneous electric field, and parameters can be precisely adjusted and detected. Laboratory experiments can help reveal the formation and evolution of ionospheric irregularities using in situ observations and theoretical studies [8] . Sheared E × B flow is one of the most familiar sources of free energy for ionospheric plasma instability excitation. Instabilities driven by sheared E × B flow are often considered potential candidates for generating ionospheric irregularities [9][10][11] . Broadband instabilities ranging from whistler to sub-ion cyclotron frequency ranges -such as the electron-ion hybrid (EIH) [12] , inhomogeneous energy-density driven (IEDD) [13] , and Kelvin-Helmholtz (KH) instabilities [14,15] -can be excited by the sheared E × B flow. Biasing electrodes such as ring electrodes [16][17][18][19] , solid plates, button electrodes [20,21] , and grid electrodes [22,23] are powerful tools to control flow and shear in the laboratory. When a positive DC voltage is biased on an electrode, electrons in the plasma will first gather around its surface because of the faster thermal speed related to the ions. The resulting negative potential of the electrode surface accelerates ions toward the surface. Once the ion and electron flow balance is established, a potential difference will be formed around the electrode surface and an inhomogeneous electric field can be generated. This is the modulation process of the plasma potential. A similar process occurs when a negative bias voltage is applied, with ions attracted and electrons repelled. Combined with the background magnetic field, a sheared E × B flow can be formed in the plasma.
In this work, the interpenetrating plasma and ring electrode methods used to trigger sheared E × B flow by generating a radial electric field were studied in the laboratory. The sheared E × B flow can excite various instabilities according to the experimental parameters. Each method exhibits unique features and can be used to excite plasma instabilities responsible for ionospheric irregularities.

Experimental setup
Experiments were conducted using the Keda Space Plasma EXperiment (KSPEX) device [24] . Fig. 1 shows the sketch of the main parts of the experimental chamber, including a vacuum chamber, six magnet coils, and two plasma source chambers. The vacuum chamber is 2.73 m in length and 0.5 m in diameter and surrounded by six magnet coils that generate a uniform axial magnetic field ranging from 20 to 1000 G (δB/B ≈ 0.01). According to the experimental conditions of these two methods, hot filament, an inductively coupled plasma (ICP), and large-area oxide-coated cathode sources can be chosen. Plasma was produced by ionizing argon gas at a desirable pressure of approximately 10 -3 -10 1 Pa. The distributions of plasma density and potential were determined using a radially movable Langmuir single probe and an emissive probe, respectively. Both probes were arranged at 110 cm downstream from the plasma source to avoid the influence of the electrode on the probe (as shown in Fig. 1). The corresponding electric field distributions were subsequently calculated from the gradient of the plasma potential. The axial and azimuthal potential fluctuations were also detected using a multiple-tip floating probe, where two tips were separated by a certain distance to detect the potential signals. The phase difference between these two signals gives the wavelength λ. The wave frequency f can be obtained by applying a fast Fourier transform (FFT) to the potential signals, and other information related to wave propagation can be calculated further using λ and f. Different electrodes (the ring electrode and Mesh 1 and Mesh 2 shown in Fig. 1) were designed and installed to adjust the plasma potential. In the interpenetrating plasma method, primary plasma was produced by a hot filament source (Source 1) and secondary plasma was produced by an ICP source (Source 2). Two stainless meshes (Meshes 1 and 2) were specially designed to obtain an interpenetration plasma layer. The outer region of the plasma produced by Source 1 (primary plasma) was blocked by a Macor blocking disk on Mesh 1 (Fig. 2). The plasma emitted from Source 2 (secondary plasma) filled this void while the central portion of Mesh 2 was blocked. Each mesh was biased by a DC power supply by which the potential of the primary and secondary plasma to generate an inhomogeneous radial electric field could be controlled.
However, in some experiments, only one plasma source could be installed. Therefore, the method mentioned above was not suitable for this condition and a new method was designed and fabricated. A ring electrode, consisting of four concentric rings (Fig. 3), was designed to generate a radial electric field. The outermost ring was a holder connected to the chamber wall to maintain stabilization. The radii of the inner three rings were 8, 5, and 2.5 cm, respectively. The electrode was installed 1.3 m away from the plasma source (shown in Fig. 1). Each ring was electrically isolated via machinable ceramics and biased by a DC power supply ranging from 0 to 300 V to independently regulate the distribution of plasma potential. The plasma column was compressed to a smaller radius by the magnetic field (14 cm for the inter-penetrating plasma method and 8 cm for the ring electrode method). The radius of the plasma is smaller than that of the vacuum chamber (25 cm); therefore, the boundary effect can be ignored in this study.

Results and discussions
In the interpenetrating plasma method, the radial electric field can be modulated by adjusting the potential difference between the primary and secondary plasmas. Mesh 2 was electrically grounded to ensure that the potential of the secondary plasma would not float randomly. Thus, a potential difference could be achieved by regulating the biasing voltage of Mesh 1. The resultant profiles of the plasma potential and electric field are shown in Fig. 4a, with Mesh 1 biased at 120 V. The average plasma potential of the primary plasma was approximately , which equaled the DC biasing voltage. The secondary plasma potential was approximately . A sheared region was formed at the position corresponding to the interpenetrating region, which is marked in gray in Fig. 4a. The "sheared region" denotes the boundary layer between the two types of plasma with different electron ci ω ci drift velocities, i.e., two radial electric field strengths. The shear strength is given by [25] . The electric field maximum appears, here, to be about with the scale length . Fig. 4b shows that the peak value of the electric field increases from to as the biasing voltages applied on Mesh 1 vary from to . This indicates that the shearing strength can be regulated by changing the biasing voltage. The electrostatic fluctuation in the ion cyclotron frequency range excited by inhomogeneous energy-driven instability (IEDDI) was investigated using the interpenetrating plasma method, whose peak frequency was as low as , where is the ion cyclotron frequency. This is a unique result because previous experiments could not produce such a low-frequency IEDDI [26] .

V
Regarding the ring electrode method, the inner ring was biased to a negative potential, and the two outer rings were connected and biased at to the ground to achieve a stable plasma condition. Plasma potential was measured using an emissive probe. Fig. 5a shows the radial distributions of the plasma potential and the electric field when the inner ring was biased at -30 V and the outer rings were biased at 10 V. The plasma potential at the boundary region is higher and almost equals the bias voltage ( ~10 V). There is an apparent sheared region where a potential drop exists between the inner and the middle rings. A corresponding electric field is subsequently produced, and the peak value is about with a scale length . The plots provide the distribution of the region because the probe holder needs to traverse half the plasma column to measure the opposite part. This will lead to a significant electrical disturbance and introduce extra errors. Fig. 5b shows the peak value of the electric field under different bias voltages. According to the profiles, when all the rings were floating (corresponding to "0 / 0" of the horizontal axis), no apparent radial electric field was generated. When the two  The electric field peak value versus different biasing voltages. The horizontal axis is in the format of "bias on the outer ring / bias on the inner ring" while " " refers to electrical floating or electrical insulation. The background magnetic field was fixed at for all these cases. 10 V 2 V · cm −1 outer rings were fixed at , the electric field peak varied slightly regardless of the bias of the inner ring and was approximately .
1.480 V 0.986 V · cm −1 As shown in Figs. 4b and 5b, the electric field peaks do not change after the bias voltage exceeds a threshold value. The collective effect of plasma plays a significant role in the response to an external electric field. The charged particles tend to weaken the impact of the external electric field. Therefore, the plasma potential is often inconsistent with the direct application of bias voltage. In addition, considering the finite charged particle number density, the ability of plasma to respond to the external electric field has a certain threshold. Both of these lead to the results shown in Figs. 4b and 5b. The average level of the error bars in Figs. 4a and 5a are close to and within the error margin ( for plasma potential and for the electric field, respectively), which indicates that both methods can control the potential with a high accuracy. . 6 shows the radial profile of the electric field distribution under two different magnetic field conditions. When the magnetic field strength was set to , the peak value of the electric field reached approximately . The magnitude of the electric field decreased by almost half ( ) when the magnetic field strength was increased to . This suggests that the peak value of the electric field decreases as the magnetic field increases, and the electric field scale length shrinks under the strengthened magnetic field. This was attributed to the frozen effect of the plasma. The stronger magnetic field squeezes the plasma into a smaller column and weakens the perpendicular mobility of the charged particles.

V
Plasma perturbation induced by an inhomogeneous electric field was simultaneously detected using multiple-tip floating probe. The power spectrum density( PSD) of the potential fluctuation varying with different bias voltages was calculated using FFT and plotted in Fig. 7. Fig. 7a shows that no plasma wave mode was excited when all the ring electrodes were floating. When a voltage was biased on the outer rings, the plasma waves were excited by the sheared E × B flows, whose frequencies were approximately 2, 4, and 6 kHz, as well as other weak harmonic waves. Three similar wave modes can also be observed when the DC voltage on the inner ring varied from to . The fundamental frequency and magnitude under biasing voltages changed slightly (Fig. 7b), but an additional E × B doppler shift could be seen when compared to the case of "10 / 0 V" (Fig. 7a). This can be ascribed to the almost unchanged or slightly changed electric field (as shown in Fig. 5b) under different inner-ring biasing voltages. Identifying the plasma wave modes is a complex issue, and more diagnostic information is required. Thus, the characteristics of plasma waves will be discussed in detail in our future work.

Conclusions
In this study, two controllable methods for triggering sheared E × B flows were investigated. The interpenetrating plasma method generated a sheared E × B flow through two-ended plasma sources and two mesh electrodes. The plasma potential  Fig. 7. PSD of potential fluctuation versus different biasing voltages on the ring electrodes. The legend is written in the format of "bias on the outer ring / bias on the inner ring" while " " refers to electrical floating or electrical insulation. The magnetic field strength was fixed at , and the radial position was fixed at .

V
17 profile could be adjusted by varying the bias voltages on the meshes, and the sheared E × B flow could be excited within the interpenetrating region. When Mesh 1 was biased to and Mesh 2 is grounded, the electric field maximum was approximately with the scale length (as shown in Fig. 4a). The peak electric field increased as the biasing voltage on Mesh 1 varied from to in intervals of , but became constant beyond 120 V biasing. This approach could produce a considerable plasma potential gradient; therefore, it would be appropriate for situations requiring a large radial electric field. However, the experimental setup was relatively complex, and the ceramic-supported Macor disk on the mesh electrode was fragile under high-temperature conditions. The ring electrode method was designed to avoid these shortcomings and only one plasma source was required, with the latter greatly simplifying the experimental configuration. This method benefits conditions when no additional ports are available for installing another plasma source or plasma sources are insufficient. In previous studies, similar electrodes were used to modulate the plasma potential, but most of them were biased as a whole [27,28] ; therefore the distribution of the electric field was not controllable. However, in our work, an independent-biasing improvement was made to allow a controllable inhomogeneous electric field profile. As shown in Fig. 5a, when the outer two rings are connected and biased to , and the inner ring is biased to , an inhomogeneous electric field with the maximum of and the scale length was produced successfully using our method. As the sheared E × B flows were excited, plasma waves were also detected from the potential fluctuation with frequencies of approximately 2, 4, and 6 kHz, and other weak harmonic waves. Detailed analysis of the sheareddriven wave modes will be conducted in our following work. Our results demonstrated that the ring electrode method was reliable and could be extended to investigate shear-driven instabilities that account for ionospheric irregularities. However, the adjusting range of the radial electric field is limited due to the collective effect of plasma especially for the ring electrode method which may reduce its availability. We will improve the methods in subsequent experiments. In spite of sheared E × B flow, these two methods also show great application in experiments where a background electric field is needed. This enable researches on instability caused by other sources of free energy to be carried on.