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Abstract
Arc plasmas are common and important phenomena, which have been widely used in scientific research and industrial fields. It is a non-intrusive way to understand the dynamic characteristics of arc plasma by measuring magnetic field distribution and applying inverse method. Aiming to investigate the motion characteristics of arc plasma, a high-speed magneto-optical imaging system was developed, which mainly consists of a laser-driven light source, achromatic collimator, beam expander, polarized beam splitter, analyzer and high-speed camera. The calibration experiment of the system, which was conducted using a Faraday indicator with a Verdet constant of −96 rad/(T·m)@632.8 nm and Helmholtz coils, shows its magnetic sensitivity reaches 1 mT, spatial resolution is about 500μm, temporal resolution is 100μs as for a circular measuring area of 42 mm in diameter. The arcing experimental results also demonstrate that the developed system can obtain the 2D magnetic field distribution in real time with relatively high spatial and temporal resolution and reasonable magnetic sensitivity. It also provides an effective method to study the motion characteristics of arc plasma inside of an enclosed chamber.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Arc plasmas, generated by arc discharges, have been utilized in various fields such as combustion enhancement, gas conversion and decomposition, surface treatment, pollution control and power industry [1–3]. Electronic temperature, morphological characteristics and motion, energy transport are the key properties of arc plasma. Optical diagnostics have irreplaceable advantages in the measurement of the arc plasma with temporal and spatial resolution, which make it possible to understand the dynamics and chemistry of arc discharge. High speed photography has been applied to survey the spatial distribution and movement of arc plasma, which enable the investigators to obtain the optical images of arc plasma and tracks the position of the arc plasma during the whole dynamic processes [4–6]. The electronic temperature and chemical composition of arc plasma column have also been surveyed by optical emission spectroscopy [7–9]. Data from a fast visible light camera were used for tomographic reconstruction to study plasma boundary [10]. As for some applications within enclosed chamber, the main drawback of the above methods is that it is necessary to drill a hole in the wall of arc chamber and mount an observation window in order to let the arc light emit out. It was found that the material of observation window is labile at high temperature and its decomposition products have dramatic influences on the gas pressure distribution and the physical properties of arc plasma [11–13]. This problem becomes worse as the arc current increases. Although optical fiber array could reduce damage to the chamber, it is of relatively low spatial resolution which depends on the amount of optical fibers mounted [14,15].
Magnetic tomography is a non-invasive means to determine the distribution of electric current via measuring the surrounding magnetic field and solving the inverse problem, which has been demonstrated by many applications in the fields of fuel cells, superconducting cables, and human bodies [16–18]. It is also an effective method to reconstruction the current distribution of arc plasma from the measured magnetic field [19]. Toumazet et al. [20] applied a combined technique of an inverse method and a voltage measurement to study arc motion. Ghezzi et al. [21] developed a magnetic inverse model for the arc plasma reconstruction of vacuum circuit breakers. In the preliminary work, we reported that a 2D arc plasma distribution can be reconstructed by only the single magnetic field component [22]. There are several useful methods to measure the magnetic field, such as Hall effect sensor, AMR sensor, GMR sensor and so on [23–25]. They have a high sensitivity and quick response but low resolution as the element density of sensor array is limited by the chip package size. Therefore, as to a specific magnetic field measurement system, the key performance parameters: detection area, sampling speed, spatial resolution and sensitivity are always contradictory with the others.
The magneto-optical imaging (MOI) technique provides a promising method to resolve those contradictions. By using the Faraday indicator, mounted in a polarizing microscope or equivalent optical setup, magnetic field distributions can be detected as a pattern of changing light intensity. Different types of MOI systems have been built for various purposes reducing some of the four contradictions. Baziljevich et al. presented a MOI setup with a view of 5 mm in diameter up to 30 000 pfs [26]. Murakami et al. [27] built a high-sensitive scanning laser MOI system of a spatial resolution less 500 nm and the sensitivity of about 5 mT. Kuhn et al. [28] set up a new apparatus for MOI investigations as large as 400 cm2 through magneto-optical scanning technique. Pabitra et al. [29] developed a high sensitivity differential magneto-optical imaging system which has a root mean square noise level of 50 mG.Hz−1/2 at a full frame rate of 1 fps with each frame being of size 512 × 512 pixels. Cheng et al. discussed several key improvements for the MOI device, including the optimization of the magneto-optical sensor, the design of the magnetic excitation device, and the image processing approaches [30]. The arc plasma varies rapidly in position and shape, which means magnetic field data with high sensitivity and high resolution in a relatively large area must be obtained simultaneously. The magnetic sensor arrays and MOI systems mentioned above can’t meet the harsh demands.
In this work, in order to overcome those problems with the existing MOI system, a large area high speed MOI system has been developed to meet the requirement of measuring the 2D magnetic field distribution of transient arc plasma in real time, which mainly consists of high intensity and stability laser driven light source, MR3-2 type magneto-optical glass, high extinction ratio polarizer and analyzer, beam expender, polarized beam splitter, and a high speed CCD camera. The main technical parameters of the proposed MOI system are as follow: imaging frame rate up to 10 000 fps, detection area of 42mm in diameter, spatial resolution higher than 500μm, and magnetic field sensitivity about 1mT. Calibration and test experiment were conducted to verify whether or not the developed MOI system meets the measurement requirements of time varying arc plasma in an enclosed arc chamber.
2. Design of MOI system
2.1 Principle of MOI system
Magneto-optical imaging system is based on the Faraday effect. The schematic diagram of the principle is shown as Fig. 1. In the presence of a magnetic field, the polarization plane of a linearly polarized beam of light will rotate when the beam transmits through a Faraday indicator. The Faraday rotation of the plane of polarization takes place as follows:
where θF is the angle of rotation (in radians), V is the Verdet constant for the material. This empirical proportionality constant (in units of radians per tesla per meter) is associated with wavelength and temperature, B is the magnetic flux density in the direction of propagation (in teslas), L is the length of the path (in meters) where the light and magnetic field interact.As shown here, the sign of Faraday rotation angle varies with the direction of applied magnetic field B. Therefore, if both the Faraday rotation angle and its sign are obtained at the same time, the strength and direction of the magnetic field can be directly evaluated.
For an ideal polarization optical system, the light intensity of a light beam traversing the polarizer, Faraday indicator and analyzer is given by the Malus law:
where I0 represents the intensity of the incident polarized light beam, ε is the absorption coefficient of Faraday indicator, θF is determined by Eq. (1).Polarized light and linear optical elements can be represented by a Jones vector and Jones matrices respectively. When light crosses an optical element the resulting polarization of the emerging light is obtained by taking the product of the Jones matrix of the optical element and the Jones vector of the incident light. So for a MOI setup, the measurement model of the optical rotation angle can be derived according to the Jones calculus.
The Jones vector of the incident light is expressed as:
where E0 is the amplitude of incident light.The Jones matrix of polarizer is as follows:
where α is the angle between the transmission axis of the polarizer and the given optic axis, σ1 is the extinction ratio of the polarizer.The Jones matrices of the polarized beam splitter in transmission J2 and reflection direction J4 are respectively expressed as:
The Jones matrix of Faraday with rotation angle θF is
The Jones matrix of analyzer is as follows:
where β is the angle between the transmission axis of the analyzer and the given optic axis, σ2 is the extinction ratio of the analyzer.The Jones vector of the emergent light is expressed as:
Then the final light intensity Qout entering into the optical imaging sensor or device, such as a high speed CCD camera, can be given as:
The relation between the gray value Gout of the magneto-optical image produced by the imaging device and the light intensity Qout is:
where ω is a positive constant that represents the transfer ratio from light intensity to gray value.Thus, the gray value Gout can be represented as a function of rotation angle,
As θF is linearly correlated with B, thus the gray value Gout will vary with the measuring magnetic field B. The relationship between Gout and B can be determined by experiment.
2.2 Integrated MOI system
The proposed MOI system consists of a laser driven light source, a high extinction ratio polarizer, beam expander, polarized beam splitter, magneto-optical glass, polarization analyzer, lens, high-speed camera and PC-based image processing system, as illustrated in Fig. 2. A miniaturized MOI system has been implemented by integrating all the optical components in several shading cylinders and box, which is shown in Fig. 3.
The laser driven light source EQ. -99-FC produces high brightness, broad-band light from DUV wavelengths through visible and beyond. Its time and spatial stability reduces the experimental error caused by light intensity fluctuation. The light emitted from EQ-99-FC, passing through the fiber, was transformed into a parallel beam (22mm in diameter) by achromatic collimator (RC12) of Thorlabs. After transmitting through the interference filter (central wavelength: 632.8 ± 1nm, bandwidth 10nm) and the expander, the beam became monochromatic and was expanded to 42mm in diameter, so as to cover the detecting area.
A piece of magneto-optical glass (MR3-2) with in-plane isotropy was used as the Faraday indicator. The size of the magneto-optical glass is 70mm in diameter and 10mm in thickness. The Verdet constant of MR3-2 glass is −96 rad/(T·m)@632.8 nm. On the incident plane of the MR3-2 glass, a wide band antireflective film with a visible light transmission of 99.9% is coated, and a mirror layer is sputtered onto the other plane to improve light reflection and prevent arc light. Thus the light reflected from the incident plane of the MR3-2 glass was decreased so that the noises caused by multi-path propagation were depressed.
The expanded monochromatic beam was split into mutually perpendicular p-light (transmission light) and s-light (reflection light) by the polarized beam splitter. The polarization plane of p-light beam rotated when passing through the MR3-2 glass as a result of the x-component of the measuring magnetic field. A negative Verdet constant corresponds to R-rotation (clockwise) when the direction of propagation is parallel to the magnetic field and to L-rotation (anticlockwise) when the direction of propagation is anti-parallel. Thus, the rotation doubled as the beam passed through the MR3-2 glass and reflected back through it.
The reflected light beam with abundant information about the magnetic field transmitted through the polarized beam splitter and analyzer. The optical signals were recorded by a high speed camera (Phantom Miro eX2) and transferred to the image processing system. The maximum resolution is 640 × 480, the maximum frame rate reaches 105 200 fps (at the lowest resolution) and the minimum exposure time is 5μs. In the future the camera can be replaced by an iCCD camera to increase the resolution and sensitivity.
3. Calibration and image processing
3.1 Calibration
The MOI system was calibrated by applying homogeneous magnetic field in optical axis direction. The magnetic field was generated by a Helmholtz coil. The MR3-2 glass was placed in the center of the Helmholtz coil and the relative position is shown as Fig. 4.
In the ideal situation, the gray value of magneto-optical image received by the camera would take on uniform distribution. However, due to machining error of lenses of the MOI system and experimental error, it was distributed as Fig. 5(a) in the initial state, that is, under the magnetic field of 0 mT and Fig. 5(b) when applying an external magnetic field of 10mT. Based on the data analysis, the ratios of gray value in the same coordinates between the magnetic condition B = 10mT and B = 0mT can be considered as constant within a margin of error, the result of which was shown as Fig. 6(a). The average ratio value was about 1.6 and the difference between maximum and minimum value was about 0.15, so that the system sensitivity of 1mT can be achieved. The image resolution of high speed camera was set to be 128 × 128 and the sampling rate was set to 10 000 fps. The diameter of the detection spot was 42mm which active area covered more than 96 × 96 pixels, thus the spatial resolution can reach 500μm.
Fig. 5 (a) The gray value distribution when B is set to 0mT; (b) The gray value distribution when B is set to 10mT.
Fig. 6 (a) The ratio of the gray value when B is equal to 10mT; (b) The relation between the ratio of gray value and magnetic flux density.
By calibration, it can be found that there was a good linear relation between the ratio of the gray level of the magneto-optical images and the magnetic flux density, as shown in Fig. 6(b). The fitting function was derived from the curve:
where B is the magnetic flux density, R is the ratio of the gray value.3.2 Image processing
In order to obtain the distributions of magnetic flux intensity over time, the each frame of magneto-optical images received by high speed camera was processed by the image processing system. The data flow diagram for the image processing system was shown as Fig. 7. There are five main steps should be dealt with before obtaining the magnetic field image. Firstly, the gray values are extracted from each magneto-optical image and divided by initial matrix to get the ratio matrix, which are linearly associated with the magnetic flux intensity. Secondly, as the ratios are not homogeneous at the edge of light spot, the measuring data of edge are trimmed off by applying an edge detection algorithm with the Canny operator to refine data. Thirdly, median filtering algorithm is adopted to reduce the measurement noise. Then, the ratio matrix are converted to magnetic field data multiplied the transform matrix. Finally, magnetic field distribution image is obtained after interpolating and pseudo color processing.
Figure 8 demonstrates the images before and after being processed. A raw image captured by high-speed camera is shown in Fig. 8(a). Figure 8(b) is the gray value image extracted from magneto-optical image. After a series of data filtering, transformation and interpolation, a magnetic field image is obtained, as shown in Fig. 8(c). The final result shows a continuous distribution of magnetic field with pseudo color over the concerned area.
4. Experimental setup and results
4.1 Arc discharge circuit
Figure 9 shows the experimental discharging circuit to test the developed magneto-optical imaging system. The test current is provided by the capacitor banks circuit which can deliver 50Hz sinusoidal current up to 5kA. When the main closing switchgear is closed and the capacitor banks imposes the short-circuit current into the arc plasma generator which consists of a pair of separable arc contacts, arc runner and shutter-shape arc splitter.
The arc contacts, arc runner and arc splitter are fixed in an enclosed chamber. The special wall material of the arc chamber will produce gas compositions of high thermal conductivity at high temperature, which is helpful for driving arc to move forward and also cooling the arc column. The details of ignition, motion, cutting, and extinction of the plasma column was recorded by the developed MOI system. For comparison an observation window was mount in the outside wall of the arc chamber and the arc motion was recorded by Phantom V10 camera at the same time whose frame rate is set to 24 000 fps and exposure time is set to 5μs. After arc plasma ignited between the separating contacts, it jumped from the ignition position to the arc runner and finally extinguished in the arc chamber, with the help of the Lorenz force and gas blowing mechanism. The arc current and voltage were recorded by a digital storage oscilloscope (Tektronix TBS1104) with a Hall current sensor and a high voltage transducer.
4.2 Arc current and voltage
The test experiments have been done repeatingly at the charge voltage of 200 V and the prospective current of 1kA (RMS). The typical arc current and voltage waveforms are shown in Fig. 10. The arcing time is 7.40ms. The zero point of time variable is defined at the instant when the current begins to appear. The current shows an approximate sine waveform and reaches a maximum of 1392 A at 3.37 ms. The arc voltage increases up to 164V at 4.78ms, then fluctuates around 100V and finally decreases to 48V at 7.40ms, as the arc plasma moves forward along the arc runner and then extinguished in the arc quenching chamber.
4.3 Magnetic flux density distribution and arc motion
The distributions of magnetic flux density were derived from the magneto-optical images. Figure 11 shows the arc motion images from 1.5ms to 5.0ms, of which the intensity was scaled to enable better view and the corresponding images of magnetic field distribution are shown in Fig. 12. In those images, profiles of the splitter, electrode and arc runner are indicated manually.
It is found that the distribution of magnetic field changes slightly from 1.5ms to 2.0ms and from 4.5ms to 5.0ms and varies significantly from 2.5ms to 4.5ms. The reason is that the arc plasma was burning between the movable contact and fix contact at the ignition stage and it kept staying statically in the arc splitter at the final stage but in the second stage the arc plasma moved quickly along the arc runner towards the arc splitter driven by Lorenz force. Mainly dependent on the current, the magnetic field value increased from 1.5ms to 3.5ms and decreased form 3.5ms to 5.0ms, which is in accordance with the Maxwell equations.
5. Conclusion
In this work, a high speed magnetic-optical imaging (MOI) system for investigating transient arc plasma was presented, an integrated MOI system prototype has been developed and the calibration and test experiments were carried out to evaluate its performance. As a result, it was found that the MOI system has 500μm spatial resolution, 100μs temporal resolution, and 1mT magnetic field strength sensitivity under the condition of a circle measuring area 42mm in diameter. With this developed system, we have succeeded in the measuring the magnetic field distribution around the arc plasma generated by a pair of separable arc contacts in an enclose arc chamber. The experimental results shows the proposed MOI system provides an effective and non-intrusive method to obtain magnetic field distribution around arc plasma in large area with a high temporal and spatial resolutions and reasonable magnetic field resolution and it can help the investigator to study the motion characteristics of arc plasma in an enclose chamber.
Funding
National Natural Science Foundation of China (NSFC) (51477129).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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