A novel approach for the improvement of the sensitivity of the flow visualization system on supersonic molecular beam of tokamak fuelling

Supersonic molecular beam injection is a robust alternative to control the particles in fusion plasma devices. It is widely used in many experimental studies on the plasma physics. Direct visualization of beam makes it possible for precise optimization of the beam characteristics. However, a normal visualization system does not fully meet the requirements of the measurement of the beam distribution in the low gas density vacuum environment. This paper reports a newly designed multi-pass visualization system without changing the schlieren mirrors. This multi-pass system is designed to make the light passing the testing area several times, where the deflection angle of the light would simultaneously increase. Thus, the sensitivity of the schlieren image is enhanced. The testing result proves the improvement of the sensitivity, which makes it possible to optimized the beam structure in low gas density working conditions.

multi-pass schlieren system, which improves the sensitivity according to the preliminar testing result. The paper is organized as follows. Section 2 describes the system design. Section 3 shows the preliminary experimental result of the multi-pass schlieren system. Section 4 is the summary.

System setup and design 2.1 Experimental platform
A testing platform has been established to test the characteristics of the SMBI system. This testing platform is composed of several facilities including the gas injection system, the vacuum chamber, the vacuum support system, and the diagnostics. The gas injection system is the input of the gas for this platform, which usually connects with the SMBI system including the high-pressure gas source, the SMB pulse time controller. It injects the SMB into the vacuum chamber with pre-set pressure and pulse duration with signal pulse mode and cycle pulse mode. The vacuum chamber includes two parts, the large cylinder chamber in the vertical direction and the long cylinder tube in the horizontal direction. The large cylinder chamber provides sufficient area for the expansion of the gas and enables the detection at the outlet of the nozzle. The long vacuum tube simulates the working environment for the fueling at the tokamak, where the status of the fueling beam could be diagnosed. The vacuum chamber and the vacuum tube are sustained by the three mechanical pumps and three turbo molecular pumps, by which the vacuum degree could be reduced to 10 −5 Pa after baking by the heaters at the inner wall of the vacuum components. In addition, film gauges are installed on the platform to supervise the vacuum degree. The diagnostics are changeable for different requirements, such as the schlieren diagnostic system, the Rayleigh scattering diagnostic system, and the high-voltage discharge system. The Zigzag schlieren diagnostic system has been already installed on the testing platform, which provides a larger field-of-view than our other attempt with the single-mirror coincident system, and the structure of the beam is clearly observed [5,6].

System design of the multi-pass visualization system
Sensitivity is a basic characteristic for the schlieren system, which is usually typified by the amplitude or grayscale contrast variations. The sensitivity of the constructed Z-type schlieren system is convenient to be illustrated by its geometrical optics. It can be derived that the schlieren image illuminance with the knife-edge cutoff can be described as [9]: where is the luminance emitted by the light sources, is the magnification factor of the image size, is the breadth of the slit, is the height of the knife edge at the focal point for the second schlieren mirror, 1 and 2 are the focal length of the first and the second schlieren mirror, separately. Considering the light deflected by the schlieren object with the deflection angle , the deflected distance at the second focal point is described by: Substituting Δ for in eq. (2.1), it can be obtained that:

JINST 16 P10013
The contrast of the schlieren image is then given by the following equation: Thus, the sensitivity for the Z type normal system is limited by the width of the slit and the focal length of the second schlieren mirror, which is hardly optimized when the system is settled. The sensitivity factor for the Z type schlieren system is given by the following equation: The ideal of the multi-pass system is inspired by the double passed system, and was theoretically proved in 1966 [10]. Since the width of the slit and the focal length is constrained by the hardware of a fixed system, another approach to increase the contrast of the schlieren image is the increase the deflection angle as shown in figure 1. The red dashed line means the interface between the regions with tiny difference on density and its normal line. The incident light passes through the test area with a deflection angle . The deflected light is reflected by a mirror and passes the test area again with the deflection angle . According to the law of the refraction, the twice pass light follows the equation below: It should be noted the deflection and the reflection happens in a small region, and deflection angle of the light ray is also small enough, which allows the light rays keeps in the similar direction to the incident light ray. Thus, under the assumption of the small angle reflection, the deflection angle for light ray passing the testing area twice is: The result shows that the deflection angle could increase by each time when the light passes through the test area. It should be noted that the deflection angle is small which makes the reflected light still almost parallel to the incident light.Thus, the forward light reflected by the mirror for times, the deflection angle is: According to this idea, two splitters are added to the original Z-type system parallel to the view windows of the main vacuum chamber on both sides as shown in figure 2. The reflection coefficients for the first beam splitter and the second beam splitter are 1 and 2 , respectively.
is the transmission coefficient across the light pass. Thus, the contrast of the system is described as following: Neglecting the transmission loss during the light path donates the = 100%. Figure 2. Schematic of the multi-pass schlieren system for SMB visualization based on the normal zigzag schlieren system. The red and blue splitters are added to the normal schlieren system to create a multi-pass system.

System testing and the initial result
As described above, the multi-pass system is installed on the testing platform. To simplify the testing process, the background pressure is set as the level of 10 4 Pa to obtain a clear beam structure. In addition, the working gas is chosen to be carbon dioxide (CO 2 ) for convenience and safety reason. This system is then carefully adjusted to ensure the secondary schlieren image would be captured, since a small aberration on the first image can be amplified in this optical system. Figure 3 clearly shows two separate schlieren images by adjusting the mirrors. The direct measurement of the schlieren images captured by high-speed camera is shown in figure 3(a). It could be observed that these two images are deliberately separated to show the first and the second schlieren images. The first schlieren image, which is obtained by the light directly passing through the mirrors, has the deflection angle to be. The second schlieren image is obtained by the light reflected twice by the second and the first splitters with the deflection angle. In addition, the intensity of the second schlieren image is less than the first schlieren image, which means the improvement of the contrast or the sensitivity is limited by the performance of the mirrors and the camera. Instead of many schlieren images in theory, several schlieren images can be obtained in practice due to the attenuation of the intensity and the growing of the aberration. The misplaced first schlieren image and the second schlieren image are aligned to be in the same place to form a superposition schlieren image by adjusting the direction of schlieren mirror 2 and the reflector 2.
-4 - The reflection coefficients for both beam splitters are 50%. According to equation (2.10), the superposition of these two schlieren images makes the contrast of the twice-pass superposition schlieren image to be 1.25, which is about 0.25 (25%) higher than the single-pass image. Figure 4 shows the comparison of the contrast of the twice-pass superposition image and the normal singlepass image. The contrast of the image is defined in equation (2.4), which is practically calculated by the captured schlieren imagesas follows: Where ( , ) is the schlieren image with the SMB captured by high-speed camera, and 0 is the background image without SMB. The contrast of the twice-pass superposition image 1 and the normal single-passing image The background noise and small structure turbulence in the figures should be omitted, which is normally in random distribution and is not repeatable with relatively low contrast (lower than 0.12) in -5 -these cases. The distinguish structure of the main stream, which is considered to be repeatable under the same working condition, is illustrated in figure 5 from superposition image in figure 4(a). Only the data in the main stream region is used, which is = [0 mm, 40 mm] and = [−1.5 mm, 1.5 mm] within about 16 × 230 pixels as marked by the dashed red box in figure 5, the data in this region is used. The intersection of the main stream structures from all the images in this region can further figure out a more accurate boundary of the main stream structure. The averaged increase of the contrast from figure 4(c) is then calculated with this accurate main stream structure, which is about 21.0%. This value is close to the value based on the theoretical estimation.

Summary
The supersonic molecular beam injection is widely used in fusion plasma fueling and physical studies. The visualization of the beam is essential for its optimization and further quantitative investigation in related physical studies. A multi-pass schlieren system is designed and investigated for the low gas density working environment, which is expected to have higher sensitivity than the normal system. Usually, the improvement of the sensitivity of the schlieren system is to enlarge the schlieren mirrors to acquire a larger focal length, dramatically changing almost the whole system. Unlike the common approaches, this multi-pass system only simply adds two beam splitters. The testing result shows this multi-pass system improves the sensitivity to be 21.0% higher with the superposition of only two schlieren images. The performance of this system could be better with more superposition images once appropriate reflection coefficients of the beam splitters are chosen. The system will be dedicated to the optimization of the SMB in the low gas density working environment.