Dealing with Asymmetrical Abel Inversion Using Fourier-Bessel Expansions

A new method is presented for dealing with asymmetrical Abel inversion in this paper.We separate the integrated quantity into odd and even parts using Yasutomo’s method. The asymmetric local value is expressed as the product of a weight function and a symmetric local value. The symmetric distribution is expanded into Fourier-Bessel series. The coefficients of the series are determined by the use of a least-square-fitting method.

Inversion techniques to obtain local rotation velocity and ion temperature profiles for the x-ray crystal spectrometer on EAST

Inversion techniques are conducted based on the tangential x-ray crystal spectroscopy(TXCS)geometry on EAST to obtain the local profiles of ion temperature(Ti)and toroidal rotation velocity(vt).Firstly,local emissivity profiles of the impurity argon are obtained using the asymmetrical Abel inversion.Then,the local vt and Ti profiles are calculated by considering the local emissivity profiles and the TXCS detailed geometry.In addition,how the changes in the vt profiles affect the accuracy in the Ti profiles is discussed in detail.It is also found that the lineintegrated Ti profiles are becoming less accurate with the increase in the radial gradient in the local vt profiles.Nonetheless,accurate Ti radial profiles are reconstructed after considering the effects of the emissivity and velocity,which are verified by comparing the inverted vt and Ti profiles with those local profile measurements from the Charge eXchange Recombination Spectroscopy(CXRS)on EAST.

Field measurement method for ultrasonic transducer based on inverse Abel transform

A new reflection approach for field distribution measurement of ultrasonic transducers was investigated. Instead of a point-like reflection target (rigid sphere) or thin wires (line-like targets), a line response function of experimental knife-edge distribution combined with the inverse Abel transforms was used to estimate the lateral beam distributions of ultrasonic transducers. The measurement steps were as follows:① A knife-edge was scanned perpendicularly to acoustic beam axis of the transducer using an ultrasonic C-scan system to obtain its ultrasonic image line response function, ② the transverse beam distribution was solved by the inverse Abel transforms, and ③ experiments were performed to obtain the lateral beam profiles of two transducers, with and without focus, and the results were compared with those from a hydrophone. The results showed that this method was effective for ultrasonic field measurement and could be as a substitute for hydrophone in most cases.

Temperature Field Reconstruction in High-Temperature Gas by Using the Colored Background Oriented Schlieren Method

A 3D temperature field reconstruction method using the colored background oriented schlieren(CBOS)method is proposed to address image blurring due to the different refractive index of the multi-wavelength light and significant errors produced when the traditional background oriented schlieren(BOS)method is applied to high-temperature gas.First,the traditional method is employed to reconstruct the non-uniform 3D temperature field.Second,the CBOS method is applied to correct the distortion.Then,by analyzing the correlation coefficient among different color points of the colored background pattern,the non-uniform temperature field is reconstructed much more accurately.Finally,the experimental results are verified by applying the Runge-Kutta ray-tracing method and the thermocouple contact measurement method.The maximum average temperature error of the CBOS-reconstructed temperature field is 12.92°C,compared with the thermocouples.Therefore,an accurate three-dimensional reconstruction of the temperature field can be achieved by the proposed method effectively.