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.

A new method of asymmetric Abel inversion for magnetic equilibrium configuration state in tokamaks

It is difficult to obtain the asymmetrical factor along the observation direction parallel to the plasma mid-plane when the detected radiation is also in the mid-plane. This paper considers the magnetic surfaces and Grad-Shafranov shift, and develops a new method for inverse asymmetric electron density information, during magnetic equilibrium configuration in a tokamak.

An Analytical Method for the Abel Inversion of Asymmetrical Gaussian Profiles

An analytical algorithm for fast calculation of the Abel inversion for density profile measurement in tokamak is developed. Based upon the assumptions that the particle source is negligibly small in the plasma core region, density profiles can be approximated by an asymmetrical Gaussian distribution controlled only by one parameter VoID and VoID is constant along the radial direction, the analytical algorithm is presented and examined against a testing profile. The validity is confirmed by benchmark with the standard Abel inversion method and the theoretical profile. The scope of application as well as the error analysis is also discussed in detail.

The Application of Barr Numerical Method to Realize Abel Inversion

An 8-channel HCN laser interferometer will be installed on HL-2A in near term. In order to get the spatial profile of the electron density Barr numerical method is adopted to realize the Abel inversion. In this article the result of the Abel inversion by Matlab GUI is given which can be updated to process the measured data of the 8-channel laser interferometer and provide the spatial distribution of the electron density.

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.

Using a Mach–Zehnder interferometer to deduce nitrogen density mapping

This work presents an optical method using the Mach–Zehnder interferometer. We especially diagnose a pure nitrogen gas subjected to a point to plane corona discharge, and visualize the density spatial map. The interelectrode distance equals6 mm and the variation of the optical path has been measured at different pressures： 220 Torr, 400 Torr, and 760 Torr.The interferograms are recorded with a CCD camera, and the numerical analysis of these interferograms is assured by the inverse Abel transformation. The nitrogen density is extracted through the Gladstone–Dale relation. The obtained results are in close agreement with values available in the literature.

Online plasma diagnostics of a laser-produced plasma

In this study,we report a laser interferometry experiment for the online-diagnosing of a laserproduced plasma.The laser pulses generating the plasma are ultra-fast（30 femtoseconds）,ultraintense（tens of Terawatt） and are focused on a helium gas jet to generate relativistic electron beams via the laser wakefield acceleration（LWFA） mechanism.A probe laser beam（λ=800 nm） which is split-off the main beam is used to cross the plasma at the time of arrival of the main pulse,allowing online plasma density diagnostics.The interferometer setup is based on the No Marski method in which we used a Fresnel bi-prism where the probe beam interferes with itself after crossing the plasma medium.A high-dynamic range CCD camera is used to record the interference patterns.Based upon the Abel inversion technique,we obtained a 3D density distribution of the plasma density.

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.

OSCILLATING MULTIPLIERS ON NONCOMPACT RIEMANNIAN SYMMETRIC SPACE SL(3,IH)/Sp(3)

The author studies the oscillating multipliers on Riemannian symmetric spaceSL(3,IH)/Sp(3).The results are analogous to that for Riemannian symmetric spaces of rank one and of complex type.