The properties of cylindrical and spherical dust–ion acoustic solitary waves (DIASW) in an unmagnetized dust plasma comprised of relativistic ions, Boltzmann electrons and stationary dust particles are investigated for the first time in this paper. By using the standard reductive perturbation method, a cylindrical/spherical KdV equation is obtained. The change in the DIASW structure due to the effects of geometry, relativistic streaming factor, ion density, and electron temperature is studied by numerical calculation of the cylindrical/spherical KdV equation. It is observed that the properties of DIASW in cylindrical and spherical geometry differ from those in planar one-dimensional geometry, and the amplitude of the solitary wave decreases with increasing electron temperature and increases with increasing relativistic streaming factor, ion density, and vice versa. It is shown that the soliton height is closely related to the nonlinearity coefficient: the height increases as the nonlinearity coefficient decreases.

Plasma density fluctuation profile measurement is an important task in fusion plasma confinement. It is necessary in physics research that the fluctuation density signal be decomposed from the density signal accurately. Recently, a new technique, the wavelet and correlation technique, was utilized in computing the density fluctuation on the HL-2A tokamak for the first time. The db5 wavelet basis belonging to the orthogonal Daubechies wavelet was chosen for density signal decomposition and reconstruction. Two diagnostics supported this work: an 18-position magnetic coil array and a newly developed multi-channel far infrared interferometer system. During ohmic heating and electron cyclotron resonance heating discharge, density fluctuation is correlated with magnetohydrodynamics by correlation analysis; one can reduce the mode m = 2 or 1, n = 1 to its elements. From Abel inversion, the conclusion shows that the fluctuation distribution is strongly peaked at the edge, and the line-integrated fluctuation profile is slightly hollow.