Proton imaging of 3D density distribution for dense DT plasmas using regularization method

Abstract

AbstractThree-dimensional (3D) density distribution of inhomogeneous dense deuterium tritium plasmas in laser fusion is revealed by the energy loss of fast protons going through the plasmas. The fast protons generated in the laser–plasma interaction can be used for the simulation of a plasma density diagnostics. The large linear and ill-posed equation set of the densities of all grids is obtained and then solved by the Tikhonov regularization method after dividing a 3D area into grids and knowing the initial and final energies of the protons. 3D density reconstructions with six proton sources are done without and with random noises added to the final energy. The revealed density is a little smaller than the simulated one in most simulated zones and the error is as much as those of 2D reconstructions with four proton sources. The picture element N is chosen as 2744 with consideration of smoothness and calculation memory of the computers. With fast calculation speed and low error, the Tikhonov regularization method is more suitable for 3D density reconstructions with large calculation amount than simultaneous iterative reconstruction method. Also the analytical expressions between the errors and the noises are established. Furthermore, the density reconstruction method in this paper is particularly suitable for plasmas with small density gradient. The errors without noises and with 2% noises added to the final proton energies are 3 and 20%, respectively, for the homogeneous plasma.