The atomic selective multi-step photoionization process is a critical step in laser isotope separation. In this work, we study three-step photoionization processes with non-monochromatic laser fields theoretically based on the semi-classical theory. Firstly, three bandwidth models, including the chaotic field model, de-correlation model, and phase diffusion model, are introduced into the density matrix equations. The numerical results are compared with each other comprehensively. The phase diffusion model is selected for further simulations in terms of the correspondence degree to physical practice. Subsequently, numerical calculations are carried out to identify the influences of systematic parameters, including laser parameters (Rabi frequency, bandwidth, relative time delay, frequency detuning) and atomic Doppler broadening, on photoionization processes. In order to determine the optimal match among different systematic parameters, the ionization yield of resonant isotope, and selectivity factor are adopted as evaluation indexes to guide the design and optimization process. The results in this work can provide a rewarding reference for laser isotope separation.
The atomic selective multi-step photoionization process is a critical step in laser isotope separation. In this work, we study three-step photoionization processes with non-monochromatic laser fields theoretically based on the semi-classical theory. Firstly, three bandwidth models, including the chaotic field model, de-correlation model, and phase diffusion model, are introduced into the density matrix equations. The numerical results are compared with each other comprehensively. The phase diffusion model is selected for further simulations in terms of the correspondence degree to physical practice. Subsequently, numerical calculations are carried out to identify the influences of systematic parameters, including laser parameters (Rabi frequency, bandwidth, relative time delay, frequency detuning) and atomic Doppler broadening, on photoionization processes. In order to determine the optimal match among different systematic parameters, the ionization yield of resonant isotope, and selectivity factor are adopted as evaluation indexes to guide the design and optimization process. The results in this work can provide a rewarding reference for laser isotope separation.
The four-color three-step selective photoionization process of atom is very important in laser isotope separation technology. The population trapping phenomena and their influences are studied theoretically in monochromatic and non-monochromatic laser fields based on the density matrix theory in this work. Time evolutions of the photoionization properties of the four-color, three-step process are given. The population trapping effects occur intensely in monochromatic excitation, while it gradually turns weak as the laser bandwidth increases. The effects of bandwidth, Rabi frequency, time delay, and frequency detuning on the population trapping effect are investigated in monochromatic and non-monochromatic laser fields. The effects of laser process parameters and atomic parameters on the effective selective photoionization are also discussed. The ionization probability and selectivity factors, as evaluation indexes, are difficult to improve synchronously by adjusting systematic parameters. Besides, the existence of metastable state may play a negative role when its population is low enough.
Photoexcitation and photoionization of atoms, the central part of atom vapor laser isotope separation (AVLIS), relate to the ionization yield and isotope selectivity directly. Doppler broadening of absorption lines is one of the parameters that influence the photoexcitation and photoionization process of atoms. When evaporation temperature is high or beam equipment is absent, Doppler broadening has obvious influence on the ionization yield because most of atoms are non-resonantly excited. In this paper, we study the influences of Doppler broadening of absorption lines on a multi-step photoexcitation and photoionization process of atoms according to the facts of AVLIS. A Doppler-broadened three-level atom system with two resonant lasers is investigated. The interaction between laser field and atoms is described by a density matrix, which is calculated by fourth-order Runge-Kutta numerical method with variable steps. The results show that the ionization yield of atoms decreases with the increase of Doppler broadening of absorption lines under the same laser parameters. At a constant laser power, the ionization yield reaches its maximum value at the best laser bandwidths, which is different from that obtained without Doppler broadening, as reported in published papers. Meanwhile, the best laser bandwidth increases with the increase of Rabi frequency and Doppler broadening when other parameters are constant. Moreover, the best bandwidth of the second laser is smaller than that of the first laser in a multi-step photoionization process of atoms. Therefore, lasers should work at the best bandwidths in AVLIS for highest ionization yield. It is advantageous to make laser bandwidths slightly bigger than the best bandwidths technically for smaller fluctuation of ionization yield, owing to incoercible stochastic volatility in laser bandwidths. The ionization yield increases with the decrease of Doppler broadening, especially at the best laser bandwidths. Therefore, it is necessary to reduce Doppler broadening of atom vapor in laser ionization zone.
Selective photoionization of ytterbium isotope is studied numerically based on a three-step photoionization scheme, 4f146s2 1S0 (0 cm−1) → 4f146s6p 3P1 (17992.008 cm−1) → (4f136s26p) (7/2, 3/2)2 (35196.98 cm−1) → auto-ionization state (52353 cm−1) → Yb+, by the density matrix theory with the consideration of atomic hyperfine structures and magnetic sublevels. To examine the physical model, the numerical isotopic abundance of ytterbium is compared with that from mass spectroscopy experiment, showing that they are in good agreement with each other. The excitation process and ionization process of ytterbium, especially for odd isotopes, are discussed and analyzed in detail on this basis. The effects of frequency detuning, power densities, spectral bandwidths, polarization of two excitation lasers, and atomic Doppler broadening on the total ionization yield and isotopic abundance are investigated numerically and the optimal excitation conditions for 176Yb enrichment are identified semi-quantitatively.
The pulse deformation and time delay, which appear when the laser propagates in a thick atom vapor, influence the ionization yield and selectivity of atomic multi-step photoionization process directly. In this paper, we study the propagation of laser pulse and atomic photoionization in a thick atom vapor medium according to the atom vapor laser isotope separation. The process of atomic multi-step photoionization and the propagation of laser in a thick medium are described by density matrix equation and Maxwell equations, respectively. The medium consists of target isotope and non-target isotope, which is non-resonantly excited. Through numerical solution of the coupled equations we illustrate the propagation characteristics of laser and the influences of atom vapor parameters and laser parameters on average ionization yield and average selectivity in a thick medium. The important results of calculation are as follows:when the atom vapor medium is rather thick, the average ionization yield increases while average selectivity decreases with the increase of laser power. When the atom vapor is relatively thin, the average ionization yield and average selectivity increase with the decrease of laser power simultaneously. Besides, there is a positive time delay between two laser pulses in which case the average ionization yield of target isotope reaches its maximum value. Moreover, when the parameters of atom vapor are constant, extending the width of laser pulses as great as possible can not only increase average ionization yield and average selectivity simultaneously, but also loosen the control accuracy of time delay between laser pulses.
Numerical computations of ionization efficiency and isotope selectivity of 176 L u have been carried out for the following three-step ladder type photoionization scheme, 5 d 6 s 2 2 D 3 / 2 ( 0.0 c m − 1 ) − − − ⟶ 540.4068 n m 5 d 6 s 6 p 4 F 5 / 2 o ( 18504.58 c m − 1 ) − − − ⟶ 535.0626 n m 5 d 6 s 7 s 4 D 3 / 2 ( 37193.98 c m − 1 ) − − − ⟶ 618.0061 n m 53375 c m − 1 A u t o i o n i z a t i o n S t a t e → L u + , by invoking the density matrix formalism for the laser–atom interactions. Equations of motion have been derived for the odd isotopes by inclusion of hyperfine levels. The line shapes and their effect on the ionization efficiency and isotope selectivity have been discussed in detail. The effects of power of excitation and ionization lasers, spectral bandwidths, pulse delays, Doppler broadening of the atomic ensemble on the ionization efficiency, and degree of enrichment have been presented. Optimum conditions for the power of excitation, detunings, and other system parameters for the selective yet efficient photoionization of 176 L u have been identified.
Abstract The laser frequency spectrum, whose full width at half-maximum in the frequency domain is the laser bandwidth, plays a critical role in atomic multi-step photoionization processes and has a significant influence on isotopic selective photoionization results. In this study, two phase-independent frequency spectrum models, that is, the mode jitter model (MJ model) based on the mode jitter phenomenon and the multi-longitudinal mode model (MLM model) based on multi-longitudinal mode output, are proposed to describe the spectral characteristics in the frequency domain. In the MJ model, it is assumed that there is a time-varying longitudinal mode in each laser pulse, with different central frequencies between adjacent pulses in the pulse train; in the MLM model, it is assumed that multiple longitudinal modes are output simultaneously with fixed central frequencies. Selective photoionization properties of these two frequency spectrum models and the chaotic field model are simulated and compared with each other under the Lorentzian frequency spectrum condition. Influences of the excitation intensity, laser frequency spectral profile and cutoff frequency on selective photoionization processes are calculated and compared among the above-mentioned three frequency spectrum models. Finally, the measurement of the laser frequency spectrum and the introduction of individual longitudinal modes’ bandwidths are discussed.