Takayuki Utsumi

Stability and accuracy of the Cubic Interpolated Propagation scheme

Abstract We have studied the stability and accuracy of the advection phase calculation of the Cubic Interpolated Propagation scheme, which solves the universal hyperbolic equation. An advection equation with a constant velocity field is examined using Fourier analysis. The results show that the scheme is stable, the group velocity is almost constant, and the gain is near unity for a wide range of wave numbers. The low dissipation and dispersion of the scheme result from an approximation that uses nodal values of both physical quantities and their spatial derivatives.

A numerical method for solving the one-dimensional Vlasov—Poisson equation in phase space

Abstract A new numerical method for solving the one-dimensional Vlasov—Poisson equation in phase space is proposed. The scheme advects the distribution function and its first derivatives in the x and v directions for one time step by using a numerical integration method for ordinary differential equations, and reconstructs the profile in phase space by using a cubic polynomial within a grid cell. The method gives stable and accurate results, and is efficient. It is successfully applied to a number of standard problems; the recurrence effect for a free streaming distribution, linear Landau damping, strong nonlinear Landau damping, the two-stream instability, and the bump-on-tail instability. A method of smoothing filamentation is given. The method can be generalized in a straightforward way to treat the Fokker—Planck equation, the Boltzmann equation, and more complicated cases such as problems with nonperoiodic boundary conditions and higher dimensional problems.

Accurate basis set by the CIP method for the solutions of the Schrödinger equation

In this paper, we propose a basis set approach by the Constrained Interpolation Profile (CIP) method for the calculation of bound and continuum wave functions of the Schrodinger equation. This method uses a simple polynomial basis set that is easily extendable to any desired higher-order accuracy. The interpolating profile is chosen so that the subgrid scale solution approaches the local real solution by the constraints from the spatial derivative of the original equation. Thus the solution even on the subgrid scale becomes consistent with the master equation. By increasing the order of the polynomial, this solution quickly converges. The method is tested on the one-dimensional Schrodinger equation and is proven to give solutions a few orders of magnitude higher in accuracy than conventional methods for the lower-lying eigenstates. The method is straightforwardly applicable to various types of partial differential equations.

Observation of strongly collimated proton beam from Tantalum targets irradiated with circular polarized laser pulses

High-energy protons are generated by focusing an ultrashort pulsed high intensity laser at the Advanced Photon Research Center, JAERI-Kansai onto thin (thickness <10 μm) Tantalum targets. The laser intensities are about 4 × 10 18 W/cm 2 . The prepulse level of the laser pulse is measured with combination of a PIN photo diode and a cross correlator and is less than 10 −6 . A quarter-wave plate is installed into the laser beam line to create circularly polarized pulses. Collimated high energy protons are observed with CH coated Tantalum targets irradiated with the circularly polarized laser pulses. The beam divergence of the generated proton beam is measured with a CR-39 track detector and is about 6 mrad.

High-Precision Measurement of the Wavelength of a Nickel-like Silver X-ray Laser

We conducted high-precision measurements of the wavelength of a 4d1S0→4p1P1 line of a nickel-like silver X-ray laser. The Lyman series lines of hydrogen-like helium ions emitted from low-density plasmas were used as wavelength references, and the wavelength of the X-ray laser line was determined to be 13.887 nm (±0.002 nm). The experimental results were compared with Multiconfiguration Dirac–Fock calculations and were found to agree with theoretical wavelengths.

The gain distribution of the transient collisional excited X-ray lasers

Abstract An atomic kinetics model of an electron collisional excited X-ray laser is developed, and the spatial and temporal evolution of the soft X-ray gain is investigated. The calculation of the gain agrees with experiment for the transient collisional excited (TCE) Ni-like Ag laser ( λ=139 A ) pumped by two 100 ps laser pulses. The mechanism of producing gain in the ionizing plasma is discussed. The calculation is applied to the optimization of the gain. It is found that higher gain can be obtained by pumping a thin foil target with 2 ps laser pulses. The saturation intensity of the X-ray lasers is also investigated through the analysis of the detailed atomic processes of the upper laser level.

Accurate numerical method for the solutions of the Schrödinger equation and the radial integrals based on the CIP method

Abstract A new accurate numerical method based on the constrained interpolation profile (CIP) method to solve the Schrodinger wave equation for bound and free states in central fields and to calculate radial integrals is presented. The radial wave equation is integrated on an arbitrary grid system by the adaptive stepsize controlled Runge–Kutta method controlling the truncation errors within a prescribed accuracy. For the continuum orbitals in the highly oscillating region, the non-linear radial wave equation in the phase-amplitude representation is used. In the evaluation of the derivatives of the radial wave function, the potential energy is approximated by the CIP method. In addition, the radial integrals encountered in the computation of various atomic process are accomplished with the CIP method using the values and their analytical derivatives at the grids. This numerical procedure can be extended in a straightforward way to solve the Dirac wave equation.

Development of a collisional radiative model of X-ray lasers

Abstract A theoretical model of plasma hydrodynamics and atomic kinetics of X-ray lasers is developed to investigate the mechanism of lasing in 4d–4p transition of Ni-like ions at short wavelength by the transient pumping scheme. The model is designed for calculations of the ion abundance and soft X-ray gain in the short pulse laser-irradiated plasmas. We develop a compact collisional radiative model which combines the detailed level structure of Ni-like ion using atomic data calculated by HULLAC, with averaged levels over a wide range of charge states using the screened hydrogenic model. The ion abundance and soft X-ray gain are calculated by postprocessing the temperature and density of the laser-produced plasma obtained by the hydrodynamics code. It is found that a large abundance of Ni-like ion can be maintained in the plasma produced from an exploding foil target showing its usefulness as a gain medium of transient collisional X-ray lasers. For improvement of the model, sensitivity of the gain and averaged charge to the level structure included in the model are discussed.

Numerical analysis of high-gain transient collisional x-ray lasers

We have developed a collisional radiative model of electron collisional excited x-ray lasers. We calculate the ion abundance and soft x-ray gain for the 4d-4p transition of Ni-like multiple charged ion, in short pulse laser irradiated plasmas. We combine a detailed model using the atomic data calculated by HULLAC code and the averaged model based on the screened hydrogenic approximation. In order to choose a proper set of the levels to be included in the atomic model, investigation of the model dependence of the gain is carried out. The population in the fine structure levels in 3d94s and 3d94f configuration, autoionizing double excited configurations of Ni-like and Cu-like ions are found to cause approximately factor of 2 difference in the soft x-ray gain. The steady-state gain and its dependence on plasma density and temperature are investigated over elements from z equals 45 to 65. The time dependent calculation for a plasma condition corresponds to a thin Ag foil irradiated by tow short laser pulse shows the transient gain which is 40 times greater than the steady state gain.

New numerical method for the solutions of the MCDF equations based on the CIP method

Abstract A new numerical method based on the constrained interpolation profile (CIP) method to solve the Multiconfiguration Dirac–Fock (MCDF) equations is presented. The radial wave functions are represented by the values and the spatial derivatives on an arbitrary grid system, and approximated by cubic polynomials. Owing to this representation, the values and the spatial derivatives of the effective charge distribution and inhomogeneous term are calculated using the previous cycles wave functions. Then the homogeneous MCDF equations are integrated to obtain two linearly independent solutions, which are used to construct the Green function, by the adaptive stepsize controlled Runge–Kutta method controlling the truncation errors within a prescribed accuracy. The radial wave function is improved by taking the convolution of the Green function and the inhomogeneous term. The effectiveness of this numerical procedure is investigated after implementing it into the relativistic atomic structure code GRASP92.