High speed numerical calculation method of rate equations for abruptly recombining plasmas.

Tsuji, Yasumasa; Oda, Toshiatsu; Furukane, Utarou

doi:10.1541/ieejfms1972.107.517

Cited by 4 publications

(4 citation statements)

References 7 publications

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“…To avoid this difficulty, the MQSS approximation was introduced in paper I as follows: Because the system of differential equations, eq. (2.1), in the numerical solution is reduced to a system of difference equations, namely, algebraic equations, when j _ n n i j is sufficiently smaller than the absolute value of each term on the right-hand side for all the levels above a critical level m, the rate equation (2.1) is given approximately by 11,13)…”

Section: Rate Equations Based On Collisional and Radiative Modelmentioning

confidence: 99%

“…In a previous paper, we proposed a modified quasi-steadystate (MQSS) approximation, in which a steady-state approximation is valid in the rate equation for an excited level population above a critical level in order to study the recombination phase in an instantaneously cooled plasma. 11) Here, instantaneously cooled plasma means that a high temperature and high density plasma is abruptly cooled to a sufficiently low electron temperature and afterward the low temperature is maintained constantly. However, real plasmas cannot be instantaneously cooled.…”

Section: Introductionmentioning

confidence: 99%

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Fast Numerical Calculation for a Set of Nonlinear Rate Equations: Application to Rapid Ionizaton Phase in Plasma

Oda¹,

Namba

Takiyama

et al. 2005

Jpn. J. Appl. Phys.

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To make a useful contribution to the development of the compact X-ray laser, a modified quasi-steady-state approximation is applied to the fast numerical calculation of rate equations for the rapid ionization phase of a laser-produced plasma, to which the usual quasi-steady-state model by Bates et al. is not applicable. The set of nonlinear rate equations for the excited level populations coupled with the electron density and temperature for the plasma are numerically calculated with sufficient accuracy for their temporal evolution. The calculation also shows that a suitable combination is possible between the power and pulse width of a heating laser so that a high-density plasma can be obtained as the X-ray laser medium. The mathematical meaning of our approximation is briefly mentioned and its applicability is discussed.

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Section: Rate Equations Based On Collisional and Radiative Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fast Numerical Calculation for a Set of Nonlinear Rate Equations: Application to Rapid Ionizaton Phase in Plasma

Oda¹,

Namba

Takiyama

et al. 2005

Jpn. J. Appl. Phys.

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“…The integration of (1) and (2) was performed by using a high speed numerical method proposed by Tsuji et al [15], using the Runge Kutta method.…”

Section: Simplified Modelmentioning

confidence: 99%

Initial Condition and Cooling Time of Recombining Helium Plasma for Stationary VUV Lasing Action

Furukane

Tsuji

Oda

1988

Zeitschrift Für Naturforschung A

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“…We have performed calculations for three cases shown in table 1. Numerical results are given as a function of time, these being obtained by use of a high-speed method proposed by Tsuji et a1 [28]. The population densities of atoms and ions, the electron density and the electron temperature are obtained by integration with the rate equations and energy balance equations (l), ( 2), ( 3), (8) and with the differential equation derived from the conservation law (5) and ( 6 ) and equation (7).…”

mentioning

confidence: 99%

Simulation of gas-contact cooling for VUV laser oscillation in recombining plasmas

Furukane¹,

Sato²,

Oda³

1989

J. Phys. D: Appl. Phys.

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Possible rapid cooling of a higher temperature plasma is investigated in a gas-contact cooling method in which the effect of finite time for mixing the plasma and the contact gas is considered. The calculation has shown that cooling under these conditions is much more rapid than that achieved by radiative loss cooling and that the gain per unit length of the He II 164 nm line is approximately 2 cm-1 for the laser oscillation under optimum conditions. The possibility of realising a laser at a shorter wavelength in a plasma with higher charge number Z is also discussed.

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High speed numerical calculation method of rate equations for abruptly recombining plasmas.

Cited by 4 publications

References 7 publications

Fast Numerical Calculation for a Set of Nonlinear Rate Equations: Application to Rapid Ionizaton Phase in Plasma

Fast Numerical Calculation for a Set of Nonlinear Rate Equations: Application to Rapid Ionizaton Phase in Plasma

Initial Condition and Cooling Time of Recombining Helium Plasma for Stationary VUV Lasing Action

Simulation of gas-contact cooling for VUV laser oscillation in recombining plasmas

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