scholarly journals Scaling laws for pressure, temperature, and ionization with two-temperature equation-of-state effects in laser-produced plasmas

1992 ◽  
Vol 10 (1) ◽  
pp. 23-40 ◽  
Author(s):  
H. Szichman ◽  
S. Eliezer
Keyword(s):  
Equation Of State ◽  
Scaling Laws ◽  
Interpolation Method ◽  
Scaling Law ◽  
Plasma Medium ◽  
Degree Of Ionization ◽  
Ablation Pressure ◽  
Two Temperature ◽  
Temperature Equation ◽  
Thermal Conductivities

A two-temperature equation of state (EOS) for a plasma medium was developed. The cold-electron temperature is taken from semiempirical calculations, while the thermal contribution of the electrons is calculated from the Thomas–Fermi–Dirac model. The ion EOS is obtained by the Gruneisen–Debye solid–gas interpolation method. These EOS are well behaved and are smoothed over the whole temperature and density regions, so that the thermodynamical derivatives are also well behaved. Moreover, these EOS were used to calculate the average ionization 〈Z〉 and 〈Z2〉 of the plasma medium. Furthermore, the thermal conductivities have been calculated with the use of an extrapolation between the conductivities in the solid and plasma (Spitzer) states. The two-temperature EOS, the average ionization 〈Z〉 and 〈Z2〉, and the thermal conductivities for electrons and ions were introduced into a two-fluid hydrodynamic code to calculate the laser-plasma interaction in carbon, aluminum, copper, and gold slab targets. It was found that the two EOS are important mainly from the ablation surface outward (toward the laser). In particular, the creation of cavitons in the distribution of the electrons is predicted here, especially for light materials such as aluminum. These studies enable us also to establish that the commonly used exponential scaling laws of the type Pa = A[I/(1014 W/cm2)]α for the ablation pressure and similar laws for the temperature are valid only for absorbed laser intensities in the range 3 × 1012-3 × 1014 W/cm2, while the degree of ionization (at the corona) follows a quite different scaling law. We also found that the parameters A and α. in the above expression are dependent on material, laser wavelength, and pulse shape. Thus we determined for the ablation pressure, using a trapezoidal Nd laser pulse, that α varies between 0.78 and 0.84 and that A varies between 14 and 8 Mbar for 6 ≤ Z ≤ 79. Beyond the range of validity the scaling laws may give values at least twice as large as those obtained by the simulation.

Two-temperature equation of state for aluminum and gold with electrons excited by an ultrashort laser pulse

2015 ◽  
Vol 119 (3) ◽  
pp. 401-411 ◽  
Author(s):  
Yu. V. Petrov ◽  
K. P. Migdal ◽  
N. A. Inogamov ◽  
V. V. Zhakhovsky
Keyword(s):  
Equation Of State ◽  
Laser Pulse ◽  
Ultrashort Laser Pulse ◽  
Ultrashort Laser ◽  
Two Temperature ◽  
Temperature Equation

scholarly journals Asymmetric Unimodal Maps with Non-universal Period-Doubling Scaling Laws

2020 ◽  
Vol 379 (1) ◽  
pp. 103-143
Author(s):  
Oleg Kozlovski ◽  
Sebastian van Strien
Keyword(s):  
Scaling Laws ◽  
Scaling Law ◽  
Period Doubling ◽  
Cantor Sets ◽  
Unimodal Maps ◽  
Renormalization Theory

Abstract We consider a family of strongly-asymmetric unimodal maps $$\{f_t\}_{t\in [0,1]}$$ { f t } t ∈ [ 0 , 1 ] of the form $$f_t=t\cdot f$$ f t = t · f where $$f:[0,1]\rightarrow [0,1]$$ f : [ 0 , 1 ] → [ 0 , 1 ] is unimodal, $$f(0)=f(1)=0$$ f ( 0 ) = f ( 1 ) = 0 , $$f(c)=1$$ f ( c ) = 1 is of the form and $$\begin{aligned} f(x)=\left\{ \begin{array}{ll} 1-K_-|x-c|+o(|x-c|)&{} \text{ for } x<c, \\ 1-K_+|x-c|^\beta + o(|x-c|^\beta ) &{} \text{ for } x>c, \end{array}\right. \end{aligned}$$ f ( x ) = 1 - K - | x - c | + o ( | x - c | ) for x < c , 1 - K + | x - c | β + o ( | x - c | β ) for x > c , where we assume that $$\beta >1$$ β > 1 . We show that such a family contains a Feigenbaum–Coullet–Tresser $$2^\infty $$ 2 ∞ map, and develop a renormalization theory for these maps. The scalings of the renormalization intervals of the $$2^\infty $$ 2 ∞ map turn out to be super-exponential and non-universal (i.e. to depend on the map) and the scaling-law is different for odd and even steps of the renormalization. The conjugacy between the attracting Cantor sets of two such maps is smooth if and only if some invariant is satisfied. We also show that the Feigenbaum–Coullet–Tresser map does not have wandering intervals, but surprisingly we were only able to prove this using our rather detailed scaling results.

scholarly journals Scaling and Similarity of the Anisotropic Coherent Eddies in Near-Surface Atmospheric Turbulence

2018 ◽  
Vol 75 (3) ◽  
pp. 943-964 ◽  
Author(s):  
Khaled Ghannam ◽  
Gabriel G. Katul ◽  
Elie Bou-Zeid ◽  
Tobias Gerken ◽  
Marcelo Chamecki
Keyword(s):  
Scaling Laws ◽  
Velocity Structure ◽  
Scaling Law ◽  
Longitudinal Velocity ◽  
Structure Functions ◽  
Length Scale ◽  
Near Surface ◽  
Vegetation Canopies ◽  
Velocity Spectra ◽  
Attached Eddies

Abstract The low-wavenumber regime of the spectrum of turbulence commensurate with Townsend’s “attached” eddies is investigated here for the near-neutral atmospheric surface layer (ASL) and the roughness sublayer (RSL) above vegetation canopies. The central thesis corroborates the significance of the imbalance between local production and dissipation of turbulence kinetic energy (TKE) and canopy shear in challenging the classical distance-from-the-wall scaling of canonical turbulent boundary layers. Using five experimental datasets (two vegetation canopy RSL flows, two ASL flows, and one open-channel experiment), this paper explores (i) the existence of a low-wavenumber k−1 scaling law in the (wind) velocity spectra or, equivalently, a logarithmic scaling ln(r) in the velocity structure functions; (ii) phenomenological aspects of these anisotropic scales as a departure from homogeneous and isotropic scales; and (iii) the collapse of experimental data when plotted with different similarity coordinates. The results show that the extent of the k−1 and/or ln(r) scaling for the longitudinal velocity is shorter in the RSL above canopies than in the ASL because of smaller scale separation in the former. Conversely, these scaling laws are absent in the vertical velocity spectra except at large distances from the wall. The analysis reveals that the statistics of the velocity differences Δu and Δw approach a Gaussian-like behavior at large scales and that these eddies are responsible for momentum/energy production corroborated by large positive (negative) excursions in Δu accompanied by negative (positive) ones in Δw. A length scale based on TKE dissipation collapses the velocity structure functions at different heights better than the inertial length scale.

High-pressure–high-temperature equation of state of KCl and KBr

2012 ◽  
Vol 85 (21) ◽  
Author(s):  
A. Dewaele ◽  
A. B. Belonoshko ◽  
G. Garbarino ◽  
F. Occelli ◽  
P. Bouvier ◽  
...  
Keyword(s):  
High Pressure ◽  
High Temperature ◽  
Equation Of State ◽  
High Pressure High Temperature ◽  
Temperature Equation
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