scholarly journals Double layer (DL) formation in laser-produced plasma

1983 ◽  
Vol 1 (3) ◽  
pp. 251-269 ◽  
Author(s):  
Shalom Eliezer ◽  
Ariold Ludmirsky
Keyword(s):  
Heat Flux ◽  
Electric Fields ◽  
Scaling Laws ◽  
Laser Energy ◽  
Scaling Law ◽  
Feedback Mechanism ◽  
High Irradiance ◽  
Laser Produced Plasma ◽  
Temperature Scaling ◽  
Wave Instabilities

It is shown that appropriate conditions for DL formation may be created in laser produced plasma. In particular, a ‘feedback’ mechanism is suggested:Wave instabilities → absorption of laser energy → inward heat flux → DL formation → heat flux inhibition → wave instabilitiesPlasma-target potentials and plasma-currents, produced by Nd. laser intensities (IL) between 1012 to 1015 W/cm2, were measured in situ. These measurements seem to be the first direct evidence of DLs in laser produced plasma. Electric fields of EDL ∼ 5 × 105 to 5 × 106 Volts/cm and widths of 10 to 100 Debye lengths are estimated for the DL.Scaling laws are derived for the measured extremum potentials (V) and currents (I): . Two different slopes were obtained experimentally, one slope equal to α = β = 1·0 for IL < 1014 W/cm2 and another of α = β = 0·4 for IL > 1014 W/cm2. These data are explained for temperature scaling law for the low irradiance and for the high irradiance. While the first scaling law is consistent with inverse bremsstrahlung absorption, the second scaling necessitates other absorption processes. Potential and current probes are suggested as useful devices in detecting wave plasma instabilities.

The origin of fluctuations and cross-field transport in idealized magnetic confinement systems

1981 ◽  
Vol 300 (1456) ◽  
pp. 547-557 ◽  
Keyword(s):  
Electric Fields ◽  
High Frequency ◽  
Scaling Laws ◽  
Scaling Law ◽  
Low Frequency ◽  
Magnetic Confinement ◽  
Upper Bounds ◽  
Transport Processes ◽  
General View ◽  
Long Wavelength

The study of plasma fluctuations and confinement in idealized systems such as octupoles and levitrons has contributed to the understanding of cross-field transport processes. The linear theory of plasma instabilities that cause fluctuations is well developed and can predict growth rates γ and wavelengths θ x around lines of force. However, the theoretical prediction of cross-field transport coefficient D ± is restricted to quasilinear estimates of upper bounds (for example, D = 1 2 γ λ x 2 ) because of the complexity of the full nonlinear calculation. Such quasilinear estimates usually far exceed the measured values and are of limited worth. A general view of the results from octupole and levitron experiments shows that under collisional conditions ( λ ei / L < 0 ) the diffusion coefficient, D , scales in the same way as classical collisional diffusion ( D α n / T e 1 2 B 2 ). Agreement is closely approached in many cases, sometimes even in the presence of fluctuations. Under collisionless conditions ( D α n / T e 1 2 B 2 ), Bohm diffusion scaling ( D α T e / B ) is found in the few cases where the scaling law has been determined. This behaviour is consistent with the general scaling laws of Connor & Taylor (1977) but is not understood in detail. In addition there is evidence, both experimental and theoretical, that long-wavelength low-frequency electric fields (convection cells) can be generated nonlinearly from high-frequency fluctuations and can contribute to cross-field transport

Siphon Flows in Stratified Coronal Loops

1994 ◽  
Vol 144 ◽  
pp. 185-187
Author(s):  
S. Orlando ◽  
G. Peres ◽  
S. Serio
Keyword(s):  
Heat Flux ◽  
Scaling Laws ◽  
Flow Model ◽  
Supersonic Flows ◽  
Coronal Loops ◽  
Characteristic Parameters

AbstractWe have developed a detailed siphon flow model for coronal loops. We find scaling laws relating the characteristic parameters of the loop, explore systematically the space of solutions and show that supersonic flows are impossible for realistic values of heat flux at the base of the upflowing leg.

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.

scholarly journals Interferometric investigations of influence of target irradiation on the parameters of laser-produced plasma jets

2007 ◽  
Vol 25 (3) ◽  
pp. 425-433 ◽  
Author(s):  
A. Kasperczuk ◽  
T. Pisarczyk ◽  
S. Borodziuk ◽  
J. Ullschmied ◽  
E. Krousky ◽  
...  
Keyword(s):  
Focal Spot ◽  
Laser Energy ◽  
Plasma Jet ◽  
Plasma Jets ◽  
Plasma Expansion ◽  
Third Harmonic ◽  
Fundamental Process ◽  
Laser Produced Plasma ◽  
Laser Facility ◽  
Planar Target

Our recent experimental results demonstrate that the formation of plasma jets is a fundamental process accompanying the laser produced plasma expansion, if a massive planar target with relatively high atomic number is irradiated by a defocused laser beam. In this paper some new results on the influence of target irradiation conditions on plasma jet parameters are presented. The experiment was carried out at the PALS iodine laser facility, with the third harmonic beam of the pulse duration of 250 ps (FWHM). The beam energies varied in the range of 13–160 J, the focal spot radii in the range of 35–600 µm. The planar massive targets used in the experiment were made of Cu, Ag and Ta. For measurements of the electron density evolution a three frame interferometric system was employed. The jets were observed in the whole range of the laser energy used. The initial velocities of the plasma jets produced in the reported experiment reached the value of up to 7·107 cm/s, the jets were up to 4 mm long including the jet pedestal and about 400 µm in diameter. Calculations of the efficiency of the plasma jet production show that it decreases with increasing the laser energy.

Scaling laws for stagnant-lid convection with a buoyant crust

2021 ◽  
Vol 228 (1) ◽  
pp. 631-663
Author(s):  
Kyle Batra ◽  
Bradford Foley
Keyword(s):  
Heat Flux ◽  
Scaling Laws ◽  
Thermal Evolution ◽  
Crustal Thickness ◽  
Plate Motion ◽  
Crustal Layer ◽  
Lithospheric Thickness ◽  
Thin Crust ◽  
Mantle Temperature ◽  
Thick Crust

SUMMARY Stagnant-lid convection, where subduction and surface plate motion is absent, is common among the rocky planets and moons in our solar system, and likely among rocky exoplanets as well. How stagnant-lid planets thermally evolve is an important issue, dictating not just their interior evolution but also the evolution of their atmospheres via volcanic degassing. On stagnant-lid planets, the crust is not recycled by subduction and can potentially grow thick enough to significantly impact convection beneath the stagnant lid. We perform numerical models of stagnant-lid convection to determine new scaling laws for convective heat flux that specifically account for the presence of a buoyant crustal layer. We systematically vary the crustal layer thickness, crustal layer density, Rayleigh number and Frank–Kamenetskii parameter for viscosity to map out system behaviour and determine the new scaling laws. We find two end-member regimes of behaviour: a ‘thin crust limit’, where convection is largely unaffected by the presence of the crust, and the thickness of the lithosphere is approximately the same as it would be if the crust were absent; and a ‘thick crust limit’, where the crustal thickness itself determines the lithospheric thickness and heat flux. Scaling laws for both limits are developed and fit the numerical model results well. Applying these scaling laws to rocky stagnant-lid planets, we find that the crustal thickness needed for convection to enter the thick crust limit decreases with increasing mantle temperature and decreasing mantle reference viscosity. Moreover, if crustal thickness is limited by the formation of dense eclogite, and foundering of this dense lower crust, then smaller planets are more likely to enter the thick crust limit because their crusts can grow thicker before reaching the pressure where eclogite forms. When convection is in the thick crust limit, mantle heat flux is suppressed. As a result, mantle temperatures can be elevated by 100 s of degrees K for up to a few Gyr in comparison to a planet with a thin crust. Whether convection enters the thick crust limit during a planet’s thermal evolution also depends on the initial mantle temperature, so a thick, buoyant crust additionally acts to preserve the influence of initial conditions on stagnant-lid planets for far longer than previous thermal evolution models, which ignore the effects of a thick crust, have found.

Polymerization of Isobutylene Initiated by Laser Vaporization of Metal Targets

1992 ◽  
Vol 285 ◽  
Author(s):  
Walter Vann ◽  
George M. Daly ◽  
M. Samy El-shall
Keyword(s):  
Electric Fields ◽  
Laser Energy ◽  
Second Harmonic ◽  
Polymeric Materials ◽  
Reaction Chamber ◽  
Laser Vaporization ◽  
Viscous Liquids ◽  
Molecular Weights ◽  
Full Characterization ◽  
Powerful Approach

ABSTRACTA novel technique involving the initiation of polymerization using laser vaporization of metal targets is being explored. In the experiment, metal ions such as Ti+, Zr+, Ag+ are generated in the gas phase by pulsed laser vaporization/ionization of a metal target using the second harmonic of a Nd:YAG laser (532 nm). The ions are pulled toward a monomer liquid(isobutylene which can only be polymerized by cationic mechanisms) by applyingappropriate electric fields across the reaction chamber. Under different experimentalconditions (temperature, pressure of a carrier gas, laser energy, electric field strength, reaction time) different polymeric products (viscous liquids or solids) were obtained with average molecular weights ranging from 200 to greater than 106. Full characterization of these materials is currently in progress. This technique could lead to a powerful approach for the synthesis of a wide variety of polymeric materials with unique properties such as stability, strength and photo and electrical conductivity.

scholarly journals Origin of the scaling laws of sediment transport

2017 ◽  
Vol 473 (2197) ◽  
pp. 20160785 ◽  
Author(s):  
Sk Zeeshan Ali ◽  
Subhasish Dey
Keyword(s):  
Sediment Transport ◽  
Froude Number ◽  
Scaling Laws ◽  
Scaling Law ◽  
Bedload Transport ◽  
Inertial Range ◽  
Channel Width ◽  
Densimetric Froude Number ◽  
Relative Roughness ◽  
Contraction Ratio

In this paper, we discover the origin of the scaling laws of sediment transport under turbulent flow over a sediment bed, for the first time, from the perspective of the phenomenological theory of turbulence. The results reveal that for the incipient motion of sediment particles, the densimetric Froude number obeys the ‘(1 +  σ )/4’ scaling law with the relative roughness (ratio of particle diameter to approach flow depth), where σ is the spectral exponent of turbulent energy spectrum. However, for the bedforms, the densimetric Froude number obeys a ‘(1 +  σ )/6’ scaling law with the relative roughness in the enstrophy inertial range and the energy inertial range. For the bedload flux, the bedload transport intensity obeys the ‘3/2’ and ‘(1 +  σ )/4’ scaling laws with the transport stage parameter and the relative roughness, respectively. For the suspended load flux, the non-dimensional suspended sediment concentration obeys the ‘ − Z ’ scaling law with the non-dimensional vertical distance within the wall shear layer, where Z is the Rouse number. For the scour in contracted streams, the non-dimensional scour depth obeys the ‘4/(3 −  σ )’, ‘−4/(3 −  σ )’ and ‘−(1 +  σ )/(3 −  σ )’ scaling laws with the densimetric Froude number, the channel contraction ratio (ratio of contracted channel width to approach channel width) and the relative roughness, respectively.

scholarly journals Scaling laws and warning signs for bifurcations of SPDEs

2018 ◽  
Vol 30 (5) ◽  
pp. 853-868
Author(s):  
CHRISTIAN KUEHN ◽  
FRANCESCO ROMANO
Keyword(s):  
Differential Equations ◽  
Scaling Laws ◽  
Scaling Law ◽  
Warning Signs ◽  
Covariance Operator ◽  
Large Classes ◽  
Practical Applications ◽  
Critical Transitions ◽  
Degenerate Eigenvalues ◽  
Adjoint Operators

Critical transitions (or tipping points) are drastic sudden changes observed in many dynamical systems. Large classes of critical transitions are associated with systems, which drift slowly towards a bifurcation point. In the context of stochastic ordinary differential equations, there are results on growth of variance and autocorrelation before a transition, which can be used as possible warning signs in applications. A similar theory has recently been developed in the simplest setting for stochastic partial differential equations (SPDEs) for self-adjoint operators in the drift term. This setting leads to real discrete spectrum and growth of the covariance operator via a certain scaling law. In this paper, we develop this theory substantially further. We cover the cases of complex eigenvalues, degenerate eigenvalues as well as continuous spectrum. This provides a fairly comprehensive theory for most practical applications of warning signs for SPDE bifurcations.

Scaling Laws From Statistical Data and Dimensional Analysis

2004 ◽  
Vol 72 (5) ◽  
pp. 648-657 ◽  
Author(s):  
Patricio F. Mendez ◽  
Fernando Ordóñez
Keyword(s):  
Dimensional Analysis ◽  
Scaling Laws ◽  
Ad Hoc ◽  
Scaling Law ◽  
Engineering Systems ◽  
User Input ◽  
Backward Elimination ◽  
Dimensionless Groups ◽  
Complex Engineering ◽  
Complex Engineering Systems

Scaling laws provide a simple yet meaningful representation of the dominant factors of complex engineering systems, and thus are well suited to guide engineering design. Current methods to obtain useful models of complex engineering systems are typically ad hoc, tedious, and time consuming. Here, we present an algorithm that obtains a scaling law in the form of a power law from experimental data (including simulated experiments). The proposed algorithm integrates dimensional analysis into the backward elimination procedure of multivariate linear regressions. In addition to the scaling laws, the algorithm returns a set of dimensionless groups ranked by relevance. We apply the algorithm to three examples, in each obtaining the scaling law that describes the system with minimal user input.

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