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  • 1
    Electronic Resource
    Electronic Resource
    A hierarchy of empirical models of plasma profiles and transport (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 2 (1995), S. 1614-1622 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Two families of statistical models of increasing statistical complexity are presented that generalize global confinement expressions to plasma profiles and local transport coefficients. The temperature or diffusivity is parameterized as a function of the normalized flux radius, ψ¯, and the engineering variables, u=(Ip,Bt,n¯,q95)°. The log-additive temperature model assumes that ln[T(ψ¯,u)] =f0(ψ¯)+fI(ψ¯)ln[Ip] +fB(ψ¯)ln[Bt] +fn(ψ¯)ln[n¯]+fq ln[q95]. The unknown fi(ψ¯) are estimated using smoothing splines. The Rice selection criterion is used to determine which terms in the log-linear model to include. A 43 profile Ohmic dataset from the Joint European Torus [P. H. Rebut, et al., Nucl. Fusion 25, 1011 (1985)] is analyzed and its shape dependencies are described. The best fit has a predictive error of 153 eV, which is 10.5% percent of the typical line average temperature. The average error is less than the estimated measurement error bars. The second class of models is log-additive diffusivity models, where ln[χ(ψ¯,u)]=g0(ψ¯) +gI(ψ¯)ln[Ip]+gB(ψ¯)ln[Bt]+gn (ψ¯)ln[n¯]. These log-additive diffusivity models are useful when the diffusivity varies smoothly with the plasma parameters. A penalized nonlinear regression technique is recommended to estimate the gi(ψ¯). The physics implications of the two classes of models, additive log-temperature models and additive log-diffusivity models, are different. The additive log-diffusivity models adjust the temperature profile shape as the radial distribution of sinks and sources. In contrast, the additive log-temperature model predicts that the temperature profile depends only on the global parameters and not on the radial heat deposition. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.871311
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  • 2
    Electronic Resource
    Electronic Resource
    Absorption of nearly perpendicularly propagating waves in the second harmonic layer (1985)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 1757-1765 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Propagation of waves nearly perpendicular to the equilibrium magnetic field and incident to the second electron-cyclotron harmonic layer is investigated in an inhomogeneous weakly relativistic plasma. The resonance region is treated by a boundary layer analysis, and the solutions are matched to the geometrical optics solutions outside the layer. This approach allows one to investigate the transmission, mode coupling, reflection, absorption, and the effects of relativistic broadening. This work extends a previous investigation with the purely perpendicular propagation. It is shown that the mode conversion and reflection rapidly cease to be of importance outside a narrow propagation cone as the doppler broadening becomes predominant. The geometrical optics approach, which breaks down in the purely perpendicular propagation, then becomes valid. It is also shown that the transmission coefficient and the reflection from the high-field side incidence are not altered within this cone.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.864917
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  • 3
    Electronic Resource
    Electronic Resource
    Applicability of the geometrical optics at the high electron cyclotron harmonics (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 1334-1336 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Nearly perpendicular wave propagation across the Nth electron cyclotron harmonic layer in a weakly inhomogeneous plasma is investigated. It is shown that, when N〉2, unlike the case for N≤2, the relativistic corrections and the mode conversion to Bernstein waves do not alter the current density to the lowest significant order in the expansion parameter, which is the ratio of the electron thermal speed to the speed of light. Thus, when N〉2, the geometrical optics method should be applicable in this case, and hence at all angles of incidence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865885
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  • 4
    Electronic Resource
    Electronic Resource
    Nearly perpendicular wave propagation at the fundamental electron-cyclotron resonance (1985)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 3572-3580 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Waves propagating nearly perpendicular to the equilibrium magnetic field across the fundamental cyclotron resonance layer are studied by a boundary layer analysis for a weakly relativistic, inhomogeneous Vlasov plasma. The plasma is assumed to be perpendicularly stratified. It is found that the wave energy associated with the ordinary mode transmitted through the layer is independent of the relativistic corrections and is given by a geometrical optics formula. It is also found that there is no reflected energy associated with this mode when it is incident from the high-field side. These results are the same as the nonrelativistic case with purely perpendicular propagation. Relativistic effects produce a significant reduction of the reflection coefficient for low-field side incidence from the nonrelativistic value. Correspondingly, for this mode there is a considerable increase in the absorption rate for sufficiently high, but moderate, electron density and temperature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865312
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  • 5
    Electronic Resource
    Electronic Resource
    Absorption of waves in the second harmonic resonance layer (1985)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 133-144 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Absorption caused by relativistic broadening of quasiperpendicular incident waves within the second cyclotron harmonic layer is investigated in an inhomogeneous electron plasma. The resonance region is treated by a boundary layer analysis, and field equations valid in this region are derived by solving the rescaled (with respect to the parameter η which is the ratio of the thermal speed and the speed of light) linearized relativistic Vlasov equation. The geometrical optics solutions valid in the nonresonant region are evaluated near the resonance, and they are connected to the asymptotic forms of the inner solutions. The energy conservation theorems appropriate for this problem allow the evaluation of fractional transmitted and reflected energy, and thus distinguish between the energy mode converted to the quasielectrostatic (relativistic Bernstein) mode and that absorbed by the plasma (which does not exist for the purely perpendicular propagation and nonrelativistic case). Numerical methods are developed which enable one to handle the computation of the excessively stiff differential equations in the high-field side. The three fundamental scattering problems are then evaluated numerically for various values of electron density and the product of electron temperature and scale length for the variation of the magnetic field for the case of perpendicular propagation. It is found that, unlike the mode coupling, the transmission of the X mode is not affected by the relativistic corrections. In the case of high-field side incidence, the reflection is still zero as predicted in the nonrelativistic approach. However, in contrast to the zero absorption in the nonrelativistic case, there is significant absorption caused by relativistic broadening, particularly in the case of low-field side incidence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865173
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  • 6
    Electronic Resource
    Electronic Resource
    Diffusion control in radiation graft polymerization with varying dependence of rate on monomer concentration (1976)
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Chemistry Edition 14 (1976), S. 3045-3066 
    Details
    ISSN: 0360-6376
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The quantitative effect of diffusion control on the rate of radiation-initiated graft polymerization has been studied theoretically for systems in which the diffusion-free reaction may show various dependencies of rate on monomer concentration other than the usual first-order dependence. The study is also very general in that it can be applied to systems involving a variety of different modes of initiation and termination. Whether the grafting process is diffusion-free or diffusion-controlled has been analyzed in terms of the interaction of the initiation rate Ri, the propagation and termination rate constants kp and kt, the equilibrium solubility M of the monomer in the polymer, the polymer film thickness L, the diffusivity D of the monomer in the polymer, and the diffusion-free kinetic order of dependence v of the grafting rate on monomer concentration. The dependence of the grafting rate for both the diffusion-free and diffusion-controlled reactions on these parameters is expressed both by mathematical experssions and graphically. Diffusion control is shown to occur at a critical value of the parameter A which is proportional to L(kpRiw/ktzD)1/2M(ε-1)/2 where w, z, and v have different values depending on the specific modes of initiation, propagation and termination in a particular grafting system. The grafting rate is shown to vary with the value of A according to specific mathematical expressions. In comparing diffusion-free to diffusion-controlled reaction, it is shown that the former is independent of L and D while the latter is directly dependent on L and inversely on D1/2. Further, the change from diffusion-free to diffusion-controlled reaction involves a change in the dependence of rate on monomer from v-order to [(v - 1)/2]-order. The nonsteady-state as well as the steady-state reaction rates have been analyzed.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1976.170141218
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  • 7
    Electronic Resource
    Electronic Resource
    A quick method for determining the diffusion coefficient for polymer-monomer systems from desorption data (1980)
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Chemistry Edition 18 (1980), S. 1647-1650 
    Details
    ISSN: 0360-6376
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1980.170180527
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  • 8
    Electronic Resource
    Electronic Resource
    Diffusion-controlled reaction. V. Effect of concentration-dependent diffusion coefficient on reaction rate in graft polymerizationFor previous articles in this series, see refs. 1-4. (1979)
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Chemistry Edition 17 (1979), S. 2601-2626 
    Details
    ISSN: 0360-6376
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The effect of diffusion on radiation-initiated graft polymerization has been studied with emphasis on the single- and two-penetrant cases. When the physical properties of the penetrants are similar, the two-penetrant problem can be reduced to the single-penetrant problem by redefining the characteristic parameters of the system. The diffusion-free graft polymerization rate is assumed to be proportional to the v power of the monomer concentration C, in which the proportionality constant a = kpRiw/ktz, where kp and kt are the propagation and termination rate constants, respectively, and Ri is the initiation rate. The values of v, w, and z depend on the particular reaction system. The results of our earlier work were generalized by allowing a non-Fickian diffusion rate, obtained from an extension of the Fujita free-volume theory, which predicts an essentially exponential dependence on the monomer concentration of the diffusion coefficient, D = D0 [exp(δC/M)], where M is the saturation concentration. It was shown that a reaction system is characterized by the three dimensionless parameters v, δ, and A = (L/2)[aM(v-1)/D0]1/2, where L is the polymer film thickness. Graft polymerization tends to become diffusion controlled as A increases. Larger values of δ and v cause a reaction system to behave closer to the diffusion-free regime. The transition from diffusion-free to diffusion-controlled reaction involves changes in the dependence of the reaction rate on film thickness, initiation rate, and monomer concentration. Although the diffusion-free rate is w order in initiation rate, v order in monomer, and independent of film thickness, the diffusion-controlled rate is w/2 order in initiator rate and inverse first-order in film thickness. The dependence of the diffusion-controlled rate on monomer is dependent in a complex manner on the diffusional characteristics of the reaction system.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1979.170170832
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  • 9
    Electronic Resource
    Electronic Resource
    Diffusion-controlled reaction. VI. Radiation graft polymerization of 4-vinylpyridine to polyethylene (1980)
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Chemistry Edition 18 (1980), S. 737-748 
    Details
    ISSN: 0360-6376
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The radiation-initiated graft polymerization of 4-vinylpyridine to high-density polyethylene was studied over a wide range of reaction conditions of radiation intensity I, monomer concentration M1, and polymer film thickness L. The conditions included both diffusion-free and diffusion-controlled graft polymerizations. The results corroborate our previous theoretical predictions on the effect of I, M1, and L on the experimental grafting rate. The grafting rate is inverse first order in L for diffusion-controlled reaction and independent of L for diffusion-free reaction. The dependence of grafting rate on radiation intensity decreases from 1/2 to 1/4 order for diffusion-controlled reaction. Diffusion control results in a decrease in the dependence of rate on monomer concentration. The observed decrease is somewhat greater than theoretically predicted.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1980.170180233
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  • 10
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    Neutron diffusion in a randomly inhomogeneous multiplying medium with random phase approximation (2012)
    American Institute of Physics
    Details
    Publication Date: 2012-06-01
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
    Published by American Institute of Physics
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