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- Combustion theory (2)
- Electromagnetic cascading and generation of trains of few-cycle, relativistically intense pulses in plasmas (1)
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- Microwave heating; Thawing; Stefan problem; Maxwell's equations; Semi-analytical solutions (1)
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- Mode coupling in nonuniform plasmas (1)
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- Reaction-diffusion equations catalytic pellet singularity theory Hopf bifurcations semi-analytical solutions Arrhenius law (1)
- Reaction–diffusion equations; Cubic autocatalysis; Michaelis–Menten kinetics; Singularity theory; Hopf bifurcations; Semi-analytical solutions (1)
- Relativistic plasma wave (1)
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- Stimulated Raman scattering of short laser pulses in plasma channels (linear theory) (1)
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Articles 1 - 6 of 6
Full-Text Articles in Physics
Application Of Detuned Laser Beatwave For Generation Of Few-Cycle Electromagnetic Pulses, Serguei Y. Kalmykov, Gennady Shvets
Application Of Detuned Laser Beatwave For Generation Of Few-Cycle Electromagnetic Pulses, Serguei Y. Kalmykov, Gennady Shvets
Serge Youri Kalmykov
An approach to compressing high-power laser beams in plasmas via coherent Raman sideband generation is described. The technique requires two beams: a pump and a probe detuned by a near-resonant frequency \Omega < \omega_p. The two laser beams drive a high-amplitude electron plasma wave (EPW) which modifies the refractive index of plasma so as to produce a periodic phase modulation of the incident laser with the laser beat period t_b = 2\pi / \Omega. After propagation through plasma, the original laser beam breaks into a train of chirped beatnotes (each of duration t_b). The chirp is positive (the longer-wavelength sidebands are advanced in time) when \Omega < \omega_p and negative otherwise. Finite group velocity dispersion (GVD) of radiation in plasma can compress the positively chirped beatnotes to a few-laser-cycle duration thus creating in plasma a sequence of sharp electromagnetic spikes separated in time by t_b. Driven EPW strongly couples the laser sidebands and thus reduces the effect of GVD. Compression of the chirped beatnotes can be implemented in a separate plasma of higher density, where the laser sidebands become uncoupled.
Stimulated Raman Backscattering Of Laser Radiation In Deep Plasma Channels, Serguei Y. Kalmykov, Gennady Shvets
Stimulated Raman Backscattering Of Laser Radiation In Deep Plasma Channels, Serguei Y. Kalmykov, Gennady Shvets
Serge Youri Kalmykov
Stimulated Raman backscattering (RBS) of intense laser radiation confined by a single-mode plasma channel with a radial variation of plasma frequency greater than a homogeneous-plasma RBS bandwidth is characterized by a strong transverse localization of resonantly driven electron plasma waves (EPW). The EPW localization reduces the peak growth rate of RBS and increases the amplification bandwidth. The continuum of nonbound modes of backscattered radiation shrinks the transverse field profile in a channel and increases the RBS growth rate. Solution of the initial-value problem shows that an electromagnetic pulse amplified by the RBS in the single-mode deep plasma channel has a …
Microwave Thawing Of Cylinders., Tim Marchant
Microwave Thawing Of Cylinders., Tim Marchant
Tim Marchant
Microwave thawing of a cylinder is examined. The electromagnetic field is governed by Maxwell's equations, where the electrical conductivity and the thermal absorptivity are both assumed to depend on temperature. The forced heat equation governs the absorption and diffusion of heat where convective heating occurs at the surface of the cylinder, while the Stefan condition governs the position of the moving phase boundary. A semi-analytical model, which consists of ordinary differential equations, is developed using the Galerkin method. Semi-analytical solutions are found for the temperature, the electric-field amplitude in the cylinder and the position of the moving boundary. Two examples, …
Asymptotic Solitons For A Third-Order Kortweg-De Vries Equation, Tim Marchant
Asymptotic Solitons For A Third-Order Kortweg-De Vries Equation, Tim Marchant
Tim Marchant
Solitary wave interaction for a higher-order version of the Korteweg–de Vries (KdV) equation is considered. The equation is obtained by retaining third-order terms in the perturbation expansion, where for the KdV equation only first-order terms are retained. The third-order KdV equation can be asymptotically transformed to the KdV equation, if the third-order coefficients satisfy a certain algebraic relationship. The third-order two-soliton solution is derived using the transformation. The third-order phase shift corrections are found and it is shown that the collision is asymptotically elastic. The interaction of two third-order solitary waves is also considered numerically. Examples of an elastic and …
Semi-Analytical Solutions For One - And Two-Dimensional Pellet Problems., Tim Marchant
Semi-Analytical Solutions For One - And Two-Dimensional Pellet Problems., Tim Marchant
Tim Marchant
The problem of heat and mass transfer within a porous catalytic pellet in which an irreversible first–order exothermic reaction occurs is a much–studied problem in chemical–reactor engineering. The system is described by two coupled reaction–diffusion equations for the temperature and the degree of reactant conversion. The Galerkin method is used to obtain a semi–analytical model for the pellet problem with both one– and two–dimensional slab geometries. This involves approximating the spatial structure of the temperature and reactant–conversion profiles in the pellet using trial functions. The semi–analytical model is obtained by averaging the governing partial differential equations. As the Arrhenius law …
Cubic Autocatalysis With Michaelis - Menten Kinetics: Semi-Analytical Solutions For The Reaction - Diffusion Cell, Tim Marchant
Cubic Autocatalysis With Michaelis - Menten Kinetics: Semi-Analytical Solutions For The Reaction - Diffusion Cell, Tim Marchant
Tim Marchant
Cubic-autocatalysis with Michaelis–Menten decay is considered in a one-dimensional reaction–diffusion cell. The boundaries of the reactor allow diffusion into the cell from external reservoirs, which contain fixed concentrations of the reactant and catalyst. The Galerkin method is used to obtain a semi-analytical model consisting of ordinary differential equations. This involves using trial functions to approximate the spatial structure of the reactant and autocatalyst concentrations in the reactor. The semi-analytical model is then obtained from the governing partial differential equations by averaging. The semi-analytical model allows steady-state concentration profiles and bifurcation diagrams to be obtained as the solution to sets of …