Collisional Approximation Research Articles

The heating phenomenon of a plasma column by electromagnetic wave injection from a semi-bounded waveguide

The plasma heating is studied due to the injection of electromagnetic waves into a semi bounded plasma column. The incident wave is injected from a cylindrical dielectric semi bounded waveguide into the plasma column. The plasma temperature will growth up via the interaction of the electromagnetic waves with the plasma, if the plasma has been considered in collisional approximation. The rate of variations of plasma temperature will be introduced as function of geometry dimensions, the function of incident wave frequency and the function of type of the plasma. To obtain the growth rate of the plasma temperature, the approximated solutions of the wave function should be obtained in two asymptote cases. The first case is, to heating of the needle shape plasma rod and the second is for the thick plasma rod covered by thin dielectric layer. The graphs of plasma temperature growing, respect to the variations of geometrical dimensions, variations of frequency of injected wave and the type of plasma in two these considered cases are investigated.

About the helix plasma antenna: effective factors on characteristics of radiation

ABSTRACT In this paper, a plasma waveguide including a dielectric cover surrounded by metallic helical sheath is investigated as a helix plasma antenna. By solving the wave equation, the components of electric and magnetic fields of hybrid modes for each region is calculated. The collisional approximation for background plasma is used at first and in the second stage a magnetized plasma will be considered as the electromagnetic media in the helical sheath. Applying suitable boundary conditions, the dispersion relation of slow waves in terahertz frequency region is investigated for two configurations mentioned above. Effect of several parameters such as the helix angle, the geometry dimensions, the dielectric constant of dielectric layer, the cyclotron frequency and the plasma frequency on the population of dispersion branches of lower hybrid modes, is investigated. Also, the graphs of normalized radiation power in plasma region to the radiation power in vacuum region are presented.

Modeling of a bimetallic eccentric cylindrical plasma waveguide based on a transmission line for TEM-mode

In this paper, a plasma waveguide made of two eccentric cylindrical metallic walls have been studied according to the theory of transmission lines. The inductance per unit length L, the capacitance per unit length C, the resistance per unit length R and the shunt conductance per unit length G are obtained. The graphs of variations of the mentioned parameters vs. geometrical dimensions of waveguide are investigated. This investigations have been done for two different types of plasma waveguide. At first stage, plasma region will be considered in cold and collisional approximation and in second stage, a drift plasma in cold collisionless approximation will be considered. Also, graphs of phase velocity variation vs. the main parameters of the waveguide are presented.

Hybrid simulations of chromospheric HXR flare sources

AbstractRecent measurements of vertical extents and positions of the chromospheric hard X‐ray (HXR) flare sources based on Ramaty High‐Energy Spectroscopic Imager (RHESSI) observations show a significant inconsistency with the theoretical predictions based on the standard collisional thick target model (CTTM). Using the hybrid flare code Flarix, we model simultaneously and self‐consistently the propagation, scattering and energy losses of electron beams with power‐law energy spectra and various initial pitch‐angle distributions in a purely collisional approximation and concurrently the dynamic response of the heated chromosphere on timescales typical for RHESSI image reconstruction. The results of the simulations are used to model the time evolution of the vertical distribution of chromospheric HXR source within a singular (compact) loop. Adopting the typical RHESSI imaging times scales, energy dependent vertical sizes and positions as could be observed by RHESSI are presented. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Plasma flows in the quiet solar chromosphere-corona transition region

This article is devoted to solving the problem of the plasma temperature distribution along a magnetic tube, one end of which is in the chromosphere, while the other is in the corona. The plasma temperature dependences of the density, pressure, and velocity of plasma are determined for various velocities of the plasma flow, which are given at the lower boundary of the transition region. In the case where gravitation can be neglected, these dependences are derived in the analytical form. The existence of three velocity ranges is demonstrated, for which: (a) the excitation of shock waves in the transition region is possible, (b) the transition region can be considered in the classical collisional approximation, and (c) the plasma heating process is close to the p = const mode and the calculated hard ultraviolet radiation coincides well with modern satellite observations. Based on the obtained results, we concluded that generally in the presence of plasma flows, the quiet transition region between the corona and the chromosphere should be considered in the classical approximation of Coulomb collisions.

Wave-particle interactions in non-uniform plasma and the interpretation of hard X-ray spectra in solar flares

Context. High energy electrons accelerated during solar flare are abundant in the solar corona and in the interplanetary space. Commonly, the number and the energy of non-thermal electrons at the Sun is estimated using hard X-ray (HXR) spectral observations (e.g. RHESSI) and a single-particle collisional approximation. Aims. To investigate the role of the spectrally evolving Langmuir turbulence on the population of energetic electrons in the solar corona. Methods. We numerically simulate the relaxation of a power-law non-thermal electron population in a collisional inhomogeneous plasma including wave-particle, and wave-wave interactions. Results. The numerical simulations show that the long-time evolution of electron population above 20 keV deviates substantially from the collisional approximation when wave-particle interactions in non-uniform plasma are taken into account. The evolution of Langmuir wave spectrum towards smaller wavenumbers, due to large-scale density fluctuations and wave-wave interactions, leads to an effective acceleration of electrons. Furthermore, the time-integrated spectrum of non-thermal electrons, which is normally observed with HXR above 20 keV, is noticeably increased due to acceleration of non-thermal electrons by Langmuir waves. Conclusions. The results show that the observed HXR spectrum, when interpreted in terms of collisional relaxation, can lead to an overestimated number and energy of energetic electrons accelerated in the corona.

Resonance potassium and sodium lines in the spectra of ultracool dwarfs

We discuss the methodological problems and results of computations of the spectral energy distributions (SEDs) of L dwarfs. Over a wide wavelength interval (λλ4000–10 000 A), the spectra of these stars are determined to a considerable extent by absorption in resonance lines of potassium (7666.961, 7701.031 A) and sodium (5891.518, 5897.489 A). We compute the extended wings of these lines using the theory of quasi-stationary broadening. We compute the cores and nearby wings (up to Δλ = 40 A from the line center) of the KI and NaI lines in a collisional approximation (van der Waals theory). In our modeling of the SED of the ultracool dwarf 2MASS J15232263+3014562 (L8), we find that the observations agree best with the COND atmospheric models of Allard et al. with T eff = 2200 K and log g = 6.0.

Time-dependent collisional approximations for two-level systems.

We derive two types of perturbative approximation for the response of collisionally broadened two-level atoms to a time-dependent field. The perturbative approximations for the inversion and polarization are valid to any desired order in the derivatives of the field. Comparison with a numerical solution of the full density-matrix equations of motion demonstrates that the new approximations significantly improve upon the adiabatic-following and collisional steady-state approximations for time-dependent pulses in the appropriate damping regime. Application of the approximations to pulse propagation, sideband instability, and population pulsations is discussed. The collisional steady-state and adiabatic-following approximations find extensive use in many areas of nonlinear optics. The deficiencies of these approximations are well known: The collisional steady-state approxirnation is valid only for monochromatic (cw) radiation and the adiabatic-following approximation is valid only in the absence of damping and only if the product of the detuning and a characteristic time is much larger than one. In spite of their manifest faults, the collisional steady-state and adiabatic-following approximations are often exceptionally good approximations, in the appropriate damping regime, for the local response of a vapor of two-level atoms to a slowly varying field. However, timedependent nonlinear processes modify a propagating field zuch that it varies less slowly and the neglected portions of the atomic response become more important. ' Therefore improved approximations for the damped atomic response to a time-dependent field are desirable. In this paper we present two improved perturbative approximations for the inversion and polarization of collisionally broadened two-level atoms induced by a time-dependent field. The adiabatic-following approximation for two-level systems was derived phenomenologically by Grischkowsky, who used it to explain certain experimental results of near-resonance laser-pulse propagation. Motivated by the work of Grischkowsky, Crisp provided an analytic derivation for the adiabatic-following approximation and obtained a quadrature for the error. The essential feature of Crisp's derivation is the expansion of the kernel of the integral representation of the off-diagonal density-matrix element p2, in a Fourier series with integration proceeding term by term. Both the adiabatic-following approximation and the collisional steady-state approximation were obtained in first order. Both Crisp and Grischkowsky used the adiabatic inversion to derive a correction to the adiabatic-following approximation for the polarization. We have shown how Crisp's method can be extended to obtain corrections to the adiabatic inversion and to improve corrections to the polarization in the absence of damping. In this paper we show how the integrated Fourier series can be used to obtain two types of perturbative approximation for the inversion and polarization of collisionally broadened twolevel systems that are valid to any desired order in the derivatives of the field. The two types of perturbative approximation to the inversion are (i) a formal solution of the rate equation for the inversion which is obtained from the density-matrix equations for the populations; and (ii) an approximation obtained using the approximation (p22 — p») —I — 4p2, P, 2, valid for weak damping. The approximations for the polarization are obtained by substituting either (i) or (ii) for the inversion in the integrated-Fourier-series expansion of p2, . The approximation obtained using the first type of approximate inversion converges most rapidly for strong damping and reduces to the collisional steady-state approximation when the magnitude and phase of the field are constant. The approximation obtained using the second type of approxirnate inversion converges most rapidly for weak damping and in first order reduces to the adiabaticfollowing approximation for zero damping. Comparison with a numerical solution of the density-matrix equations demonstrates that retention of higher-order derivatives by retaining more terms in the integrated Fourier series results in a significant improvement in accuracy for a time-dependent field. However, Rabi oscillations, which can be an important component of the nonlinear response, ' cannot be obtained by finite-order approxi

Fluctuation-dissipation relations. Role of the finiteness of the correlation time. Quantum generalization of Nyquist's formula

The fluctuation-dissipation relations (FDR) in physical systems are studied at all levels of the statistical description. The most general FDR are the relations for the fluctuations of many-body distribution functions. It is pointed out the problem of formulation of FDR is related to the problem of deriving irreversible equations based on the reversible equations of classical and quantum mechanics. The FDR are divided into two classes: 1) FDR for fluctuations with infinite correlation times (collisionless approximation), which correspond to infinitely narrow resonances, and 2) FDR for fluctuations with finite correlation times (collisional approximation). The corresponding spectral densities have finite widths, determined by the collision integrals. The fundamental questions about which different viewpoints have been published in the literature are critically analyzed: 1) the limits of applicability of the Callen-Welton formula and 2) the quantum generalization of Nyquist's formula for the intensity of a Langevin source of oscillatory systems. It is shown that the traditional form of the quantum Nyquist formula, is not well-founded and leads to unphysical consequences. A different expression, used in the literature, for the quantum Nyquist formula is examined. It is not universal, but holds in many important cases. Its region of applicability is determined by the corresponding quantum kinetic equations. The consequences of the two forms of the quantum Nyquist formula, which can be checked experimentally, are studied. The question of the formulation of the quantum Nyquist formula is studied as a part of the general problem of determining the intensity of a Langevin source and the corresponding diffusion coefficient in quantum systems. It arises, in particular, also in quantum electrodynamics in the calculation of the Lamb shift (Sec. 12). In this connection two derivations of Bethe's formula for the Lamb shift are analyzed. It is established that the subtraction formalism of quantum electrodynamics corresponds to the nontraditional form of the quantum Nyquist formula. The exposition is illustrated with many specific examples.