Parabolic Density Research Articles

Propagation characteristics of obliquely incident THz waves in inhomogeneous fully ionized dusty plasma using the scattering matrix method

The scattering matrix method is applied to investigate the propagation characteristics of obliquely incident terahertz (THz) waves in inhomogeneous fully ionized dusty plasma. The propagation coefficients of THz waves are analyzed with different physical parameters in the case of parabolic electron density distribution. The results show that the transmissivity of lower frequency THz waves have a noticeable variation with the change of physical parameters. However, the transmissivity values can rapidly approach 1 in higher frequency band. We notice that there is a critical value fc≈0.045 THz. When f>fc, the transmissivity increases as the dust particles density and radius increase. However, it is somewhat opposite when f<fc. Significantly, the THz waves exhibit a greater propensity for penetrating fully ionized dusty plasma compared with the weakly ionized dusty plasma. To a certain degree, the investigation results provide new ideas for addressing the issue of “blackout”.

Numerical model for linear stimulated Raman scattering in inhomogeneous plasmas

Numerical model for calculating convective gains and absolute thresholds of stimulated Raman scattering (SRS) in inhomogeneous plasmas is constructed based on the Fourier-space method. The model is valid for arbitrary density profiles and scattering geometries, including both backscattering and side scattering. It is shown that 90 deg side scatter has a lower absolute threshold than other scattering geometries. Backscatter, on the other hand, has a relatively large absolute threshold under conventional direct-drive ignition conditions. For a parabolic density profile, the absolute threshold of backscatter decreases dramatically at the peak of parabola, but is still much larger than that of side scatter. We also discuss the absolute thresholds of side scatter under different density profiles, showing not big differences with the linear density profile as well as the analytic formulas. Convective gains, however, are sensitive to the density profiles and collisional damping. The k-space numerical model is verified via analytic formulas and real-space envelope model, and it offers us new perspective on the scattering angles compared with previous models for SRS.

Multipaths’ statistics for scatterers with inverted elliptic–parabolic spatial density around the mobile

The joint and marginal probability densities of multipaths’ angles-of-arrival (AOA) and times-of-arrival (TOA) at the cellular base station are developed in closed form in this paper. Unlike the general simplification assumption in the open literature in which the scatterers are assumed to be located in a circular region for non-uniform spatial densities, the scatterers in this paper are assumed to be located in an elliptical region to properly model the elliptical footprint around the mobile station from the elevated base station with directional antenna. The inverted elliptic–parabolic spatial density was adopted to model the non-uniform distribution of the scatterers around the mobile. The uplink’s AOA–TOA joint distributions, AOA and TOA marginal distributions were analytically derived in closed form. How the eccentricity of the elliptical scatterer region affects the probability density functions is discussed. Furthermore, the derived AOA marginal distribution is compared to that of the elliptic conic and inverted parabolic models. The proposed model is shown to have better least-squares fit to some empirical AOA data compared to the elliptic conic and inverted parabolic models.

On Frequency/Time Invariance of Certain Temporal and Complex Transfer Functions for the One-Dimensional Interfacial Monochromatic Neutron Density Wave

Abstract Optimization of dynamical multibeam neutron cancer therapy has recently been shown to be possible via employment of the beam frequencies of neutron waves as a control variable. The concepts of transfer functions (TF), addressed in this paper, can be essential ingredients of such optimization. Accordingly, the paper studies the dynamics of a one-dimensional (1D) monochromatic neutron density wave generated by time modulation of a boundary neutron current. It is demonstrated that a certain temporal transfer function (TTF) of both parabolic (diffusion) and low frequency hyperbolic (P−1 transport) interfacial neutron density wave happens to be frequency noninvariant with a vibrating boundary neutron current. It is proved that, only at high frequencies, both parabolic and hyperbolic interfacial neutron waves turn out to have a fully frequency-invariant and time-invariant temporal transfer function relative to such a vibrating neutron beam at the boundary. The frequency response of an associated complex transfer function is studied and demonstrated to change behavior, from a lag compensator to a fixed gain amplifier, with changing the frequency, neutron absorption and employed theory for neutron diffusion. A highlight of this paper is its illustration that mere continuity of these transfer functions can be a reflection of the correctness of the transport theory employed for modeling the neutron density waves.

Generalized Gauss-FFT 3D forward gravity modeling for irregular topographic mass having any 3D variable density contrast

A fully numerical forward model for estimating gravity anomalies in the Fourier domain is presented for irregular topographic mass distributions. Modified Parker’s formula using the Gauss-FFT method is utilized for getting better accuracy than the standard FFT algorithm. Existing frequency domain forward modeling for topographic surfaces uses common analytically derivable density functions for evaluating gravity anomalies. But in the real scenario, subsurface mass distributions can take any functional form of depth. Our presented algorithm provides a generalized approach for evaluating forward gravity anomalies due to any horizontal and vertical variation of density distributions. The computational cost depends on the irregularities of the topographic surfaces and the complexity of the functional form of density distributions. The presented algorithm is compared with analytical solutions and space domain prismatic model approximation. A complex, analytically non-integrable density distribution was also considered and compared with the space domain model. The presented algorithm accurately estimates gravity anomalies in all cases, and the results are close to the space domain prismatic model. Finally, an observed gravity anomaly of the real sedimentary basin and its corresponding inverted basement depth for parabolic density variation is considered to evaluate forward anomalies using our presented algorithm. The estimated gravity anomalies provide close approximations to observed gravity anomalies, revealing the proposed algorithm’s reliability for any 3D topographic forward modeling.

Asymptotic Behavior of the Solution of Doubly Degenerate Parabolic Equations with Inhomogeneous Density

In this paper we study the large time behaviour for solutions to the Cauchyproblem for degenerate parabolic equations with inhomogeneous density.Under the suitable assumptions on the data of the problem and on the behaviour of the densityat infinity we establish new sharp bound of solutions for a large time.One of the main tool of the proof is new weighted embedding result whichis of independent interest. In addition, the proof of uniform estimatesof the solution is carried out by modified version of the classical methodof De-Giorgi--Ladyzhenskaya--Uraltseva--DiBenedetto. Similar resultsin the case of power-like density was obtained by one of the author~[10].The approach of this work can be applied for example when studying the qualitativeproperties of solutions to the Neumann problem for a doubly nonlinear parabolic equationwith inhomogeneous density in domains with non-compact boundaries.

Thermoelectric Coefficients Of Heavily Doped N-Type Silicon

In this study the thermoelectric effect is investigated in terms of thermoelectric power, Figure of merit(ZT), and power factor. The calculations were carried out based on Boltzmann transport equation by taking ionized impurity scattering as a dominant mechanism for heavily doped n-type silicon at 300K with charge concentration varies from 2×1018 /cm3 – 20×1020 /cm3. It is known that doping of materials can induce Fermi level shifts and doping can also induce changes of the transport mechanisms. The result of this study shows doping also induces changes in thermoelectric power, Figure of merit, and power factor. The magnitude of the change is different for consideration of parabolic density of states and non-parabolic modified density of states which amounts to 16.7% for thermoelectric power, from 0.059% - 84.1% for Figure of merit(ZT) in favor of non-parabolic consideration respectively. There is also a difference of 39.9% for power factor with respect to relaxation time between the two cases in favor of the parabolic consideration.

Design and characterization of a single-channel microwave interferometer for the Helicon Physics Prototype eXperiment

A heterodyne interferometer for measuring the plasma electron density in Helicon Physics Prototype eXperiment (HPPX) has been developed and characterized in the laboratory. The heterodyne-type interferometer uses a probing beam of 85 GHz and a reference beam of 85.7 GHz by using two Gunn oscillators for facilitating frequency modulation. The cutoff density for this frequency is 8.96×1019 m−3 that is much higher than the nominal electron density of the HPPX plasmas. The maximum deflection angle due to the refraction effect is estimated to be 0.63° assuming a parabolic electron density profile, and the impact on the measurement is negligible for the plasmas with a size of 100 mm. Two identical HDPE lenses act as the vacuum windows, and the lenses working together with the transmitter and receiver horns, form a beam with the beam waist of about 20 mm located at the plasma center. The characterization results of the lens and the critical microwave components show good performance. The plasma electron density measurement results are in line with the expectation. Furthermore, the Signal to Noise Ratio (SNR) of the measurement is defined as SNR=20lg(n¯e/S), where n¯e and S are respectively the average electron density and the standard deviation of the signal, and the SNR is 80 dB. This demonstrates the system's capability of providing a clear and detailed density resolution.

Disorder-induced Anderson-like localization for bidimensional thermoelectrics optimization

Disorder-induced Anderson-like localization for bidimensional thermoelectrics optimization

Output tracking for a radiative density optical communication system with unknown disturbance

This paper deals with boundary tracking problem for a radiative density parabolic equation (RDE) coming from an optical communication system. First, the radiative intensity is modeled by a radiative transfer equation (RTE). The idea of this work is to use the fact that the signal sent by the laser beam is collimated in consideration of the radiative density flux. Therefore, the control problem of the RTE model is transformed into a boundary control for an RDE based on the time-dependent SPN approximation. Then, we investigate a boundary output tracking problem of one dimensional parabolic density equation where the unknown disturbance enters the system from one part of the boundary. By utilizing one side boundary measurement, we construct an extended state observer to estimate the system state and the external disturbance. An output feedback boundary control is then designed using the states of the servo system and observer. It is shown that the closed-loop system and the control are uniformly bounded with output being tracking the reference and the closed-loop is internally exponentially stable. The numerical simulations are presented to illustrate the effectiveness of the proposed output feedback method.

Low jitter parabolic profile low density plasma channel in 3D printed gas filled capillary

A parabolic profile plasma channel formed by an electric discharge inside a gas filled capillary are currently used to achieve optimal conditions for laser guiding and electron acceleration. Acceleration of high quality externally injected electron beam by laser induced wake field requires precise synchronization between several systems. In our experiment the measured jitter in plasma ignition was on the scale of 1 ns, providing possibility for the synchronization with high intensity laser and other auxiliary systems (e.g injectors). We confirmed the existence of a parabolic density plasma profile inside the capillary using an 84 MHz oscillator laser and found its duration to be approximately 300 ns.

Acceleration of electrons by a lower hybrid wave in a magnetic mirror

In the present study, a theory of electron acceleration by a very large-amplitude lower hybrid wave (LHW) in a magnetic mirror having frequency less than the plasma frequency is developed. The LHW has a Gaussian mode profile and is localized due to the parabolic plasma density and the magnetic field profile. The mode can be excited by launching an electron beam from outside into the magnetic mirror. Large-amplitude LWHs have potential to axially trap the electrons when they are moving nearly parallel to the phase velocity, where parallel refers to the direction of the axial magnetic field. The energy of the electrons is enhanced at the instant of interaction between the wave and the electrons. The acceleration of electrons possibly stops as the electrons gets out of phase with the wave. The transverse field of the mode favors stronger mirror confinement and increases the dephasing length. This theory can accelerate electrons up to keV energies and can be employed in the heating of electrons in a magnetic mirror.

Stimulated Raman Scattering of X-Mode Laser in a Plasma Channel

Stimulated Raman forward scattering (SRFS) of an intense X-mode laser pump in a preformed parabolic plasma density profile is investigated. The laser pump excites a plasma wave and one/two electromagnetic sideband waves. In Raman forward scattering, the growth rate of the parametric instability scales as two-third powers of the pump amplitude and increases linearly with cyclotron frequency.

Opposite Behaviors of Short Laser-Pulses as Moving Solitons in Fully-Relativistic Plasma Channels

Assuming a circularly polarized Gaussian laser pulse propagating in a plasma channel with a parabolic density profile, an effective potential and the evolution equation of the laser spot size with ...

Direct refractive index retrieval from interferometry measurements.

We present an alternative numerical method to the Abel inversion technique, which can be applied to complex non-symmetrical systems. A comparison with the Abel inversion algorithm was conducted. For benchmarking, the method was applied to a synthetic trace representing a plasma waveguide characterized by a constant parabolic density profile. Furthermore, the temperature and refractive index of a plume of hot air surrounding a non-cylindrical soldering iron were retrieved. Temperatures between 50 °C and 200 °C were successfully retrieved within the instrument precision. The proposed method allows robust and fast data retrieval while maintaining the accuracy and resolution of well-known methods, as Abel inversion.

Lax pair, conservation laws, Darboux transformation, breathers and rogue waves for the coupled nonautonomous nonlinear Schrödinger system in an inhomogeneous plasma

Abstract Plasmas are believed to be possibly “the most abundant form of ordinary matter in the Universe”. In this paper, a coupled nonautonomous nonlinear Schrodinger system is investigated, which describes the propagation of two envelope solitons in a weakly inhomogeneous plasma with the t-dependent linear and parabolic density profiles and nonconstant collisional damping. Lax pair with the nonisospectral parameter and infinitely-many conservation laws are derived. Based on the Lax pair, the Nth-step Darboux transformation is constructed. Utilizing the Nth-step Darboux transformation, we obtain the breather and rogue wave solutions, and find that the amplitude of the nonzero background is nonconstant and dependent on the inhomogeneous coefficients in the system under investigation. Characteristics of the breathers and rogue waves are discussed, and effects of the inhomogeneous coefficients on the breathers and rogue waves are analyzed. Breathers and rogue waves with the dark or bright soliton together are also constructed and their characteristics are discussed. We find that the dark and bright solitons can coexist and generate the breather-like waves.

Zemax ray tracing model for plasma waveguides

Plasma-based waveguides are currently employed for laser wakefield acceleration to extend the focal region of laser beams. A parabolic transverse plasma density profile, suitable for laser guiding, can be established in a dielectric capillary as a consequence of a discharge in gas. In this work, we report on a new ray tracing model, based on the Zemax software, able to simulate the envelope of a laser beam propagating through a plasma waveguide. The potentialities offered by Zemax in terms of geometries and materials and the possibility to create custom objects do allow the simulation of complex and various scenarios, as for example curved plasma waveguides.

Gravity gradient tensor of a vertical pyramid model of flat top and bottom with depth-wise parabolic density variation

As an alternative to the popular rectangular parallelepiped model, we have developed a novel 3D analytical forward-problem solution for the gravity gradient tensor of a vertical pyramid model with parabolic density contrast variation. Its flexibility and effectiveness are demonstrated with the help of synthetic simulations and a case study involving Chintalapudi subbasin, India. We have addressed the singularities and numerical stability in numerical implementation of our algorithm for modeling and practical implementation.

Correction to: A Core-Envelope Massive Distribution with a Parabolic Density Distribution in the Core

The study carried out by Negi et al. deals with the construction of a core-envelope model of static and spherical mass distribution characterized by exact solutions of Einstein’s field equations.

Effect of the bubble deformation in the3D nonlinear laser wake-field acceleration

A new analytical approach for bubble deformation was used for optimization of the electron acceleration in the 3D highly nonlinear laser wake-field regime. Injection of the electron bunch with initial velocity in the bubble was considered in the inhomogeneous plasma with parabolic density ramp. The researchers show that deformation of the bubble shape has an efficient role on the trapping of the electrons in the acceleration region. The influence of the parabolic density ramp on the electron bunch trapping ratio and its mean energy was considered by the numerical method.