Wave Propagation In Magnetized Plasma Research Articles

Parallelization of a 3D FDTD code and physics studies of electromagnetic wave propagation in fusion plasmas

Numerical codes for electromagnetic wave propagation in magnetized plasmas are mainly based on frequency-domain asymptotic methods, which provide a fast solution and are thus valuable for experiment design and control applications. However, in several cases of practical interest (e.g. mode conversion), these tools run close to their limits of validity and should be compared to full-wave solutions. The code RFFW solves Maxwell's equations with the finite-difference time-domain method in 3D geometry, for scenarios involving high-frequency waves with arbitrary electric field spectrum in plasmas with axisymmetric equilibrium. In fusion-related problems, the code may conduct investigations of wave propagation and absorption relevant to auxiliary plasma heating and current drive, reflectometry and instability control. The code has been parallelized with a hybrid OpenMP-MPI scheme, which has allowed exploiting the much larger processing power and memory of current-day supercomputers. In this work, we present the main aspects of the physics implemented in the code, and also refer shortly to the parallelization scheme. Furthermore, we show results that exhibit the strong scaling performance of the code, and examine cases of electron-cyclotron heating application in medium-sized tokamaks.

Numerical Accuracy of Finite-Difference Time-Domain Formulations for Magnetized Plasma

The finite-difference time-domain (FDTD) has been widely used to analyze electromagnetic (EM) wave propagation in complex dispersive media. Over the past three decades, a variety of FDTD approaches for the EM wave propagation in magnetized plasma has been presented. In this work, we perform a comprehensive study on the numerical accuracy of four FDTD formulations for magnetized plasma including the JE convolution (JEC) method, the exponential time differencing (ETD) method, the H-J collocated auxiliary differential equation (ADE) method, and the E-J collocated ADE method. Toward this purpose, the numerical permittivity tensor of magnetized plasma in the four FDTD formulations are derived and then we analyze them to determine which approach can provide the best accuracy. It is found that the E-J collocated ADE method can lead to the best accuracy. Numerical examples awere performed to validate our investigations.

An Efficient Numerical Formulation for Wave Propagation in Magnetized Plasma Using PITD Method

A modified precise-integration time-domain (PITD) formulation is presented to model the wave propagation in magnetized plasma based on the auxiliary differential equation (ADE). The most prominent advantage of this algorithm is using a time-step size which is larger than the maximum value of the Courant–Friedrich–Levy (CFL) condition to achieve the simulation with a satisfying accuracy. In this formulation, Maxwell’s equations in magnetized plasma are obtained by using the auxiliary variables and equations. Then, the spatial derivative is approximated by the second-order finite-difference method only, and the precise integration (PI) scheme is used to solve the resulting ordinary differential equations (ODEs). The numerical stability and dispersion error of this modified method are discussed in detail in magnetized plasma. The stability analysis validates that the simulated time-step size of this method can be chosen much larger than that of the CFL condition in the finite-difference time-domain (FDTD) simulations. According to the numerical dispersion analysis, the range of the relative error in this method is 10−6 to 5×10−4 when the electromagnetic wave frequency is from 1 GHz to 100 GHz. More particularly, it should be emphasized that the numerical dispersion error is almost invariant under different time-step sizes which is similar to the conventional PITD method in the free space. This means that with the increase of the time-step size, the presented method still has a lower computational error in the simulations. Numerical experiments verify that the presented method is reliable and efficient for the magnetized plasma problems. Compared with the formulations based on the FDTD method, e.g., the ADE-FDTD method and the JE convolution FDTD (JEC-FDTD) method, the modified algorithm in this paper can employ a larger time step and has simpler iterative formulas so as to reduce the execution time. Moreover, it is found that the presented method is more accurate than the methods based on the FDTD scheme, especially in the high frequency range, according to the results of the magnetized plasma slab. In conclusion, the presented method is efficient and accurate for simulating the wave propagation in magnetized plasma.

Analysis of Electromagnetic Wave Propagation in Variable Magnetized Plasma via Polynomial Chaos Expansion

A 3-D stochastic finite-difference time-domain algorithm is developed and applied to electromagnetic (EM) wave propagation in collisional magnetized plasma characterized by a variable electron density, collision frequency, and background magnetic field. The proposed stochastic model is based on the expansion of the random/variable time-domain electric and magnetic fields in terms of orthogonal polynomials in independent random variables representative of the variable ionospheric content. EM wave propagation in magnetized plasma having low variability (small deviations) and also high variability (large deviations) of the electron density, collision frequency, and background magnetic field is studied. The stochastic algorithm is validated against brute-force Monte Carlo results. The algorithm is considerably more computationally efficient than Monte Carlo. When applied to EM wave propagation in the ionosphere, the variability of the Earth’s magnetic field and ionospheric parameters can be accounted for due to naturally varying space weather conditions and day-to-day variations, measurement errors, and so on. Although only electrons are considered here, positive and negative ions may be accommodated in a straightforward manner.

3-D FDTD Modeling of Electromagnetic Wave Propagation in Magnetized Plasma Requiring Singular Updates to the Current Density Equation

A new finite-difference time-domain (FDTD) algorithm for electromagnetic wave propagation in magnetized plasma is proposed. This algorithm permits the use of two time step increments: one for Maxwell’s equations, ${\Delta t}$ , and the other for the current density equation derived from the Lorentz equation of motion, ${\Delta }{t}_{c}$ . A major advantage of this algorithm over previous approaches is that only a single update iteration is needed for the current density equation even when ${\Delta }{t}_{c} . This provides significant time savings that can make previously infeasibly long simulations now practical. The algorithm’s implementation is also relatively simple and it has relatively low memory requirements. The algorithm is validated against analytical results. A stability analysis is performed.

An Iterative WLP-FDTD Method for Wave Propagation in Magnetized Plasma

We previously developed a tri-diagonalized finite-difference time-domain (FDTD) algorithm based on the weighted Laguerre polynomials (WLPs) for modeling wave propagation in magnetized plasma. The algorithm demonstrated dramatic CPU time reduction in comparison with the original WLP-FDTD algorithm. However, a splitting error was caused owing to the additional perturbation term. In this paper, an iterative scheme is introduced to the tri-diagonalized WLP-FDTD algorithm to further reduce the splitting error. Numerical example shows the accuracy and effectiveness of the proposed algorithm.

Tridiagonalized WLP-FDTD Implementation for Wave Propagation in Magnetized Plasma

We present an efficient implementation of the unconditionally stable finite-difference time-domain (FDTD) algorithm based on the weighted Laguerre polynomials (WLPs) for the modeling of wave propagation in magnetized plasmas. The sparse matrix equation is tri-diagonalized by using a factorization-splitting (FS) scheme, leading to a significant reduction in computational time. The algorithm is validated by numerical experiments.

An Efficient 3-D FDTD Model of Electromagnetic Wave Propagation in Magnetized Plasma

Modeling electromagnetic wave propagation in the upper atmosphere is important for space weather effects, satellite communications ionospheric modification experiments, and many other applications. We propose a new methodology for solving and incorporating the current equation into the finite-difference time-domain (FDTD) form of Maxwell's equations for modeling electromagnetic wave propagation in magnetized plasma. This approach employs a version of Boris's algorithm applied to particle-in-cell plasma computational models. There are four primary advantages of this new method over previously developed three-dimensional FDTD models of electromagnetic wave propagation in magnetized plasma. Specifically, it: 1) requires less memory; 2) is more than 50% faster; 3) is easier to implement; and 4) permits the use of two different time step increments when solving the current equation versus Maxwell's equations that is useful for modeling high collisional regimes. The new algorithm is faster because it solves all the equations explicitly and there is no need to solve complicated matrix equations. Modeling of higher altitude ranges and higher frequency electromagnetic waves is much more feasible using this new method. Results of the new FDTD magnetized plasma model are provided and validated.

FARADAY ROTATION AND PRIMORDIAL MAGNETIC FIELDS CONSTRAINTS ON ULTRAVIOLET LORENTZ VIOLATION WITH SPACETIME TORSION

Recently Kahniashvili et al.9 presented a unified treatment for ultraviolet Lorentz violation (LV) testing through electromagnetic wave propagation in magnetized plasmas, based on dispersion and rotation measured data. Based on the fact discovered recently by Kostelecky et al., 3 that LV may place constraints on spacetime torsion, in this paper it is shown that on the limit of very low frequency torsion waves, it is possible to constraint torsion from Faraday rotation and CMB on a similar fashion as Minkowski spacetime plus torsion. Here, the Maxwells modified equations are obtained by a perturbative method introduced by de Sabbata and Gasperini [Introduction to Gravitation (World Scientific, 1980)]. Torsion is constraint to Q CMB ≈10-18 GeV which is not so stringent as the 10-31 GeV obtained by Kostelecky et al. However, Gamma-Ray Bursts (GRBs) may lead to the more string value obtained by Kostelecky et al.Another interesting constraint on torsion is shown to be placed by galactic dynamo seed magnetic fields. For torsion effects be compatible with the galactic dynamo seeds, one obtains a torsion constraint of 10-33 GeV which is two orders of magnitude more stringent that the above Kostelecky et al. limit.

Wave propagation in magnetized plasma and some applications

In the past several years come up interest of laser devices in plasma applications. Interaction between a laser beam and magnetized plasma is very important for the next use of the laser beam to increase the plasma temperature.

Painléve Analysis and Backlund Transformations for Coupled Generalized Schrödinger–Boussinesq System

Painléve analysis of coupled generalized Schrödinger–Boussinesq system with arbitrary parameters has been carried out. We identify two branches of leading singularities in the Painléve formalism for PDEs as developed by Weiss et al., [ J. Math. Phys, 24, 522 (1983) ] . The coupled system is shown to be completely integrable in one of the branches, for which case the associated Bäcklund transformation is explicitly given. Relevance of the results for coupled nonlinear wave propagation in magnetized plasmas is pointed out.

Cyclotron resonance effects in a fluorescent lamp plasma

A plasma physics experiment is described, which is suitable for undergraduate courses in electromagnetism as well as for independent projects. Using the plasma of a fluorescent lamp inside a conducting cavity that is immersed in a magnetic field, the experiment shows the effect of electron cyclotron motion of plasma electrons on the resonant modes of the cavity. An added benefit of the magnetic field is the ability to measure the plasma density through a frequency shift technique, but without having to know the mode frequencies in the absence of plasma. Density measurements made using this technique are consistent with those described in an earlier article on the unmagnetized fluorescent lamp plasma, and with the literature on fluorescent lamps and gas discharges. Understanding the experiment described here will give the advanced undergraduate experience in the theory of electromagnetic wave propagation in magnetized plasma, in the theory of resonant cavities, and in microwave and instrumentation techniques.