# Development of an Exactly Solvable Model of Resonance Tunneling of Electromagnetic Waves through Gradient Barriers in a Nonuniform Magnetoactive Plasma

## Abstract

An exactly solvable one-dimensional model describing resonance tunneling (reflectionless transmission) of a transverse electromagnetic wave through wide layers of magnetoactive plasma is developed on the basis of the Helmholtz equation. The plasma layers include a set of spatially localized density structures the amplitudes and thicknesses of which are such that approximate methods are inapplicable for their analysis. The profiles of the plasma density structures strongly depend on the choice of the free parameters of the problem that determine the amplitudes of plasma density modulation, characteristic scale lengths of the density structures, their number, and the total thickness of the nonuniform plasma layer. The plasma layers can also include a set of random inhomogeneities. The propagation of electromagnetic waves through such complicated plasma inhomogeneities is analyzed numerically within the proposed exactly solvable model. According to calculations, there are a wide set of inhomogeneous structures for which an electromagnetic wave incident from vacuum can propagate through the plasma layer without reflection, i.e., the complete tunneling of thick plasma barriers takes place. The model also allows one to exactly solve a one-dimensional problem on the nonlinear transillumination of a nonuniform plasma layer in the presence of cubic nonlinearity. It is important that, duemore »

- Authors:

- Russian Academy of Sciences, Shmidt Institute of Physics of the Earth (Russian Federation)
- Russian Academy of Sciences, Space Research Institute (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22763215

- Resource Type:
- Journal Article

- Journal Name:
- Plasma Physics Reports

- Additional Journal Information:
- Journal Volume: 44; Journal Issue: 10; Other Information: Copyright (c) 2018 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-780X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ELECTROMAGNETIC RADIATION; EXACT SOLUTIONS; LAYERS; NONLINEAR PROBLEMS; PLASMA DENSITY; RESONANCE; THICKNESS; TUNNEL EFFECT

### Citation Formats

```
Erokhin, N. N., E-mail: nerok1986@gmail.com, Zol’nikova, N. N., E-mail: nzolnik@iki.rssi.ru, and Mikhailovskaya, L. A..
```*Development of an Exactly Solvable Model of Resonance Tunneling of Electromagnetic Waves through Gradient Barriers in a Nonuniform Magnetoactive Plasma*. United States: N. p., 2018.
Web. doi:10.1134/S1063780X18100033.

```
Erokhin, N. N., E-mail: nerok1986@gmail.com, Zol’nikova, N. N., E-mail: nzolnik@iki.rssi.ru, & Mikhailovskaya, L. A..
```*Development of an Exactly Solvable Model of Resonance Tunneling of Electromagnetic Waves through Gradient Barriers in a Nonuniform Magnetoactive Plasma*. United States. doi:10.1134/S1063780X18100033.

```
Erokhin, N. N., E-mail: nerok1986@gmail.com, Zol’nikova, N. N., E-mail: nzolnik@iki.rssi.ru, and Mikhailovskaya, L. A.. Mon .
"Development of an Exactly Solvable Model of Resonance Tunneling of Electromagnetic Waves through Gradient Barriers in a Nonuniform Magnetoactive Plasma". United States. doi:10.1134/S1063780X18100033.
```

```
@article{osti_22763215,
```

title = {Development of an Exactly Solvable Model of Resonance Tunneling of Electromagnetic Waves through Gradient Barriers in a Nonuniform Magnetoactive Plasma},

author = {Erokhin, N. N., E-mail: nerok1986@gmail.com and Zol’nikova, N. N., E-mail: nzolnik@iki.rssi.ru and Mikhailovskaya, L. A.},

abstractNote = {An exactly solvable one-dimensional model describing resonance tunneling (reflectionless transmission) of a transverse electromagnetic wave through wide layers of magnetoactive plasma is developed on the basis of the Helmholtz equation. The plasma layers include a set of spatially localized density structures the amplitudes and thicknesses of which are such that approximate methods are inapplicable for their analysis. The profiles of the plasma density structures strongly depend on the choice of the free parameters of the problem that determine the amplitudes of plasma density modulation, characteristic scale lengths of the density structures, their number, and the total thickness of the nonuniform plasma layer. The plasma layers can also include a set of random inhomogeneities. The propagation of electromagnetic waves through such complicated plasma inhomogeneities is analyzed numerically within the proposed exactly solvable model. According to calculations, there are a wide set of inhomogeneous structures for which an electromagnetic wave incident from vacuum can propagate through the plasma layer without reflection, i.e., the complete tunneling of thick plasma barriers takes place. The model also allows one to exactly solve a one-dimensional problem on the nonlinear transillumination of a nonuniform plasma layer in the presence of cubic nonlinearity. It is important that, due to nonlinearity, the thicknesses of the evanescent plasma regions can decrease substantially and, at a sufficiently strong nonlinearity, such regions will disappear completely. The problem of resonance tunneling of electromagnetic radiation through gradient wave barriers is of interest for various applications, such as efficient heating of dense plasma by electromagnetic radiation and transmission of electromagnetic signals from a source located in the near-Earth plasma or deep in the plasma of an astrophysical object through the surrounding evanescent regions.},

doi = {10.1134/S1063780X18100033},

journal = {Plasma Physics Reports},

issn = {1063-780X},

number = 10,

volume = 44,

place = {United States},

year = {2018},

month = {10}

}