Propagation of Short Pulses in Plasma Half-Space (Ionosphere)

Propagation of Short Pulses in Plasma Half-Space (Ionosphere)

The exact solution of the problem in the half-space of non-homogeneous plasma is obtained, and an asymptotic method for the same task as well. The estimations of the non-linearity and the electron-atom collisions influence regarding the problem are carried out.

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Бібліографічні деталі
Дата:2002
Автор: Gutman, A.L.
Формат: Стаття
Мова:English
Опубліковано: Радіоастрономічний інститут НАН України 2002
Назва видання:Радиофизика и радиоастрономия
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/122335
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Propagation of Short Pulses in Plasma Half-Space (Ionosphere) / A.L. Gutman // Радиофизика и радиоастрономия. — 2002. — Т. 7, № 4. — С. 359-361. — Бібліогр.: 3 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling irk-123456789-1223352017-07-03T03:03:06Z Propagation of Short Pulses in Plasma Half-Space (Ionosphere) Gutman, A.L. The exact solution of the problem in the half-space of non-homogeneous plasma is obtained, and an asymptotic method for the same task as well. The estimations of the non-linearity and the electron-atom collisions influence regarding the problem are carried out. Получены точное и асимптотическое решения задачи распространения коротких импульсов в полубесконечном пространстве с неоднородной плазмой. Дана оценка влияния в этой задаче нелинейности и столкновений електрон-атом. Отримано точний та асимптотичний розв'язки задачі розповсюдження коротких імпульсів у півнескінченному просторі з неоднорідною плазмою. Дано оцінку впливу у цій задачі нелінійності та зіткнень електрон-атом. 2002 Article Propagation of Short Pulses in Plasma Half-Space (Ionosphere) / A.L. Gutman // Радиофизика и радиоастрономия. — 2002. — Т. 7, № 4. — С. 359-361. — Бібліогр.: 3 назв. — англ. 1027-9636 http://dspace.nbuv.gov.ua/handle/123456789/122335 en Радиофизика и радиоастрономия Радіоастрономічний інститут НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description The exact solution of the problem in the half-space of non-homogeneous plasma is obtained, and an asymptotic method for the same task as well. The estimations of the non-linearity and the electron-atom collisions influence regarding the problem are carried out.
format Article
author Gutman, A.L.
spellingShingle Gutman, A.L.
Propagation of Short Pulses in Plasma Half-Space (Ionosphere)
Радиофизика и радиоастрономия
author_facet Gutman, A.L.
author_sort Gutman, A.L.
title Propagation of Short Pulses in Plasma Half-Space (Ionosphere)
title_short Propagation of Short Pulses in Plasma Half-Space (Ionosphere)
title_full Propagation of Short Pulses in Plasma Half-Space (Ionosphere)
title_fullStr Propagation of Short Pulses in Plasma Half-Space (Ionosphere)
title_full_unstemmed Propagation of Short Pulses in Plasma Half-Space (Ionosphere)
title_sort propagation of short pulses in plasma half-space (ionosphere)
publisher Радіоастрономічний інститут НАН України
publishDate 2002
url http://dspace.nbuv.gov.ua/handle/123456789/122335
citation_txt Propagation of Short Pulses in Plasma Half-Space (Ionosphere) / A.L. Gutman // Радиофизика и радиоастрономия. — 2002. — Т. 7, № 4. — С. 359-361. — Бібліогр.: 3 назв. — англ.
series Радиофизика и радиоастрономия
work_keys_str_mv AT gutmanal propagationofshortpulsesinplasmahalfspaceionosphere
first_indexed 2025-07-08T21:32:05Z
last_indexed 2025-07-08T21:32:05Z
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fulltext Radio Physics and Radio Astronomy, 2002, v. 7, No. 4, pp. 359-361 PROPAGATION OF SHORT PULSES IN PLASMA HALF-SPACE (IONOSPHERE) A.L. Gutman Voronezh State Forestry Engineering Academy, Department of Physics 4140 Irvington Ave.#42. Fremont, CA 94538,USA E-mail: agtm22@yahoo.com The exact solution of the problem in the half-space of non-homogeneous plasma is obtained, and an asymp- totic method for the same task as well. The estimations of the non-linearity and the electron-atom collisions in- fluence regarding the problem are carried out. 1. Introduction This paper is the continuation of [1] where the rigor- ous solutions to the problem of short pulse propaga- tion in plasma half-space for simplest models of the electrons density. Here, the asymptotic solution is presented enabling to approach the real distribution of electrons. The 2-nd part of this work is on the peculiarities of taking into account the plasma electrons collisions with the atoms as short pulses are passing through. 2. The Asymptotic Solution As a “large” parameter is proposed 0 ,Lk t c = where 0t – the initial pulse duration at the medium boundary, L – the linear size of the pulse propaga- tion region, c – the velocity of light. In this case the field ( ) ( ) ( ),u z t Z z T t= obeys the equation ( ) 2 2 ,d Z k p Z d ζ ζ = where /z Lζ = , ( ) ( )[ ]2 2 2 0 pp tζ ω ζ ω= − , pω – the plasma frequency, and the ordinary equation for ( )T t . If the field decreases as ζ increases relatively arbitrary cross-section 0ζ , we obtain [2]: ( ) ( )( ) ( ) 04 0 exp , , ,p B ddZ k p d k p ζω ζ ω ς ς ζ ζ ζ ω ω ζ = − − − > > ∫ ( ) ( ) ( ) 0 4 0 exp , , .p B d dZ k p d k p ζ ω ζ ω ς ς ζ ζ ζ ω ω ζ   = −     > < ∫ If 0z = at the plasma region boundary, then ( ) ( ) 2 2 0 0 2 24 0 0 , | exp . p t B d TdZ i t k t ω ζ ω ω ω ω = = − = − The incident onto the plasma field at 0z = [1] is as ( ) ( ) ( ) 0 2 2 0 0 32 2 0 | 1 5 1 exp , 4 0,25 y TdZ E t R i t d t ζ ω ω ω π ω = = − + − + where R – reflection coefficient. As these fields are equal as well as their corresponding normal deriva- tives and in view of 1dZ dZ dz L dζ = , one can obtain 0 0 0 0 0 0 1 , . 1 R ct ct t L t R R L ct t L ω ω ω ωω ω + −= = − + Thence the frequency component of the Poynting vector of the reflected field is as ( ) 2 22 2 0 0 0 0 0 2 32 2 0 00 1 5 . 64 0,25 y x d E H t ct t L d ct t Lt ω ω ω ωπ ω Π =    − −       ++  Thence it is easy to obtain Poynting vectors of the re- flected and transmitted fields. In particular, the latter is like A.L. Gutman 360 Radio Physics and Radio Astronomy, 2002, v. 7, No. 4 ( ) 0 0 2 2 22 2 0 0 0 32 2 0 000 64 1 5 1 . 0,25 y xE H t ct t L d ct t Lt π ω ω ω ωω ∞ Π = ×     − −    −      + +   ∫ 3. The Peculiarities of the Collisions The non-linearity of the electron-atom (ion) colli- sions in the plasma excludes any making use of the canonic results for monochrome fields and radio im- pulses when the short pulses are dealt with. When the magnetic field influence is ignored, the system of equations for the directed movement of the plasma electrons under the electric field is as in [3]: ( ) ,2 3 e e p my eE m y dT eyE T T dt ν δν β = − = − −  where 231.38 10β −= ⋅ J/Kelvin – the Boltsmann constant, δ – the number of electron-molecule colli- sions per sec, eT , pT – temperatures of the electrons and plasma, m , e –electron's mass and charge. Between the collisions the electron obeys the equation: 0; ,eEmy eE y t y m = = + where 0y – velocity of electron after the previous collision. The work by the field between the colli- sions is as 2 2 2 2 2 2 mean , 2 2 me E me EA τ ν = = where τ – the mean time span between collisions. As a result of a recurrent collision the electron looses the part of its energy specified by the multi- plier 2 /m M , where m , M – the masses of elec- tron and the molecule. In this way the kinetic energy of the directed move due to the 1-st collision is equal to ( ) 2 0 1 2 2 my m M − , which replies the new velocity 1 00 1 2my y M = − . As this process continues, we obtain ( ) 00 1 21 . i n n ii meE My y m ν= − = ∑ Here it is allowed for iν to vary in-between col- lisions depending on the electron temperature varia- tion. Thus for the electron-atom and the electron- molecule collisions. ef e p T Tν ν= , where efν – the effective number of collisions at e pT T= . One can get convinced that in the ionosphere conditions, at the achievable short pulse power levels as the ionosphere is reached, and the number of colli- sions is small enough, one obtains 1e p T T ≈ . Therefore ( ) ( ) 00 0 1 00 0 1 2 / 1 1 2 / . 1 1 2 / n i n m i n m eEy y m M m Me Ey m m M ν ν = = + − = − − + − − ∑ When the pulse duration is less than the collision-to- collision time span, the initial system of equations is as 0 , for .2 3 e pte my eE T TdT eyE dt β = =  ==  Thence 2 2 2 0 0 3e t e E tT T mβ= = + . After a short enough pulse has left, the equa- tions determining the dynamics of leveling of the temperatures of the electrons and plasma are valid: ( ) ( )[ ] ( ) ( )[ ] 2 2 2 0 , exp , 3 exp . e e p e p dT T T dt e E tT T t m y y t δν δν τ β τ ν τ = − − = + − − = − − In the ionosphere, for layers “E” and “F” correspond- ingly 5 2 E F E F 1 110 s , 10 sτ τ ν ν − −= ≈ = ≈ . Consequently, the pulses with duration not greater than 10-6 s should have passed through without any collision effect at all. References 1. F.L. Gutman, AMEREM 2002, 2-7 June, Annapolis, Maryland, USA, p. 78. (2002). 2. V.А. Fock. Tables of the Eirie functions. М. pp. 10-14 (1946). 3. V.A. Ginzburg. Propagation of Electromagnetic Waves in Plasma. М., Physmathgiz. pp. 503-507. Propagation of Short Pulses in Plasma Half-Space (Ionosphere) Radio Physics and Radio Astronomy, 2002, v. 7, No. 4 361 РАСПРОСТРАНЕНИЕ КОРОТКИХ ИМПУЛЬСОВ В ПЛАЗМЕННОМ ПОЛУПРОСТРАНСТВЕ (ИОНОСФЕРЕ) А.Л. Гутман Получены точное и асимптотическое решения за- дачи распространения коротких импульсов в полубес- конечном пространстве с неоднородной плазмой. Дана оценка влияния в этой задаче нелинейности и столкно- вений електрон-атом. РОЗПОВСЮДЖЕННЯ КОРОТКИХ ІМПУЛЬСІВ У ПЛАЗМОВОМУ ПІВПРОСТОРІ (ІОНОСФЕРІ) А.Л. Гутман Отримано точний та асимптотичний розв'язки за- дачі розповсюдження коротких імпульсів у півнескін- ченному просторі з неоднорідною плазмою. Дано оцін- ку впливу у цій задачі нелінійності та зіткнень елект- рон-атом.

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