THOMSON-LIKE RF SCATTERING BY SMALL OVERDENSE PLASMA PARTICLES

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Submitted on 1 Jan 1979

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THOMSON-LIKE RF SCATTERING BY SMALL OVERDENSE PLASMA PARTICLES

William Janos

To cite this version:

William Janos. THOMSON-LIKE RF SCATTERING BY SMALL OVERDENSE PLASMA PARTI- CLES. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-753-C7-754. �10.1051/jphyscol:19797364�.

�jpa-00219360�

JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment au n07, Tome 4 0 , JuiZZet 1979, page C7- 753

THOMSON-LME RF SCATTERING BY SMALL OVERDENSE PLASMA PARTICLES

William A. Janos.

ConsuZtant, 8381 Snoubbird Drive, Huntington Beach, CaZifornia 92646.

ABSTRACT

Linear perturbation theory is employed to estimate

k

= ~ J / L z LT-)A, ; b. = plasma conductivity the scattering amplitude and cross section of a AI-~CA-V~) z 1 at scatterer, zero otherwise.

small overdense plasma particle of linear dimension INTEGRAL EQUATION FOR THE SCATTERED FIELD much less than the skin depth of the incident radi- The integral form of (2) of interest is obtained ation. It is shown that the scattering properties through inversion by the free space Green's dyad.

so derived are Thomson-like and can exceed the con-

c s c k ) = E C ~ ) - E > C I = i kzldz (C )$%($ * g )

⁽³⁾

O h

ventional sharp boundary Rayleigh-Mie results by

Fs

is the scattered field,-and

2 ,

^{( 4 .Y')/I!}

several orders of magnitude. BORN APPROXIMATION FOR A SMALL SCATTERER

INTRODUCTION The first Born Approximation,

.kg, - (r

⁾ to the .scat- The reradiation effects giving rise to scattering tered field would arise by replacing

Eif)

^{in the}

of monochroiatic electromagnetic waves incident on integrand on the right of (4) by

E 6 < r 1 ) .

^Under

metallic or overdense plasma surfaces are generated the condition

by the free electron constituents of the plasma

6

^LC

=

²

6 , ~ " )

^{( 4 )}

within a layer of thickness of the skin depth,

gs ,

namely, particle size much less than skin depth, it of the incident waves. Thicknesses much greater can be shown that the relative error in scattered than this

sS

are essentially superfluous in scat- field amplitude due to the first Born Approximation, tering. Thus it would appear that a very thin or neglecting all of the higher order scatterer terms small scatterer, which has virtually all of its is bounded as

conduction electrons exposed to the incident radi- Inax

I Es - Es, j _f: - J-

^{r c /}

a5L) - s

⁽⁵

ation, reradiates most efficiently in terms of

I'sI

scattered power to mass ratio. Here we consider Thus with (5), the first Born Approximation applies such a case and treat it by linear perturbation and 'can be replaced by

5;

in the integrand on the theory. Consider the scattering of an incident right of ( 3 ) . It also follows that all of the terms

L

electromagnetic wave of frequency bi;Hr) in the integrand are virtually constant over the by a small dense charge-neutral plasma agglomerate small plasma volume. The scattered field

_- cs,

^then

of characteristic length

&

much less than the skin takes the simplified form depth i 9 ( o 1

.

More specifically, let

S r d

²

Sscbj

^{( 1 )}

I - ,

^Ly

WAVE EQUATION wherely is a mean location of the scattering

The time independent wave equation for the diver- volume, AVu.

genceless electric vector is then

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797364

SCATTERING AMPLITUDE AND CROSS SECTION Phen. Ion. Gases, Eindhoven, 1975, 11.3.a.

The scattering amplitudep and cross section

s,,

^{are 3.} Janos, W.A., "RF Propagation Effects of Metallic Aerosol Distributions,'' N.C. Christophilos Intn'l Summer School and Conf. in Plasma Phys., Spetse, Greece, July 1977.

cP =

\ A p / L = & 4 L ~ F ) L ~ ~ ~ 7 ; n L ( ~ ~ f . - l p ) (8)

-

COMPARISON WITH RAYLEIGH SCATTERING

The Rayleigh-Mie scattering cross section,

5 ^,

^for

an ideal conducting particle (of infinite conductiv- ity) with the same volume is given (as in reference

Thus the ratio of the cross section (8) and (9) is

s*/,& .

⁽¹⁰⁾

Since for metals g - 1 0 1'7 je);.'

,

the above ratio can be large in the RF

-

microwave range.

CONCLUSION

It appears that in the limit of small particle size, much less than the skin depth of the incident radi- ation, the plasma electrons act collectively and additively with their individual scattering ampli- tudes to give rise to a composite Thomson scatterer.

For high conductivity metals, of correspondingly high collision frequency p

,

the total Thomson cross-section of the conduction electrons is modi-

L

fied by the

ratio[^/^,) .

Application of the scat- tering effects considered here has been made in reference (2) and (3) to coherent forward scatter- ing, where the estimated radio frequency permitivity of weak concentrations of small metallic scatterers has been shown to produce strong reflection, and for weaker concentrations, diluted an order of magni- tude, strong absorption.

REFERENCES

1. Van den Hulst, H.C., "Light Scattering by Small Particles," J. Wiley, N.Y., 1957, Chapter 6.

2. Janos, W.A., "~icrowave Reflection and Absorp- tion by Contaminated Plasma," XI1 Int. Conf.

*Partially performed at MDACW,~EC.