American Institute of Aeronautics and Astronautics

1

THE NATURE OF SURFACE MW DISCHARGES

Kirill V. Khodataev*

Moscow Radiotechnical Institute RAS, Russia

In MRTI are received and investigated the microwave discharges of average and high gas

pressure, developing in the field of radiation with amplitude, significantly smaller critical

value, exclusively along a surface of dielectric. The discharges initiated by means of passive

electromagnetic vibrators, located on a surface of dielectric, look like a net of thin channels

pressed to a surface of dielectric. Experiments with dielectric plates from quartz, textolite,

glass-reinforced textolite, usual and quartz glass, ceramics and polyethylene have specified

in independence of discharge properties on a kind of dielectric material. Special interest was

presented by experiments with thin dielectric films. At a thickness of films even 100мкм

discharges have the same properties, as discharges on a surface of unlimitedly thick plates.

Experiments were spent on installations with wavelength of MW radiation 8.9 cm and 2.5

cm. As the reasons, causing primary propagation of streamer discharge over a surface of

dielectric, the electrostatic effects and physical-chemical surface processes in presence of the

discharge were considered. But the second factor was classified as a factor, which is not

defining the reason of indifference of phenomena to a material of dielectric testifies.

However, attraction to the phenomena theory of first factor, the processes of electrostatic

effect, changing distribution of MW field in a vicinity of the head of the growing streamer,

has appeared uneasy because the calculations have shown, that the increase in amplitude of

a field at a head of a streamer near surface of dielectric with dielectric permeability ε ~ 2-4

(typical values for used materials) does not exceed 10-15 % for thick dielectric layers and

very small for thin films, that is obviously not enough for maintenance of primary

propagation along a surface. But more detailed calculations at both electrostatic and

electrodynamic approach have shown, that presence of a dielectric layer with ε ~ 2-4

displaces a maximum of amplitude of a field in a streamer head towards a surface (not

changing essentially its amplitudes) if the thickness of a dielectric layer is more than distance

from the streamer head to a surface. By earlier numerical modeling it has been shown, that

the streamer develops towards a maximum of amplitude of a field defined by the sum of a

primary field and field generated by currents induced in discharge channels and forgoing to

a head of streamer. At presence of dielectric the charges, induced in dielectric, displaces a

field maximum nearer to surface so a streamer, keeping the tendency to extend in direction

of field maximum, continuously slides over a surface. It is possible to assert, that the

electrostatic factor is the defining factor for the surface streamer MW discharges.

I. Introduction

During of many years cycle of investigations have been obtained and been studied the

initiated subcritical streamer microwave (MW) discharges of average and high gas pressure

developing exclusively along a surface of a dielectric material1,2,3,4

. The surface discharges

initiated by means of passive electromagnetic vibrators, located on surfaces of the dielectric

material, are similar to a streamer network of usual volume discharges, but pressed to the surface

of the dielectric material. As the reasons causing primary propagation of the discharge over a dielectric material

surface the electrostatic effects and physical - chemical surface processes in the presence of the

discharge were considered. The goal of this work is defined the main factor ordering the

discharge propagation over dielectric surface.

* Head of department MRTI, Prof., member AIAA

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition4 - 7 January 2010, Orlando, Florida

AIAA 2010-1378

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

American Institute of Aeronautics and Astronautics

2

Experiments with dielectric plates of textolite, fiber glass, usual and quartz glass,

ceramics and polyethylene have revealed independence of the discharge properties on a sort of a

dielectric material (see the Fig.1). The properties of surface discharge, developing over surface

of dielectric plates of rather different material and thickness are the same.

Special interests represent experiments with thin dielectric films. At a thickness of films

even 100 m the surface discharge possesses the same properties as discharges on a surface of

unlimited thick plates. Experiments have been carried out with installations with a wavelength

8.9 cm and 2.5 cm of MW radiation and show the identical results.

(a) (b) (c) Fig.1.Discharge streamer net structure does not depend on a dielectric material layer: (a) –

polyethylene film, 0.02 cm thick, (b) – fiber glass, 0.2 cm, (c) – quart glass, 1.0 cm

Therefore the second factor was considered as inessential. An indifference of the

phenomenon to a dielectric material testifies this. The written below is devoted to study of

electrostatic and electrodynamic effects influence on MW streamer discharge behavior near

surface.

II. The task formulation

At calculations the special attention has been given to electric field amplitude distribution

in vicinity of the streamer head located over a surface of dielectric layer at distance, much

smaller its length and comparable with its diameter as it is observed in experiments. At

calculations the streamer was simulated by ideally conducting thin cylinder. The task

formulation is shown in Fig.2.

Fig.2.The problem statement about electric field amplitude distribution near the thin

conductor located over a dielectric layer of a small thickness at a small distance

American Institute of Aeronautics and Astronautics

3

III. The field calculation in electrostatic approach

If the length of the cylinder is smaller than a half length of MW radiation wave then

calculations can be carried out in a static approach, which allows to use the analytical rates for

extremely accurate results achieving. It is essentially important because small geometrical

parameters in formulation of task create quite hard difficulties in numerical calculation of fields

near ends of conducting wire.

The electrostatic approach has advantage of the known solution for potential of a point

charge located over a dielectric layer of finite thickness Eq.(1):

1 02 2

0

1 0 2 0

0 0

2 0

0

1exp ,

, exp exp ,

exp ,

A J r z d z dr z

r z B J r z d B J r z d d z d c

A J r z d d c z

(1)

where

1 2

exp 2 exp 2

1 exp 2

b dA

c

2

2 2

1

1 exp 2A

c

1 2

1

1 exp 2B

c

2 2

1 exp 2

1 exp 2

bB

c

1

1

b c d c - a thickness of a dielectric layer,

d - distance from an axis of a conductor to a surface of a layer,

- permittivity of a layer.

The linear charge distribution q(x,t) in a conductor with a half length L and with linear

conductivity σ, located under a dielectric layer along the electric field Е0, was defined by means

of the numerical solution of the integral-differential equation Eq.(2)

2 2

1 1, , ,0

L

L

q x t x q x t x x a dxt x x

(2)

а –conductor radius (а<d).

The stable solution obtained in calculations has turned out close to the known analytical

solution Eq.(3) for a conductor in the static electric field in free space

American Institute of Aeronautics and Astronautics

4

0

2 2 2

2

,

ln 4 1

0,

E xx L

L x aq x

a

x L

(3)

In Fig.3 we compare both solutions.

Obtained charge distribution allows to find the electric field distribution with a help of

relations Eq.(4) and Eq.(5)

2 2

1 1 1, ,

L

L

x z q x x x a z dx (4)

0,E x z E (5)

Fig.3. Linear discharge distribution along the conductor of 2L length in electric field E0.

Red curve -solution Eq.(3), black curve - solution of the Eq.(2)

Involvement to the surface discharge theory of the first factor (the electrostatic effect

changing distribution MW of a field near a head of a streamer, causing the increase field

amplitude in maximum) has met some difficulty. The calculation executed for thin wire located

over unlimitedly thick dielectric plate have shown, that the increase in the field amplitude near a

streamer head located over surface of dielectric with permittivity ε ≈ 2-4 (typical values for used

materials) does not exceed 10-15 % just for thick dielectric layers (Fig.2) and of course must be

even less for thin layers.

It is absolutely insufficient for insurance of primary propagation of a streamer along a

surface even at very large undercriticality Ecr/E0. In this connection more detailed calculations

have been carried out for exact calculation of peculiarities of field distribution in area between

streamer head and surface.

Distributions of electric field magnitude calculated in static approximation, using the

Eq.(1)-Eq.(5), for various thickness and permittivity of a layer are shown in Fig.4. One can see

that magnitude of field maximum near streamer head is changed insignificantly but its location is

shifted from streamer axis toward the surface.

American Institute of Aeronautics and Astronautics

5

Fig.2. Dependence of increase in a maximum of a field in a vicinity of a head of the

"streamer" located over a dielectric surface with respect to its permeability

Fig.4. Distributions of the module of electric field for various thickness and permeability of

the layer, calculated in static approach. Red color corresponds to area of large

values of the module of electric field

American Institute of Aeronautics and Astronautics

6

The shift is observed only if distance between streamer axis and surface much less of its length

and comparable with its radius from one side and smaller than dielectric layer thickness. All

those conditions are satisfied in real experiments with real streamers, propagating over surface.

IV. Field calculation in electrodynamic approach

It was important to ascertain that the maximum field location shifting takes place too at

case of the streamer length comparable with wave length.

At the length of a conductor (streamer) close or equal to a half length of a wave for

determination of electric field amplitude distribution the calculations in electrodynamic approach

on basis of Maxwell equations are necessary. Such calculations have been carried out by means

of program CST MW Suite Studio. In the Fig.5 the example of the electrodynamic calculation

for a thin "streamer" of resonant length is represented. Calculation parameters: wave length of

MW radiation λ =11.6 cm, 2L=5 cm, 2а=0.2 cm, d=0.2 cm, the dielectric material thickness is

с=0.1 cm, ε =4 (see Fig.2). A wave of MW radiation propagates normally to the film surface (in

the Fig.4 from below upwards), wave electric field is oriented along the "streamer". Those

parameters corresponds to typical conditions of real experiments.

Fig. 5. Distribution of the electric field amplitude round the conductor of resonant length

located under a thin dielectric film with ε =4

It was defined that electrodynamic approach gives the same result: the electric field

amplitude maximum location is shifted to dielectric surface just in the case of very thin layer and

permittivity more 2.

V. Conclusion

The calculations executed both in electrostatic and at electrodynamic approaches, have

shown, that presence of the dielectric layer displaces a maximum of amplitude in the field of a

streamer head to a surface (not changing essentially amplitudes in the maximum). In the Fig.6

dependence of the rate, characterizing the shifting of field maximum, on thickness and

permittivity is represented. It can be seen, that the shifting is essential if thickness of the

dielectric layer is greater than the distance from an axis of the streamer to the surface, and the

permeability is ε> 2.

American Institute of Aeronautics and Astronautics

7

Fig.6. dependence of the value characterizing displacement of a maximum of a field on

a thickness and permeability of the field

Executed earlier numerical modeling of initiated streamer discharge propagation in free

space (in the absence of a surface) has shown, that the streamer develops towards to the

maximum of the field amplitude, defined by the sum of a primary field and a field of charges

created by currents in the streamer channels and located ahead the streamer head5,6

. The carried

out research has shown, that at presence of the dielectric material the charges, induced in the

dielectric, shift the electric field amplitude maximum closer to the surface of the dielectric.

Thereof the streamer, supporting the tendency to propagate in the direction of the field

maximum, continuously slides over the surface. As arising asymmetry of the field distribution

does not depend on the undercriticality degree then the surface MW discharges is observed in all

area of the subcritical discharges existence.

Thus, electrodynamic interaction of the streamer with the dielectric material is a principal

reason for propagation of the streamer discharge over the surface.

It is possible to assert, that the electrostatic factor is the defining and for DC surface

discharge too.

Acknowledgements

The work is performed with financial support of EOARD (Project ISTC №3784р)

References

1 K.V.Alexandrov, L.P.Grachev, I.I.Esakov and K.V.Khodataev. Surface streamer microwave discharge. Technical

Physics, V.47, N. 7/ July 2002. 2 S.Popovic, L.Vuskovic, I.I.Esakov, L.P.Grachev and K.V.Khodataev. Subcritical microwave streamer discharge at

the surface of a polimer foil. //Appl. Phys. Letters, 2002, v.81, Nu.11, pp.1964-1965. 3I. Esakov, L. P.Grachev, K.V. Khodataev, V. L. Bychkov, D.M.Van Wie. Surface Discharge in a Microwave Beam. IEEE Transactions on Plasma Science, Vol.35, No.6, December 2007 4 Konstantin V. Alexandrov, Eugeny B. Alfeev, Lev P. Grachev, Igor I Esakov, Alexei I. Khomenko, Kirill V.

Khodataev, Vyacheclav A. Vinigradov. Experimental investigation of a surface discharge in focused beam of

microwave radiation at wavelength of 2.5cm and 8.9cm. 47th AIAA Aerospace Sciences Meeting and Exhibition. 5-

8 January 2009, Orlando, Florida. Paper AIAA 2009-845.

American Institute of Aeronautics and Astronautics

8

5 Kirill V. Khodataev. Investigation of undercritical microwave discharge ability to propagate limitlessly by

continuous branching of the streamer. 44rd AIAA Aerospace Sciences Meeting 9-12 January 2006, Reno, NV.

Paper AIAA-2006-0789 6 Kirill V. Khodataev. Propagation of Microwave Subcritical Streamer Discharge Against Radiation by Brunching

and Looping. 46th AIAA Aerospace Sciences Meeting 7-10 January 2008, Reno, NV, USA. Paper AIAA-2008-140