The initial phase of initiated undercritical microwave discharge*

Kirill V. Khodataev† UFSF “Moscow Radiotechnical Institute of RAS”, Moscow, Russia

khodataev@tochka.ru

The initiated undercritical attached microwave discharge is very usable discharge in area of plasma aerodynamics both in physical experiments and in future applications especially for plasma assisted combustion. Parameters of the discharge are difficult for measurement. Any contact of diagnostic gauge changes the discharge. The spectrum diagnostics are not complimentary in this case because the discharge is strongly inhomogeneous thin object. But understanding of physics of attached discharge development is needed for optimization of process in different cases of application. The developed phase of attached discharge (both in a still gas and in supersonic flow) was investigated numerically by means of designed models. But these models have not described the very initial phase sufficiently. In this connection the numerical modeling of the initial phase of an initiated undercritical discharge have been performed. The designed model takes into account electrodynamics of initiator, the ionization balance, heating, diffusion (both free electron diffusion and ambipolar diffusion, caused by difference between electron and gas temperatures).

Nomenclature E, = effective amplitude of electric field of microwave radiation c = light velocity ω, λ = microwave radiation frequency and wave length σ = plasma electrical conductivity k = 2π/λ , wave number, cm-1 ψ = ionization coefficient De = free electron diffusion coefficient D = effective electron diffusion coefficient τeg = time of electron temperature relaxation Tg = temperature of heavy component Te = electron temperature h = dispersion of initial distribution of ψ νi = total frequency of ionization, attachment and recombination a = initiator radius

T I. Introduction he

robabl undercritical initiated microwave (MW) discharges are most interesting as from the point of view of

p e appendices and as insufficiently investigated form of the gas discharge. For initiation of the discharge the passive metal vibrators, representing the metal cylinders (in general case elliptic shaped metal objects) oriented along an electric field, more often are used. On sharp tips of the vibrators, placed in an external MW field, there is the field of the polarization many times exceeding initial not perturbed value. The radius of curvature on the end of the vibrator is less in comparison with its length, the it is more increase of a field. Especially big increase of a field is possible to achieve, if the length of the vibrator comes nearer to half of wavelength of a radiation (in this case

* Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved † Professor, Head of Plasma Physics department, member AIAA

American Institute of Aeronautics and Astronautics

1

43rd AIAA Aerospace Sciences Meeting and Exhibit10 - 13 January 2005, Reno, Nevada

AIAA 2005-598

Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

there comes an electrodynamic resonance). Accordingly for initiation of the discharge the smaller level of radiation is required.

Determination of a breakdown threshold usage of the initiator, which size is small in comparison with wavelength of MW radiation and for which the size of increase of a field is precisely known, allows to determine enough confidently the absolute size of amplitude of a radiation field. To these conditions satisfies the initiator of the spherical form. Small metal ball is simple in manufacturing and a field vacuum around of it is described by precisely analytical ratio

ϕ−∇=Er

(1)

where

−⋅⋅−= 2

2

0 1rarE rr

ϕ (2)

The spherical initiator is widely used in researches of undercritical discharges. On undercritical discharges with its participation the big observant data is saved up. It also is convenient and at modeling of the initial stage of the undercritical discharge, as it allows to expect the electromagnetic field at the presence of the discharge, developing near to the initiator, in quasistationary approximation.

The initial stage of the initiated discharge till now is not represented enough clear. Undercritical MW discharge initiated in dense gas with the help of the metal initiator, rather quickly develops into the streamer (or several streamers), adjoining to a surface of the initiator. Further, depending on factor of undercriticality of field, the streamer or creates the system of streamers, freely extending towards to radiation, or remains attached to the initiator. Supervision show that development of the discharge begins with formation of diffuse areas poorly ionized gas directly at a surface of the initiator. However at the further development in increasing ionized areas it starts to be shown the heterogeneity, formed later into the streamer or a row of streamers. On Fig. 1 it is given a photo of the discharge initiated by the spherical initiator 1.

On a pole of sphere the field precisely three times exceeds the value of not perturbed field Ео. The sphere is highlighted by UV radiation causing photoemission of free electrons which derivate avalanche growth of ionization if the field at a surface of the initiator is higher than breakdown value.

Figure 1. Appearances of low and high temperature forms of the MW discharge initiated by the ball, p = 60 Torr, 2a = 0.5 cm, E0/E0 br = 1: τdis = 35 µs;

The purpose of research is modeling dynamics of development of initial stage of discharge attached to initiator and definition of the factors determining development of instability of an initial plasma cloud.

II. Initiation of the breakdown As it was noted earlier the streamer microwave discharge can exist and propagate in the field that is much less

than the critical one. But creation of these discharges needs the start initiation. The role of initiator can be performed by thin long metal body (which can be shaped as sphere, ellipsoid or cylinder) placed in the undercritical field.

American Institute of Aeronautics and Astronautics

2

A. The field arising on the top of a metal initiator In the quasi-stationary approximation the spatial distribution of a field potential ϕ at presence of arbitrary

distributed electrical conductivity σ is described by Puasson’s equation

041 =∇⋅

⋅−∇+∆ ϕ

ωπσϕ i . (3)

For the special case of a spherical symmetry of conductivity distribution and azimuth symmetry of the electric field the Eq. (3) can performed in the 1D form by changing of variables

( ) ( ) ( )θθϕ cos, ⋅= rfr , (4)

where (r,ϕ,θ) – spherical coordinates. Instead of the Eq. (3) we have now the 1D equation for f:

01222

2

2=

∂∂⋅

∂Σ∂

⋅Σ

+⋅−∂∂⋅+

∂

∂rf

rf

rrf

rr

f. (5)

The electric field is defined by equation:

))()sin()()(cos())cos()(( θθθθϕ irrfi

rrfrfE r −∂

∂−=⋅−∇=−∇= , (6)

The solution of Eq. (5) for the case of metallic sphere in homogeneous external field E=Ez in spheroidal coordinates (r,ϕ,z) is represented on Fig.2.

0

1

2

E /Eo

z

r

Figure 2. The spatial distribution of the field amplitude around the sphere.

The equation (5) is especially interesting because allows investigate the any conductivity distribution with spherical symmetry.

For the metallic ellipsoid, oriented along the external electric field, the famous analytical solution 2 can be used if the sizes of body are much small comparatively wavelength of MW radiation. Using the analytical solution for not charged metal ellipsoid with sizes mach smaller radiation wavelength, placed in homogenous external field E0, one can calculate the field distribution in its vicinity. The sample of such distribution is shown on Fig.3. For the field on the pole the expressions are simplified and we have Eq. (7) for the increase coefficient Q (Ref. 2)

American Institute of Aeronautics and Astronautics

3

( ) ( )( ) a

llalaArth

lalaQ ⋅

−−−

−=

11

31, )4( λ<l (7)

The graphic of the Eq. (7) is given on Fig.4.

0

2

4

6

8

E /Eo z

r

Figure 3. The spatial distribution of the field amplitude around the ellipsoid.

The approximate calculation of the field on the top of metallic thin cylinder gives the expression (Ref.2):

( )

−

⋅

⋅

⋅=

28ln

2

ala

llaQ , )4( λ<<< la . (8)

1 10 1001

10

100E /Eo

l /a

Figure 4. The increase coefficient Q dependence from the relation between ellipsoid half-length and radius of curvature at its pole

But the expressions (7) and (8) can describe the top field only if the length of the initiator is much less than half wavelength of microwave radiation. In the case of an equality between initiator length and half wavelength the increasing of the top field is significantly more because the electric-dynamical resonance. At the resonance the top field is limited by only so named radiation resistance and can be successfully described by Eq. (9)

American Institute of Aeronautics and Astronautics

4

( )awRacE

topEaQ λπ

λλ ⋅≈⋅

⋅== 255.02

0 (9)

where

cwR 5.2≈

is well known the radiation resistance of the vibrator, which at the resonance approximately equals to 75 Ohms in system of measurement SI. The factor in the numerator λ/π - is so named the acting length of a resonant vibrator. The values of the increasing coefficient Q for resonant length in dependence on a/λ (λ–wavelength) achieved by Eq.(9) and by integral equation are compared with experimental data on Fig.5. The measurement data for two magnitudes of wavelength (8.9 cm and 12.5 cm) are present on the picture. It must be noted that the experimental points for 12.5 cm wavelength are submitted by supposition of Eo=100 V/cm.

Figure 5. The coefficient of field increasing Q=Etop/E0 dependence on aspect ratio a/l for resonant length of initiator. The solid line – the values calculated by integral equation, the dotted line – Eq.(9), circles and boxes – the values measured at λ=8.9 cm and 12.5 cm accordingly.

B. The electron diffusion influence on the breakdown field at presence of an initiator Balance of electrons (electron concentration) in air in linear approximation can be described by the equation (at

small ionization degree, when the process of dissociative recombination of electrons and positive molecular ions, , is insignificant) MMe 22 →+ +

nainDtn )( νν −+∆=∂∂

, (10)

Here n – is electron concentration, νi and νa – frequencies of ionization and attachment in processes: - ionization ( M=N++→+ 22 2 MeMe 2, O2), - dissociative attachment, and D is coefficient

of a diffusion. In the case of our interest we can accept for the breakdown criterion the following condition

−+→+ OOOe 2

0/ =∂∂ tn .(11)

American Institute of Aeronautics and Astronautics

5

It means that the ionization is compensated by the electron attachment and diffusion losses of electrons from a breakdown area. Usually ionization frequency is approximated by the formula 3

β

crEE

aνiν

⋅= , β=5.3, (12)

where E is local value of the field amplitude,

+= 2/21230 cpcrE νω , V/cm (13)

is the amplitude of the critical (breakdown) field, ω - circular frequency of electromagnetic field,

1s;4104.6 −⋅= paν (14)

is the frequency of attachment,

;910.4 pc =ν s-1 (15)

is transfer collision frequency of electron-neutral molecule collisions. Here and in analogous formulas air pressure p is expressed in Torr.

If a ball of radius a<<1/k (k=2π/λ - a wave number) is placed into the microwave field E0 the field amplitude is maximal on the ball's poles (where a vector of the external field E0 is perpendicular to its surface) and equals 3E0. At the ball equator the field equals zero. Hence the best breakdown conditions are realized at polar areas of the ball. The electric field at the pole is directed along the external field Eo.

At taking away from the ball's pole along E0 the field is being decreased up to E0 by the law

( )

+⋅=

3/

210 arEE . (16)

where r is distance from the ball center. The equation (16) is right if the body is small in comparison with a wavelength, the boundaries are far from the

body quite enough and the situation is far from electric-dynamical resonance. In this case the field structure is insensible to the ball presence so it does not influence on the general field distribution and field initial level. The ball is creating only local deviation described by Eq.(16). The refraction wave generated by the ball is small enough and is possible being not taken into account.

The ionization process will start near the ball pole where the maximal electric field equals to 3E0 and exceeds the critical value. It is easy to see that at 3E0/Ecr-1<<1 the ionization area represents the thin layer near the pole. It allows to simplify the task and to find the stationary solution of Eq.(10) in a frame of the 1D approximation.

The breakdown at the ball presence comes to the one-dimension problem of searching of a stationary distribution of electron concentration n(r) that would satisfy diffusion equation (10) at the condition (11) in non-uniform field of form (16). Moreover n has to become equal to zero on the ball's surface at r=a and to decrease to zero at taking away from it. The required values of a field E0 and pressure p are present at the obtained distribution as parameters.

The diffusion equation (10) is reformed into the Airy equation (in the result of linearization of the Eq.(12)) for νi near the ball's surface relative to a value E):

American Institute of Aeronautics and Astronautics

6

0222

2=+

∂

∂ ϕϕ

Bb

z

z, (17)

Solution of Eq.(17) is known 4,5:

( ) ( )

<

−−+

−−⋅

−

>

−+

=

0,3

2/323/13

2/323/1

2/1

0,3

2/323/13

2/323/1

2/1

zbBzI

bBxIz

zbB

zJbB

zJz

Сϕ (18)

where J±1/3(x), I±1/3(x) are the Bessel functions. It automatically satisfies the condition posed on the distant boundary ρ→∞ (z→-∞), since there it is exponentially small.

Here we introduce the follows dimensionless parameters: b=νaa2/D, ε0=E0/Ecr, A=(3ε0)β-1, B=2β(3ε0)β, and variables: ρ=r/a, ϕ=nρ, z=bA - bB(ρ-1).

The condition of the ball's surface ϕ(ρ=1)=0 is satisfied at

2⋅z3/2/(3bB)=2.338. (19)

The higher eigenvalues are disregarded because ϕ is alternating in sign. On the surface of a ball we have z=bA and from Eq.(19) finally appears the required relation between E0/Ecr and

p

( )

( )

2/3

032,7

1031βεβ

βε

−

=≡aal

b. (20)

Here

a

Dal ν= (21)

is a diffusion length of the electron attachment, which is the air pressure's function. In Eq. (21) under D we have to mean an ambipolar diffusion coefficient

p.

aDD41041 ⋅

== , cm2/s. (22)

Indeed, if the UV radiation source maintains some electron concentration in a gas near the isolated body's surface at some electron temperature Te then after a time

td ≈ 1/(4πσ), (23)

American Institute of Aeronautics and Astronautics

7

where σ is plasma conductivity, the potential of this body rises to a value about of several Te. So the further entering of plasma electrons into a body can take place only by ambipolar type. With accounting of Eq.(13) and Eq.(22) the Eq.(21) for diffusion length of the electron attachment can be changed into

la=0.33/p, cm. (24)

The dependence Eq.(20) in coordinates (3E0/Ecr - la/a) is represented in the Fig.6. From Eq.(20) follows also that at high p, i.e. at la/a→0, the breakdown takes place in the polar ball's areas as if in

three times increased field. In this case the breakdown field is E0=(1/3) Ecr. With the decrease of the pressure the electrons begin to diffuse intensively from the polar ball's areas, where the field is increased, so as the breakdown takes place at a value E0 that is approaching to Ecr. In this case the presence of a ball only stabilizes the breakdown by emission of the initial photoelectrons near its surface. Note that at relatively low pressure, i.e. at high value of la/a, the presented theory is quantitatively inapplicable to the description because of assumption (la/a)-1<<1 accepted at its formulation. The field of its applicability was determined experimentally. For the illustration on the Fig.7 on the basis of Eq.(16) and Eq.(18) the graphs of dependence: n[(r-a)/la] was depicted. It corresponds to area near the ball's poles at parameter value la/a=0.1.

Figure 6. The dependence of the normalized breakdown field Ebr/Ecr from the attachment length; line – Eq.(20), points – experimental data.

Figure 7. The electron density distribution near the sphere surface at the pole. la/a=0.1.

By the same way as in the case of the sphere that have discussed above the diffusion influence on the breakdown field is stronger in the case of a long body.

Using the same method of calculation as at the chapter 3 one can get the expressions that is analogical toEq.(20)

( )

( )

2/3

2,7

1

βεβ

βε

br

braal

−

= (25)

where εbr=(Etop/Ecr)br. The Eq.(25) with Eq.(13) and Eq.(21) taking into account gives the needed equation F(Ebr,p,a)=0

American Institute of Aeronautics and Astronautics

8

( ) ( )( )( ) ( )( )

0

2/3

2,7

133.0

=⋅

−⋅−

⋅ ββ

β

pcrEbrEolaQ

pcrEbrEolaQ

pa . (26)

The Eq.(25) in common with Eq.(21) allows to get the universal dependence of (Etop/Eo)br on the product of pressure p on the initiator radius a for any length of initiator (see Fig.8). It is clear from Fig.8 that diffusion influence on the breakdown with initiator is insignificant if the product ap>10 cmTorr.

Figure 8. The breakdown field Ebr related to one without the diffusion influence Ebr0 dependence from product (a⋅p). Experimental points: circles – a=0.25 cm, cross – a=0.019 cm.

Figure 9. The dependence of the breakdown field Ebr from the pressure with different values of the radius of curvature a at the top of the sub-resonant initiator which are shown on the right and corresponds to solid lines from above downwards; dot line is the critical field Eq.(13), experimental points: box - a=0.125 cm, cross - a=0.019 cm. λ=8.9cm

The solution of Eq.(26) (that follows from Eq.(25)) in common with expressions for Q let to find the needed dependencies. Fig.9 shows the breakdown field Ebr dependence on the pressure for initiator of 2 cm length (it is so

American Institute of Aeronautics and Astronautics

9

named sub-resonant initiator) at wavelength 8.9 cm. The initiator is shaped as cylinder with semi-sphere on the ends. The dependencies are given for several values of cylinder radius. Consequently the same dependence for the resonant initiator with length that equals to half of wavelength is shown on Fig.10. One can see that resonant initiator with the same radius allows to get discharge at the more pressure (approximately at 2-3 times). It is important because very thin initiators are less rack to heating by the MW current inducted in it by the external field.

Figure 10. The breakdown field Ebr dependence from air pressure p at different radius a of cylindrical initiator of the resonant length. The lines are the solution of Eq. (26) together with Eq.(9). at – parameter of the theoretic curves, cirkles –the experimental points at initiator radius 1.1, 0.55, 0.25, 0.125 cm from the top downward

It is two-time smaller the value, which corresponds to power output of the generator. The comparison of the theory with experiment points on Fig.8-10 gives the satisfactory consent.

III. Modeling of initial stage of undercritical MW discharge

A. Formulation of task In external homogeneous field Е0, oriented along z-axis, in the beginning of coordinates the metal sphere of

radius a is located. About its surface initial distribution of ionization coefficient of gas is set at the given pressure and room temperature. As gas the air is used because the greatest number of supervision is carried out in air. Calculation interrupts at distance of border of the discharge from a surface of the initiator more, than on radius a as used approximation lose admissibility.

The model consists from usual system of gas dynamics

( ) ( )( ) ( )

⋅+∇⋅∇+⋅∇−⋅=

nETTn

TTTnVTTTnCdt

dT geegegg

geg

g2,,,

,,, ,,,

1 ψσψϑ

ψ (27)

( )eg nTnTdt

ψρ

+∇⋅−=dV 1

(28)

Vndt

⋅∇−=dn

(29)

Equation of ionization balance

American Institute of Aeronautics and Astronautics

10

( ) ( )( )ψψψψνψ∇⋅∇+⋅= gegei TTnDTTn

dtd ,,,,,, (30)

And Poisson equation

( )

0,,,4

1 =

Φ∇⋅

⋅+⋅∇

ωψπσ ge TTn

i (31)

(32) Φ−∇=E

The functions, which are included in the equations, are designed for an air mix in the assumption of thermodynamic balance of heavy components (molecules, atoms and their ions). Diffusion coefficient takes into account transition from the free diffusion at small electric conductivity of gas (σ>>ω/4π) to ambipolar diffusion at the big conductivity (σ<<ω/4π). The electron temperature is determined by the equation

( )( )

0,,,

,,,

2

=

⋅−

−

nETTn

TTnTT ge

geeg

ge ψσψτ (33)

where τeg – t time of electron relaxation.

B. Boundary and initial conditions The sizes of calculation area have big enough values, so variables remained to be not perturbed by development

of the discharge. They keep initial values. Development of near-surface avalanche occurs on exponential law with diffusion taken into account. Initial

distribution of factor of ionization ψ described by normal distribution with dispersion h

( )eNiν

eDh ln⋅= , 0>iν (34)

where Ne – electron surface number density. This distribution arises during time

( )iν

eNt

ln= (35)

At ln (Ne) =10 (ψ≈10-7 ) the heating of gas yet does not result in change of density of gas that allows to count at the initial moment gas not perturbed.

C. Results of modeling Below the following investigated variant are presented: radius of spherical metal initiator a = 0.3cm, air pressure

1 atm, parameter undercriticality E0/Ecr = 0.4, 0.5, 0.75. The scenario of the process is same for all investigated variants in main details. Let us describe it on sample of

variant E0/Ecr=0.75. Because the field near pole of metal ball is higher than critical value the ionization of gas increase the electric

conductivity and electron diffusion moves the boundary of plasma creation away from surface. Together with plasma boundary the maximum field location moves, saving its magnitude (see Fig.11). The heating of gas creates the shock wave, behind of which the gas density is decreasing (Fig.12a and Fig.12b).

American Institute of Aeronautics and Astronautics

11

a) b)

Figure 11. Spatial distribution of electric field amplitude near spherical initiator: a) - at initial time (t=0) and b) - at finish time (t=4µs)

In plasma the electric field decreases accordingly to gas density decreasing, so the rate E/N beside front of ionization is constant and equals to critical value (Fig.12c). Correspondingly the effective frequency of ionization in average equals to zero (Fig.12d).

Figure 12. Spatial temporal distribution of discharge parameters at z-axis (r=0)

On Fig.13 the profiles of the ionization wave on z-axis at the moment of time t=3.3 µs are shown. It is visible, that behind of front of ionization the amplitude of a field traces the change of density of gas, satisfying condition

American Institute of Aeronautics and Astronautics

12

E/N=(E/N)cr. Ahead of discharge front the ionization is fully absent. It confirms that fact, that for streamer propagation the preliminary ionization of gas by UV radiation of discharge is not needed, Ref.(6). The propagation is caused by free electron diffusion into area, where electric field is more than critical; it is near the streamer (or initiator) head. On border of a wave of ionization the amplitude of a field keeps initial maximal value. At the further development of discharge into the streamer the size of a maximum should grow, as grows the relation of streamer length to its radius.

The front of the discharge moves with constant speed, that it is visible on Fig. 14, where the degree of luminance corresponds to a level of electron temperature (black area - the initiator). Its magnitude is directly proportional to parameter of undercriticality of the external field at the given form of the initiator (Fig. 15).

Figure 13.Distribution of discharge parameters along z-axis at time t=3.3 µs. Radius of ball a=0.3 cm

Figure 14. Plot of the electron temperature, demonstrating the front trajectory.

As with growth of the streamer length the amplification of a field on its end grows, the speed of movement of the streamer end should grow also. We shall note, that the calculated values of speed of front of the discharge at an initial stage are lower than the values determined by estimation of average speed of streamer undercritical discharge, given in Ref.( 7):

American Institute of Aeronautics and Astronautics

13

⋅⋅

⋅=

cmVETorrp

cm

sV

/

30ln

5106.3

λ

, cm/s. (35)

Equation .(35) for conditions of the task gives value of 1.25-2.25 km/s (see Fig.15). It is explained by that circumstance, that at an initial stage the radius of the discharge is determined by radius of curvature of the initiator, while the radius of developed streamer, determined by its properties, is smaller than radius spherical initiator in the given numerical experiment

Figure 15. Dependence of discharge front velocity on parameter of undercriticality. Numerical experiment – solid lin with cicules, dadot – estimation Eq.(35), dashed line - |E0|/Ecr

At initial stage of initiated discharge the shock wave leads the discharge. At further stage< when discharge have developed into the streamer, the bow shock wave changes into conic divergent shock wave and further into radial shock wave. It surely was shown in Ref.(8), where the initiated undercritical discharge has been numerically stood.

IV. Discharge front instability The found peculiarities of initial phase of undercritical initiated discharge allow to explain the observed process

of transformation of near-surface discharge (named in Ref.(1) by “plasma hat”) into thin streamer. Basis of this process is electromechanical instability.

Performed numerical modeling have shown that depth of ionization front if thin enough comparatively with thickness of discharge some time after start. Behind the front this is plasma with quite high conductivity. One can deduce that It is easily to show, that originally homogeneous field above a flat well conducting surface at its infinitesimal perturbance

( )kxzz f sin⋅∆+= (36)

also will be perturbed under the law

( ) ( )( )fzzkkxkEEE −⋅−⋅⋅∆⋅⋅+= expsin00 (37)

It means, that above convexities the field grows, and above concavities decreases. The carried out modeling has shown, that speed of front of the discharge is proportional to amplitude of a field before front:

American Institute of Aeronautics and Astronautics

14

cr

f EE

VV ⋅= 0 , V (38) scmo /105=

It will result to that convexity will leave forward, and concavities will get behind. That is the amplitude of perturbance will increase. Thus, at the certain stage of development of the discharge this instability should be shown.

The increment of the instability is

0fVk ⋅=γ (39)

where

cr

f EE

VV 000 ⋅= (40)

The spatial spectrum of instability is limited from above and from below. The minimal size of unstable perturbance is limited to thickness of front of the discharge, and maximal - depth of the discharge. On linear stage the thin streamer (single or branched) arises. Accepting the depth of the plasma hat equal to 1.1 cm and taking in to account Eq.(38) and Eq.(40) one can estimate the time of the instability development. The estimated value ~1 µs corresponds to the observations quite well.

The described mechanism of instability quite well explains a usual picture of initiation of MW undercritical discharge, in particular, a photo on Fig.1.

V. Summary The carried out research confirms developed before representations about undercritical MW discharges and

supplements them regarding an initial stage. Formation of the streamer near to a surface of initiator is consequence of display electric-plasmadynamic instability at its nonlinear stage.

Though its development does not need participations of UV radiation generated by the discharge, a role of this radiation on development of other processes occurring in complex MW discharge structures is certainly great and demands attentive studying.

Acknowledgements

This work was supported by European Office of Research and Development (EOARD), Project #2429p and Project #2820p. Author is grateful to L.P.Grachev and I.I.Esakov for the provided experimental data and useful discussions.

References

1 V.L. Bychkov, I.I. Esakov, L.P. Grachev Experimental determination of the microwave field threshold

parameters insuring realization of a streamer discharge of the high temperature form. 42-nd AIAA Aerospace Sciences Meeting 5-8 January 2004, Reno, NV. Paper AIAA-2004-0181. 2 L.D.Landau, I.M.Lifshits. Electrodynamics of solid mediums. Moscow. ”Nauka”. 1982 3. W.Sharfman, T.Morita. IEEE Trans., AP-12, 6, 709,1964; W.Sharfman, T.Morita. Appl. Phys. 33, 2016, 1964. 4. R.O.Kuzmin. Bessel functions. 1935. 5. V.L.Ginzburg. Propagation of electromagnetic waves in plasma. Moscow. ”Nauka”. 1967. 6 K.Khodataev, B.R.Gorelik. Diffusion and drift regimes of a plane ionization wave propagation in UHF field. //Physika plasmy, 1997, v.23, 3 pp. 236-245 7 K.Khodataev. Numerical Modeling of the Combustion, Assisted by the Microwave Undercritical Attached Discharge in Supersonic Flow. 43rd AIAA Aerospace Sciences Meeting 10-13 January 2005, Reno, NV. Paper AIAA-2005-0985 8 O.I.Voskoboynikova, S.L.Ginzburg, V.F.D’achenko, K.V.Khodataev. Numerical investigation of subcritical microwave discharge in high-pressure gas. // Tech. Phys. Vol.47, No. 8, pp. 955-960.

American Institute of Aeronautics and Astronautics

15