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Effective Area of Microwave Discharge Interaction with

EM Beam Exciting It

D.V. Bychkov *, Lev P.Grachev,† I.I. Esakov‡ , Kirill V.Khodataev§

Moskow Radiotechnical Institute RAS, Moscow, 117519, Russia

In this work the research results of the electric discharge in supersonic air stream are

described. The discharge is lighted in the field of linearly polarized quasi-optical

electromagnetic beam of the microwave (MW) of wavelengths range, which initial level

is substantially smaller than critical breakdown level. Electric breakdown is initiated by

the tubular electromagnetic vibrator of resonant length placed in the MW beam. The

internal hole of the vibrator is an outlet section of submerged supersonic air stream

formation duct. The discharge burns in this flow and is attached to the stern end of the

initiator. Measurements of spatial distribution of stagnation temperature and pressure

of the stream in the wake of the discharge area have allowed to estimate energy

deposition into the discharge plasma and to determine the effective area of power

interaction of the discharge with the MW field exciting it. Results of experiments and

their analysis have shown that this area substantially exceeds the cross section area of

plasma discharge area.

I.Introduction

orm and properties of the gas electric discharge in the quasi-optical electromagnetic (EM) beam of

MW wavelengths range essentially depend on an initial level of EM field electric component E0 and pressure of a gas p Ref.Ref.[1]. Experiments have shown, that a plasma of such a discharge, at rather

high gas pressure p in EM beam with overcritical (E0> Ecr) and subcritical (E0 <Ecr) field is energetically

effectively interacts with this field. Here the critical level of the field Ecr is understood as its minimum amplitude, which still insures independent, electrodeless MW air breakdown. It is natural that at subcritical

discharge realization the electric breakdown of a gas should be initiated. One of such initiation ways consists in

location of the linear metal EM-vibrator into the MW beam. The MW discharge initiated by such a vibrator can be lighted also in the EM-beam with deeply subcritical

level of the initial field (E0 <<Ecr). Plasma areas of the MW discharge realized in this case are attached to the

ends of the initiating vibrator. There is a question on efficiency of EM-energy put in the plasma of such

discharge form. It is necessary to mark, that at high gas pressure p overcritical and subcritical MW discharge forms can be

carried out only in a pulse EM-field at the maximum duration of the MW pulse in tens of microseconds. For

their realization it is required to use rather unique powerful MW generators. Initiated deeply subcritical MW

discharge can be lighted also in a continuous mode using widespread rather low-power MW generators. In case

of high efficiency of EM-energy put into the plasma of such discharge form this circumstance essentially expands space for search of ways of its practical application.

One of possibilities of the specified efficiency experimental definition is lighting of deeply subcritical MW

discharge initiated by the vibrator in a stream of air and measurement of the stream parameters in the wake of

this system. In the present work experimental results of definite realization of such a possibility and results of

their analysis are described. In the experiments the design of the initiator accounting experience of works in the

given researches direction Ref.[2] was used.

II.Conditions of experiments carrying out

The basic scheme of carrying out of experiments is placed in a Fig. 1.

* Senior engineer, Department of plasma physics † Group manager, Department of plasma physics. ‡ Deputy director on Sci., PhD § Professor, Head of Plasma Physics department, member AIAA.

F

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

AIAA 2010-1002

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

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Fig.1. The scheme of research experiments of deeply subcritical MW discharge properties in quasi-

optical EM-beam in supersonic air flow

In experiments the EM-wave with the wavelength of = 12.3 cm from an exit of the MW-generator with a power Pgen = 1.5 kW propagates over a waveguide with the sizes of the internal cross section 45x90 mm. The

waveguide ends up with an antenna conic horn 150 mm in length and the opening aperture area 90x90 mm. As a

result in the working chamber of the installation linearly polarized EM-wave of = 12.3 cm is radiated in a form of the quasi-optical MW beam.

The copper tube 1 with an external diameter dout = 4 mm and internal - din = 2 mm is located in the beam

symmetrically its axis. The tube axis, as is shown in a Fig. 1, is parallel to a vector of the EM-field electric component E0 and stands from the radiating horn opening aperture at the distance of 90 mm.

In Fig.2 one can see general appearance and a calculations result of the electric field amplitude distribution

calculation in a waveguide, horn and in a near zone in absence of the tube. In Fig.3 is shown a distribution of

MW energy density flux along an axis of the system. Vertical markers correspond to a position of the horn

opening and a place where the tube will be located.

Fig.2. Electric field amplitude distribution in the plane y=0 inside the radiator and in the near zone.

A ratio of calculated values of the energy density flux in the near zone and in the waveguide allows to

connect energy density flux in the near zone w with the power Pg of the generator:

0.21gP

wab

(1)

here a, b – are sizes of internal waveguide cross section. The equation (1) at known power of the generator

(Pg=1500W) and sizes of the waveguide cross section (2a=b=90 mm) gives the value of the energy density flux

in the place of the vibrator location w=7.8W/cm2. This corresponds to the field amplitude E0= 76.5 V/cm.

One end of the tube is flat, and another has three triangular sharpened ledges. Ledges are 4 mm by depth and

distributed in regular intervals on a tube's butt end. One of them is located towards the Umov-Pointing П vector

of the EM-beam. On the end of a tube with ledges the quartz tube-nozzle 2 is densely put on. Its external

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diameter is 5.5 mm, total length is 22 mm and length of the section spreading out the pointed ends of the

vibrator is Lout = 9 mm.

Fig.3. A distribution of MW energy density flux along the axis of the radiator.

The tube is located over the metal screen 3 which is perpendicular to the vector of energy density flux П.

The distance between a tube axis and a screen surface is h = 30 mm ≈ (λ/4), i.e. it is placed in a loop of the EM-

field of initial size ~ 2E0.

In electrodynamic sense the tube 1 is the EM-vibrator. The induced field on its ends can substantially exceed

a field exciting it and to exceed the field necessary for air breakdown. At a tube length 2L ≲ /2 the induced

charges are equal to zero in its central area. This allows to fix the tube on a metal rack 4 strengthened on the

screen 3 not influencing the EM properties of the tube. The rack has size along the tube, equal to 10 mm, and across - 2 mm.

On plainly cut off end of the tube-vibrator for the length 6 mm the polyethylene tube 5 with internal

diameter 4 mm and thickness of a wall 1 mm is densely dressed. It comes from the installation working chamber

where in its rupture an electrically operated valve 6 is included with the conditional diameter equal to 10 mm.

The polyethylene tube is connected with a balloon 7 with a volume Vb = 5.2∙103 cm3. Pressure of air in the

balloon can be set in a range pb = (760 ÷ 3) Torr and to be controlled with an accuracy ±1.5 Torr.

In the Fig. 1 on the right side of the screen the source of ultra-violet (UV) radiation 8 is shown. Its purpose

and the scheme will be explained below.

The vibrator is placed in the working chamber of the installation of 0.5 m3 volume. Air pressure in the

chamber pc can be set in a range from 760 to 3 Torr and controlled with the same accuracy, as pressure pb. At

pc < pb at opening of the valve 6 air from the balloon starts to leak in the working chamber, and on an exit of a

quartz nozzle 2 the flow of air is formed. Its stagnation pressure pstag and stagnation temperature Tstag can be measured by means of a Pitot tube and the thermocouple. If necessary, one of these measuring instruments is

fixed to electrically operated motion device. It allows without chamber depressurization to pace a working

element of the measuring instrument in set "point" of the stream with co-ordinates x, y, z shown in the Fig.1.

Thus the axis х is counted from the stern plane of the quartz nozzle 2.

Metal Pitot tube used in the experiments has internal diameter 2 mm, and external - 2.9 mm. The inlet

section of this tube is directed towards the stream. Other end of Pitot tube is connected with “bridge”

electromechanical measuring scheme. The signal from it is proportional to a pressure difference on the entrance

end of Pitot tube and atmospheric pressure; it goes to an oscilloscope inlet. It allows to detect both invariable

pressure in time, and its differences with millisecond fronts.

For measurement Tstag the sensor on a basis of chromel -alumel thermocouple is used. For prevention of MW

noise, the wires departing from "hot" junction of thermocouple are placed into a metal tube-screen with external diameter 4 mm. Junction comes out the screen butt for 1 mm. At measurements the tube butt face is placed

towards the air flow. “Cold junction” of the thermocouple is the entrance scheme of the oscilloscope. Average

sensitivity of the used sensor in a stable time mode of measurement is SТ = 24.5 °К/mV at the temperature of the

hot junction up to 1100 °C. Feature of measurements by the given temperature Tstag sensor with its "sharp"

differences will be described below.

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III.Resonant properties of the tubular EM-vibrator

The resonant length 2Lrez of the EM-vibrator essentially depends on its diameter dout Ref.Ref.[4]. In the

present work has been experimentally determined the length 2Lrez of the tubular vibrator used in the basic

researches with the quartz nozzle dressed on its end. Used experimental installation for the solution of this problem allows to controllably change pressure in the

working chamber pc and, placing in the EM-beam the EM-vibrators of various make to define maximal pc at

which the given vibrator still initiates air MW breakdown pbr. In the Fig. 4 corresponding experimental values

of pbr corresponding to different lengths 2L of the investigated tubular vibrator are placed.

The basic experiences were supposed to be carried out at duration of MW radiation τMW ≈ 0.2s. However,

initial experiments on determination of resonant properties of the EM-vibrator have shown, that at such τMW in

consecutive MW pulses under invariable conditions air breakdown could occur or not. This instability,

especially at pc insignificantly smaller than pbr, is explained by a small volume of the area adjoining to edge

sharpened parts of the vibrator, with induced field Е > Ecr and absence in it during τMW of free electrons

necessary to start development of breakdown avalanches.

For liquidation of this instability in the scheme, as is shown in the Fig.1, the source of UV-radiation 8 has been included. This radiation is generated by a spark burning between an internal vein of a high-voltage (HV)

cable and a surface of the screen 3. The corresponding HV-pulse is given to the cable simultaneously with

switching on of a HV feeding of the MW-generator. Experiments have shown, that the irradiation of the end of a

tube 1 with ledges by the UV-radiation stabilizes MW breakdown process. Thus it develops at this end of the

vibrator in the quartz nozzle.

150

200

250

300

40 42 44 46 48 50 52 54

2L, мм

pb

r, Т

ор

р

Fig. 4. Resonant properties of the tubular linear EM-vibrator with the quartz nozzle

From data in the Fig. 4 follows that the resonance occurs at the tube length 2Lrez ≈ 48 mm. It is for 13.5 mm

smaller than /2 = 61.5 mm. The vibrator in such execution in the given field can ensure air breakdown up to pbr ≈ 280 Torr. Its electric quality factor is Q ≈ 5.5.

In the basic experiments the vibrator with 2L = 47 mm was used.

IV.Parameters of the initial submerged air stream

In the experiments it is supposed to investigate the MW discharge in the supersonic (SS) air stream. Let us

designate the sizes characterizing air in a balloon 7, where air speed is v0 = 0, by an index “0”. In the

experiments in the balloon in an initial condition it is set pb = p0 ≈ 750 Torr at room temperature T0 ≈ 300 °K.

According to the theory Ref.[4] follows, that at pc ≲ 0.5 p0 on flow out duct section having the minimal area

of the cross section, the stream will be characterized by the Mach number M = 1. M <1 down the flow from this

critical cross section of M <1, and M > 1 above it. In the described duct the cross section with the minimal area

is in internal channel of EM-vibrator 1. Hence, at pc ≲ 0.5 p0 on a section from the balloon to this channel the

flow will be subsonic (SubS), and in the outlet channel of the flow duct it will be SS, i.e. in the internal channel

of the quartz tube 2.

The knowledge of the ratio of the area of cross section of any section of the duct and the area of the critical

cross section allows to calculate stream parameters in the considered section Ref.[4]. So, at the specified ratio of pressure pc and p0 in the outlet channel of the quartz nozzle 2 at the ratio (dout / din) 2 = 4, the Mach number is

Mout = 2.94, the static air pressure is pout = 24 Torr, static temperature is Tout = 110 °K, concentration of

molecules nout = 2.3∙1018 cm-3 at air density out 110-4 g/cm3, and speed of the stream vout = 600 m/s. To these parameters corresponds the mass flow rate of air m = 0.7 g/s.

The pressure drop Δpb measurement in the balloon 7 for fixed time τv of the valve 6 opening allows to

estimate experimentally a value of m and to compare it with the obtained estimation. In experiment during τv ≈

0.7 s the value of Δpb in various switching on of the scheme stably lays in the range 51÷54 Torr. At known

volume Vb these values to within 10 % give the value of m, coinciding with represented above its theoretical

estimation. The basic experiments were carried out with this time τv. The specified value of Δpb equals

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approximately to 7 % from the initial p0. Hence, it is possible to consider that the parameters of the stream

represented above during time τv change no more, than on this value.

As it is known Ref.[4,5] the stagnation pressure pstag and temperature Tstag in a flow are connected

with the static pressure pstat and static temperature Tstat by Eq.(2) andEq.(4) respectively:

stag statp p F M , (2)

where

211111

1

12

12

1 2, if 1

2 12

11

11 , if 1

2

MM

MF M

M M

(3)

211

2

stag

stat

TT

M

(4)

here М –is local value of the Mach number.

Corresponding dependences are shown in a Fig. 3.

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4

M

ps

tag /

p

1

1,5

2

2,5

3

3,5

0,5 1,5 2,5 3,5

M

Ts

tag / T

Fig. 5. Dependences of ratios of pstag and static air pressure and Tstag and static air temperature in

a stream via its Mach number

For the submerged stream formed in experiment quite fair is an assumption of its equilibrium at which is

valid the condition of equality of static pressure in the stream and the external pressure - pressure in the chamber

stat cp p (5)

The measured values of stagnation pressure pstagexp and temperatures Tstag with a help of Eq.(2), Eq.(4) and

assumption Eq.(5) completely define the stream parametres. The equation (6)

exp

0c stagp F M p (6)

(Solved numerically) defines a value of the Mach number M. Its substitution in Eq.(4) together with the

measured value of the stagnation temperature Tstag gives the value of the static temperature. Then the local

values of the stream parametres are defined trivially:

the speed of the stream

0

stats

TV MC

T (7)

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where Т0 is room air temperature, Cs - sound velocity at room temperature, and the concentration

c

B stat

pn

k T (8)

where kB –is Boltzmann constant.

For analyzed in this section adiabatic flow temperature Tstag T0 and the basic information about the stream is in the waveforms for pstag.

In a Fig. 6 one can see waveforms from the measuring instrument of pstag at pc = 21 Torr and at pc = 27 Torr

in a "near" zone of the stream at x = 5 mm over its axis - y=z=0.

(a) (b)

Fig. 6. The pressure measured by Pitot tube pstag of the submerged air stream at х = 5 mm and

y=z=0. (a) - pc = 21 Torr, (b) - pc = 27 Torr

In these waveforms, as well as in all placed further in the text the time scale is kt = 0.1 s/div. In them the

initial horizontal section corresponds to pressure pc, and the signal amplitude Up counted from it characterizes a dynamic component of pressure pstag:

stag p cp Torr k Up p Torr (9)

here Up Ref.[mV]- is the oscilloscope readings, kp Ref.[Torr/mV] – is the calibrating coefficient.

In the waveforms a signal growth begins with the moment of the valve 6 opening. The signal grows to Up during time ~ 0.06 s and remains approximately constant during 0.6 s. Their sum gives actual time of the flow

out τv = 0.66 s. Final falling of a signal level in the waveforms traces leaking of "residual" air with p > pc from

the duct of the stream formation.

Both values of the amplitude Up in Fig.6(а) and Fig.6(b) by Ошибка! Источник ссылки не найден.

give the value pstag = 280 Torr, that coincides with the value following from the ratio pstag / pout = 11.7, obtained

by the corresponding graph in the Fig. 5 at Mout = 2.94.

In a Fig. 7a there is the dependence of pstag (pc) on the stream axis in its near zone constructed using the

corresponding waveforms.

(a) (b)

Fig.7. A dependence of pstag on pc of the air stream at х=5 mm and y=z=0

The pressure pstag in the given cross section rises with pc growth and the Mach number drops with respect

with Eq.(6) (see. Fig.7b)

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This result is understandable. External pressure at pc > pout in greater degree “compresses” the stream. Its

diameter decreases reaches the diameter of the critical cross section and the Mach number drops but the pressure

pstag grows.

In Fig.8 one can see an experimental dependence pstag(x) along the stream axis at pc = 27 Torr, and at Fig.9 at

the same pc one can see the dependence of pstag(y) over the diameter of the transversal cross section of the stream

at x = 20 mm. The dashed horizontal line in the Fig.9 marks the level of pc .

100

150

200

250

300

0 5 10 15 20 25 30

x; mm

psta

g;

To

rr

Fig.8. A dependence of pstag(x) of the air stream at y=z=0

0

50

100

150

200

-4 -3 -2 -1 0 1 2 3 4

Y; mm

ps

tag;

To

rr

Fig.9. Values pstag (y) of the air stream at z = 0 and x=20 mm

Mach number distributions corresponding to Fig.8 and Fig.9 represented in Fig.10 allow to judge the sizes

ans characteristics of the stream.

Fig.10. Mach number distribution in the stream:(а)- over у at the distance of x=2 cm from the nozzle

opening, (b) - over х at the stram axis.

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V.Deeply subcritical MW discharge in SS air stream

In the analyzed situation on the SS-section of the flow out to a concentration nout there corresponds an

equivalent pressure peq ≡ nout kBT0= 65 Torr at a room temperature. For it Ecr = 2.7 kV/cm Ref.[6], and air

breakdown should be realized at subcritical fields (Ecr/2E0) = 22.5. According to Ref.[1] in motionless air to experimental values of peq and 2E0 there corresponds an area of deeply subcritical streamer MW discharges.

In a Fig. 11 photos of the MW discharge lighted under the considered scheme at several values pc are placed.

Their exposition time τexp> τMW.

Fig. 11. Appearance of deeply subcritical MW discharge initiated by the EM-vibrator in SS air

flow

In the Fig. 11 the form of the stern end of the EM-vibrator with the quartz tube is given, and on the right side

over its axis there is the measuring instrument of Tstag. Its end butt has co-ordinate x=20 mm, that can serve as

scale of images. In the photos one can see, that the discharge partially burns in the quartz tube. It results in

increase of p in it Ref.[7], and can cause flow reorganization in a transversal direction. The last is demonstrated

in a Fig. 11. In experiences at pc ≳ 50 Torr the discharge area loses its axial symmetry.

In a Fig. 12 characteristic waveforms for pstag at the discharge burning in the flow are placed.

х=5 mm x=10 mm

Fig. 12. Waveforms from the measuring instrument of pstag at MW discharge burning in the air

stream at pc = 21 Torr, y=z=0 and х=5mm and x=10mm

In experiments MW generation begins after 0.1 s after signal giving on opening of the valve 6 and lasts

approximately 0.2 s. In the waveforms one can see that, as well as follows, through 0.1 s after the beginning of initial stream formation the current picture changes. Through (0.04÷0.08) s it becomes again stationary up to the

termination of τMW, but already at new level. Counted from the initial horizontal section of a signal its stationary

value Up dis at burning of the discharge also defines a value of pstag at this time under the Eq.(1).

In a Fig. 13 dependences of pstag (x) over the axis of the stream during the discharge burning are placed at

pc = 21 Torr and pc = 36 Torr.

They illustrate the experimental fact of that at small pc values of pstag along a stream axis fluctuate. In

process of pc growth the amplitude of fluctuations decreases, and they stop to be detected at pc ≳ 36 Torr.

Considering this fact and that at pc ≳ 50 Torr the discharge starts to influence also on axial symmetry of the stream, the basic experiments with the discharge were carried out at pc = 36 Torr.

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50

100

150

200

250

300

0 5 10 15 20 25 30

x, mmp

sta

g,

To

rr

Fig 13. Dependence of pstag (x) at burning of the MW discharge in SS stream at y=z=0 (a

continuous line - pc = 21 Torr, dashed - 36 Torr)

In a Fig. 14 at pc = 36 Torr and x = 20 mm two typical waveforms from the measuring instrument of Tstag are

represented at burning of the discharge in SS stream with the discharge. The left waveform (a) corresponds to

position of the thermocouple sensor on the stream axis at y=z=0. The right one (b) - at the sensor displacement

from the stream axis at y = - 3 mm and z=0.

(a) (b)

Fig. 14. Typical waveforms from the measuring instrument of Tstag for the stream excited by the

MW discharge

The signal starts to grow from the moment of lighting of the discharge and to fall - from the moment of it

extinction, that gives time of the discharge burning τdis = 0.16 s. It of a little bit smaller the time interval τMW

between giving of signals on switching on and off of MW generator.

From a Fig.14 follows, that the measuring instrument of Tstag is slow-response. If to assume, that at "step"

growth of Tstag the signal from the sensor at the MW switching on changes in time t under law U = U0 ∙ Ref.[1 -

exp (-t / τT)] then from the waveforms follows, that a time constant is τT = 0.21 s. During time t = τdis the signal

grows to Um. This value allows to calculate U0: U0 = 1.8 ∙ Um. Real value of the stagnation temperature is defined with accounting of this factor

0 01.8stag T m disT K k U T K T T (10)

where kT- is the calibrating coefficient of the thermocouple. The temperature ΔTdis also characterizes the energy

gotten by a gas in MW discharge Ref.[7].

In the Fig. 14 in the left waveform the amplitude is Um = 6.8 mV and by (4) ΔTdis = 300 °К. In the right one

– the value Um = 13 mV and ΔTdis = 570 °К.

In Table 1 and Table 2 with a step of 1 mm are placed obtained experimentally values of signals Up dis from

the Pitot tube during burning of the discharge and the amplitude of signals from the thermocouple sensor Um at

pc = 36 Torr in the plane x=20 mm.

VI. Power of MW discharge interaction with EM field exciting the discharge in SS

air stream

For determination of the power released in the discharge created in a supersonic stream of gas, the method

used earlier in Ref.[8] has been applied.

In cross-section section of a stream, in a plane x=20 mm, with step of 1 mm have been measured during the

discharge burning values of stagnation temperature and pressure at pc = 36 Torr. Results of measurements are

presented in the form of matrixes H (Table 1) and G (Table 2).

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Data of Tables 1 and 2 allow to calculate MW discharge power interaction with EM field exciting it.

Following Eq.(6), Eq.(7) and Eq.(8) we get matrixes of Mach number values, velocity and concentrations in the

flow

, , 0c m n m np F M G (11)

,

, ,

0

m n

m n m n s

HV M C

T (12)

,

,

cm n

B m n

pn

k H (13)

Local value of the energy density flux put into the stream is defined by the equation

, , , , 01

m n m n m n B m nw n V k H T

(14)

Distributions of the Mach number and energy density flux in the plane х=20 mm are represented in

Fig.15. The full power released in the discharge is determined by integration over the cross section in its

wake

2

,m n

m nS

W wds w (15)

Summation Eq.(15) gave the result W=256 Ref.[W]

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Fig.15. Distributions of the Mach number M and energy density flux w in the plane х=20 mm.

An interaction efficiency of the vibrator loaded by the discharge (with a reflector) and EM is characterized

by the absorbtion energy

0

ef

WS

w (16)

As it was indicated above w0 = 7.8W/cm2 in conditions of the experiment, this gives a value of an effective cross section Sef = 53.6 cm2. It is convenient to express the effective cross section through λ2, or

2

0.21efS

(17)

Obtained value η=0.21 is greater than the theoretical value for optimally loaded resonant vibrator (η =0.15).

This excess caused by influence of a reflector, can be large at compensation of the system resonance detuning

by the discharge plasma.

YII. Conclusions

Thus, we have realized initiated by the linear EM-vibrator deeply subcritical MW discharge in initial SS air flow in the field of linearly polarized quasi-optical EM beam. Measurements of the stagnation pressure and

temperature distributions in the wake of the discharge trace area have allowed to calculate the effective area of

interaction of the discharge plasma with the EM-field exciting the discharge. This area essentially exceeds the

area of the discharge area cross section.

In the conditions of experiments the EM beam energy put into the discharge is about of 17 %.

The estimation of energy released in the discharge can be a little underestimated. The question requires

additional research: whether all the energy gotten by molecules of air in the discharge has relaxed in heat in the

course of measurements.

The executed researches allow to consider variants of the given scheme application in practical devices as

microwave plasma generator.

Acknowledgement

The work is performed with the financial support of EOARD Project ISTC # 3572p.

References

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45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 9-12 Jan. 2007, AIAA 2007-0433

2. Esakov I.I., Grachev L.P., Khodataev K.V., Vinogradov V.A. and Van Wie David D. Effiency of

Propane-Air Mixture Combustion Assisted by Deeply Undercritical MW Discharge in Cold High-Speed Airflow //44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 9-12 Jan. 2006, AIAA 2006-

1212

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3. Drabkin A.L., Zuzenko V.L., Kislov A.G. Antenna-feeder devices. Sovetskoe radio. Moscow. 1974.

536 p.

4. Loitsyansky L.G. Mechanics of liquids and gases. Nauka Publishers. Moscow. 1970. 904 p. I. Esakov, L.

Grachev, K. Khodataev, and D. Van Wie. Efficiency of Microwave Discharges for Propane Ignition in Cold High-Speed Airflows. 43nd AIAA Aerospace Sciences Meeting 10-13 January 2005, Reno, NV. Paper AIAA-2005- 0989

5. Gorlin S.M. Experimental aeromechanics. Vysshaya shkola. Moscow. 1970. 423 p.

6. MacDonald A.D. Microwave Breakdown in Gases. John Wiley & Sons, Inc. NY-London-Sydney. 1966..

7. Bartlma F. Gasdynamics of Combustion. Energoizdat. Moscow. 1981. 274 p.

8. I. Esakov, L. Grachev, K. Khodataev, and D. Van Wie. Efficiency of Microwave Discharges for Propane

Ignition in Cold High-Speed Airflows. 43nd AIAA Aerospace Sciences Meeting 10-13 January 2005, Reno, NV.

Paper AIAA-2005- 0989