A Flame Attenuation Analysis Using State-of-the-Art Millimeter Techniques A. H. GREEN, JR. Abstract-Maintaining reliable guidance links between in- flight missiles and ground-based radar or radio guidance equipment is a problem becoming more difficult with advanced system concepts and electromagnetic environment complexity. A major difficulty encountered is signal loss caused by the ionization characteristics of the rocket motor exhaust (plasma), particularly for advanced propellants. This article summarizes briefly the present state-of-the-art in millimeter technology, particularly as it may relate to exhaust plume studies, and describes initial efforts expended in the investigation of millimeter wave techniques with application to plume diagnostics. INTRODUCTION FOR SEVERAL YEARS in both government and private industry the usefulness of millimeter waves has been discussed, but few applications employing this part of the electromagnetic spectrum have ever been completely realized. The state-of-the-art in millimeter technology continues to advance unabated, albeit a very slow process. When one thinks of the frequencies available in the millimeter spectrum the first ideas which normally emerge are concerned with radar, communications, or missile guidance techniques. These ideas arise natu- rally, since one normally would anticipate applying microwave techniques to millimeter waves to obtain such qualities as enhanced resolution, tighter (narrower) beamwidths, small components, lighter weights, or greater bandwidths. But another facet to which the em- ployment of millimeter waves seems appropriately ap- plicable is the study of the effects of rocket exhaust plumes upon radar signals. One reason that guidance difficulties occur in some Army missile systems is because the exhaust plume of the rocket apparently attenuates the guidance signal. Consequently, it becomes necessary to determine the cause of the attenuation, to determine if attenuation is the only problem or just part of the problem, and to dis- cover methods to alleviate the problem and still main- tain desirable performance capabilities of the missile. Since it usually is impractical to work with full-size rocket motors in a laboratory, then one is required to perform investigations with small scale motors. There are many factors which must be considered in this type of analysis. The most important and most difficult problem is how to scale from large motors to small Manuscript received October 26, 1964; revised November 19, 1964. The author is with the Advanced Circuits Branch, Electromag- netics Lab., Directorate of Research and Development, U. S. Army Missile Command, Redstone Arsenal, Ala. motors in order to relate results from tests on small motors to what actually occurs in large motors. This is one purpose for which the experiments have been planned. This article has two objectives, 1) to discuss briefly the present state-of-the-art in millimeter technology, particularly as it may relate to exhaust plume studies, and 2) to summarize efforts expended to date in the in- vestigation of millimeter wave techniques with its ap- plications to plasma (exhaust plume) diagnostics. Because this was the first year (fiscal year 1963) for the Electromagnetics Laboratory, Directorate of Re- search and Development U. S. Army Missile Com- mand, Redstone Arsenal, Ala., to explore millimeter technology, much of the effort was applied to reviewing literature, acquiring and evaluating equipment, study- ing millimeter techniques, and designing experiments. Several exploratory experiments were performed, but limited data was obtained. However, the knowledge gained enabled the planning and design of more detailed diagnostic experiments with small scale liquid motors and solid motors using advanced propellants. The limited experiments performed yielded valuable experience and contributed greatly toward the solution of instrumentation problems. The position has been reached whereby more useful data can be obtained. The gravity of the flame attenuation problem in certain missile guidance links warrants continued investigation in this area. A lengthy bibliography, not included in this paper, is available upon request. This bibliography contains ref- erences for work which continues to advance the state- of-the-art and which is progressing in exhaust plume studies. STATE-OF-THE-ART Millimeter Wave Generation Generally, tubes for millimeter wave generation have been developed as scaled versions of tubes operating in the microwave region, since there has not yet been dis- covered an electron beam-RF interaction mechanism which will produce these high frequencies at desirable output powers. However, considerable progress has occurred in the development of scaled tubes which pro- duce high frequencies with relatively high output pow- ers. The tube which is most noted for the generation of relatively high powers in the millimeter spectrum is the backward wave oscillator. Magnetrons are the tubes which have been most successfully scaled to the higher 172
Transcript
A Flame Attenuation Analysis Using State-of-the-ArtMillimeter Techniques
A. H. GREEN, JR.
Abstract-Maintaining reliable guidance links between in-flight missiles and ground-based radar or radio guidance equipmentis a problem becoming more difficult with advanced system conceptsand electromagnetic environment complexity. A major difficultyencountered is signal loss caused by the ionization characteristicsof the rocket motor exhaust (plasma), particularly for advancedpropellants.
This article summarizes briefly the present state-of-the-art inmillimeter technology, particularly as it may relate to exhaust plumestudies, and describes initial efforts expended in the investigationof millimeter wave techniques with application to plume diagnostics.
INTRODUCTION
FOR SEVERAL YEARS in both government andprivate industry the usefulness of millimeterwaves has been discussed, but few applications
employing this part of the electromagnetic spectrumhave ever been completely realized. The state-of-the-artin millimeter technology continues to advance unabated,albeit a very slow process.When one thinks of the frequencies available in the
millimeter spectrum the first ideas which normallyemerge are concerned with radar, communications, ormissile guidance techniques. These ideas arise natu-rally, since one normally would anticipate applyingmicrowave techniques to millimeter waves to obtainsuch qualities as enhanced resolution, tighter (narrower)beamwidths, small components, lighter weights, orgreater bandwidths. But another facet to which the em-ployment of millimeter waves seems appropriately ap-plicable is the study of the effects of rocket exhaustplumes upon radar signals.One reason that guidance difficulties occur in some
Army missile systems is because the exhaust plume ofthe rocket apparently attenuates the guidance signal.Consequently, it becomes necessary to determine thecause of the attenuation, to determine if attenuation isthe only problem or just part of the problem, and to dis-cover methods to alleviate the problem and still main-tain desirable performance capabilities of the missile.
Since it usually is impractical to work with full-sizerocket motors in a laboratory, then one is required toperform investigations with small scale motors. Thereare many factors which must be considered in this typeof analysis. The most important and most difficultproblem is how to scale from large motors to small
Manuscript received October 26, 1964; revised November 19,1964.
The author is with the Advanced Circuits Branch, Electromag-netics Lab., Directorate of Research and Development, U. S. ArmyMissile Command, Redstone Arsenal, Ala.
motors in order to relate results from tests on smallmotors to what actually occurs in large motors. This isone purpose for which the experiments have beenplanned.This article has two objectives, 1) to discuss briefly
the present state-of-the-art in millimeter technology,particularly as it may relate to exhaust plume studies,and 2) to summarize efforts expended to date in the in-vestigation of millimeter wave techniques with its ap-plications to plasma (exhaust plume) diagnostics.
Because this was the first year (fiscal year 1963) forthe Electromagnetics Laboratory, Directorate of Re-search and Development U. S. Army Missile Com-mand, Redstone Arsenal, Ala., to explore millimetertechnology, much of the effort was applied to reviewingliterature, acquiring and evaluating equipment, study-ing millimeter techniques, and designing experiments.Several exploratory experiments were performed, butlimited data was obtained. However, the knowledgegained enabled the planning and design of more detaileddiagnostic experiments with small scale liquid motorsand solid motors using advanced propellants.The limited experiments performed yielded valuable
experience and contributed greatly toward the solutionof instrumentation problems. The position has beenreached whereby more useful data can be obtained. Thegravity of the flame attenuation problem in certainmissile guidance links warrants continued investigationin this area.A lengthy bibliography, not included in this paper, is
available upon request. This bibliography contains ref-erences for work which continues to advance the state-of-the-art and which is progressing in exhaust plumestudies.
STATE-OF-THE-ART
Millimeter Wave GenerationGenerally, tubes for millimeter wave generation have
been developed as scaled versions of tubes operating inthe microwave region, since there has not yet been dis-covered an electron beam-RF interaction mechanismwhich will produce these high frequencies at desirableoutput powers. However, considerable progress hasoccurred in the development of scaled tubes which pro-duce high frequencies with relatively high output pow-ers. The tube which is most noted for the generation ofrelatively high powers in the millimeter spectrum is thebackward wave oscillator. Magnetrons are the tubeswhich have been most successfully scaled to the higher
Fig. 1. Millimeter wave sources. Approximate frequency and peak power capabilities presently available.
frequencies, but even these seem to have approached a
limit.The state-of-the-art in millimeter wave generation
continues to advance with design centered on the scalingof microwave tubes. Figure 1 is a chart depicting com-
mercially (unclassified) available tubes in terms ofapproximate frequency and power capabilities. Al-though this chart is not complete, an overall view of thestate-of-the-art can be realized.
Components
Most millimeter wave components are built as scaledversions of the rectangular waveguide in microwavehardware and operate principally in the same manner.
The primary advantage is in utilizing the dominantmode. This results in propagating only this mode sinceother modes are severely attenuated. However, prob-lems, such as increased attenuation, lower power-
Lens-corrected antennas and horns are used in thestudy of plasmas at microwave frequencies, but havenot often been employed for such use at millimeter fre-quencies. These antennas and horns are available withvarious focusing lengths and are capable of narrow
beamwidths and extremely sharp focusing.A very necessary component for good receiver design
has apparently been given little attention by various
manufacturers. This component is a mixer, either bal-anced or single-ended. A good broadband mixer for fre-quencies above 30 Gc/s is most difficult to locate. Amixer is required for designing a superheterodyne re-
ceiver which is certainly a must for the low power levelspresently available.
Transmission Techniques
A novel method of transmission involves a new typeof waveguide called H guide, which was introduced tothe millimeter community by F. J. Tischer. The advan-tage which the H guide has over the standard rectangularwaveguide is that the attenuation is much lower.Another approach to the transmission problem has
been introduced by G. Goubau of the Army ElectronicResearch and Development Laboratory, Fort Mon-mouth, N. J. This approach uses beam waveguideswhich consist of a series of lenses which attempt tofocus the radiation from lens to lens. The losses in thistype of guide are: 1) dielectric, 2) reflection, and3) diffraction.Another method of reducing attenuation in milli-
meter transmission is to use oversize waveguide. Theprimary difficulty with this method is that higher-ordermodes may be present. If the additional modes can betolerated or reduced, the gain in lower values of attenu-ation is worth while.A new concept in millimeter transmission without the
use of waveguide is based upon free-space transmission
400 -
350 -
300 -
250 -
uv5 200z
: 150al
100
173
l
.7
3,8 4 a
m a
IEEE TRANSACTIONS ON MILITARY ELECTRONICS
components performing the same functions as ordinarywaveguide components and instruments. Results ofextensive measurements of transmission loss for variousdistances show 30 dB less loss than for conventionalwaveguide at distances of up to 75 feet for wavelengthsof 4.3 and 8.6 mm employing several different antennasizes. Reflectors were used to obtain around-the-cornertransmission with losses no higher than those obtainedin straight-line transmission. Applications of this tech-nique to communication and radar systems requirefurther investigations.
Signal DetectionA device which has been used successfully in low-level
millimeter detection is the backward diode or tunneldiode. To evaluate the performance of the diodes, milli-meter waveguide circuits which were originally designedfor silicon point-contact diodes have been employed. Forlow-level millimeter signals (below -20 dBm) the low-impedance video current sensitivity of the diodes is anorder of magnitude greater than that of selected existingdiodes for the same frequency range. The "open-cir-cuit," low-level baseband voltage sensitivity of high-impedance units is at least comparable to that of thebest silicon point-contact diodes. For both of the abovecases, the devices have acted as square-law detectors.When incorporated into millimeter wave frequency con-verters (mixers), unbiased tunnel diodes have revealed aminimum conversion loss comparable to that of the bestunbiased conventional diodes when operating at beat-ing oscillator power of one milliwatt, but the optimumbeating oscillator power level is significantly less thanone milliwatt. The worst tunnel diode noise factor at IFfrequencies in megacycles is approximately that of con-ventional diodes. However, at low audio frequencies alarge reduction in noise, compared to point-contactdiodes, occurs.The tunnel diodes have been tested at selected milli-
meter frequencies up to 300 Gc/s. Because of the powerlevel generated by these diodes, they do not yet lendthemselves for incorporation into a millimeter radarsystem for use as a local oscillator. Perhaps, with moreresearch, the tunnel diode can become useful as a localoscillator in a superheterodyne receiver when incor-porated into a radar missile guidance system.Some of the newer millimeter components which have
been designed and built for use in receivers include har-monic generators, mixers, and detectors. The resultshave been improved performance, utilization of thesedevices at higher frequencies, and improved reliability.Extensive measurements have been performed at 140,235, and 420 Gc/s.
Gallium arsenide and silicon have performed equallywell in the harmonic generators. A usable dynamicrange of more than 55 dB has been achieved at 140Gc/s using 30 to 40 mW of 70-Gc/s power.A solid-state oscillator at 68 Gc/s is currently under
development by Sylvania Electronic Systems. This os-
cillator is designed for a fundamental frequency in Xband. The millimeter frequency of 68 Gc/s is to beobtained by a frequency quadrupler. The design goalsare for a power output of 10 mW at 68 Gc/s and a pack-age weight of less than 10 lb.At the present time low-noise RF amplifiers are not
available, but development is proceeding on a devicewhich is hoped to accomplish this purpose. This deviceis the millimeter maser. While such a device is at presentbulky, weighty, and cumbersome, new techniques areevolving which will make the maser gain in importanceas an integral component of a receiver system.
THE FLAME ATTENUATION STUDYThis area of interest has been studied in as much de-
tail as any other area, because of the facilities availablelocally, the adaptability of the equipment available,and the gravity of the problem. An extensive searchof literature applicable to this problem has been con-ducted and is continuing to be conducted. Sources,titles, and authors of the literature relevant to the topicare listed in the available bibliography.
A pplicable Electromagnetic TheoryThe theory behind the experiments is obtained by
combining elements of Newtonian mechanics, electro-magnetic theory, and the kinetic theory of gases. Thedevelopment presented here is intentionally detailed sothat the theory is complete.When an electromagnetic field is impressed on an
ionized medium, the electrons in the gas are set intooscillatory motion. The subsequent collision with neu-tral gas molecules causes energy to be abstracted fromthe wave. It is possible to write an intuitive equation ofmotion for a single electron, and account for the power(energy) losses by adding a first-derivative term in theequation of motion.
Consider a region where free electrons exist with adensity of N electrons per cubic centimeter.' The elec-tromagnetic field, E, produces a movement of the elec-trons, and hence, creates a conduction current with adensity of magnitude
J,= Nev = crE (1)where N is the electron density, e is the electroniccharge, oa is the complex conductivity, and v is the aver-age instantaneous velocity in the direction of the electricfield. If there are collisions between the electrons andneutral gas molecules, energy is lost in the form of heatto the gas. This "frictional" force is assumed to be pro-portional to the average velocity of the electron. Hence,the equation of motion may be written as
dvm -+ mvv = Ee
dt (2)
where m is the mass of an electron, v is the frequency1 Adler, J. P., Measurement of the conductivity of a jet flame,
J. Appl. Phys., vol 25, Jul 1954, pp 903-906.
174 April
Green: Flame Attenuation Analysis
of collision, and dv/dt is the change in the velocity of theelectron with respect to time. The electric field is as-sumed to be of the form
E = Eo exp[j(ct+yy)] (3)where w is the electromagnetic frequency in radians,and y is the propagation constant. The expression forthe velocity obtains from a solution of the differentialequation, namely,
Ee=
mv + jxm (4)
Equation (4) is substituted into (1) so that the equa-tion for the current density becomes
Ne2EJ= Nev =:S
mY + jrm (5)
Equation (5) is separated into its real and imaginarycomponents yielding the equation for the conductioncurrent density
NeIvE jfNe2EJc= (6)_m(v2 + Co2) m(V2 + w2) (6)
The conduction current in the gaseous media, therefore,has a component of current in phase with the impressedelectric field and a component of current in quadraturewith the electric field. From (1) the relation is obtainedin terms of conductivity
Fig. 2. Coordinate system for the field components of a plane wave.
and
AD bEV X H = Jc +- = Jc +
At bt (11)
Assume that the E vector has only the component alongthe y axis and the H vector only the component alongthe z axis as shown in Fig. 2.From Maxwell's vector equations a set of scalar equa-
tions is then obtained, namely,
b -z Ey-~~~~E-= o-Ey -+Ax 6t (12)
ar = aR + j0-1 (7)where
Ne2vR m(V2 + (,2) (8)
Nelc_ __= (9)
Mm(V2 + 2)
In formulating Maxwell's equations for ionized media,the conduction current density term must be added tothe displacement current density term that appears inthe free-space form of the equations.No electromagnetic waves can exist within a perfect
conductor. However, if the conductivity is finite, propa-gation can occur. A good conductor is defined as one inwhich the displacement currents are negligible whencompared with the conduction currents. If the reverseis true, the medium is defined as an imperfect dielectric.Since the ratio of these two currents is frequency de-pendent, a medium may be a conductor in one regionof the frequency spectrum and a dielectric in anotherregion. In the case of laboratory flames under investiga-tion, imperfect dielectrics will be of primary concern.
In the conducting region Maxwell's equations takethe form
and
1x
(HZ= (13)
To solve the equations, differentiate (12) with respectto t and (13) with respect to x. This obtains
12Hz BE, 62EY==-a +
(x(t At at2 (14)
and
(2EY (22HZBx2 btcx
(15)
Equation (14) is now substituted into (15) yielding
1 62EV SEy (2EV--- a + e
A ax, at at2(16)
If E, is assumed to be of sinusoidal variation withrespect to t, then
Ey= Eo exp (jwt) (17)First and second derivatives of (17) are now taken so
that
(SEa= jwEo exp (jwt)
_ tB AHV X E = --=-A=
bt At
,Hz
DIRECTION OFPROPAGATION
1965 175
y
(10) (18)
IEEE TRANSACTIONS ON MILITARY ELECTRONICS
and
82EV-=Ey - w2Eo exp (jwt)
When (18) and (19) are substituted into (16) the e(tion
6X2 (jw/.ps - w2/.Ae)E,
for the quadratic equation
(19) ax2 + bx + c = 0 (30)
qua- is used. Since the solution is concerned with plus or
minus a square root term, it is determined that only theplus sign is of significance since (3 is a real number. Con-
(20) sequently, the expressions for A and a are determinedto be
(31)
and
=Vf[fL)2R(232
is obtained. Let2 =jCOa-W2
then62E
_=2 7Ey
A solution for this yields
The cases of interest in the experiments are 1) v>>w, and(21) 2) v =w. For case 2) the equations for a and : do not
easily simplify, but for case 1) o-f becomes negligible,and the equations simplify such that
(22)(33)
andE, = Eo exp (-yx),
whereby y is recognized as the propagation constanthaving real and imaginary components such that
1 = a + j# (24)
where a is the attenuation constant and d is the phaseshift constant. The components of oy are now solved.From (7), (21) and (24)
a2 - (2 = - (cyoWT + C02/.E) (25)
(34)
Since the medium of interest is essentially an imperfectdielectric, then
we->> 10R
(35)
Now, by the binomial theorem
/ cy 2 \1/2 1 o. 2R1 2_2_)1 + 2 2**R1+=1+-1 --- R
2\(&Y/ 2 W21E2
Equation (26) is solved for a with the result substitutedinto (25). This yields as the expression for A
( R _ 2 = -(Cv,ua + W2jAC)
Equation (27) is simplified so that
34 + (COIArtT + W2A()f2 R = 04
To solve for : the general solution
-b ± Vb2 - 4acX =
2a
with other terms neglected since they are small in com-
parison with the first two terms. This result is substi-tuted into (33) and (34). Hence,
(27)(37)A
= _/ _((R2 +4W2E2)
(28)
(29)
and
a= (38)
Therefore, a wave traveling in an ionized medium v>>whas the form
E, = Eo exp (-j,Bz) exp (-az) (39)
(23)
and
2a# = wAo/1R (26)(36)
2 2# = CO
juf al 0-r O-R1 + + 1 + +
2 we wc- we
/if 0-ra = w - I +
2 2
2-A ea = w -I + I +
2
176 April
(32)
2 -
# = CO1.4cI + I + O'R
2 WC
Green: Flame Attenuation Analysis
INCID
H WAV
REFLEC4-WAVE
ROCKETFLAME
ENT INCIDENTgo ze&rE X z /, HZ WAVE X/fEXTRANSMITTED ZWAVE REFLECTED
TED WAVE
CONDUCTINGMEDIUM
BOUNDARY BOUNDARY 2
Fig. 3. Plane wave transmitted through conducting medium atnormal incidence with no charge in polarization and no loss.
and
a= L(/1+ + I + + 2
INCIDENT
2 WAVE X
(44)
Since imperfect dielectrics are considered, the condition(.e/aR)>l) applies. Now, by the binomial theorem withall terms after the first two terms neglected as before
This result is substituted into (43) and (44) so that
For the problem under consideration where the condi-tion »>>w applies, wave transmission through a dielectricslab, namely the flame, is similar to that shown in Fig. 3.A rigorous analysis would require a consideration ofboth the transmitted and reflected waves at boundaries1 and 2. However, with the flames under consideration,reflection is to be assumed negligible. Consequently,the equations for the square of the amplitude of thesignal with ,B neglected become
W V(2++R W:2 )
and
a = w (V/i()
Equations (46) and (47) are simplified so that
(48)A = (2w2l2 + 2wEaR + a-R2)(40)~~~~\/
and and(Ne svd
(El,) I = E02 exp - \IAIe m(V2 + W2)) (41)
where d is the thickness of the slab. The power ratio is,therefore,
(Eyl)l r _ Ne2vd 1
(Ey2)2 =MexpL-/ (V2 + W2) j (42)
Usually, the phase shift constant, (, will be measuredin order to determine more accurately the value for thecollision frequency. Since both the electron density andthe collision frequency are the only unknowns in theequations for a and (, these parameters may be calcu-lated from the measurements for a and A. It is possibleto determine a value for the collision frequency by meas-
uring the electron temperature of the flame, but such a
method is inaccurate because of the difficulties inherentin measuring exact temperature. The measurement ofgives a more accurate value for the collision frequency.
For the case 2) where v-=w, (31) and (32) may besimplified. Since v=W, then Oa,UR. Consequently,
+ / + 2 [21 (43)
aR ACi = _ /
N/2 / > (49)
As previously stated, the reflection is assumed negligibleand the power ratio becomes
(El)2 - 1 Ne2,d__
(exp -L m(V2 + W2)_ (50)
If (50) is compared to (42), the exponential is seen todiffer by a factor of 1/2. This means that the signal isbeing attenuated less, and, as w increases, the implica-tion is that the signal begins to propagate through themedium.
Experimental EffortThe experimental effort of this laboratory has been to
utilize the millimeter equipment as a tool in the studyof plasmas. This type of experimentation has been pur-
sued primarily because of the availability of facilitiesand equipment and because of the desire to more com-
pletely understand the properties of plasmas withregard to propagation of electromagnetic waves. Ex-periments have been proposed for this investigation ofvarious solid propellant mixtures and structures bymillimeter probes of plasmas created by small solidmotors, and similar experiments have been designed for
(46)
2(Ell= Eo
(47)
(40)
1771965
IEEE TRANSACTIONS ON MILITARY ELECTRONICS
millimeter probes of plasmas generated by small liquidmotors in test firings of advanced fuels.The microwave equipment was arranged for use in
these proposed experiments as shown in Figs. 4 and 5,respectively. Since measurements at the small solid-motor facility were planned on a cooperative basis (aspart of an existing project), only measurements ofattenuation were to be performed. Because of smallnessof the test area and the complexity of the instrumenta-tion, a limitation on the type of measurements per-formed was required. Only the necessary measurementsof attenuation and frequency were planned. Otherparameters of the plasma were to be approximated fromtemperature and thrust characteristics of the rocketplume.Three series of several firings have been completed
on the small solid motors with limited data gleaned.These firings, however, have led to a solution of themajor instrumentation problems and the last firing heldindicated that the equipment was functioning properly.Another series of firings was proposed for the future andthe expectation is that much improved data will beobtained.
Linear polarization in the vertical plane is planned.The transmitting frequency is to be near 75 000 Mc/s.The transmitter employs a continuous wave klystronmanufactured by Varian Associates of Canada andtunable from 74 000 to 76 000 Mc/s, and an antennaapproximately six inches in diameter with a beamwidthof approximately 1.50. The receiver employs a hornhaving a beamwidth of approximately 250 and lN53crystal as a detector. All data are to be taken at the exitplane of the rocket motor.The major instrumentation problem was associated
with the detector mount. This mount was subject tovibration, shock, and pressure waves generated by therocket motor. Two difficulties had to be overcome,1) insufficient mass of the mount, and 2) the physicalinstability of the crystal within the mount. These diffi-culties were solved by constructing a mount for thedetector mount itself. This new mount was constructedof heavy aluminum utilizing welded construction.Within this mount the detector mount was installedand embedded in foam rubber. Teflon was used to serveas a pressurizing window for deflecting the pressurewave and was mounted directly on the horn. Figure 6is a pictorial representation of the mount constructedfor the detector mount. Figure 7 depicts the mountingof the horn within the teflon pressurizing window. Thisteflon device is assumed to have negligible effect on theelectromagnetic wave.The complete instrumentation is shown in Fig. 8.
The horn antennas are used for performing attenuationmeasurements in X band or near 10 000 Mc/s. The smallantenna shown in approximately the center of the pic-ture is situated directly over the receiving horn whichis mounted within the white structure. The mount con-taining the detector is shown just to the right of the
base of the concrete pedestal.The instrumentation for the experiments proposed
on small liquid motors is expected to yield the morecomplete and useful data. This is because of the caretaken in determining the position of the antennas andthe rocket motor. Figure 9 illustrates a simplified ver-sion of the test equipment configuration for the experi-ments proposed for the small liquid motor facility.The motor is mounted on a carriage which is free to
ride on a set of rails, as shown in Fig. 10. The carriageis to be driven hydraulically with exact position of thecarriage to be determined by a voltage reading from aprecision potentiometer. The arm of the potentiometeris attached to the carriage and is movable, but thepotentiometer itself remains fixed. The transmittingand receiving equipment is to be mounted on tablespermanently fixed in relation to the carriage. The trans-mitting and receiving antennas are to be accuratelyaligned with the longitudinal axis of the motor by usinga transit. The transmitting antennas with a beamwidthof approximately one degree emit beams which areessentially collimated. The distance between receivingand transmitting antennas is of the order of 40 cm.
Because no firings have been conducted, the instru-mentation problems which will undoubtedly occur areunknown. However, there should be no problem sosevere that its solution cannot be resolved.
Literature Search
There are many articles in the literature which treatthe plasma diagnostic problem. The majority of thesereport experiments which have utilized frequencies lessthan those of millimeter waves. But millimeter wavesare being used more frequently because of the advan-tages offered by millimeter techniques. The followingadvantages are cited: 1) the small beamwidth attainableby millimeter antennas, 2) the small size of the com-ponents which allows more flexibility in instrumenta-tion, 3) the ability to scale from high frequencies andsmall motors to perhaps lower frequencies and largermotors, and 4) high resolution obtainable with milli-meter waves.The more useful and appropriate articles are listed
in the available bibliography. The difficulties and suc-cesses are reported in great detail in these articles; con-sequently, no useful purpose is attained in reportingthese details. But one implication is gleaned from nearlyevery report--that a more satisfactory method forstudy of plasmas needs to be created. Several people feelthat millimeter may offer a solution; others differ, butwork that has been done indicates a useful future formillimeter wave techniques in the study of plasmas.From a theoretical point of view, the millimeter waves
under consideration, that is, for a frequency of 75 000Mc/s, are hopefully operating at the point where v;wor where electromagnetic waves begin to propagatethrough the medium. Thus, the medium is approaching
178 April
Green: Flame Attenuation Analysis
Fig. 4. Microwave instrumentation for attenuation and phase measurement.
Fig. 5. Microwave instrumentation for attenuation measurements.
1965 179
Recorder = Detector -Attenuator Tuner
- Precision
11
IEEE TRANSACTIONS ON MILITARY ELECTRONICS
Fig. 6. Receiving horn mounted within a teflon pressurizing window.
Fig. 9. Simplified physical layout of test equipment forsmall liquid motor facility.
Fig. 7. Crystal detector mounted within a heavy mass structureand embedded in foam rubber.
Fig. 10. Roller-mounted carriage for use in measuringattenuation of small liquid motors.
Fig. 8. Complete X band and millimeter instrumentation formeasuring attenuation of small solid motors.
that of conducting medium and is ceasing to be a di-electric medium. It is, rather, an imperfect dielectricand/or a quasi-conductor.Theory indicates that millimeter waves should be
extremely useful in the study of plasmas because of theinherent advantages associated with a short wave-length. The two primary reasons are the narrow beam-width attainable and small component size.
Because attenuation and phase can be measuredfairly accurately with available commercial equipment,the two unknown parameters, collision frequency andelectron density, can be determined with reasonablygood accuracy. These two parameters determine to alarge extent the characteristics of plasma.
The experiments proposed and described herein wereplanned for a continuation of the study of plasmas atmillimeter frequency. It is felt that the results whichwill be obtained will be applicable to tests of largermotors by using a scaling factor. However, the mostimportant result to be gained from these experiments isthe characteristics of the plasmas and their effect uponpropagation of electromagnetic waves.
APPENDIX
BASIC ESSENTIALS OF IONIZED MEDIA
Contained herein is a compilation of the basic essen-tials presently used in the study of ionized media. Asummary of formulas and a diagram for ionizationstudies for a cavity of the TM1o0 mode at Jet PropulsionLaboratory are given.2 This method is regarded as oneof the most basic for evaluating the parameters of anionized media. Essential to the evaluation of the proper-ties of an ionized media is the determination of the tem-perature of the media. Two of the best known methods,
2 Adler, op. cit., pp 903-906.
180 April
Green: Flame Attenuation Analysis
BASIC ELECTROMAGNETIC EQUATIONS FOR THE STUDY OFTHE PARAMETERS OF IONIZED MEDIA
Complex propagation constant y = a + j
Attenuation constant a = 9V 2 ( 1/ + ft- 1)
Phase constant A1+ - +1
N 22 V/ 2
Real part of conductivity -e
1 + (V______1 + (VC/co)2
Ne2 1Imaginary part of conductivity a; = N 1
Attenuation constant as a func-tion of plasma parameters a - 1(,p/,)2]1/2(approximation)
Phase constant as a function of X 1plasma parameters c [1 - (cp/w)2]1/2
Cavity technique employed at Jet Propulsion Laboratory.
SUMMARY OF FORMULAS FOR IONIZATION STUDIES BYMEANS OF THE TM010 CAVITY
Real part of conductivity ob- attained from TMoio cavity as = 1.69 X 10-s3 - (r -1)measurement
Imaginary part of conductiv-ity from TM0jo cavity meas- aj = 47rc0 -
2
J Ji2(ka)urement
b Jo2(ka)+ J,2(kb)
Collision frequency from cavity , = R
measurement ai
Electron density from cavity MM= (A-+-o\+-+
measurement E2 \i OR
McAr I1-jw\Complex conductivity (=JRR-jJ i
m \1+w,2A
EXHAUSTPLUME
RFGENERATOR
CALIBRATED
ATTENUATOR
X MOTOR
RECORDER
!\AMPLIFIER
AND
AVERAGING
iii ~~VOLTMETER
> DETECTOR
Electromagnetic probe system used by NRL.
Acoustic method of measuring gas temperature.
SYMBOLSX= signal angular velocitya= cavity radiusb = flame radiusQ =unloaded cavity QV= collision frequency = IITn =electron densityAf=frequency shift from no flame to flamem =electronic massT =mean time between collisione=electronic charger =ratio of field strength at the receiver with and without jet
flame presentJo(ka) = Bessel function of first kind, zeroth orderJ1(ka) = Bessel function of first kind, first order
, = phase constanta= attenuation constantc =velocity of light
w,= plasma frequency
which are given in pictorial diagrams, are the electro-magnetic probe system in use at the Naval ResearchLaboratory, Washington, D.C.,3 and the acousticInethod used at Harry Diamond Laboratories, Wash-ington, D.C. The most useful electromagnetic equa-
tions and definition of the symbols employed are given
for reference.
ACKNOWLEDGMENT
Referring to various industrial and governmentalsources which are pursuing studies in flame attenuation,and which are engaged in advancing the state-of-the-art in millimeter technology, aided in the preparation ofthis work. The author is indebted to these sources,which are too numerous to mention, for their support.
3Balwanz, W. W., The plasmas of rocket flight, 1961 IRE Inter-natl. Conv. Rec., pt 1-10, pp 3-9.
