<( 0( 1S I -~m -f 7CD N RADC-TDR-63-435 4915-13-Q = RL-2116 MICROWAVE PLASMA COMPONENTS STUDY! TECHNICAL DOCUMENTARY REPORT NO. RADC-TDR-63-435 November 1963 Techniques Laboratory Rome Air Development Center Research and Technology Division Air Force Systems Command Griffiss Air Force Base, New York * 0 -Project No. 5573, Task No. 5,(Prepared under Contract No. AF30(602)-2605 by Andrejs Olte and E.K. Miller, The University of Michigan, Ann Arbor, Michigan)

Suggested Keywords: Magneto-plasma resonance isolator, microwave circuit application ABSTRACT First order theory is presented for a magnoto-plaslma resonance isolator employing the TM mode in:a rectangular -aveguide. The effect 1 of non-uniforrm rmagnetostatic field on the non-reciprocal transmission properties of the device is investigated. The beginning of experimental study to improve the stability of plasma package in the i.?icro\.ave circuit application is presented. PUBLICATION REVIEW This report has been reviewed and is approved. For further technical information on this project, contact Mr. Joseph Schenna, RALTM, Ext. 4251. Approved: i ~:? J SE PI CHENNA Pro jectngineer Directorate of Aerospace Surveillance & Control Approved: 44 / (;a 6 ARTHUR J FROHLICH Chief, Techniques Laboratory Directorate of Aerospace Surveillance & Control AIR FORCE, Cato Show Prtg. Co. 11/25/63 - 142

TABLE OF CONTENTS Page I. Thcoretical Derivation of Absorption in the Electron Cyclotron Resonance Isolator 1 II. E.xerimncntal Study of Plasma Packalge Stability 19 11I. Conclusions 22 IV. Future Plans 23 iii

LIST OF FIGURES Figure Page 1-1 Isolator Geometry 2 1-2 Ratio of Power Transmission to p2 as a Function of Y, Calculated from the Extraordinary Wave Approximation Equation (1. 31) 12 1-3 Ratio of Power Transmission to p2 as a Function of Y, Calculated from the Extraordinary Wave Approximation with Elliptic Polarization Accounted for Equation (1.47) 18 2-1 Vacuum System 20 v

INTRODU CTION This Quarterly Progress Reports presents work done on Air Force Contract AF 30(602)-2605 for the period 1 April to 30 June 1963. This report has three sections. Section I presents partially completed theoretical ws'ork on the mode of absorption of the electron cyclotron resonance isolator. Section II gives an account of the progress mnade in the experimental phase of the effort. Section III presents a brief statenent of the plans for the second quarter. Previous work on these prolle-l:s is su.u marizedl in Radition Laboratory Report 4915-1 -F(RADC-TDR -3 -54). I. THEORETICAL DERIVATION OF ABSORPTION IN THE ELECTRON CYCLOrTRON RESONANCE ISOLATOR. We want to compute the powscr transmnission coefficient through a plasma cyclotron resonance isolator. The pertinent dimensions of the isolator and the coordinate systems are shown in Fig. I-1. A TMll mode propagates in the squatre cross section ewaveguide in the positive z-direction. A thin plasma slab in the bottom half of the waveguide extends from vwall to wall in the x-direction. A magnetostatic field is impressed on the plasma in the + x-direction. The power flow at each point in the z-direction, for any waveguide, may be characterized by an absorption coefficient a that is defined by +Note: Although this is called Quarterly Status Rce:ort No. 13 it should be noted that it covers work done in the first quarter of the second year. The first 12 reports were monthly. 1

y a Y, z FIGURE I-i. a 7.6cm, b =7.7cm, yj =1. Ocm, and Y 2.5 cm.

(assuming propagation in the positive z-direction) P(z) = Pinexp -2 5 (z')dzj (1.1) where Pin is the input power, and P(z) is the remaining power as the wave progresses through the guide. Differentation of (1. 1) yields, Y(Z) 1 dP(z)(1.2) ) 2P(z) dz (1.2) But since the time average of the divergence of the Poyntings vector, V S S, gives the negative density of the po wer absorbed in the medium we obtain, dP() JV S dx dy, (1.3) A where A is the guide cross section. On substituting (1.3) in (1. 2) we have (z) — 21( J^V dx dy (1.4) A The power tramslnission coefficient (PTC) of the isolator may now be defined by P out PTC 10 log- (1.5) in Neglecting the reflections from the ends of the isolator we have 3

b PTC - 4.34 a(z')dz' (1.6) and since P(z)=-Ref S a dxdy (1.7) z A we have from (1.4) and (1.6) that <b fv Sdxdy PTC = 4.34 A dz (1.8) 0 ReffS azdxdy We see that in order to calculate the PTC one must have a model that describes the plasma-electromagnetic wave interaction so that the divergence of the power flow may be obtained. The magneto-ionic plasma has a permittivity of the following form in our coordinate system: E 0 0 11 ~ = 0 22 23 (1.9) 0 C32 C33 The tensor elements are given by 4

c4j P ] L j(v ~j) - C22 C33 C0L17V77(.0 23 32 jL(V~j)2 ~y2j - where P z- p/ W, ", - V vi Ljo, Y=W,, / W The time, average divergence of Poyntings vector for an anisotropic dielec-tric is given by v. E. (111 In the above formula the tensor notation is used. Substituting (1.9) and (1.10) in (1.1 1) wve have = j {(Ci I -,Efj)9ElE+(c-22 -E*2)(-E*E + E*E) 4 2c 2E-EE23 1.3a with -I,, 2jc0 N7 (I. 12b) C. j ----— V - -(1. 12 c).1. vp2 y c + (-I =4co y2V2 12, (1..12 d) 2 3 2 3 0 V2J2+2) 5l

The isolaltor is operated normally a stalte such that the following conditions on the parameters hold true: V <<1 (1.13a) and Y = ltiY, /Y| <<1. (1.13b) The conditions (1.13 a and b) imply that the first term on the right hand side of (1.12a) is negligible compared to the remaining two terms. Thus further we consider only that V ' -j (22 2)(E E2+ E3 E -E23+ 3)(E* E3-E3E2) 4 22 22 2 2 3 3 23 23 2 3 3 2 (1.14) A special case of considerable interest is when the electrical field part containing E2 and E3 components is circularly polarized. Then E3 j E2 (1.15) and V.S -E VP2 (2+y )2:'V2 IF2 (1.16) 02 (V22 — i.)2 V)2 I where IEI2;2IEI;2 F2 IE - 2 |E2 +- 2 Es and the + signs are correlated with the signs in (1.15). Applying conditions (1.13) to (1.16) and taking the leading terms we have in the case of the (-) sign;

V2S() V \to\2 p(1.17) and in case of the (+) sign 7V e vP2 V1P- E l(1.18) (+) 0 (V y)2+v2 Equations (1. 17) and (1.18) show that the time average divergence in the vicinity of the cyclotron resonance very strongly depends on the sense of the circular polarization of the electric ficid in the plane normal to the magnetostatic field. This is clue to the fact that the sense of rotation of the electrons in a plane normal to the magnetostatic field is fixed, and in the case of (1.18) the electric field is rotating in the same sense whereas in (1.17) the electric field is rotating in the opposite sense to the natural direction of the electron rot ation. Hence we have the striking difference in the time average of the Poyntings vector divergence. For the moment we leave this thread of reasoning and consider the following. The time average divergence of the Poyntings vector in an isotropic medium that has only dielectrical losses may be written as V' c, Ed. (1.19) 2 where e tt -j Coa is the permittivity of the medium and clearly is a scalar constant. iHowever, also in the special case of a circularly polarized plane 7

wave that is propagating along the magnetostatic field line the electrical flux density is related to the electrical field by a scalar constant; an equivalent permittivity so to speak. We distinguish two waves: ordinary and extraordinary, depending on the sense of polarization of the electrical field. For the extraordinary wave the sense of polarization of the electrical field is the same as the direction of rotation of electrons in the magnetostatic field, while for the ordinary wave they are opposite. One may be tempted to believe t-at it is permissible to take the imaginary parts of these equivalent permittivities and substitute them in (1.19). Then we obtain that in the case of extraordinary wave V'S VP, E - - * 1.20) cOx. 0 2 (Y -1 )2+v E * E ) and in the case of ordinary wave V.S =- VP1 E E (1.21) ord. 0 2 V y+1)2+V2 E E The absorption for the ordinary w\ave should correspond to (1.16) with the (-) sign xlwhile the same equation swith the (4) sign would apply to the absorption of the extraordinary <a':ve. Equat ion (1.16), however, does not reduce any further, and we have to conclude that (1.20) and (1.21) in general are not correct. But here, we arc not interested in the total domain of the variables. We are interested primarily in conditions (1.13). \ihen we apply conditions (1.13) to (1.20) and (1.21) \ve have respectively: 8

ex. 2 P ()+ E E (1.22) ~ 02 (Y Y)2 +V2 and -7 VP -e Vp2E E (1.23) ord(. 02 4 It is clear that (1.22) corresponds to (1.18) and (1.23) corresponds to (1.17). Wo may conclude that (1. 20) and (1.21) are a good approximation to the actual absorption in the magneto-ionic medium in the case when the microwave frequency is close to the electron cyclotron frequency and th1e electron col - lision frequency is small comnpared to the first. With these approximations in mind we will be using (1.20) and (1.21) in the first set of calculations. To shorten the notation we introduce the following. eo. C 2 1 (1.24) (Y'-)2 +V2 and C - "o vp2 ( 1 _ (1.25) Before we can proceed with the calculation of the power transmission coefficient we have to write down the form of the fields m the isolator. We consider the fields of the TMI1 mode propagating in the positive z-dircction in an empty guide. Wiithin an arbitrary constant and assuming C time dependence they iare de nd they are 9

-TX 7x - x y - E- x a cos - sin x-j 3 as rcos-ay a a a a y +2rsinX _sin _ z eI z a a z TX yJ. - 1 - jw ca sin - cos -a -cos —sin -a ' a a x a a j (1.26) (1.27) where 11-JZ c -2 (a)2 11 0 a In the context of using formulas (1.20) and (1.21) we neglect E and hence we have E -2 x2 I 2 Sin2 7rX Si2 E =E a2 31 eCs2 sin - + 47 sin2 x sin2! - a a a a (1.28) Furthermore we have that f s a dxdly - 2Re A A ExH- 4 dxdy ExH g dxdy = 4 (1.29) We observe that (1.24) has to be used together with the fields of (1.26). Thus we have V - - [a2 2 sin 2 Cos! 9! 4-sin sin2 ax cs2.+42 in2 aX a- a] a a a a (1.30) Substituting (1.29) and (1.30) in (1 8) we have 10

PTC= -8.68 (dz dy A sin2 X cos2 y Ia a a 2 1 7 + s in2 rsn2 + (1.31) 31a a ] c When C' in the preceding equation is independent of coordinates, we may easily carry out the intcgration, and aa2 PTC a 17 2-.136 (1.32) I 0 For a frequency of 3. 9 Gc the equation (1. 32) reduces to PTC: - 5.6 (y (1.33) In Fig. I-2 the ratio PTC to P2 of (1.33) is plotted as a function of Y for f = 3. 9 Ge and v = 0. 8 Gc. The magnetostatic field strength is taken at the c center of the plasma. We observe a sharp resonance at Y=l, i.e. o=i_. Measurements on the magnetostatic field show that the field at the center of the plasma chamber is about 15 percent less than that at the edges. Since c" is dependent upon the cyclotron frequency and hence on the magnetostatic field strength, it follows that (1.32) is not strictly applicable in our case. 11

OP PTC -- p * -, - Cn 0 -0 yI ~I. FIG. 1-2: RATIO OF POWER TRANSMISSION TO P2 AS A FUNCTION OF Y, CALCULATED FROM THE EXTRAORDINARY WAVE APPROXIMATION [EQUATION (1.31)

In order to determine the effect upon the PTC of a non-uniform magnetostatic field, the integration of (1. 31) was performed assuming a parabolic and a linear variation of the magnetostatic field in the x- and z-directions. Since the extent of the plasma in the y-direction is rather small compared to the waveguide size, the magnetostatic field in this coordinate was assumed constant. The integration was performed numerically, using, as before, a microwave frequency of 3. 9 Gc and a collision frequency of 0. 8 Gc. In Fig. 1-2 we have shown the PTC to P2 ratios for the parabolic and linear field variation. We notice that the resonance absorption peaks are considerably broadened, and reduced in amplitude by approximately one-half as compared to the constant magnetoslatic field case. For Y=l the PTC/ P2 was computed for the measured magnetostatic field variation. It is slightly larger than the preceding two magnetic field variation cases. At this point we should summarize the approximations which have not been pointed out explicitly in the calculation of the graphs of Fig. 1-2. (1) The field in the plasma has the same transverse variation as in the empty guide and there is no reflected wave in the plasma section of the guide. This assumption will also be used in subsequent calculations. 13

(2) The longitudinal electric field of the TM11 mode is not circularly polarized throughout the plasma cross section, but we are proceeding as if it were. (3) The magneto-ionic plasma slab does not convert energy from the TM, 1 mode into the TElo or TE o mode which are also propagating modes in our square waveguide. When the direction of propagation of the TM 11 mode is reversed, i. e. it is propagating in the negative z-dircction, then the PTC may be computed from (1. 31) by substituting for C' the imaginary part of the equivalent permittivity for the ordinary wave, E, given by (1.25). This loss is negligible for V << 1 and Y~l; our region of interest. In the preceding discussion it was assumed that the longitudinal field of the TM, 1 mode was circularly polarized throughout the plasma slab. The assumption holds only for the center plane of the slab. In the rest of it the field is elliptically polarized. We may remove this approximation, if we decompose the elliptically polarized electric field into two oppositely rotating, unequal amplitude, circularly polarized fields. We thus let E [A + ]e (1.34) with A+ =A2 a +jA3 (1. 35a) B Bay -B3 a (1.35b) 14

and A2 A3- B3 - B3 The longitudinal electric field then is resolved as A in a 1- cos+ 27r sin a] (1. 36a) 2 2 a a a B2: j - sin 31 cos - 2 sin I (1.36b) 2 2 a L a aI We notice that for our range of parameters B2 << A2 The time average divergence of the Poyntings vector becomes V2 L A- A + ~ A+C+ B*. (1.37) At would appear that we are mis-using superposition to obtain the above formula. In fact we are not using that principle in either sense. We may easily show that the power absorption in the magneto-ionic medium does not couple for the ordinary and the extraordinary waves. We consider a medium that has only dielectric losses. Then aD-E (1.38) at Considering two circularly polarized waves: DIl-I CI El j Eil (1.39a) and D2 2E2; E2=E -j e (1. 39b) ].5

with El E (a+j; ) (1.40a) E2 = E2(a -j (1. 40b) \We introduce complex notation in (1. 38) by letting 1 - -,) 1 -', E -- (E + 1) (E 2 ) (1.41) *E* 1 (1.42) ~-t) ~ (j;,Cl-j; E t)+ (ji e2E2-j e2 E (1. 42) and substituting the two preceding equations in (1. 38) we obtain 9 E1 c E-+ e E2 E] 2-(cl)E1 E,2+(El-E )E l E (1.43) Applying (1. 40a) and (1.40b) in (1. 43) we see that E E 2(x ).( +j ) = 0 (1.44) 1 2 x y x y 14- E1E) ( a + a) 0 (1.45) and hence the second term vanishes in (1. 43) and consequently we have established that (1. 37) is valid, subject only to approximations discussed previously. 16

We return to the calculation of the power transmission coefficient. In (1. 37) we may neglect the second term. Substituting the remainder in (1.8) in the same sense as before we obtain: + i2 4rxr4r2 2 nl PTC= -4.34 dz dy dx sin2 a + sin +2 PL --- a a a 0 Vi 0 (1.46) + 1 sin cos I a a For constant magnetostatic field we can integrate the above equation to (1.47) PT C = - -h E 0.136 + 0.197 -— + 0.173 -2 ] (. 47) We have calculated the ratio of PTC to P2 for f = 3. 9 Gc and v = 0. 8 Gc. c The results are plotted In Fig. 1-3. Comparing this with the corresponding curve in Fig. I-2, we notice that in this Ix rticular case the absorption is about 20 percent less on the db scale than it was for the circularly polarized calse. 17

FIG. 1-3: RATIO OF POWER TRANSMISSION TO P2 AS FUNCTION OF Y, CALCULATED FROM THE EXTRAORDINARY WAVE APPROXIMATION WITH ELLIPTIC POLARIZATION ACCOUNTED FOR EQUATION (1.47 f=3.9 Gc,v =O. 8 Gc, Y = P. 120 100 2( Y 1.5.6.7.8.9 1.0 1.1 1.2 1.3 1.4 1.5 18

II. EXPERIMENTAL STUDY OF PLASMA PACKAGE STABILITY 2.1 VACUUM SYScTEM A Varian designed vacuum system employing a 140 liter/sec ion pump was used to evacuate the glass envelope which serves as the plasma chamnber. The vacuum system is connected to a glass manifold through a 1 in. copper line. A pressure gauge sensing element, gas inlet port and taper to which the plasma envelope is connected form a part of the glass manifold. A diagram of the vacuum system is shown in Fig. 2-1, A mechanical forepump is used to take the glass manifold and copper line from atmosphere to about 20 microns Hg. The valve to the Varian -3 system is then opened. A pressure of about 10 mm Hg was attained at the taper to which the plasma envelope is connected with the Varian system valve fully opened. The ion pump pressure under these conditions is less than 5 x 10 mm Hg. 2.2 PLASMA TUBE A glass envelope 6 cm x 7 cm x 1. 5 cm was blown of Pyrex glass. A cathode consisting of 4 straight pieces of thoriated tungsten wires 0. 010 in. in diameter welded at the ends to 0. 10 in. diameter tungsten rod which served as feed-throughs was placed across the 6 cm end. An anode, also of 0.10 in. diameter tungsten rod, was put across the other end of the envelope. The pumping outlet was located on the anode end of the chamber. 19

Pressure sensing 1 inch valve ( 1 inch diameter copper line element Kovar-glass transition 12 mm glass tubing Kovar to glass transition Taper TBrass Bellows. Taper for gas bottle Flasma Chamber Valve OQ 2 mil lass Stopcock Forc- pu..ip 6 ) 6 mm Glass Stopcock FIGURE 2-1: VACUUM SYS'.:i

The cathode design was tested by inserting a second cathode in a glass envelope and heating the cathode to temperatures as high as 3000 K after evacuation of the envelope. The welds held satisfactorily at these temperatures, which are much higher than the normal operating temperatures of 1800 to 19000K. The temperature limited emission of the cathode was calculated to be about 1 ampere at 1900 K. 2.3 CATHODE DEVELOPMENT A small oven was constructed of toaster heater elements for baking the plasma envelope. Temperatures as high as 550 C could be attained and were varied by means of a variac. The envelope was baked at 3500C for 2 days, while either on the Varian system or being evacuated by the mechanical fore pump. The initial attempt to bake out the chamber revealed the presence of an intermittant leak through two of the feed-throughs. After reworking of the chamber, the chamber was evacuated, and while it was being baked, the Varian system remained at a pressure less than 5 x 10 mm Hg with the valve fully open, with no indication of a leak. Cathode temperature measurements were made by use of an optical pyrometer and measurements of the cathode resistance. The resistance has been used previously as a temperature indication and has been found to correlate quite well with the optical pyrometer. 21

The cathode activation was begun by heating the cathode to about 1000 K while baking out the chamber. When the outgasing had ceased, the cathode temperature was further increased to 1800 K. The activation was continued by flashing the cathode to temperatures between 2200 to 2500 K for periods up to 30 seconds and then returning to 1800 K. A voltage was then applied between the cathode and anode to determine if there was a measureable emission. In this manner, the cathode emission was gradually increased to 3 ma at an anode potential of 200 V. Shortly after, the emission began to decrease, and eventually fell to about 4 ua at 200 V. Efforts to return the emission to its former value proved fruitless. We concluded that the decreased emission was most likely the result of either (1) poisoning of the cathode by gas sputtered from the anode or (2) evaporation of all the free thorium from the cathode. In order to remedy this situation, future anodes will be baked out separately at higher temperatures and we will attempt to use lower activation temperatures. III. CONCLUSIONS The theoretical work provides tractable formulas to predict the optimum performance of the magneto-ionic resonance isolator. The implications of these formulas need to be studied and compared with existing data from the experimental model of the device. 22

IV FUTURE PLANS In the next quarter, attention will be directed towards the cathode development. A helical design will be tried, as well as the possibility of obtaining a suitable commercially manufactured cathode. With a successfully developed cathode, the plasma envelope will be placed in an rf cavity, and the plasma frequency and collision frequency investigated as a function of gas type and pressure. Reproducibility of the results will be emphasized in this work. This data will be used to find the optimum gas parameters to be used in a sealed plasma envelope for electron cyclotron resonance interaction.