^ecknlcal vjote 
 
 \^,m, 
 
 151 
 
 MODE CONVERSION IN THE 
 EARTH-IONOSPHERE WAVEGUIDE 
 
 THE UNIVERSITY LIBRARY 
 
 |THE PENNSYLVANIA STATE UNIVERSITY 
 STATE COLLEGE, PENNSYLVANIA 
 
 JAMES R. WAIT 
 
 U. S. DEPARTMENT OF COMMERCE 
 NATIONAL BUREAU OF STANDARDS 
 
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NATIONAL BUREAU OF STANDARDS 
 
 technical ^Lote 
 
 151 
 
 JUNE 8, 1962 
 
 MODE CONVERSION IN THE 
 EARTH-IONOSPHERE WAVEGUIDE 
 
 James R. Wait 
 NBS Boulder Laboratories 
 
 NBS Technical Notes are designed to supplement the Bu- 
 reau's regular publications program. They provide a 
 means for making available scientific data that are of 
 transient or limited interest. Technical Notes may be 
 listed or referred to in the open literature. 
 
 For sale by the Superintendent of Documents, U.S. Government Printing Office 
 Washington 25, D.C. - Price 20 cents 
 
CONTENTS 
 
 Page 
 
 1. Introduction 2 
 
 2. Formulation ■ 2 
 
 3. Discussion of Formulae 13 
 
 4. References-- 17 
 
 Figures 18 
 
 li 
 
MODE CONVERSION IN THE EARTH-IONOSPHERE WAVEGUIDE 
 
 by 
 
 James R. Wait 
 Central Radio Propagation Laboratories 
 National Bureau of Standards 
 Boulder, Colo. 
 
 Abstract 
 
 An approximate theory for conversion of modes in an earth- 
 ionosphere waveguide is propounded. The model is two concentric 
 spherical reflecting boundaries which have prescribed surface 
 impedances. The localized irregularity at either the ground or the 
 ionosphere is idealized by a "black screen" which effectively blocks 
 the cross -section of the waveguide over a portion of its area. In 
 this sense, the method is a union of approximate Kirchoff diffraction 
 theory and rigorous mode theory. 
 
 The research reported in this document has been supported, in 
 part, by the Advanced Research Projects Agency. 
 
-2- 
 
 1. Introduction 
 
 In the theory of VLF propagation it is usually assumed that the 
 ionosphere is concentric with the surface of a spherical earth. In 
 many actual cases, this is often an excellent approximation. In fact, 
 even if the ionospheric height changes slowly in a horizontal direction 
 the modes do not change their individual character. However, if the 
 changes are abrupt, and occur in a very localized region, conversion 
 of energy from one mode to another may result [Wait, 1962a]. 
 
 In this paper the general problem is studied from a fresh view- 
 point. A localized irregularity is imagined to be equivalent to block- 
 ing the aperture -which is the cross-section of the -waveguide. The 
 method is applicable to irregularities at both the ionospheric reflect- 
 ing layer as -well as at the earth' s surface. An example in the last 
 category would be a mountain ridge -which is transverse to the propa- 
 gation path. 
 
 The method is based on a union of approximate Kirchoff diffraction 
 theory and rigorous mode theory. To simplify the discussion, the 
 problem is considered to be two-dimensional in nature and, thus, 
 the equivalent source is a line dipole. 
 
 2. Formulation 
 
 We initiate the analysis -with a simple model. The earth' s surface 
 and a reflecting layer are represented by two concentric cylindrical 
 surfaces with curvature radii of a and a + h, respectively. In terms 
 of cylindrical coordinates (r,0, z) concentric surfaces are r =a and 
 a + h. The situation is illustrated in Fig. 1. The surface impedances 
 at the lower and upper surface are denoted by Z and Z., respectively. 
 The fields are assumed to vary according to exp (i oo t). 
 
-3- 
 
 The fields in such a region can be expressed as a superposition 
 of transverse electric (TE) and transverse magnetic (TM) modes. 
 We will just consider the TM modes since they are of greatest 
 practical interest at VLF. The analysis for the TE modes is al- 
 most identical. 
 
 For the TM modes the magnetic field has only an axial com- 
 ponent H (i. e. , out of the paper in Fig. 1). The electric field has 
 only r and 9 components and they can be obtained simply 
 
 by differentiating H. 
 
 We now imagine that the fields at the aperture plane 9 = 9 
 
 are known. For example H(9 , r) is specified over the interval 
 
 o 
 
 a < r < a + h. Thus, for the region 9 > 9 the field will consist 
 of TM modes travelling in the positive 9 direction. Furthermore, 
 these modes must satisfy the boundary conditions 
 
 E Q = - Z H at r = a (1) 
 
 U g 
 
 E Q = Z. H at r=a + h. (2) 
 
 u 1 
 
 Under the assumptions 
 
 ka > > 1 , 
 h/a < < 1 , 
 9 < < 1 , 
 
 it was shown previously that [Wait, 1961] the field could be represented 
 
■ 4- 
 
 in the form 
 
 H = H(x,y) = 
 
 A $(t ,y) e 
 
 n n 
 
 i(x-x Q )t n 
 
 n = l, 2,3 
 
 where 
 
 1 J. 1 1 
 
 x=(^)0, X q =(^) O , y =(—■) k(r-a), andy^^kh 
 
 (3) 
 
 The function 3? satisfies the differential equation 
 
 (4) 
 
 and t are obtained from 
 n 
 
 *(t ,y) + q*(t ,0) = 
 
 dy n n 
 
 y = 
 
 (5) 
 
 ■where 
 
 and 
 
 v * Z 
 
 . ka. g 
 
 *(t ,y) 
 
 d y n 
 
 q. $(t ,y ) = 
 
 l no 
 
 y = y„ 
 
 (6) 
 
 where 
 
 1 3 Z ' 
 
 ka x 
 
 1 q i = { — ] fZoW ' 
 
-5- 
 
 The latter two equations are equivalent to the boundary conditions 
 given by (1) and (2). 
 
 Solutions of (4) are linear combinations of the Airy integral 
 functions w x (t-y) and w 2 (t-y). In terms of the functions A i(a,) 
 and Bi(ct), defined and tabulated by Miller [1946], 
 
 wi(ct) = ^t [Bi(a) - i Ai( a )] 
 
 (7) 
 
 and 
 
 w s (a) =N/fr[Bi(a) + iAi(a)] 
 
 (8) 
 
 It is easy to verify that 
 
 $(t ,y) 
 
 n 
 
 Wl (t -y) + A(t ) w 2 (t -y) , 
 n n n 
 
 where 
 
 (9) 
 
 A(t) = 
 
 rwj, (t - y Q ) + q^ w^t - y n ) 1 
 Lw^ (t-y ) + q. w 2 (t-y )J 
 
 (10) 
 
 satisfies (6). Furthermore, if 
 
 A(t ) B(t ) =1 = e 
 
 n n 
 
 - i Z TT 
 
 n 
 
 (ID 
 
 where 
 
 B(t) = 
 
 -[ 
 
 w 2 (t) - qw P (t) 
 w{(t) - q w x (t) 
 
 (12) 
 
 it is seen that 3? also satisfies (5). 
 
-6- 
 
 It should be mentioned at this stage that the surface r = a + h 
 can be regarded as a reference surface where the ratio of the tangential 
 fields are specified . In the general case Z. or q. may be a function 
 of the eigen-values t . However, for VLF it is a good approximation 
 to regard Z. or q. as constants. This is equivalent to stating that 
 the surface impedance does not depend on the angle of incidence. In 
 a similar manner Z or q can be regarded as constants. 
 
 The orthogonality properties of the modes are now studied. We 
 
 consider two sets of values, t and t , which satisfy the boundary 
 
 n m 
 
 equations (5) and (6). However, for any value of y these must also 
 satisfy 
 
 $ . (t -y) $ =0 , $ = $(t ,y) (13) 
 
 dyn nn n n 
 
 and 
 
 ■—9 - (t -y) $ = , $ = $(t ,y) . (14) 
 
 d y m m m m m 
 
 After multiplying the first of these equations by $ and the second 
 
 m 
 
 by 3? they are subtracted from one another. Both sides of the re- 
 
 n 
 
 suiting equations are then integrated with respect to y over the 
 range to y . This results in 
 
 fo 
 
 n d y m m d y 
 
 d d 7o C~ 
 
 $ -rr- $ _ $ -1L $ = (t -t ) \ $ & dy . (15) 
 
 dy nj n m J n m 
 
 o o 
 
-7- 
 
 In view of the boundary conditions on 3? and 3? at y = and 
 
 n m 
 
 y = y , the left-hand side of the preceding equation is zero. Thus, 
 o 
 
 the integral on the right also vanishes if t is not equal to t . 
 Therefore, we have the important result 
 
 C 
 
 $ (t , y) $ (t , y) dy = if m * n . (16) 
 
 J m n 
 
 o 
 
 It now follows that, if both sides of (3) are multiplied by 
 
 3?(t , y ) and integrated from to y , 
 mo o 
 
 3 H <v 
 
 y) $(t , y) dy 
 
 n 
 
 A = -Q . (17) 
 
 n Yo 
 
 c 
 
 [»(t ,y)] 3 dy 
 n 
 
 The normalizing integral 
 
 y 
 
 N = U*(t , y)f dy (18) 
 
 n J n 
 
 o 
 
 is now expressed in a more convenient form. This is accomplished 
 by noting that 
 
 U*(t .y)] 3 dy = - (t -y)[*(t . y)] a + [<&• (t, y)] 3 . 
 
 (19) 
 
This can be proved by differentiating both sides with respect to y 
 and making use of (13). Then using the definition of 3?(t , y) in terms 
 of Airy functions, it follows that 
 
 $(t , 0) = - -n r^ ; r (20) 
 
 n' w»(t ) - qw ? (t ) V ' 
 
 n ^ n 
 
 and 
 
 $(t , y ) = - — n rr 77 r ( 2 i) 
 
 v n y o w'(t -y ) + q. w 2 (t -y ) v ' 
 
 rf n o l no 
 
 where use is also made of the Wronskian condition 
 
 wjt) Wj(t) - wj(t) w 2 (t) = - 2 i (22) 
 
 which is valid for any value of t. Finally, on making use of (19), 
 (20), and (21) along with (5) and (6), it is found that 
 
 N = 
 
 4 ^-q 5 ) 
 
 [w 2 '(t ) - q w 2 (t )] 
 
 ^ n ^ n 
 
 4 (t n -Yo - 3j ) 
 
 [w 2 (t -y ) + q. w 2 (t -y )] 
 L a n o l ** n o 
 
 (23) 
 
 This can be regarded as a fairly important result. 
 
 Equation (17) ior the coefficient A can be written in the con- 
 
 n 
 
 venient form y 
 
 \ H(x , y) *(t , y) dy 
 
 2A " ° 
 A = 2. ° (24) 
 
 " Y o [*(t ,0)f 
 
 n 
 
where 
 
 y. 
 
 A = -f-kt -q*) - (t -y -q s )C ,^"n'-, qW 'V }1 .(25) 
 
 n 2 L n n o 1 Vw^t -y ) + q. w 2 (t - y )} _ 
 
 n o 
 
 It is now imagined that the incident field results from an equiv- 
 alent line magnetic source at x =0 (i. e. , 9 = 0). Thus, 
 
 H(x, v) = ) a $( t ,y) e ~ 1Xtm for x<x (26) 
 
 } [_. m m o 
 
 m 
 
 where a is a coefficient which does not depend on x or y. It is 
 
 m 
 
 assumed that in the aperture plane x =x is obstructed in such a 
 
 o 
 
 manner that the effective aperture is a slit extending from y = y x 
 
 to y 2 (i. e. , r - a = z x to z 2 ). The situation is illustrated in I ig. 2. 
 
 Thus, within the Kirchoff approximation, 
 
 H(x , y) = Y a $(t ,y) e" ' X o tm for Yl > y > y 2 (27) 
 
 o /_ . m m 
 
 = for o<y<yi 
 = for y 2 < y < y Q • 
 
 In other words, ve are assuming that the field within the aperture 
 of the slit has the same value as if the slit were not present. It is 
 known from a study of the rigorous solutions of diffraction by slits 
 that this is an excellent approximation [Born and Wolf, 1959] pro- 
 vided the width of the slit is greater than about a wavelength. 
 
■ 10- 
 
 The field in the region x > x can now be expressed in the 
 
 form 
 
 H(x, y) = 
 
 A (m) ft(t ,y) e " i(x - X o )t: n e" iX o **> (28) 
 n n 
 
 m n 
 
 where 
 
 A 
 
 (m) 
 
 y 2 
 
 $(t , y) $(t , y) dy 
 
 <-- A J m n 
 
 n _ Zl 
 
 n 
 
 [3(t , 0) 
 
 n 
 
 m 
 
 (29! 
 
 We see clearly that the incident mode of order m excites modes of 
 order n where m and n are positive integers. 
 
 It is convenient to write 
 
 A (m) = r p (m) + Q (m) 
 n L n 
 
 n 
 
 m 
 
 (30) 
 
 where, for m 
 «(m) 
 
 * n , 
 
 n 
 
 *(t , o) X 1 
 
 2 A_ $(t , , 0) 
 
 y 
 
 o n 
 
 and 
 
 Q 
 
 (m) 
 
 n 
 
 2 A $(t ,0) ^o 
 
 £ *F7^) J C m (y)G n ( y )dy , 
 
 n V 
 
 Y2 
 
 y 
 
 whe re 
 
 G (y) 
 
 n 
 
 *(t ,y) 
 
 n 
 
 $(t ,0) 
 
 n 
 
 (32) 
 
 (33) 
 
■11- 
 
 and 
 
 *(t , y) 
 
 m 
 
 G m (y) = *(t , 0) 
 
 m 
 
 (34) 
 
 In obtaining the above forms for P and Q use has been made 
 
 n n 
 
 of the orthogonality condition given by (16). 
 When m = n , we have 
 
 A 
 
 (n) 
 
 n 
 
 p(n) + Q (n) 
 
 n n 
 
 n 
 
 (35) 
 
 where 
 
 P (n) = i 
 
 n 
 
 2 A f 
 
 -^ ] [G a (y,] 
 
 dy 
 
 (36) 
 
 and 
 
 Q (n) = 1 
 
 n 
 
 2 A Xo 
 
 2- f [G (y)]»d 
 
 y 
 
 y a 
 
 (37) 
 
 where use has been made of (23). 
 
 The integrals over the range to y\ in the preceding equations 
 can be regarded as the influence of the obstacle on the ground, where- 
 as the integrals over y 2 to y are related to the protuberance at 
 the ionosphere. To evaluate these integrals it is desirable to expand 
 the G functions as a power series in y. 
 
 Since 
 
 G (0) = 1 
 
 n 
 
 (38) 
 
-12- 
 
 [dG n (y)/dy] 
 
 -q 
 
 y = 
 
 (39) 
 
 and 
 
 d 5 G(y) 
 
 dy 2 
 
 = (t -y) G(y) for any y, 
 
 (40) 
 
 it is not difficult to show that 
 
 t y 2 (1 + t q) 
 
 G n (y) = 1 - qy + 
 
 n 
 
 y 
 
 (41) 
 
 Thus, 
 
 G (y) G (y) 
 
 n m 
 
 1 - 2 qy + (t^ + t_ + 2 q 2 ) X 
 
 n m 
 
 3 
 
 (1 + 2 t q + 2 t q)^- + 
 n mi 
 
 (42) 
 
 2 . 
 
 m 
 
 and the expansion for [G (y)] is obtained by simply replacing t 
 by t in the preceding result. 
 
 The integrations for the P integrals are now readily carried 
 out. They yield 
 
 2 A 
 
 Am) 
 
 y. 
 
 - U»[ R -" ! + (t n + t m + 2 ^»^ 
 
 (1 + 2 t q + 2 t q)^" + 
 n m 1& 
 
 (43) 
 
 where 
 
 $(t ,0) w 2 (t ) - q w 2 (t ) 
 
 m n n 
 
 'm, n $(t , 0) ' w'(t ) - qw 2 (t ) 
 
 n m m 
 
 (44) 
 
and 
 
 -13. 
 
 p i n) ^-VH-^+'v^ 3 
 
 (1 + 4 t q) $- + 
 n l£ 
 
 (45) 
 
 Q 
 
 (m) 
 
 The Q integrals are evaluated in a very similar manner. Thus 
 2 A 
 
 n 
 
 y 
 
 — S G (y ) G (y )j(y -y 3 ) - q.(y - y ? ) : 
 
 Tm, n mo noLo - l o 
 
 + (t + t +2q 2 ) (y ° 7 y ^ - (1 + 2 t q. + 2 t q.) {y °' Y? ^ + 
 i o n i m l 1c 
 
 n m 
 
 and 
 
 Q (n) = 1 
 
 n 
 
 2 A 
 
 y 
 
 — [G (y )] 2 f"(y -y 3 ) - q.(y -y 2 ) : 
 noLo i o 
 
 (46) 
 
 + (t + q?) (y Q -yp) 3 . (i + 4 t q .) (y " ' y ^ 4 + . 
 
 n i J n l 1<S 
 
 (47) 
 
 Due to the typically large values of q. at VLF, the preceding series 
 for the Q functions are probably not useful. It would be better to 
 work directly with equations (32) and (37). 
 
 3. Discussion of Formulae 
 
 Some of the previous results are now discussed briefly. For 
 purposes of illustration, it is assumed that the ionosphere is a 
 
 sharply bounded medium whose effective conductivity is e to where 
 
 -12 ° r 
 
 e =8. 854 x 10 . Under this condition extensive numerical values 
 o 
 
-14- 
 
 of the coefficients t satisfying equation (11) are available [Spies 
 
 n 
 
 and Wait, 1961], Using these values, the various quantities entering 
 into the formulas for the modal coefficients can be evaluated in a 
 straightforward manner. 
 
 It is seen that the modal coefficients, given by equations (43), 
 
 (45), (46), and (47) all contain the factor A . This factor is a modal 
 
 n 
 
 excitation factor and it is a measure of the efficiency of excitation 
 of a given mode from a line or dipole source [Wait, 1961, 1962b] . In 
 the present context it is normalized so that it approaches unity for 
 perfect ground conductivity (q = 0) and a flat earth (a = oo). In 
 
 general it is a complex quantity. To illustrate its behavior co is 
 
 5 
 set equal to 2 x 10 and h is taken as 70 km. Furthermore, the 
 
 ground is assumed to be perfectly conducting. Under these conditions 
 
 A for n = 1 has the following complex values for the frequencies 
 
 indicated: 
 
 Ai = 0.95 |3. 8° (10 kc/s), 0. 79 |3. 0° (15 kc/s), 
 
 0. 59 J4.6° (20 kc/s), 0. 37 j 7. 4° (25 kc/s), 
 
 0.19 1 10. 6° (30 kc/s). (48) 
 
 This mode corresponds to the mode of least attenuation. It is 
 
 characterized by an excitation factor which decreases approximately 
 
 as the inverse of the frequency. Under the same conditions A , 
 
 * n 
 
 for n greater than 1, is roughly unity over the same frequency range 
 [Wait, 1962b]. 
 
-15- 
 
 The modal coefficient P n defined by (45), in the case of n = 1 
 
 n ' 
 
 can be written 
 
 Pl (1) « 1 - 2 Al i- . (49) 
 
 Here, h-i/h is the ratio of the heights of the obstacle on the ground 
 to the height of the ionosphere. This quantity would never be greater 
 than about 0. 5 and thus the modification of the first mode by even 
 an extremely high mountain range would be small. This is particularly 
 the case at the upper end of the VLF band where the excitation factor 
 is small. 
 
 The relative conversion of the field from an incident mode of 
 
 ( TCiS 
 
 order 1 to a mode of order 2 is obtained from the factor P de- 
 
 n 
 
 fined by (43) for m = 1 and n = 2, Approximately, this can be 
 written 
 
 P. 
 
 (1) 
 
 2 
 
 2 A, g 1)2 (h x A) . (50) 
 
 The complex quantity g ? is defined by equation (44) for m = 1, 
 
 1> ^ 
 
 n = 2, and q = 0. For the same conditions, its magnitude for the 
 frequencies indicated are given as follows 
 
 |g | = 1. 72 (10 kc/s), 1. 47 (15 kc/s), 1. 08 (20 kc/s), 
 1> ^ 
 
 0. 70 (25 kc/s), and 0. 41 (30 kc/s) . (51) 
 
 Since |A 2 | is of the order of unity, it is thus apparent that the con- 
 version to higher modes may be significant. 
 
-16- 
 
 The influence of the protuberance on the upper boundary is de- 
 scribed by equations (46) and (47). The situation is similar to that 
 of the ground obstacle except that the factors G (y ) appear. Actually, 
 these are the ratio of the field just below the ionosphere reflecting 
 layer to the field at the ground. 
 
 Of particular interest is the possibility that, as a consequence 
 of an ionospheric irregularity, a mode of order 1 may be excited by 
 an incident mode of order 2. The magnitude of this first-order mode 
 relative to amplitude of the second-order mode is obtained from 
 equation (46) with m = 2 and n = 2. Thus, approximately 
 
 o[ Z) e -2 Al g 2jl G 2 (y ) G i(y ) (nr 2 *- ( 52 > 
 
 The numerical magnitude of the excitation factor A x has already 
 been discussed. As noted, it may be quite small for frequencies of 
 the order of 25 kc/s. However, in certain cases, the height-gain 
 function G x (y) ,. is somewhat greater than unity. Thus, the con- 
 version to the lower-order mode may be quite significant. This 
 point can also be demonstrated directly from equation (32) which, 
 in this special case, has the form 
 
 ~^- l. , , \ »>.-, (v) <:...< Y> <ly . «''o) 
 
 o 
 
 i Z) = - T^gz.i J G 2 (y) G i(y> d y • 
 
 y 2 
 
 Modes of the "whispering gallery" type [Budden and Martin, 1962], 
 also known as "earth-detached modes" [Wait, 1962b], are associated 
 with a low excitation efficiency (i.e. , A a is small). However, the 
 
-17- 
 
 height-gain function G x (y) for a "whispering gallery mode" is an 
 
 increasing function of height. Thus, the product of the integral over 
 
 y 2 to y and the excitation factor Aj may be of appreciable magnitude. 
 
 4. References 
 
 Born, Max and Emil Wolf, Principles of optics (Pergamon Press, 19 59), 
 Budden, K. G. , and H. G. Martin, The ionosphere as a whispering 
 
 gallery, Proc. Roy. Soc. Ser. A, 265 , 554-569 (1962). 
 Miller, J.C. P. , The Airy integral, giving tables of solutions of the 
 
 differential equation y n = xy (Cambridge University Press, 1946). 
 Spies, K. P. , and J. R. Wait, Mode calculations for VLF propagation 
 
 in the earth-ionosphere waveguide, NBS Technical Note No. 114 
 
 (Jul. 17, 1961). 
 Wait, J. R. , A new approach to the mode theory of VLF propagation, 
 
 J. Research NBS £5D (Radio Prop. ), No. 1, 37-46 (Jan. -Feb. 1961). 
 Wait, J. R. , An analysis of VLF mode propagation for a variable 
 
 ionosphere height, J. Research NBS 66D (Radio Prop. ), No. 4, 
 
 (Jul. -Aug. 1962a). 
 Wait, J. R. , Electromagnetic waves in stratified media (Pergamon 
 
 Press, New York and London, 1962b). 
 
0=0 
 
 (REFERENCE 
 REFLECTING LEVEL) 
 
 r=a + h 
 
 «s^Sr 
 
 X AV r=a 
 
 0=0, 
 
 Fig. 1 - The waveguide model and the spherical coordinate system 
 
 (r,M> 
 
 x=o 
 
 y=y, 
 
 / y=o 
 
 x=x ( 
 
 Fig. 2 - The waveguide model showing idealized obstructions in the 
 
 aperture plane x = x . Here, the natural coordinate system 
 (x, y) is being used. 
 
 U.S. GOVERNMENT PRINTING OFFICF : 1962 — S519>J 
 
U. S. DEPARTMENT OF COMMERCE 
 
 Luther H. Hodges, Secretary 
 
 NATIONAL BUREAU OF STANDARDS 
 A. V. Astin, Director 
 
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 WASHINGTON, D. C. 
 
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 Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tropo spheric Measurements. 
 Tropospheric Analysis. Propagation-Terrain Effects. Radio-Meteorology. Lower Atmosphere Physics. 
 Radio Systems. Applied Electromagnetic Theory. High Frequency and Very High Frequency Research. Modula- 
 lation Research. Antenna Research. Navigation Systems. 
 
 Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. Ionosphere and Exosphere Scatter. 
 Airglow and Aurora. Ionospheric Radio Astronomy. 
 
 RADIO STANDARDS LABORATORY 
 
 Radio Physics. Radio Broadcast Service. Radio and Microwave Materials. Atomic Frequency and Time-Interval 
 
 Standards. Millimeter-Wave Research. 
 
 Circuit Standards. High Frequency Electrical Standards. Microwave Circuit Standards. Electronic Calibration 
 
 Center. 
 
PENN STATE UNIVERSITY LIBRARIES 
 
 ADDD 
 
 D71 
 
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