ENGINEERING RESEARCH INSTITUTE THE UNIVERSITY OF MICHIGAN ANN ARBOR GENERAL DESIGN PROCEDURE FOR HIGH-EFFICIENCY TRAVELING-WAVE AMPLIFIERS Technical Report No. 24 Part II Electron Tube Laboratory Department of Electrical Engineering By Joseph E. Rowe Harold Sobol Project 2750 CONTRACT NO. AF30(602)-1845 DEPARTMENT OF THE AIR FORCE PROJECT NO. 4506, TASK NO. 45152 PLACED BY: THE ROME AIR DEVELOPMENT CENTER GRIFFISS AIR FORCE BASE, NEW YORK February, 1958

-iiiEXPLANATORY NOTES 1. Theoretical Development of Design Procedure. In Part I of this report a general design procedure is developed for the design of high-efficiency traveling-wave amplifiers. The procedure is first developed for helix-type tubes and is then extended to cover traveling-wave amplifiers with other types of r-f structures. The same design curves are used for these dispersive structures with appropriate correction factors. 2. Design Curves. In Part II all of the available design curves useful in the actual design of high-efficiency amplifiers are compiled. Immediately preceding each section of curves there is a list of parameters for which the particular curves have been calculated.

-ivTABLE OF CONTENTS Title Page EXPLANATORY NOTES iii SECTION A: Efficiency 1 SECTION B: Impedance Reduction Factor 8 SECTION C: Space Charge vs. Stream Diameter 18 SECTION D: Space Charge vs. Voltage 379 SECTION E: Space-Charge Correction Factor 398 SECTION F: Optimum Electron Injection Velocity 402 SECTION G: Perveance 409 SECTION H: Perveance Correction Factor 435 SECTION I: Electron Stream Characteristics 439 SECTION J: Space-Charge Reduction Factor for Dispersive Structures 450 SECTION K: Tube Length and Change in Phase Shift vs. Input-Signal Level 459

SECTION A EFFICIENCY The efficiency curves are presented for selected values of the parameters C, B, and QC in the indicated ranges. Parameter Range C 0.05 to 0.20 B 0.5 to 1.5 QC 0 to 0.75 -1

60 -- 50 40 Z 30~___0 B=1.5 20 ----------— C ---- ------— B = 1.0 B= 0.75 B= 0.50 10 0 0.2 0.4 0.6 0.8 1.0 SPACE -CHARGE PARAMETER, QC FIG. A.I SATURATION EFFICIENCY VS. SPACE CHARGE. b- ADJUSTED FOR MAXIMUM 3s (C 0.1, d = 0)

's. 60'50 40 20 1.0 I 0 0.2 0.3 0.5 Q C B FIG. A.2 SATURATION EFFICIENCY VS. SPACE CHARGE AND BEAM DIAMETER. b - ADJUSTED FOR MAXIMUM 7/s. (C=0.1, d =O)

60 50 - 50 _____ F 30 LJt0 1 C0.2, B\. \__ C0.i, 0 JU~1 \\ 10 _C =0.05, B = 0.5 0 0.2 0.4 0.6 0.8 1.0 SPACE-CHARGE PARAMETER, OC FIG. A.3 SATURATION EFFICIENCY VS. SPACE-CHARGE PARAMETER. b- ADJUSTED FOR MAXIMUM %. (B: 0.5, d=O)

60 50 LWI P- 30 0C =0.20, B= I 201 I 0.10, B=1 C 0.05 B = I 0 0.2 0.4 0.6 0.8 1.0 SPACE-CHARGE PARAMETER, OC FIG. A.4 SATURATION EFFICIENCY VS. SPACE- CHARGE PARAMETER. b- ADJUSTED FOR MAXIMUM ig. (B =I, d O)

60 50 4 QC = 0.125 40~ QC o.252QC-= 005l l -l l l l! ll l 0,00 PA~aMETR QC o -- hii 0 0.1 0.2 0.3 0 Ui 30 20 QC 0. 75 I0 0 0.1 0.2 0.3 GAIN PARAMETER, C FIG. A.5 SATURATION EFFICIENCY VS. GAIN PARAMETER. b- ADJUSTED FOR MAXIMUM XI. (B 1.0, d =O)

60 - _-_ — --- -----' —_- -—' i.QC = 0.125 -QC 0.05 50 I I I I QC: 0 QC o0.25 40 z 0 Ct 30Li I:,, ~ ~ ~ -~ --—'-'= QC = 0.5 2 QC = 0.75 10 0 0.1 0.2 0.3 GAIN PARAMETER, C FIG. A.6 MAXIMUM SATURATION EFFICIENCY VS. GAIN PARAMETER. b - ADJUSTED FOR MAXIMUM 9i. (B= 1.0, d =O)

SECTION B IMPEDANCE REDUCTION FACTOR The impedance reduction factor curves are arranged according to ascending values of the dielectric loading factor. Parameter Range DLF 70 to 100 -8

;;l; I. —- \ If \ 1:: W..... T..NARROW TAPE HELIX 0I I I I I;:fll | I | 11 1._ il I I _ I _ I I 1I_[lls I I J _ 1LII r r _Y1 _ I rl 1rfi l I I III I I I Ill I III I I II1 i _! __. r rr-T IT.__ 10. 0.9 0 O QI~0. 0.2 0.3 I. I ifI 0. I FIG_. _______._TI IMPEDANCE REDUCTION FACTOR F F 11 F2 FOR A TAPE HELIX. (EXTENSION OF _TEN'S CALCULATIONSV. I fill _ _ _ _. T I (ETNSO OF I CACULATIONS_) -=1 W11ll 95' l - s - - - - T x _ _ _ _ _i _

1.0 o. l I I! I I I I I 1 1 111 11 1 1 1 1 1 1 11 1 I I1L 0.9 I I AL | if nl I || 0 0.0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 (a.) (b.) FIG. B.2 (a.) IMPEDANCE REDUCTION FACTOR Fl FOR DIFFERENT CURRENT DISTRIBUTIONS. (b.) FACTOR FI COMPUTED USING CURRENTDISTRIBUTION — a FOR'o 1, 1.5,4. COURTESY OF P (COURTESY OF.K.TIEN). —-----—.(. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 >.l II I. 3 k.-.. * -- -.. -. _ -.- - < ^ - - - - - - - - - - - 0 Illll.3lllll l ll li il;! ^ ^__:::=: I ~ ~ ~ (CUTS OFl [i K. IEN) i

F ~11 |||||'N| 1 ^11 * |____I____ ____________ 77 1E. 8 0. 0.6 ------ 70 809010 DIELECTRIC LOADING ]FACTOR IN PERCENT 0. 0 0.1 0.2 0.3 70 80 90 100 k a DIELECTRIC LOADING FACTOR IN PERCENT FIG. B.3 IMPEDANCE REDUCTION FACTOR F2 FOR A TAPE HELIX. (COURTESY OF P.K.TIEN)

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SECTION C SPACE CHARGE vs. STREAM DIAMETER The curves of the space-charge parameter vs. the stream diameter are arranged according to increasing values of the parameters V, a'/b' and DLF successively. Parameter Range Vo 1 to 14 kv a'/b' 1.2 to 2.0 DLF 70 to 100 -18

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0 w Lr) InLI) w 0~ ____________________________________________z_ Q QI 33 U)) IC,) LJ) 2 43 cr. w cr cr I- 0 CM~ ~ ~~~~~~~~~~~~~~C LAJ __ __ W La.. In___ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s L& Q 4La LI) d" r~~~~~~~~~~~~~~~~~~c _ _ _ _ _ dL J,I P~~~~~~~~ 0"0;!^ ^^ ^ N, m a -S^S. - i^ -. UJ -C o 0o 0 (q3 + I )3'3N\\\ \OtS ~ uj < 0 cc., ____________, ^~~~~~~~~~~~~~~( ^t r o 0 QD <0 ^U ON -d 6i di d (q0 + \ )/300 ^OUHO 33VJS

0 lLJ z__ 0 0 J., < I____ ___ ________-___ 01 w 9-00 w 4400 _ W Il Lf., o 0 CD > I w 0 (q I )/D'3&P H 3 d a (43~~~~ \\\ 1)333$>33fd

I o a: tZ c.S _J -— __W --- - 0~j (qS | )30'98v" 3- o0 w _____ ___ ___ ___ ^s~s "s "s^ ______ __ ___ 0 u 5 __ W La.. a......._II~~~~~~~~~t aI (qO + (q3+)/3O'3DVH3 3OVdS

0 cr II. a0 IZ U' Go f,__ 0 wi > ww a a — 4 —- 0 U OD T7..77...^\\ a.... ~i__ __ 111 i Ull i i 00 - c cd o (q) + 1)/30'3gUVHO 33VdS

i0 I(C iI 0 0 -- ^ -- -- -- I _ _ _ 0 I I II~d K 1 1, t I 1E\S\1/1, P o — ^ ^^ ^ -^^ — ao I'CI d Io u'd —o'j w I- 0 0 0 U a (J - o c~o d o (qO + I )/O0 *39aVHO 3OVdS

jc IU. 0 Wb W..~~~~, o <~ ~'~~~~~~~~~~ w LU U I-, J ^^ o _ 9d I \ ~ 0 o dl I I \Y -' E 00 m s ~r vo<\ o ~(qO~ + I ~)/D0'39:~HO~ 3JdS a. __ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ o) s~~~L O QD 10 ~ ~~~~~U O~ d ci cS d~~~~~~~~~~~~~~~^ ___ ____ ___ ____ ____________________________ r

--- -- -- -- -- -------- -- --- --- CI ___ ~~~~~~~~~~~w I__ ~~~~~~~~~~~~z LJ 0 ^__ __ __ ___ __ __ __ __ __ ______ __ __ wn Ir) I cr 0 ao w cr w LUl.04 d OD~~~~~~ 0~~~~~~~~ w LL 0 ~ ~ ~ ~ ~ ~ I w a a L(n _ _ _ — - - -------------------- LU d IC)~~~~~~~~~~~ OgV,~~~~~~~, II O W~~~~~~ ^^^~i I n? n\I\I u c~ IL) m —. ------- LL ----- ^^ ^ — s o d ~ >\\ 403 + 1)/3~'3~ L~t~w3 N 0. ci~~~~~~~~~~~~~~~~~~ ci --- --- ------------------------------ dS

ILaJ W _e~ ~Sz 3; r. 0 (9 l l)In, i — r ^ ^^ ^v" \ 0- w'0 0 0~~'0 "'q3+ I)/D Hd O O ci O O O ( 0 CD a < w U tO 0 0d~~ 0 UabC~~) ^ C" 0I - 6 d oa

r -. 0L 0 d LO r o oG0 J Us 00C > 0 I I 1 w- ITT IV II 1 1 <o-: ^"^ -—.' Iq -I+ I I I I I/ I3 I> I O 1 ______ o 6 _\ \\__ 5 0 (q93 + 1 )/9'3 9 3~0 dS (q3 + I )/00'39OUVHO 33VdS

0 4, I__ I I. w - w Ld) J: I. $ c( it~~ i~~~ P WI 00 V) IsO 1, \\_ 1 I 8 -— __- ---- )O 09110'8H3d0 --- ^ _ — - -- -o o - o~,S ~ { "\ \ { { ------— ^ -~ —— ^ c~ c~c __ __ _ __ ____ __(qO- + )0'-VO O

0 II I I — ---- ---- ~ ^ -- 0 I Il_ o ___ _ __ ___ 1I — 0 In or -~~~~W -- I i(q + W A 10 o - 6 d d 0 (qO + I)/310'391VH0 3OVdS

N0 Q: U. It LLJ,- 0 w 0 __ __ W L... m I_LL I0 C, n C.) 0,, (q9 +J. IJ.' *"o^ ~ ~ ~ ~ I 0 C) d > 0, ui ^s..- o 0 0 w. 0,, o r\ W + 10) 10n (qO + 1)/30)'3SSVH3 330VdS

0 I44 UbJ -.... - -. T\ ---- I ~ 0 tO I —' ~" -'' _0 C)IC) Q: 0 0 c 0 6 0 o 0 -.: 6 c i d (qO + I)/O0'39L~VH0 33VdS

i CM 44 0 W l-j Lb'_ _ _I 0 w:E cr 0 i-!L -- of 0a~~~- > __ U0 oO~~~~ d rC)&~~~~~ _La IL __ --- --- --- --- — 1 1 4 ) I. ~ u ": 0 (qO + I)/~O'39~VHo 3VdS (43 4 I )/00'39MVHO 30VdS

_ _ _______ _______ ______ _______ _____ ____0cr In _ _ _ _ _ _ w~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~- - - _-. -- - _ ~ -. - * - - 0. In IU Li. 2 0 Cl) co w w ------------------------------- L e ) to 0 w aP LJ __ __ LE)Jo~~~~~~~~~~ w J d Ln ^^O~ (0 "^s^^ ~i \I fId __ _ _ S: -__ ___ _ ot __ _ _ __LS 40 In ___ ___ __ _ __ o_ o_ 3') \ \ \ _ __ U 2 w C cn C2 C0 0 o (q3 + i )/DO'3OLlfVH< 37dS

i O0 ILAJ Cr 0 z ILi. __ ___ ___ ^ ^^ ^______ ___ ___ 0 w 7^^7\~~ ~ ~w w / —— 7/777^^^- i a 0 U. o 0 o ~ o o __ —_ _ —-,0 > d d d wU. c o In 0) c, _ m. m -. m0LL 0 0 ci 0d (q0 + 1)/Z0'3DUVHO 33VdS

O Q: -- LqJ z U. 0 w _C Gu.'I) im > w - s0 U. iP 0 cS > 0 U ~a L. tn 0 t.) (0,___ ~ _ _ ii. - d ci c o (qO + 1)/Z0'39UVHO 3OVdS

SECTION D SPACE CHARGE vs. VOLTAGE The plots of the space-charge parameter vs. the stream voltage are arranged according to increasing values of the parameters B and DLF successively at a fixed value of a'/b'. Parameter Range B 0.5 to 1.5 DLF 70 to 100 a'/b' 1.4 -379

I"_ 0 \ I in 1 1 1 LU I I \ l I 1 l, l I 01 1 1 01 J, 9 I__ __ __l_____ I __ _ 1 1t w w a.' I \ III I _ _I I 1'I I 1 \ I I o 1 T _ _ I \ _ _; T >0 0 ~' > w @ <~ ~j 0 ~o > > ) 0 U. o o o o o cO O (qO + I )i/gOC'3951dVHO 3VIdS oI N ci: C) _ _ _ 0..~~~~~~~Q

o - /I1 \~ i! I - > i Q) >~ D o \ \ \ \ \ \ \ | O I/0~~~~ 0 O Q >0 w LI.0 I) a (a

a SI C-) ~~~~~~~0,\ \ \\0 o-T~oi OD ~ nl>C D 0a0 0 mci~~~m a > cr _ _/__ __ 1 1011x L0 < - 6 6C (I 0 W w I do 0 ( I/'NH 00CdS

0 w i~ ~~~~~l l ~~~~~~LU w z UI 0 w l 1 l I 1 1 I ~ ~o., \ 1o I' U) ______ "-1______ __]__ 00 __ 0~ -' a' > 0 In T~ r~i \ \ \> w.\ ~~~~~~~ \L~~~~~ l los~~~~~ LI w 0 >cD X is o\ o I o oo __ _\ __\___ + 1)___'\_ _ > U) \ t o......... 0r IJ 0 m ~ q. twl o LU _4__-V- _\ c-gm c c a( 0 - -____I_____ II- - - - I —0 — ____ 0 (qO+ 1)/30'398XH3 30VdS

w ci 0 LU C6 0 > 0I~~ 0"~~ U) w > -J U-! > O i 0 o w LL wJ Lc W i, O.

-— t 1 1 ill t — -- o a I o L. I - -- -- -o -, —1-4 - -[ - -- ---- >L0, N I I I I 1 0o o w N LL.. 0w -!/ 0 - d O O d (q9 + D /OO t vH0 mvdS wo OII dn o 0 ci,, ~ #~~~~~~~~~~~~~~~~~~~~~~c -* d o o c~~~~~~~~~~~~~~~L (qO + I}/00'3~)~1.10 30~d$~~~C

w Ii CL LI1 0~ __ ~ ~ ~ ~ ~ ~ ~ ~ ~ r I= 111 II IL w __..J____" ____ __ " ___.>.4 Y 4 0 o 1 0 UJ.Al. N a 6 W0 0 o 0 \I I1II I, 0 0 0 w~~~~~~~~~~~~~~~~~..0 I V~~~~~~~~~~s CD~~~~~~~~~~~~~~~~~~ so 4~~ 1 >J:5 U.3 w _ _ _ _ 4~~~~~~~r, 4 L i ft~~~~~~~~~~~~~~~~~~I ri I-i wO Xu OD C C 4 U ('4 ___ \ ___\~ ___\ ~ \ --- --- 1 --- --- A --- --- --- L --- 0 -- ---. —-L -- ->O L \ \ 11tjd __ _ -_ L _ _LA__ _K_ -_ - IL~~~~~~~~~~~~~~~~~~~~h 4. C 0 NO(i (qO+I)/3o'39yiVHO 33fVdS

a\/ X!X I D z w ___ 0 o, (I) 0 0 0n 0 o) 0. _ LLJ w W oI od 0 0 0 W ~~~0 IA~ 0'A~ 0 ~~ i (qO+ I )/QO'398VH0 3

____ ___1 1 _ < w o a_ __0 I. - -0 - (q9+ /9' H 39>dS _LL -n O0 _1 > 0 C,,o w 0a r)o o wL. (qO'+ 1)/100'39BiHO 30~dS

a t- aI — Li I It ill 9 + I )/90'398tH9 39UdS ~~ L I c9 O LL. -- --- | --- -- --— _ —--- ---- - -- -__L -_L__' ____ (:[ 11 - O UO X I0 o d0 0 -6 -: 0 0 0 0 d ~o c5~ o 6 o (qO + )/00'39IVHO 30VdS

/I I 0 I III 1 1 1 II 1 I...... l I U. -J 0L 0 0 t Cn @i > 0 >U O o O O ~ o o d S O (qO + I)/'39lvHO 9 OdS IaJ ___ 0~~~~~~~~~~~~~~~~~~~I

@1 w _ \ _ \ \ I I 10 I~ \ I0 \0I \R I~ \~ I I 11 1 1 1 o \ \ - -- -- — _ __\ - -- -\ — \ - -- - - -- z _ 0 LI W I\ I LL 1 I I \ I\ 0 I I 0cU~ ~0 o w o (Iq +l )/00' 3dVHO 30VdS "U >0 w a., ci oi ci ci i co o 66 0 0 0 0 6 (q9O+ I )/30'3 9VH 39~dS6

w z I0 W Q0 |or 61 0,?, > r 0 0 1 o o > o II.~ LO t -~~O 0t) x jLL:I 0.0 I0 0 __ < ~> I 10 0 0 0 __ __ _L __ 1 __ __ __ __ __ > *~~~~~~~~~~~~~~~~~~~~~~~pC -- --- -- \ \ --- -t - --- -V - - - --- 1 -- ----- ^ o~~~~~r ill 1 ~ "~~~~~~~~~~~~~~~C cJ O Q) U) ~\\ c -— ^ -l _ -4 —---- S O d ~ ~ ~ l I ~ d - - - t - -v -i — - - \ - - + -73 3ttl3~ 3d

^_r 4i~n__, J!' -I^ " I0! " I ^ > z UI 0 o U) 0 C el N \ 60__ ____ __ 1 —- 60 0 w, >o \\^ ^\ - ~rOr C LL i\ \' IW WI O. On I D U)C ) ( cu N d d d ___ Nddddbo

w ID I i. ^ l 1l "~ll i.. S. I — ___ S CDo 0 I I c I c \ I I \ I \ I I I I I I. m> ___ INI I 1\1cm 0 0 in I I_ I I I Im~ I I'a - i zzMlsC.) ) _ oOO O O O o;o'i@_o d I, ~ 0I0 x LL in W oJx vi o n I...... r 0LI) CD Ccj 4 t) W i U) a.~

, ___!~~~~~~~~ ___.~~~~~ IILL CC! I I i I -! O D w N___0 000 XI -J 0 1ci~~~~ > >0 I () 0 -— i ------- (q3'J)/3Q'398VH3 XO~dS i o o I / I I, (/ (q9+ 1)/DO'39VH 9 3 |9VdS

.L. c( l > z w <o 0 > ) NI~~~~ 0' 0~~~~~ Co 0 0 so o> > 0 C) o! d d ) (q!+ I)/90 II~yVH_ IV i -'C LL L > _ O ~ a. ci

A__ l_ oC ol ~ ~,c z LI) 0 w I 0 0 _J m -g 0c A 0 >: -o c1 0 d o diN c i(q + _/9VO w > 0. 0 C 4) w 4 4:V 6 6 0 0 0 0 6 0 6 6 0 6 -1 ~ (q3~~ ~ ~ ~ + )3 JQ~H Od

SECTION E SPACE-CHARGE CORRECTION FACTOR The space-charge correction factor curves are arranged according to ascending values of the gain parameter. Parameter Range C 0.05 to 0.20 -398

1.6 — ---- 1.4 1.2 1.0 uj / / D 0.8 0=/ () 0.6 - 0.4 - MAXIMUM 7ls 0.2 MAXIMUM X, 0.2 0.4 0.6 0.8 1.0 1.2 QC I +Cb FIG. E.I SPACE-CHARGE CORRECTION. (C = 0.05, d = O)

1O.6 1.4 I. - 1.0' — I 07 —-- ---- ---- ---- ---- --- + Cb a G. E.2 SPACE-CHARGE CORREC 0.6___ _ OA - MAX. /" 0.2 A MAX. X, _______ 0 0.2 0.4 0.6 0.8 1.0 1.2 1+ Cb FIG. E.2 SPACE-CHARGE CORRECTION. (C:O.10, dOQ)

1.8 ---- -- 1.6 1.4 1.2 / 1.0'I) L ii 0s 0.6| |_ ___/ 0.4 / MAXIMUM 7S MAXIMUM XI 0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 QC I +Cb FIG. E.3 SPACE-CHARGE CORRECTION. (C =0.2,d =0)

SECTION F OPTIMUM FT.ECTRON INJECTION VELOCITY The curves of the optimum electron injection velocity are arranged according to ascending values of the loss parameter. Parameter Range C 0 to 0.3 QC 0 to 1.0 d- 0 to 1.0 -402

-----.4 QC =1.0 QC:0.75.2 I I I I I I I 11- - - QC = 0.60 7Q QC — = C 0.50 \ A\C 0.30.2 - - --- -— \T -r yo co.5 — o C -0 8/ 0.20.0 I 1____ - -\\\ 00.15 X, M AX. CF b A MAX. VS. X MAX. C AS PARAMETES. (d - 0 1.6 o 0. 0. 2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 X| MAX. G. F.I b AT X) MAX. VS. XI MAX. WITH C AND QC AS PARAMETERS. (d - Q)

3.6 _QC:1.0 3.4 3.2 3.0 2.8!. ~~/ 00:QC=0.50 L o2 lo k.6 / 2.4 - /00.2 2.2 C 0. 2.0 1.8 0 \0 \ 0 0 0 0 069 QC=.0.125 0. FT 0.6 0.4 0 OJ 0.2 0.3 0.4 0.5 0.6 0. 8 0.9 1.1 1.2 1' X, MAX.

3.6 2.8 _ -1 —/ ~4QC =0.5 2.6 2.4 /.2 s \ / / 2.0 2.8 / 1_6_/ /__ 0.2 0.3 /.07.. QC =0.25 1.4 1.4 ____ __ (d/ / 0 /QC0.I25) / _ / / 0:0.3 0.8 6 --------- C 2 0.1 0 O.I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 X, MAX. FIG. F.3 b AT XMAX. VS. X1MAX. WITH C AND OC AS PARAMETERS. (d 00.125)

3.6 QC ~ 1.0 3.4 / 3.2 3.0 / Q Ioc 0.5 2.e -4H e-A_I \ / I_ / 2.4 2.0 1.6 I QC 0.25 1.4^~/ Z I/ CO.3 1.2 / \X. 0.2 1.0 C z 0.1 0.8 0.6 0.4 0 0 2 0.3 0. 0 0.6 0.7 0.8 0.9 1.0 1.1 FIG. F.4 b AT X MAX. VS. Xo MAX. WITH C AND QC AS PARAMETERS. ( d: 0.5)

QC=I.0 __ __ __ /_ -/ ____ 6 41o./ 0. 04.07QC 0..5.4 _. _ / AT __ VS - W C A Q AS TE c-o. ).6 1.4 ---- - -- -- - --- -- - C C=0.2 0.2 0.3 0.4 0.6 0.7 0.8 0.9 1.0 1.1.2 1.3 MAX. FIG. F.5 b AT X1MAX. VS. X(MAX. WITH C AND OC AS THE PARAMETERS. (d: 1.0)

3.4 3.2- b- ADJUSTED FOR MAXIMUM Xl -- b - ADJUSTED FOR MAXIMUM 7s 3.0 C =0.2 2.8 --- 2.6 I> 2.4I / ~0 0 2.2 C: 0.2 I 20^ —I__ __ __ __ _ 2.0 i-\4 ~~~~~~SA/0 CZ -j C0. 0.050. _ cRo.:I /d w 1.8 0.6 4. 0.2 ____ /C 0. 05 0.6 0. 2 0 0.2 0.4 0.6 0.8 1.0 1.2 SPACE-CHARGE PARAMETER, QC IG. F.6 RELATIVE INJECTION VELOCITY VS. SPACE- CHARGE PARAMETER. (B I, d= 0)

SECTION G PERVEANCE The curves of the electron stream perveance vs. the stream diameter are arranged according to ascending values of the parameters a'/b' and C in succession. Parameter Range a'/b' 1.2 to 2.0 C 0.05 to 0.20 -409

4.0 3.0 I+ 2.5 _ _ _ _ _ _ _ _ 0 2. 0 02 1.0 QC = 0.5' ____.5..25. QC = 0. 2" QC = 0.25 QC = 0.05 0 0.5 1.0 1.5 2.0 BEAM DIAMETER, B FIG. G.I MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C= 0.05, a'/b' 1.2)

4.0 3.5 3.0 2.5 2.0 1-.5 —-— QC / — 1.0 — QCIO _______ __________I I - 0.5 ~ QC' 0.50 PO QC0.5 --- --- M_-l QC- 0.125 0 0. 5.O 1.5 2.0 BEAM DIAMETER, B FIG. G.2 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C 0.05,a/b': 1.4)

4.0 3.5 2.0 - - - -- - -- -- 3.0 CW. ~ O 2.0C S E A P. / 0.5 C) V____ __ _ w 1.0 _QC 2 = I.05 -- 0.5 QC 0.50 1 2 BEAM DIAMETER, B FIG. G.3 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OFQ THE SPACE-CHARGE PARAMETER. (C 0.05,'/b' 1.6)

4.0 C 3.5 3.0 ~2.5 2.0 1.5 2.0 -- 0. QC * 0.50 lI QC 0.3 - QC = 0.25 QC F 0.20 0 0.5 1.0 1.5 2.0 BEAM DIAMETER, B FIG. G.4 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C 0.S,a'/b': 1.8)

3.5 Q. 2.5 wI z w 2.0 a: asl0 2____.5 —--- -- QC =01.5 QC = 0. 25 QC = 0.25 QC: 0.0=5 0 0.5 1.o 1.5 2.0 BEAM DIAMETER, B FIG. G.5 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER.(C = 0.05,'/b'= 2.0)

4.0 oQC= 1.0 3.0 2.5 A 2.0. _o, QC = 0.50 i.e _____ _____ QC=0.35~- QC = 0.20~~ QC= 0.125 - -- QC= 0.05. —-----— ~ —-" ~o0 O.S 10.5 2.0 BEAM DIAMETER, B FIG. G.6 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER (C 0.08, a/b' 1.2)

4.0 A _ 3.5 QCU 1.0 3.0 " Lo~o~ FT=t _/ a. 3o 2.5 _ —-- CMJ W 2.0 P 0 _ QC.0.15 e___^___ 1.0 J.S 1. 1.52. 0o.5 o-QCo= 02 ~ 0.5 QC 0.235 QC: 0.25 2 QC! 0.10 5 QC. 0.05 BEAM DIAMETER, B FIG. G.7 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C=0.08, a'/b': 1.4)

4.0 3.0 l.. — - - - - -- - / 1QC __1.0 _ 2.5 2.0 / 1.5 1.0 O ____ _ 0.5______ QC = 0.05 —0 "QC= o0.20 QC = 0.25 QC = 0.05 0 0.5 1.0 1.5 2.0 BEAM DIAMETER, B FIG. G.8 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C=0.08, a'/b' 1.6)

4.0 3.5 QC: -I.O. z > 2.0 OC 0.50 1.0 QC = 0.35.0 QC= 0.125 ——' QC. —---— 0 5 0 0.5 1.0 1.5 2.0 BEAM DIAMETER,B FIG. G.9 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C = 0.08, a'/b': 1.8)

4.0 3.5 3.0 2.5 QC =1.0 1.10 _=0.50.__ —/' OC: 0.35 O. 5.5 20 00=0.05 --- - -- ~~ --- """" BEAM DIAMETER, B FIG. G.10 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C: 0.08, a'/b' 2.0)

4.0 3.5 3.0 QC 0.50 it ___ a2.50 z w 2.0DIAME, w QC =0.35 w FIG. G.II MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (CO.IO,1 a'/b' 1.2) QC = 0./0 QC= 0.05THE SPACE- CHARGE PARAMETER. (C=. IO0, a'/b'=I.2)

4.0 3.5 3.0 s,,I I IQ I1.35 1.0 QC —-- --- -7 —- 0.25 QC 0. —-20//X 0.5QO.50 1 2 - - - - - -^ — QC- I 0 0.5 --- QCO0.125 0 0.5 1.0 1.5 2.0 BEAM DIAMETER, B FIG. G.12 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C 0.10, a'/b' 1.4)

4.0 3.5/ / l y / 3.0 e 2.5 P, QC - 0.50 LU.5 O —-- ---- --—. —-- ---- ETR --— VAR ---- ---- WO < QC =-0.35 QC = 0.20 —--- 0.5 QC - 0.05.0 01.0 1 2.0. BEAM DIAMETER, B FIG.G.13 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (CO.IO, a/b': 1.6)

40 i.0 i __ _ 3.0 QC - 0.50 l 2.5 1 0______ ____ ___ QC z=0.2035'1 0 0.5 1.0 1.5 2.0 BEAM DIAMETER, B FIG. G.14 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C O.1O, atb' -1.8) LI OF THE SPACE-CHARGE PARAMETER. (C:= 0.10, o'/b'= 1.8)

4.0 QC= 1.0: 3.5 3.0 2._ 0/ 2.0 Ms / w 0 I,0 QC z 0. 2 0.5 _= ~QC= 0.125, —, QC = 0.05, 0.5 1.0 1.5 2.0 BEAM DIAMETER,B FIG. G.15 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (Co=0.1, a'/b' 2.0)

4.0 a__ — 3.5 _ _ QC= 0.25< f 3.0 _-_ ___ 2.5 --- - QC 0.20 / /e 2.005 10 15 2.0 LI THE SPAQCE-CHARGE PARAMETER. (C 0.150.15 b' 1.2) i.5 Q C0.5 _ _._I o / - 0. 7 5 0.5~~BEAM DIAMETER, B THE SPACE-CHARGE PARAMETER. (C:,0.15, o/b' 1.2)

4.0 cm QC /0.25 / 2.5 j/ 0o / c 2.0 -- QC'0.20 A w a. 1~~ ~QC:0.15 w v c. ___________0_ 125_____ _____ 1s — -- OC0 ---- -~QC 0.10,0 0.5 0 0.1.0 1.9 2.0 BEAM DIAMETER, B FIG. G.17 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C: 0.15, o/b'/b1.4)

4.0 X, 1 / A/ 3.5 H 3.0 L _, _ — ___ 2.0 _2 QC =0.205 _ _ _0.15/_ 1.0 I QC 0.05 0. 1.0 1.5 2.0 BEAM DIAMETER, B FIG. G.18 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C: 0.15, Q'/b' 1.6) QC z 0-0 -o~oo~ oc —~~~~~~~~~o.,, // []' I~~~~~~~~~~~~~~~~~~~~~~~~~~~~001 QC.07 oc~~~~~o,2~/ /~~~~.00 0.5~ ~ ~~~~~~ QC 0./5

4.0 QC: 0.35 o 2.5 w 0___ 2.0_ w a.____ _ T0C/ QC =0.05. ---— x^ -^ ~ QC= 0.205 / 0 _0.5 9.0. 2.0 THE SPACE-CHARGE PARAMETER. (C - 0.150- /b' - 1.8)

4.0 3.5 3.0 0 QC=0.35-,C I I o I / I I 2.BEAM DIAMETER, 2.0 / / /. GQC.20 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF20 QC E-CHARGE PARAMETER. 0.150.15 /b 2.0) QC z 0.1251000" QC= 0.10-;, 010.5 ---- - QC=0.0750OC =0.05 BEAM DIAMETER, B

4.0 0035 - - 0.153.5 QC. l/ l__ 0 ___ Q0.15 CL1 r I OC 0.10 w 2.0 0 /. Li.C 20.075 1.0Q —-— O _C 0.05 —0 0.5 1.0 1.5 2.0 BEAM DIAMETER, B FIG. G.21 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C 0.20, c/b' -1.2)

4.0 _ __ _ 3.5 3.0 OC 0.15e., + 2.5o M./ / 0 QOCw C 0.125P. > 2.0 -- -- ---- ^ — ------------ a./ 0 0.5 1.0 1.5 2.0 BEAM DIAMETER, B FIG G. 22 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C 0.20, a'/b' 1.4)

4.0 _____ _____ QC =0.20/ o~. o o / 3.5 3.0 0. o 2.5 QC.10 1 I5 2 + Fw 1.2 OPA E T0 QC =0.075 I.0 QC = 0.05 0 0.5 1.0 1.5 2.0 BEAM DIAMETER, B FIG. G.23 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C=0.20, 5ib:1.6)

4.0 3.5 3 2.05 —-- BEAM DIAMETER, B G. G.24 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THEC C 0.20 /b' 1.8) QC DIMEER IG. G.24 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF TH SAC-CARE ARMEE. C OZOa'bif18

4.0 I I I I I M 1X \=2 3.5 LS 0o r ocro o T30 --- QCE- 0 PE ( 0.2 — --- __- - f, — / -/ 2.) 1" QC=O.15 < o y oi 0.- QCIO..125 0 i cr. GQC 0.075 QC = 0.05... 0 0.5 1.0 1.5 2.0 BEAM DIAMETER, B FIG. G.25 MICROPERVEANCE VS. BEAM DIAMETER FOR VARIOUS VALUES OF THE SPACE-CHARGE PARAMETER. (C= 0.20,a'/b' 2.0)

SECTION H PERVEANCE CORRECTION FACTOR The curves of the perveance correction factor vs. the space-charge parameter are arranged according to ascending values of the gain parameter. Parameter Range C 0.05 to 0.20 -435

1.0 0.96 0.92 -- MAXIMUM Xi. 0.88 - / MAXIMUM Ms 0.84 0.80 0.76 0.72 1 0 0.2 0.4 0.6 0.8 1.0 1.2 QC FIG. H.I PERVEANCE CORRECTION FACTOR. (C 0.05, d=O)

0.98 0.94 0.90 MAXIMUM XI 0.86 0.82 _____ 0.78 - 0.66 0.62 0 0.2 0.4 0.6 0.8 1.0 1.2 FIG. H. PERVEANCE COC FIG. H.2 PERVEANCE CORRECTION FACTOR. (C=0.10, d-O)

0.92 0.84 0.76 _ 0.68 iv, [a I\ I MAXIMUM Xi 0.60 0.52 MAXIMUM __7 0.36___ 0.28 --- 0 0.2 0.4 0.6 0.8 1.0 1.2 QC FIG. H.3 PERVEANCE CORRECTION FACTOR. (C =0.2, d=O)

SECTION I ELECTRON STREAM CHARACTERISTICS The following useful electron stream characteristic curves are included: 1. QC vs. B with (p/) as the Parameter. C = 0.05; a'/b' = 1.4, 2.0. C = 0.10; a'/b' = 1.4, 2.0. C = 0.20; a'/b' = 1.4, 2.0. 2. Rn vs. B with a'/b' as the Parameter. 3. Electron Stream Perveance and Power. 4. Nomograph of Stream JPerveance and Power. 5. Magnetic Field Required for Brillouin Flow. -439

0.28 1 - ----- ---- - - — 0.4 I'0~~~~~~~~=0 0 0.2 0.40.60.6 w STREAM DIAMETER, B / FIG. I.1 SPACE CHARGE VS. STREAM DIAMETER WITH NORMALIZED PLASMA FREQUENCY AS THE PARAMETER. (C 0.05, ~a0./b' - 1.4) o I 0.6 (U:0,1 0 o~e.. 0.6 0.8 1.0 1.2 1 / /.6 1.8 2.0 2 STREAM DIAMETER, B FIG. I.I SPACE CHARGE VS. STREAM DIAMETER WITH NORMALIZED PLASMA FREQUENCY AS THE PARAMETER. (C =0.05, aI/b' = 1.4)

I —- -0.2 02 X0.4 1.0 w L IDLW 0(C., a b 2.0. 0 w 0.4 (D 0.6 I 0. () 0.4 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 STREAM DIAMETER, B FIG. 1.2 SPACE CHARGE VS. STREAM DIAMETER WITH NORMALIZED PLASMA FREQUENCY AS THE PARAMETER. (C =0.05, a'/b':2.0)

1.2 ---- ----- Wp --- 0.5 1.0'-I p I. 0.6 w Wp 1.0 — --- - l l 0.4 _ I / / p A w 0 C., - 0... 2. 2. FIG. 1 ISPE CRE S STREAM I WI 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 STREAM DIAMETER, B FIG. I.3 SPACE CHARGE VS. STREAM DIAMETER WITH NORMALIZED PLASMA FREQUENCY AS THE PARAMETER. (C 0.1, a'/b' 1.4)

l~~- o.5 1.0 - ~ 0.8 C U --- -:060 6' A /-0.4 2 0I/l / 0. 0.6 0 0.4 0.6 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 STREAM DIAMETER, B FIG. 1.4 SPACE CHARGE VS. STREAM DIAMETER WITH NORMALIZED PLASMA FREQUENCY AS THE PARAMETER. (C 0.1, a'/b' 2.0)

1.2 -- -I — - — ii-i-ii 1.0 20.8 0 0wp 0tov~~~~~~~~~~~~ rm 0.6'Q: 0.6 ~~~~z (Up ~~~~~~~~~~~~= 0.5 a I 0.4 PI - -— ^wp,. x ^^'w0.3 STREAM DIAMETER, B FIG. 1.5 SPACE CHARGE VS. STREAM DIAMETER WITH NORMALIZED PLASMA FREQUENCY AS THE PARAMETER. (C =0.'/b.4) 0 —.2 0.4 0.6 o.e 1.0 1.4 16 1.. 2.0 2.2 STREAM DIAMETER, B FIG. [.5 SPACE CHARGE VS. STREAM DIAMETER WITH NORMALIZED PLASMA FREOUENCY AS THE PARAMETER. (C =0.2, a'/ b'=1.4)

1.0 I - - - - - - - - 0.8,tp 0.6 w C,) 0 0.2 0.4 06.6 0.6, 1.0 1.2 1.4 1.6 1.8 2.0 2.2 STREAM DIAMETER, B FIG. 1.6 SPACE CHARGE VS. STREAM DIAMETER WITH NORMALIZED PLASMA FREQUENCY AS THE PARAMETER. (C = 0.2, a'/b'y 2.0) a, I O~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0...-.. 2 14 16... STREAM DIAMETER, B 5 O. d/b'r- 2-0)~ ~ ~ ~

-F —i —- - C 0 o a -0 m c Q c- s 0'- Q uj 0- ___ ___-___ I - ____ ------ _ _ _ - - | e: " m + ___ 11.g-__-:_________^ z L~~~~~~~~~~~~~~~~~~~(I,___ __ _. 0 0 m ( 0 m c. - 00

, x"7 / 1,/ / /1 3 I/' / / / /// \\' Z,_ /////,,Z///,,/ / W Z_/xy y///X9/.,><\\ 1,-//, / y///o \ \ \ ~ \\,/// / //// ooL 0 lo IO c 0 w o W ~~0. \ x^<- / / / / 0 - 00 I..A /s /\/\ x -'p. / / 0 / / / S 0 W ac o /x^ ^. ~~ y' ~,~ ~ - I,77 / / /.^ I __ _ ~ w oo o o o oA o) o o(^) SS\^\.\2^^^^7 Z__4^^7^~~~~~~~~ Y/VN)?^^\ / x X v V / ^ ~7 / / / / / ^0 S~~~svS^^^^^-^7-^^^7~~~~~~~~~~ I ^ K~~~~~v^X^^V^V ^yy/// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^W^^^^-^^^^^- ^~~~~~~ Q\~D~~ u'xx \/ N \ \ ~7// / /'0 1 X/^S/x'/x0000 0^\ 0 0^ 0 s\^V ^ /^/y\^\>(\\ W ^K V^~~A>SI/) / / A

40 100 30- 50 10 1000 40- 9 30 8 500 7 20 400O 20 300- - 6 200 6 ~~00~ I 10- 5 100 50 4 10 40 - 9 30 3 8^ ~20- 2 8- 7 10 6.0 2 6~~~~~~~~~ 42 5 3 2 - 0.5 421 0-1^ 8~0.4 4 1.0 0.3 0.2 1.0 3 0.5: 0.4 0.9 0.3- 0.1 0.9 0.2 0 0.7 2.0 o0.1 0.0 0.6 0.04 - 0.05 0.03- 0.5 0.04 - 0.03 — 0.02 0.020 1.0- 0.01- 0.01 0.9 0.3 0.8 0.005 0.73 PoW IA0.004 - 0.005I 0.7 0.003 0.004 0.6 0.002 0.00302 0.~~~~~~000 — 0.0020.5 0.001 0.002 0.4 0.001 0.3 Po,(KW) I (AMP.) 0.1 0 BEAM BEAM P. BEAM POWER CURRENT MCROPERVE 0.2 MICRO PERVE \(IOAMP/ VOL 0.IVQ (KV) BEAM VOLTAGE FIG. 1.9 NOMOGRAPH RELATING CURRENT, VOLTAGE, POWER AND PERVEANCI IN AN ELECTRON STREAM.

0 IL\\'S\\ \ \\\\ X\\\' —, \ Stt4o I 00 I\\ \\ 1\1\ \\\\ \1\o \ o IN 0,~ o I 1\\ \\\ \, \\ \\ ~\\\ \,j -T__ ^ ^S l5_ I I I\\e\\ \\\__ - = z 9 5?1 \ \ o i -- -— ^ ^^^,W? to. Cy t ooo o oo _ _ 0_ -. o \ I' d ~ -- ^ —-— ^^\\ -i _ ~ ~,,.. I.L _S l _ > CD___W. -- o o - -1 W oc''0 0 0 0 0 0 4 N 0 ('NI-SSflV) P~8

SECTION J SPACE-CHARGE REDUCTION FACTOR FOR DISPERSIVE STRUCTURES The space-charge reduction factor curves for dispersive structures are arranged according to ascending values of the parameters Vo, a'/b' and DLF successively. Parameter Range ~V0o~ 5k5 kv and 10 kv a'/b' 1.2 and 2.0 DLF 70 and 90 -450

CM n n l m m 11 i n — | LL n X <1 AI l l IU. o m - U I I ~.i V: C ^ 1E an so i Xoul< XTIir iI.- Iw - w:E1 0 s < < m TUX I IllTII> o -oX I n | * Q-'d I' a < 39/ V Ul l 0 ] >~ | or a~~1>3 ______.4.- I: 0, __ II __ rJiA I I-~~~~~ oI~~~~~ o0~ o oc~I C.I -- - - ml SM. *I 10 I* I0 U 0 0 ____ ____ 0OioV1 NOlGno3BI [(qo+ )vO] / ____ I I I I I I 0 -. i o I 6 -doooL L L L.\

0 o H0 -- o J w J' —.. o —--- -- - -' - 0 I C _2 I I__I____ I- I_ - _-_ -4 *_ --- ~o i T _| | N|| < _,J l I I - -. —. -- ~- _ N1 - -+-+-4-1 -— 2 III ci l I I I I I II_ _ iI _ -- -- --- _- I.I S I I:11 111 1 II IS I 1 m 0 CN W 00 2 " 39UVHO-30V/dS I=: P[(qO + / I/:0]

HJ I1 0 N I\ \ \\ 1 - _-V LL 0 Uul %! I I 6o m ~ OLLJ ili 0 0 2 > N __ __ __ _ _ — -- -- -- -- _ 0 C) 0 _ ii 6I n1i ~A ~I~I u f o wo ~n LrJ )o'0 39uH-3OVdS P[(qn O l)/00], II U I I I 9 6l*333d Pq3 130] oI I

LL. LL o own% -- I \IU\ \\ 1 \ \\ I i, ll 1 \ 1,,.,\ I \1\ 1 1 1 1 0 0 _ W. o < > -.- _ \ -- I \ \ \ \\ I I I I iIo L,__ _Jit4i;^ ii -- Z cn I- 0 LU 0 CM a<' /id d o N i II II' II I ~~~~ ~CI) I.. L.. U) 398.tH3-33\ dS + - I I t I 1 I I, _ "LL - d d d 6

- - --- L LIII ~1111 ~7~" u —1 i -- -. L -- m - 0 IQC I loralull IililnIro -t l ~ o -- - -- ------ - - _I — o o Io F I —-- - -[-+ -tIr — I-'Id IY -. ^ I I I IX II *I 2 C 2 ) -n o I I) ____l__ —-__ I-I - d o O - 0 o od

V 0 1~T 1 - - - I O 1 X1xr I No II I I I I II 1 I I o LL cr. z -- _ _0 C) I 5 W w I W I 2I1 il I <vt o I I _ _ _ 6 o | 0 >n1 o o1 ~ ~it U. U — - U. - U- - to - d o 0 d 0 0 00 o QN - __ __ _ aoi v d N io au [0+ 6 /oo] 0_ __ __ d 6 aoyvHO -aovds''P""'^ <o ^ I | 9t93vS I P(3 ) 9 ]l aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa Ic I L oI I> II II wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwd-t o rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

s i \ it~~~~~~~~~~~~~~n'i~~~~~~~i ~i i nj"~~~~~~~~~~~~~ II UJ w c \\ i. i \fo sU. w w iia~~~~~~~~~~~~~~~~~: I \ \\ \ \ \\ i -u- i Q I \ ~- o LL I \\\\\\ z l I w l a. co L - - - T'l~ i ni-A —.s >> w C-;- - -~-1+~~ ~~~ —- - 1' - - -t 0 0 c~i - I I l i I \ \ \ * I o r s- - - -~~~~L. _ _ ml ^\ \^ - - j~ ~~~~~~~L. LL. LL L i. L L) 10~~ IL o 0 0 0 0 0 0 0 0 1 _____ _____ " ___M __._~._ >1_.._____ U 00 d d __ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~?WC.> Ir,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I ___ _ 801 1~O NOJ0110038 ^[(q0+IDOO] ___ ~ --- ---- --- 398MVHO-33VdS ---- ~s — -- -- > - -~~~~~~U If of mm %.. LL- LL La- w U- W L 0 0 0 0 6 (~ -do ~ 6 (3 ~~~~3 ~~~~3 ~~3 (3 (3 L3 L3 O~~~~~c

C — N + Or. o.I' c. \, d — __ __ __ | — n-n~-\-14 -1-44-H-\- - -_ 0: Is?3 i iL \ l \rrT -w mii li 0- - -- — 11 1 - 1 I: 0 O ob.. LA- Li U.. Lp. io 0 - o d d doL~~~~~~~Sd d 0~~~cd O 0hO ~ ~ ~ L U N t c). m Q o. L. L U- o

SECTION K TUBE LENGTH AND CHANGE IN PHASE SHIFT vs. INPUT-SIGNAL LEVEL The optimum tube length and the change in phase shift through the tube are given as functions of the input-signal level 4, relative to CIoVo. Parameter Range C 0.1 B 1.0 QC 0, 0.05, 0.125, 0.25, and 0.5. -459

FIG. K.I 4, INPUT-SIGNAL LEVEL IN db BELOW C IVo, VS. TUBE LENGTH AT SATURATION IN UNDISTURBED WAVELENGTHS. b IS ADJUSTED FOR MAXIMUM SATURATION GAIN (C 0.1, d O, B * I, a'/b' ~2) 0 10 LJ co 40............................. 0a. 30 2. OC — o0. 50 \ - 0.05 40 0 2 6 8 10 0 12 __ 16 18 20 22 24 2. bT 1.5 QL, N.5 QC2N U125.WAVE75 \ b=.,25 b 5. 60 2 4 610 12 14 16 18 20 22 24 26 TUBE LENGTH, Ng, IN UNDISTURBED WAVELENGTHS

1.8 FIG. K.2 QC =,.5b= 1.5 CHANGE IN PHASE SHIFT AT 1.7 Ng. 5.5 VS. ~ FOR FIXED TUBE 1.6 LENGTH WITH VARIABLE 1.s INPUT-SIGNAL LEVEL,.4 (C 0.1, d O, Ng =5.5, B Ia'/b' 2) 1.3 1,2 QC = 0.25 b=1.25 QC = 0.125 1.0 i._____ / b=1.5'0 /f / i C: 0.05 0.9 -- - - --- - --- b 1.75 ___ ___ ___ I QC 0 _ L ~8 - - - - - - ~ ~r -j I /r b -.2.0 u 7i0.7 / / 1 0.6 o.A __'-L _ —5 0 30 20 10 0 INPUT POWER LEVEL BELOW CIoVo>,,db

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