Charge Storage in Cathode-Ray Tubes

PROCEEDINGS OF TIHE I.R.E.

Charge Storage in Cathode-Ray Tubes*C. V. PARKERt, SENIOR MEMBER, IRE

Summary-The charging process in cathode-ray tubes used forstatic storage of information is analyzed for both a stationary spotand a linear scan, with and without redistribution of secondary elec-trons. Approximate equations are derived for the surface potentialsand charging current as functions of time and other parameters, suchas primary beam current, writing speed, and initial potentials. Theresults are presented graphically in special cases for comparisonwith photographs of experimental wave forms.

INTRODUCTIONT HE PHENOMENON of static storage of electric

charge in cathode ray tubes has recently foundwide-spread application and is therefore worthy of

intensive theoretical and experimental study. The pur-pose of the present paper' is to attempt an approximateanalysis of the charging action and to deduce the effectsof various parameters of the process on the output cur-rent. The analysis is undertaken in four well-definedparts which arise naturally from the increasing com-plexity of the phenomena. Parts I and II apply approx-imately to cathode-ray tubes containing grids closelyspaced to the insulating surface2-5 while parts III andIV apply to ordinary cathode-ray tubes used for storagepurposes.6-8 An analysis9 of a barrier-grid tube with"backing-plate" modulation was published recently withresults similar to some described in Part II of this paper,but differing in detail because of a different approach.The generalized storage tube consists of an evacuated

envelope containing at least the following parts: anelectron gun, deflecting plates, a collector electrode, anda target electrode made up of an insulating materialbacked up by a conducting plate. The collector electrodeis normally at the highest potential of any electrode inthe tube (usually ground potential). The output ter-minal is the conducting plate of the target electrode

* Decimal classification: R138.31. Original manuscript receivedby the Institute, June 26, 1950; revised manuscript received, Decem-ber 11, 1950.

t 18 Bolling Road, RFD #1, Alexandria, Va.1 Condensed from Naval Research Laboratory Report 3648, dated

March 17, 1950.2 A. V. Haeff, "A memory tube," Electronics, vol. 20, pp. 80-83;

September, 1947.3 A. S. Jensen, J. P. Smith, M. H. Mesner, and L. E. Flory, "Bar-

rier grid storage tube and its operation," RCA Rev., vol. 9, pp. 112-135; March, 1948.

4 R. C. Hergenrother, and B. C. Gardner, "The recording storagetube," PROC. I.R.E., vol. 38, p. 740; July, 1950.

6 J. V. Harrington, and T. F. Rogers, "Signal-to-noise improve-ment through integration in a storage tube," PROC. I.R.E., vol. 38,p. 1197; October, 1950.

6 R. A. McConnell, "Video storage by secondary emission fromsimple mosaics," PROC. I.R.E., vol. 35, p. 1258; November, 1947.

7F. C. Williams, and T. Kilburn, "A storage system for use withbinary-digital computing machines," Jour. IEE, Part IIIA, vol. 96,p. 81; March, 1949.

8 J. P. Eckert, Jr., H. Lukoff, and G. Smoliar, "A dynamically re-generated electrostatic memory system," PROC. I.R.E., vol. 38, p.498; May, 1950.

9 J. V. Harrington, "Storage of small signals on a dielectric sur-face," Jour. Appi. Phys., vol. 21, p. 1048; October, 1950.

which is connected to the collector through a suitableoutput resistor.

PART I-SPOT CHARGING WITHOUT REDISTRIBUTION

It is by this time well known that current flows in theoutput resistor when the primary beam is first turned ondue to the charging current to the capacitance formedby the spot under the electron beam with the back plateof the target electrode. A secondary current, consistingof a secondary electrons (on the average) for each pri-mary electron, is emitted from the spot, which will tem-porarily be assumed to be initially at collector potential.These secondaries will be carried by their initial kineticenergy to the collector. If 5 is greater than unity, thespot will charge positively due to the loss in electrons.Those secondaries with the lowest kinetic energy ofemission are pulled back to the spot by its positivecharge; the apparent secondary emission ratio is re-duced. Higher and higher energy secondaries are pulledback as the spot charges until eventually a condition ofequilibrium is reached in which the apparent secondaryemission ratio is unity.

Referring to Fig. 1, the number N of secondary elec-trons of initial energy between E and E+dE electron-volts emitted per second is assumed to vary with Eaccording to a function f(E). The total area under the

Ni

az0

0.

(3

wIC'

Ee E

EMISSION ENERGY IN ELECTRON VOLTS

Fig. 1-Energy distribution curve for secondary electrons.

curve represents the number of electrons emitted persecond 8Io, where 1o is the beam current. The area notcross-hatched represents the number of secondary elec-trons which return to the spot per second after theequilibrium potential has been reached; the cross-hatched area represents the current 10 which flows tothe collector.

A ugust900

Parker: Cathode-Ray Storage Tubes

In order for a secondary electron to escape from thespot and reach the collector, it must possess at least asmuch kinetic energy initially as its potential energy inthe field of the spot just before reaching the collector.If the penetration of the fields of auxiliary electrodesinto the region of interest is negligible, this potentialenergy in electron volts is simply the potential of thespot. Thus, in this case of no redistribution, the ab-scissa E of Fig. 1 may be identified as the potential ofthe spot V. Hence, the fractional part of the secondarycurrent bIo which returns to the spot may be defined asS61o from which S is defined as

S- f(E)dE ff(E)dE. (1)

In the case of thermionic emission, the energy distribu-tion of escaping electrons is Maxwellian. A plot of thisdistribution'0 curve has the same general shape" whichhas been found experimentally for secondary electronsfrom metals as in Fig. 1. Hence, we obtain

s L 2(E/ET)112e EIETd(E/EriI2 = 1 - IVIET (2)

where ET is the average energy due to Z-directed motion

(the Z axis is taken perpendicular to the surface from

which the electrons are emitted).The output current consists of three components:

The primary beam current (-lo), the secondary emis-sion current (3Io), and the secondaries which return to

the surface after emission (-SbIo), as given by the fol-

lowing formula:dV

I-=bo-lo-Salo=C- (3)dt

where C is the capacitance between the spot and theconducting back plate, and d V/dt is the time rate ofchange of the effective potential of the spot. Using thevalue of S from equation (2), there is obtained:

dV 3Io Io_-___ e-VIET + =!0.

If the initial potential of the spot is Vi, and y =Io/CET,the solution is

V = ET In [3 + (evilErT

Note that the potential approaches V.=EErln6. Theoutput current is

I C dV (3 - eViTET)e-I6- - -6rVIr- 1 = -- > ~~~(6)Io Io dt 3i- (3 e ET)e-tY

which may be approximated to a fair degree of accuracyby a linear function of potential and a simple exponen-tial function of time. These results would be obtained

10 W. G. Dow, "Fundamentals of Engineering Electronics," JohnWiley and Sons, Inc., New York, N. Y., p. 237; 1937.

11 H. Salow, "Die Sekundarelektronenemission,". Fern. Tech.Zeit., Heft 6, p. 161; June, 1949.

if the exponential in equation (2) were expanded in apower series and only the first two terms retained; i.e.,e-x -1-x. In order to obtain better agreement be-tween the more exact expressions and their simpler ap-proximations over a wide range of the independentvariables, a constant factor m may be introduced sothat S=m V/Er. This approximation is useful in morecomplicated cases.The physical situation makes it clear that the maxi-

mum output current obtainable is (- 1)1o and theminimum current is -1o so that 0<.S .1. If the po-tential V is made negative, either by positive bias onthe collector or by the deposition of negative charge onthe dielectric surface, the derived equations do notapply since the output current can be no greater than(- 1)Io. However, if V is made more positive than theequilibrium potential, equation (6) correctly predictsthe limiting current -Io. In either case the chargingprocess automatically brings the surface to zero poten-tial with respect to the collector after which the derivedequations apply.The assumed condition of no redistribution may be ap-

proximated in the practical case by use of a wire meshclosely spaced to the insulating surface compared to thespot size. Only a small fraction of those secondary elec-trons whose Z-directed energy is insufficient to permitthem to reach or pass through the wire mesh butwhose radially-directed energy is large will fall outsidethe boundaries of the spot. The number of such elec-trons approaches zero with decreasing spacing betweenwire mesh and surface. Hence, it is only necessary toconsider the Z-directed energy. The closer the physicalsituation approaches one of no redistribution, thecloser we may expect our derived equations to apply.

PART II-SCANNING WITHOUT REDISTRIBUTIONAs we have seen, the output current is a function of

the potential of the spot. As long as the spot is sta-tionary, the potential may be assumed the same overthe entire spot. When the beam begins to move, theleading edge of the beam strikes a region whose potentialis that left by preceding scans or the initial potentialof the surface. The trailing edge of the beam strikes aregion which has already been under bombardment forat least the time required for the beam to move fromits initial position to its present position, and the partsof the beam between the leading and trailing edges strikeregions at intermediate potentials. It is necessary, then,to integrate over the area of the spot.The beam (and, hence, the spot) will be assumed rec-

tangular in cross section of width a in the direction ofscan and height b perpendicular to the direction ofscan, and the writing speed W=dx/dt will be assumedconstant. The assumption will also be made that thepreviously derived equation for the potential may beapplied to each incremental area bdx of the spot with thefunctional dependence of S upon the potential of theincremental area the same as in the case of the station-

1951 901

PROCEEDINGS OF THE I.R.E.

ary spot. Defining the capacitance per unit area as C/ab,it follows that

C dVdl =-bdx

ab di (7)

is the contribution of current from area bdx. The totalcurrent is

jaC dVI-= --dx.

JOa dt(8)

When the beam is first turned on and the scan begins,a transient current flows, but after the time requiredfor the spot to move its own width, a steady-state con-dition is reached in which the total current is constant.Since W=dx/dt, the integral for the steady-state cur-rent may be evaluated by changing the variable ofintegration from x to t. Thus:

C alW dV WC a- Wdt= v(t= --v (9)a JO di a (W9

Using the value of V from (5)

I W wcvi- - In [£ + (eVtIET w- )eaw] - (10)1o 'ya alo

Fig. 2 shows I/Io and V/ET plotted as functions ofya/W=Ioa/WCET for the case of Vi = 0, a = 4. TheV/ET curve also indicates the way in which the outputcurrent in the steady state varies with primary beamcurrent, since from (9) I is linear in V.

3

2 3 4 5

Or~~~~~~X

W WCET

Fig. 2-Steady-state output current and potential versus -ya/W forb=4, V,=o. Scanning beam with no redistribution.

In the transient state, the integration over x must becarried out with t held fixed, and d V/dt expressed as afunction of x. Referring to Fig. 3, the initial and presentpositions of the spot are indicated by the dotted andsolid lines, respectively. The time rate of change of

r- --

F

c'

- AT 0

1 1

Tb

Fig. 3 Initial and present positions of spot for scanningbeam transient analysis, no redistribution.

potential is the same for all points between A and B butvaries between x=0 and x= Wto (point A). Thus, theintegration must be carried out in two parts

c x=wto dV C dV x=aI =-J --(x)dx +-- (to) dx (11)a J0 dt a dt J xwtO

I W WCVi- In [£ + (eV/ET -6)e-7O] - -10

Io z (a aIo

(devi1ET)e--"o(1 t

+ (12)£ - (£ - eViIET) e- to

It will be noted that when to= a!W, this expression re-duces to that for the steady state, but that for to<a! W,the output current contains a component having theform of the stationary spot current multiplied by(1- Wto/a). The form of the resultant current is shown

3

3aW 4

\ _

va4

0 1 2 3 4 5 6yto

Fig. 4-Transient output current versus -yto for 6=4, Vi= 0.Scanning beam with no redistribution.

in Fig. 4 for three different values of ya/W in the specialcase of 5 = 4, Vi= 0. The higher the writing speed thegreater is the final output current. The initial currentis independent of writing speed and is directly propor-tional to the beam current.

- ~ ~~~~~~I

902 August


Figs. 5 and 6 are photographs of the experimental out-put current obtained on an early model of the Haeffmemory tube.2 All parameters except writing speed wereheld constant for these photographs. The beam currentwas turned on for 20-microsecond intervals in a sequenceof three times on, followed by an off period during whichthe hold gun was pulsed on to provide erasure. Thephotographs show the large output on the first scan(after erasure) which charges the surface to equi-librium except at the beginning and end of the onperiods. Hence, transient outputs appear at thesepoints at subsequent on times. The off times show inthese photographs as mere closures of the base line sincethe output during erasure is not shown. The similarityof the output current on the first scan after erasure tothe curves of Fig. 4 is apparent including the de-pendence on writing speed.

PART III-SPOT CHARGING WITH REDISTRIBUTION

In this case it is necessary to consider the effect ofthose secondary electrons which return to the regionaround the spot. Since the secondary emission ratio isclose to zero for low energies, most of these electrons"stick" where they land and depress the effective po-tential of this region. In the absence of these redis-tributed electrons, the dielectric surface in the vicinityof the positively-charged spot would be at a positivepotential with respect to ground which varied inverselywith distance from the spot. Thus there is a tendency forthe returning secondaries to pile up in the immediatevicinity of the spot and for their number to fall off withdistance in the same general way as the potential does.It is quite certain experimentally that most of the re-turning secondaries are deposited within two or threespot diameters of the center of the spot, although evi-dence of their presence is found out to many spotdiameters. In order for additional secondaries to arriveat any point, the resultant potential of that point muststill be positive with respect to the collector.

In order to handle this complex charge distribution

Fig. 5-Output current wave form obtained with early model HaeffMemory Tube. Writing speed, 0.0152 inch per microsecond.

even approximately, the idealizing concept of anequivalent constant-potential region of negative chargesurrounding the spot is introduced. This region ofnegative charge will be designated as Region Two (2),with Region One (1) designating the positively-chargedspot. The actual potential of any point of the screenmay be written as some fraction of the potential of thespot VI, plus some fraction of the (negative) potentialof Region Two V2, the fractions depending on thedistance of the point from the center of the spot andthe size of the spot.Now the Z-directed initial energy required of a sec-

ondary electron to permit it to land at a given pointdepends not only on the location of the point, but alsoon the initial direction of emission. Those electronsemitted almost normal to the surface may possess con-siderable initial energy and still return to the spot whilethose electrons making a large angle with the normalmay land in Region Two with much smaller amounts ofZ-directed initial energy.The argument of Part I must now be modified since

there are two regions of interest at different potentialscharging at different rates. Hence, there are two dif-ferential equations:

dVjI1 = lo -Io- S1bIo = C-

dt

12 = - S2e3TodV2

= C2-dt

(13)

(14)

These equations are not independent, however, ;incethe fractional number of secondaries which return toRegion One (S1) depend on the potential of bothRegions One and Two, etc. Hence, it is necessary toaverage over these regions by defining some new param-eters dependent on the geometry, chiefly spot size,and the angular distribution and energy distribution ofthe secondaries characteristic of the emitting material.Then, by an argument similar to that of Part I, andmaking the approximation that was indicated in Part I

Fig. 6-Same as Fig. 5, except writing speed is 0.00715inch per microsecond.

9031951


as being reasonable, e-VIlT 1-(m V/ET), we have

Si = mlVl + m3V2 + S01 (15)82 = M2V1 + m4V2 + 502. (16)

Both S1 and S2 have been increased by the constantterms So, and S02 in order to take account of residualfields which may penetrate in some cases to the regionaround the spot to cause the return of some secondaryelectrons to the screen, even when the screen bears nopositive charge. The restrictions on S mentioned inPart I apply here also in the form 0< (S1+S2) < 1,limiting the total output current to ( -1)Io and -Io,respectively. The differential equations now become

dV,C -= (a - )Io - o(SOI + mlVl + m3V2) (17)

didV2

C2-- = - 1O(SO2 + m2V1 + m4V2) (18)dt

with the solutionsV1 = Xle7bIoNit + Yle-SIoN2 + Ve. (19)

V2 = X2e-SIoNIt + Y2e-81ON2-+ Ve2 (20)

where N1 and N2 are given by the two solutions

N = 1 [m+ m2 Cl C2

/ ml m42 m M4-2M3+(miC1 + Cm) - 4 (TT' _ . (21)

We will designate by N2 the value of N correspondingto the use of the positive sign and by N1 the negativesign. Hence, N2 will represent the sum of two positiveterms while N1 represents their difference. The outputis the sum of I, and I2 or

I_ = [HI(Vel- Vil) + H2(V.2 - Vi2)]e-O°Nlt

+ [H3(V.1- Vil) + H4(V.2 - Vi2)Je-rO'N"', (22)where Hi, H2, H3, and H4 are constants involvingC1, C2, ml, ml, m3, and M4. From their definitions, N2would be expected to be larger than N1. This is borneout experimentally with the factor N2/N, being large.The output current turns out to be the sum of a smallamplitude, long time-constant component; and a largeamplitude, short time-constant component. The lattercomponent is of positive polarity experimentally if bothinitial potentials are near zero and may be interpretedas chiefly representing the net positive current to thespot which, having small capacitance to ground becauseof its small size, charges rapidly to its equilibrium po-tential. The former component may be interpreted asthe redistributed-electron current which continues tocharge the relatively-large capacitance of the regionabout the spot for a long time. Experimentally, thislonger time-constant does not seem to remain constantwith time, but approaches a limiting value which is

independent of beam current after hundreds of micro-seconds. Apparently the initial assumption that RegionTwo remained fixed in area indefinitely is not validafter a sufficient time, as might have been expected,but that, on the contrary, the higher-energy secondariescontinue to land on the border so that the boundaryslowly spreads out.The general behavior of the output is experimentally

as predicted, however, as shown by Figs. 7 through 9.

Fig. 7-Photograph of output current from a stationary spot withredistribution. Commercial SJPS cathode-ray tube. Beam current,0.130 microampere.

Fig. 7 is an oscilloscope photograph of the outputcurrent versus time, clearly showing the two com-ponents referred to above. The experimental techniquewas to pulse the primary beam on for several intervalsinstead of for one longer interval, and record all theresults on the same photograph. Thus, the output dur-ing several hundred microseconds is shown with thepositive peak indicating the start of the process. Fig. 8

Fig. 8-Positive peak current versus beam current. Stationary spotwith redistribution. Crosses show experimental points.

904 A ugust


shows the amplitude of positive peaks of such curves asdetermined experimentally, plotted versus beam cur-rent over nearly a 100-to-1 range. Fig. 9 is a plot of thereciprocal of the time constant of the positive com-ponent over the same range in beam current. The spotdiameter for Figs. 8 and 9 was 0.6 cm representing a

To (MICROAMPERES)

Fig 9-Reciprocal of time constant of positive component versusbeam current. Stationary spot with redistribution. Crosses showexperimental points.

purposely defocused beam in order to permit more ac

curate measurements. Since the N1 and N2 factors varyinversely with the capacitance coefficients, increasingC1 and C2 by increasing the spot size increases the cor-

responding time constants.

PART IV. SCANNING WITH REDISTRIBUTION

The general procedure of Part II may now be repeatedusing the values for the potentials obtained in Part III,but it must be recognized that this formal processignores some fundamental physical facts of redistribu-tion. The secondary electrons returning to Region Twofall in part ahead and in part behind the scanning beam,as well as on each side of the line of scan. Thus, whenthe beam reaches any particular point, it finds an

initial potential which is more negative than it was

before the beam approached its vicinity and, after thebeam has passed by, the point again goes negative inpotential since it is again in a Region Two of nearbypoints. Furthermore, points off the line of scan are bom-barded by secondary electrons during the time that thescanning beam moves several times its own width incontrast to the no-redistribution case of Part II inwhich the steady-state current and potential were

reached in the time required for the beam to move

just once its own width. Also, the division of second-aries between the different regions of the screen may be

affected by the potential of the line of scan, both aheadof and behind the spot.These complications might be taken into account, at

least approximately, but the process involves expres-sions so unwieldy that a simpler if less accurate analysiswill be given here. The final establishment of the limitsof validity of the results can only (as in any case) beobtained by resorting to experiment. We proceed thento find the steady state output current by integrationover the areas shown in Fig. 10. As in Part II, the cur-rent to Region One is

pa C1 dV1 WC, a, (

JO a, dt a1 L ww)7(23JAs an approximation, the current to Region Two is a2/a,times the current to an area b2 in height and a1 in width,or

a2 ral C2 dV2 WC2F/ a,\12 - -dx= V2 t-- -Vi2 .

a, JOa2 dt a, W(24)

Introducing the expressions for the potentials fromPart III, we haveI = II + I2

W=- -[KI(Ve - Vil) + K2(Ve2 - Vi2) je-6IoNiaIIw

a,

[K3(Ve1 - VFi) - K4(Ve2 - Vi2) ]eIoN2aljW+ Cl(Vel - Vil) + C2(Ve2 - i2) (25)

where K1, K2, K3, and K4 are constants involvingC1, C2, Ml,Mi2, m3, and M4. The output current is zerofor beam current zero and approaches a constant value

2

2 Ill-1- -- :-b4K8,

K-0-I p-- 02 H

b,

b2

Fig. 10-Instantaneous position of moving spot showingidealized Regions One and Two.

for very high beam current. The first exponential in (25)is relatively close to unity so that the approximationex 1-$x may be used, and, for easy comparison withexperiment, (25) written in the abbreviated form

I = a3( -e-IOIa) -

in whicha= W/1ajN2A&=N2 [(K1+C1) (V 1- Vi1)+ (K2+C2) (Vc2 Vi2) ]-= N1 [K1(Vol- V1)+K2(V e2- Vi2) ]-

(26)

(27)

Equation (26) is plotted in Fig. 11 as a function of beamcurrent using values for a, A, and y which produce afit with the experimental points. Secondary emission

9051951


ratio was 3.76 for P-5 phosphor operating at 1,400 voltsaccelerating potential. The linear dependence of a uponthe writing speed has been checked by locating thepoints at which the output current is zero in the steady

4.2

+.2 _ _ _I_ _

I-

,- _ _ \_I"0

w-.

_3 _ ____

0

.2 4 f .8 `0 t2 I.,BEAM CURRENT IN MICROAMPERES

the method used in Part II with a similar result.

WI = _[(C,X, + C2X2)eaI0N1" + (ClYl + C2Y2)e bI0N2t

al

+ Cl(Vel - Vil) + C2(Vc2 - Vi2)]

- o [ ..!±] [Nl(ClXl + C2X2)e-'f"N'tI alI+ N2(ClYl + C2Y2)e-SIoN2ij. (28)

Considering only the first component, as t goes throughits possible values from zero to al/W, the output currenttakes on the same values as the steady-state outputcurrent does when the primary beam current goesthrough its possible values from zero to 1o. Thus, if thesteady-state output current is less positive than itwould be at a lower beam current, corresponding tooperation to the right of the maximum in Fig. 11, theoutput current would start at zero, increase to a maxi-mum, and then decrease to the steady-state current,which might be either positive or negative. If, however,the operation is to the left of the maximum, the firstcomponent of output current would increase mono-tonically to its steady-state value.

Fig. 11-Steady-state output current versus beam current for scan-ning beam with redistribution. Writing speed, 0.20 inch per mi-crosecond. Crosses show experimental points. Curve is plot ofequation

I = 0.325(1 - e-Io/0190) - 0.460 Io.

state. The beam current at these points is directly pro-portional to the writing speed. For the three writingspeeds 0.0247, 0.0817, and 0.200 inch per microsecond,the proportionality checked to within one per cent. Theprobable error of the experimental points in general,however, is not that good, due principally to uncon-trolled variations in primary beam current.The transient current which flows when the primary

beam current is first switched on may be obtained by

Fig. 13-Same as Fig. 12, except beam current is0.650 microampere.

Fig. 12-Photograph of transient output current obtained with com-

mercial 5JP5 cathode-ray tube. Writing speed, 0.150 inch per

microsecond. Beam current, 0.130 microampere, 2-microsecondmarkers.

Hence, the total output current begins at the peakvalue of the stationary spot output current and theneither increases gradually to its final positive value orelse first increases to a maximum and then decreases toeither a positive or negative steady-state value depend-ing on the primary beam current. Some examples ofthese transients as observed experimentally are shownin Figs. 12 through 15.

In practice, the leading edge of the pulsed signal ap-plied to the control grid of the cathode-ray tube ap-proaches fairly closely the action of an ideal switch, butthe trailing edge is usually not quite so good. This maygive rise to a peculiar effect at the end of the pulse:As the primary beam current decreases towards zero,

August906


outp)ut current goes through normal variation with Io,which may involve an increase in output current.

flection of the beam, or by variation of the voltage be-tween target and collector may be handled by point-by-point computations if the period of the modulationis long compared to the time required for the beam tomove its own width. Otherwise it is necessary to findthe solutions of the differential equations for the surfacepotentials corresponding to the applied function anduse these in carrying out the subsequent integration.Much experimental work remains to be done in check-

ing the validity of the theory presented here. In par-ticular, the effect of variation in initial potentials needsquantitative investigation in view of the complex phe-nomena which has been neglected in the simplifiedtheory as pointed out at the beginning of Part IV. How-

Fig. 14-Same as Fig. 12, except beam current is0.780 microampere.

It will be observed in Figs. 12 through 15 that theactual distance on the face of the cathode-ray tube re-quired for the output current to reach a constant valueis many times a spot diameter. This distance is reallya measure of the extent of Region Two along the lineof scan which was neglected in this approximate an-alysis. It appears to be approximately independent ofbeam current or writing speed in the range so far in-vestigated. No information is yet available on its varia-tion with spot size or other parameters.

APPLICATIONS

The theory so far developed may be extended asnecessary to cover various interesting special cases, al-though the details will not be given here. Thus theeffect of intensity modulation by an ideal square pulsehas already been indicated. Modulation by a con-tinuously varying voltage on the control grid, by de-

Fig. 15-Same as Fig. 12, except beam current is1.30 microamperes.

ever, the experimental work so far carried out indicatesconformity with the simple theory for the range ofparameters investigated.

ACKNOWLEDGMENTThe experimental results in this report were obtained

by W. A. White and J. E. Scobey, of the Naval Re-search Laboratory.

CORRECTIONDonald B. Harris, author of the paper, 'Product

Phase Modulation and Demodulation," which ap-

peared on pages 890-895 of the August, 1950, issue ofthe PROCEEDINGS OF THE I.R.E., has brought to theattention of the editors the following typographicalerrors:

1. Equation (1) should read

ei = [57Fan(t) cos nwt + ZFbn(t) sin nwt].2. In the line following equation (19), "k" should read

UK."3. Equation (33) should read

Q f Iodt = IaTy.

907I I.

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Charge Storage in Cathode-Ray Tubes