Propagation on Dielectric Coated WiresE. T. Kornhauser Citation: Journal of Applied Physics 22, 525 (1951); doi: 10.1063/1.1700000 View online: http://dx.doi.org/10.1063/1.1700000 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/22/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Transforming dielectric coated tungsten and platinum wires to gaseous state using negativenanosecond-pulsed-current in vacuum Phys. Plasmas 21, 112708 (2014); 10.1063/1.4902364 Domain Wall Propagation in Thin FeRich GlassCoated Amorphous Wires AIP Conf. Proc. 1003, 301 (2008); 10.1063/1.2928970 Effect of a dielectric coating on terahertz surface plasmon polaritons on metal wires Appl. Phys. Lett. 87, 071106 (2005); 10.1063/1.2011773 Propagation along a dielectriccoated cylinder immersed in a magnetoplasma J. Appl. Phys. 68, 1931 (1990); 10.1063/1.346589 Propagation along a dielectriccoated cylinder immersed in plasma J. Appl. Phys. 45, 4795 (1974); 10.1063/1.1663137

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LETTERS TO THE EDITOR 525

Decay of Spectral Components in Isotropic Turbulence

HIROSHI SATO

Institute of Industrial Science, University of Tokyo, Chiba, Japan (Received January 8, 1951)

ALTHOUGH many measurements have been reported for determining the energy spectrum of turbulence,l,2 there are

only a few data about the decay of spectral components. The author observed it by a rather direct method and some interesting results were obtained.

The wind tunnel used is of the single open-jet type, having a rectangular cross section of 60cm X 60cm. A wooden grid is placed at its opening. The dimensions of the grid are as follows: mesh length= 1 in., rod breadth = ! in., depth = ! in. The electric circuit for the hot-wire anemometer consists of three elements: the pre­amplifier, the filter, and the power amplifier. The amplifier is an ordinary one. The filter is of the phase-shift band-pass type, Q being about 50. The output current is read by a thermocouple-type milliammeter. A new method of measurement was adopted. We traveled the hot wire longitudinally, fixing the tuning frequency of the filter. The output meter indicated the decay of spectral components. This method has many advantages: the required time is short; if we consider the energy ratio only, we need not know the sensitivity and frequency response of the hot wire and amplifier. Therefore, the accuracy of measurement is high.

Experiments were made for the wind speed U = 5 m/sec and 10 m/sec. Both results coincide when the relative energy is plotted against the wave number. The decay curve for U = 10 m/sec is shown in Fig. 1, where x is the distance behind the grid, and E is

on/~~ __ ~~~L-__ L--L~ __ ~ __ ~

0.01 aJ J JO

wave number /em FIG. 1. Decay of spectral components; x, distance behind grid;

E. relative energy component.

the relative energy component, taking x=40 em as unity. From this result it may be concluded that (1) the decay law of energy is different for components of various wave numbers; and (2) there exists the component for which the decay is most severe, the corre­sponding wave number decreasing during the decay.

The result obtained is of the so-called "initial period."a The author is now engaged in the more extensive measurements, whose details will be published in the Journal of the Physical Society of Japan.

The author would like to acknowledge the valuable advice of Professor I. Tani and Professor H. Kumagai.

, H. L. Dryden, Proc. V Intern. Congr. App!. Mech. 362 (1938). 'Liepmann, Laufer, and Liepmann, Final Rep. N.A.C.A. Contract

NAW 5442 (1948). • G. K. Batchelor and L. A. Townsend, Proc. Roy. Soc. (London) AI93,

539 (1948).

Propagation on Dielectric Coated Wires E. T. KORNHAUSER

Lyman Laboratory, Harvard University, Cambridge, Massachusetts (Received February 5, 1951)

I N his interesting paper on the theory and application of di­electric coated wires as wave guides, G. Goubau1 obtains the

straightforward solution for the rotationally symmetric E-wave,

JoC-fia')NkYia)-JO('Yia)No('Yia') h' 'i HoW(i'Y'a')

J1('Yia')No('Yia) -Jo('Yia)N'('Yia') 'Yi .;. H 1<1l(i'Y'a') (1)

In obtaining a useful approximation to this equation, Goubau restricts himself to the case of ')';a'«1, so that the left-hand side of (1) becomes -')'ia' In (a' fa).

However, it might be pointed out that this logarithmic approxi­mation has a considerably wider applicability than the restriction imposed in obtaining it would imply. For the case [(a' fa) -1]«1, Goubau has mentioned that a first-order approximation by Taylor series is possible, yielding -'Yi(a' -a) for the left side. It may be noted that this result is in first-order agreement with the previous approximation if, indeed, we have [(a'/a)-I]«1.

Moreover, a second-order approximation by Taylor series is possible here, a somewhat similar calculation having been per­formed by L. Brillouin.2 In this calculation, terms in [(a' fa) -1]2 are retained, and the second derivatives are eliminated by use of the bessel equation of order zero. The resulting approximation to

TABLE 1. Examples of approximation to F(,),a' ')'a) _ J,(,),a')N,(,),a) -J,(')'a)N,(')'a').

, - Jt(,),a')N,(,),a) J,(,),a)N, (')'a') (a) Logarithmic approximation, ')'0' In(a' ja). (b) Second-order Taylor series, !')'(a'+a) [(a'ja)-I]. (c) First·order Taylor series, ')'(a'-a).

Approximations ')'a' ')'a OF (')'a', ')'0) (a) (b) (c)

0.02 O.o! 0.01386 0.01386 0.01500 O.o! 0.1 0.02 0.1617 0.1609 0.2400 0.08 0.1 0.05 0.06939 0.06932 0.07500 0.05 0.1 0.09 0.01053 0.01054 0.01056 0.01 0.5 0.45 0.05273 0.05268 0.05278 0.05 1.0 0.9 0.1057 0.1054 0.1056 0.1 5.1 5.0 0.1013 0.1010 0.1010 0.1

the left side of (1) is -'YiHa'+a)[(a'/a)-I], which can be seen to agree with the logarithmic approximation through terms in [(a'/a)-I~. Hence, it appears that the logarithmic approxima­tion is a good one even in the less restrictive case of [(a' fa) _1]2 «1. The accompanying table serves to indicate the usefulness of this approximation in cases in which its original condition is ful­filled, as well as cases in which it is not.

, G. Goubau. J. App!. Phys. 21, 11 19 (1950). 2 L. Brillouin, Spiraled Coils as Waveguides (ONR Technical Report No.

10, Cruft Laboratory, Harvard University, March 10, 1947).

Coefficients of Thermal Expansion of Au-Cd Alloys Containing 47.5 Atomic Percent Cd

LO-CHING CHANG

Columbia University, New York, New York' (Received January 31. 1951)

T HE coefficients of thermal expansion of single crystals of Au-Cd {3, alloy (CsCI structure, two atoms per unit cell)

and 1" alloy (orthorhombic structure, four atoms per unit cell), containing 47.5 atomic percent Cd, were determined by means of x-ray single-crystal oscillation method. The {31 alloy undergoes a diffusionless transformation to {3' on cooling to about 60°C, and the reverse diffusionless transformation from {3' to {31 takes place on heating the {3' alloy to about 7D-SO°C.l

The experimental procedures used are: First, rotate the desired

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526 LETTERS TO THE EDITOR

II) l-i :;)

)( ¥

(I) z 0 C Go II)

a: C z C ..J Go a: III .... ~

.7438

.7437

.7436

.7435

.7434

.7453

.7412

.7431

.7430

.7411

.7428

o (024) PLANE

• 101lZ) PLAN!

X (420) PLANE

,"0

• 7427 '---j68'--'--~76;;-"'-:'-;e4-;;-.L-9~2;;--~10:-::0:-'--1::!0~8-'--:-!-1I6:::-­TEMPER ATURE • C

FIG. 1. Spacings versus temperature of (420) type plane of til alloy (crystal No. 12).

plane of the single-crystal specimen (mounted on a goniometer) into position for high angle reflection (1J=75° or higher) by x-ray characteristic radiation of accurately known wavelength. Second, control the specimen temperature to within ±l ° of the desired value, oscillate the specimen about 2!0 each way, from the reflecting position, and obtain an exposure. Third, rotate the camera 180° about the axis of the x-ray beam and obtain a second exposure. Thus, the film will have two diametrically opposite spots, the distance between which, 2/, is related to the film specimen distance, L; the interplanar spacing, d; the Bragg angle, (J; and the wavelength of x-ray, A; by the following equations:

I/L=tan(1800-2(J), (1)

A=2d sinlJ. (2)

Knowing I, L, and A, the interplanar spacing d at any given tem­perature can be calculated from Eqs. (1) and (2). The interplanar spacings are thus determined at about SoC intervals. This method, although rather laborious, has the advantage of measuring

II) .... i :;)

)C ¥

III ! C) C "-II>

a: c z c oJ Go II: III I-!

.,81110

4.11180 -g

4,8540 ~(OOIlPLANE 4,81120 ~ .. , 4,8500

4,8480 8

4.1551

4,n50

~~ ... 4,7&48

4,7548

.,7544 ~o 4,7542

4,7540

3,"00

~o ',ISSO

J,1500 ~o

',14110

2,313.0 / 2,1110

2,3110 ~npLANr 2,1100

2,30'0 ~ 2,3080

U 26 30 34 :sa 42 46 TEMPERATURE 'C

FIG. 2. Spacings Versus temperature of various planes of fJ' alloy (crystal No. 13).

directly the coefficient of thermal expansion of a single plane of a single crystal, over the conventional powder method which yields the average value of the coefficients of expansion of many crystals. The accuracy of measurements depends very much on the Bragg angle. The Bragg angles used in the present study varied from 72° to 88°. The over-all accuracy of the determination of coefficients of thermal expansion is about ±3 percent.

The results, plotted in Figs. 1 and 2, yield the following coeffi­cients of thermal expansion of the {jl and {j' alloy: {jl alloy (cubic) 33X 10-6 per °C (70-105°C). {j' alloy (orthorhombic), directions perpendicular to:

(100) plane 216X 10-6 per DC} (010) plane -12 X 10-6 per °C ° (001) plane -74X 10-6 per 0C (20-45 C). (111) plane 99X 10-6 per °C

* This work was assisted by the AEC. I L. C. Chang and T. A. Read, J. Metals (Japan) 191, 47 (1951).

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