RD-A158 059 RESONANCE BETWEEN BETATRON AND SYNCHROTRON OSCILLATIONS i/iIN A FREE ELECTRON LASER: A 3-D NUMERICAL STUDY(iJ)NAVAL RESEARCH LAB WASHINGTON DC C M TANG El AL.

UNCLASSIFIED 3e JAN 85 NRL-MR-5499 F/6 2e/5 NL

Ehhhhhhhh.om

11111 1.0 1 811111 *,_ _ __

MICROCOPY RESOLUTION TEST CHART

NATIONAL BUREAU OF STANDARDS- 1963-A

FPRlOM ICF 1 Ar GOVERNMFJT I"'XPENSE

NRL Memorandum Report S499

Resonance Between Betatron and SynchrotronOscillations in a Free Electron Laser: 0

A 3-D Numerical StudyC. M, TANG AND P. SPRANGLE

Ln Plasma Theory BranchO Plasma Physics Division

January 30, 1985

This work was sponsored by the Defense Advanced Research Projects Agencyunder Contract 3817.

Jc;TE

K' - ~~~NAVAL RESEARCH LABORATORY E * S>:ci2

kpproved for public release;, distribution unlimited.

85 0 810

- - -. %;- -

.1

IL UI 1 L LA'SIfIC.ATION~ OFi TiiIS PA,t ,j;,A~ b ~ ~ '.REPORT DOCUMENTATION PAGE

'a RE PORT SECLR1'Y C.ASS PICATION 'b RESTRICTIVE MARKINGSUNCLASSIFIED

2a SECURTY CLASS, ICAThON ALTHORITY 3 DISTRIBUTION/ AVAILABILITY OF REPORT

2o DEC-ASSiFCATION DOWNGRADING SCHEDULE Approved for public release; distribution unlimited. " .

4 PERFORMiNG ORGANIZATION REPORT NUMBER(S) S MONITORING ORGANIZATION REPORT NUMBER(S)

NRL Memorandum Report 5499

6 7a NAME OF MONITORING ORGANIZATION " "(IF applicable)

•

NAME

-

Naval Research LaboratoryCoe49"-"'.

6: ADDRESS (City. State, and ZIPCode) 7b ADDRESS (City, State. and ZIP Code)

Washington, DC 20375-5000

8a NAME OF FUNDING, SPONSORING Sb OFFICE SYMBOL 9 PROCUREMENT INSTRUMENT IDENTIFICATION NUMBERORGANIZATION (If applicable)

DARPA

8c ADDRESS (City, State. and ZIPCode) 10 SOURCE OF FUNDING NUMBERSPROGRAM PROJECT TASK WORK UNIT

Arlington, VA 22209 ELEMENT NO NO NO ACCESSION NO

11_TITLE_(includeSecurityClassification)_ 62301E I I IDN980-37811 TITt (Inlude Security Claification) Resonance Between Betatron and Synchrotron Oscillations in a Free

Electron Laser: A 3-D Numerical Study

12 PERSONAL AUTHOR(S)

Tang, C.M. and Sprangle, P.13a TYPE OF REPORT 13b TIME COVERED 14 DATE OF REPORT (Year. Aonth, Day) S PAGE COUNTInterim FROM TO 1985 January 30 22'6 SuPPLEMETARY NOTATION

This work was sponsored by the Defense Advanced Research Projects Agency under Contract 3817.17 COSATI CODES 18 SUBJECT TERMS (Continue on reverse if necessary and identify by block number)

FIELD GROUP SUB-GROUP Free electron laser,

Betatron-synchrotron stability,, --

19 ABSTRACT (Continue on reverse if necessary and Identify by block number) -.-

We analyze the effect of betatron and synchrotron resonance on the gain process of the free electron laser(FEL) including betatron oscillations, finite beam emittance, self-consistent electron dynamics and a 3-Dradiation field. Betatron oscillations force the electrons to be affected by an oscillatory radiation amplitudeand phase in a Gaussian resonator radiation field. We show that not only can the radiation phase variationcause a resonance between approximately twice the betatron wavenumber and the synchrotron wavenumber,but the radiation amplitude variation in an FEL with efficiency enhancement schemes or just a taperedmagnetic wiggler field amplitude Bw can also have a similar resonance effect. Numerical results for a 10 pmFEL are given. We find that for short wigglers, the effect of the betatron-synchrotron instability on the gain_."-is negligible for Gaussian electron beams with radius less than 0.8 times the radiation beam spot size. . . -

20 S'Q -3,, O*ii AVAILABILITY OF ABSTRACT 21 ABSTRACT SECURITY CLASSIFICATION.] ASS, F ED NLMITED 03 SAME AS RPT COTC USERS UNCLASSIFIED

.':a %AVE 0 RESPONSIBIE NDIVIDUAL 22b TELEPHONE (Include Are Code) 22c OFFICE SYMBOL

C. M. Tang (202) 767-4148 I Code 4790DO FORM 1473,B4 VAR 93 APR editior may be used until exhausted -

All Other edtOns are obsolete

SECURITY CLASSIFICATION OF TIS PAGEI _I

CONTENTS

INTRODUCTION ............................................. 1

BETATRON OSCILLATIONS IN A TAPERED WIGGLER...............2

RADIATION FIELD ........................................... 3

EQUATION OF PHASE......................................... 4

NUMERICAL EXAMPLES ....................................... 7

ACKNOWLEDGMENT.........................................9

REFERENCES.............................................. 17j

Acc-essiocn For

410%)S%s.

RESONANCE BETWEEN BETATRON AND SYNCHROTRONOSCILLATIONS IN A FREE ELECTRON LASER:

A 3-D NUMERICAL STUDY

INTRODUCTION -r

In this paper, we will examine the resonance between the synchrotron waveilumber,

i.e., the wavenunber associated with the bounce of the electron in the ponderomotive

potential well, and twice the betatron wavenumber [1-5]. Betatron oscillations are caused

by the transverse gradient of the wiggler [6-12]. There are a number of different sources

for this resonance. In this paper, we will concentrate on the one caused by the Gaussian

resonator radiation field first discussed by M. Rosenbluth in Ref. [1]. Another source of

the resonance, described in detail in Ref [5], requirt, a tapered wiggler, but no; a 3-D

radiation field.

The wavefronts of the Gaussian TEMQ0 resonator radiation are spherical; the curva-

ture is a function of radial and axial position. As electrons execute betatron oscillations in

the transverse direction, the electrons are forced to sample varying wavefronts or a varying

phase of the radiation field. The effect of that on the axial electron motion is eq-iivalent

to varying the radiation frequency, which results in a forced driving term in the modified

pendulun equation with a wavenumber of 2k,3, where ka is the betatron wavenunber.

The amplitude of the TEMy,, resonator radiation field has a Gaussian profilei in the

radial direction. As electrons execute betatron oscillations in the transverse direction,

the electrons are forced to sample varying radiation amplitudes. In an FEL ewploying

efficiency enhancement schemes, we find that the amplitude variation also contributes

forced driving terms in the modified pendulum equation with wavenumber 2k,. P

Betatron oscillations, in a wiggler whose magnetic field amplitude B,,, is lapered,

result in a spatially dependent axial electron momentum. The wavenumber of the axial

nmomentun variation is also 2k! (see Ref. 151).When 2k9 becomes approximately equal to the synchrotron wavenumber K,, tie phase

of the electrons in the ponderomotive potential well can become unstable and electrons can

become detrapped from the b)uckets. Since the principle of efficiency enhancement schemes

[13-10] for the FEL is based on trapping the electrons, the loss of trapped electr ins will

Manuscript approved October 17, 1984.

* -. ,, .. -

'% " ° ".' - *o ° .. " . o" .'. " " .' - '" . -• . ,**.. . ,o . . .° . , •° 1 °

. - a l

reduce the gain. In an FEL oscillator, a slightly reduced gain will increase the start-up

time necessary to reach saturation. A iignificantly reduced gain per pass will also reduce

the final saturated field amplitude as well.

amplitude as well. -

In this paper, we will consider a realistic, arbitrarily tapered, linearly polarized, mag-

netic wiggler. The vector potential of the wiggler is expressed as

A A,, (z)cosh(k. (z)y) cos(jIt) '-:)e,.1

where A,(z) and kw(z) are the slowly varying amplitude and wavenumber. We will con-

sider an electron beam that is cold but possesses a finite emittance. The radiatinm field

initially is taken to be a Gaussian TEA0o0 resonator mode with slowly varying amplitude

and phase. Modeling of an exact 3-D radiation with higher order modes can be acheived

with minor modifications.0|

BETATRON OSCILLATIONS IN A TAPERED WIGGLER

For a linearly polarized wiggler, there exists a constant of motion in the x-direction,

- L(2)

C

where the constant Pxo is the canonical momentum. To obtain the betatron orbits, we will

take A - A,,• e, and p. "llAx + Pxo. The particle motion in the x-direction can be

obtained by integrating the momentum in the x-direction,(Z)z

x z----cosh(k (z)p) sin k.(z')d'), (3)

k,, -+ (z) fwZdj

where 1 - zo + foz, #go = pzo/'(moc, 1 is a function of (yo,pyo,z), x. and yo are the

initial transverse coordinates, and pgo and Pyo are the initial transverse momentums, and. .

Oo± = IeIAw /('moc2).

The particle motion in the y-direction is due to the finite z-component of the wiggler

field,

d p~ Le iAZBZ (4)dt c

2

. . -. - - - - -- ,.. ,-•.

We will assume that the fast oscillatory terms are unimportant. Replacing v, by " in the

appropriate places, we find that

d 2j + 1t25,(z)k,(z)sinh(2k (z)i,) = 0. (5)dz 2 4.-r-

Taking k,(z)j, << 1, this equation can be integrated to give

(k'."- 1/2

-Y k ) cos( kp(z')dz' + ), (6)

where kd = = + = p, o/kO)n0)MoC 2 '

and 0, = cos-'(y0 /y,).

RADIATION FIELD

The radiation field can be written in terms of Gaussian resonator modes. For the

purpose of illustrating this resonance, only the TEMoo mode wiln be considered, i.e.,

AR(xy, z, t) - -Aoo(z)Goo(z,y, z)exp(i(kz - wt))6& + c.e., (7)

where .4oo(z) = IAoo(z)l exp(i~oo(z)) is the slowly varying self-consistent complex ampli-

tude,

Goo(z,y, z) goo exp ioo), (8)Wo -(z2 + Y2,

goo (Xy, Z) - W(Z) eWp w(Z) '-'-..:

+ Z2 + y2 ." "

Ooo(z,y,z) = 2 (Z)

(z - L,)Izo is the normalized axial distance, w(z) = w(1 + 2)1/2, W and k = W/c L

are the frequency and wavenumber of the radiation, w0 is the waist of the resonator mode,

"- = w 2k/2 is the Rayleigh length, and L, is the axial location of the minimum waist.

Gaussian decomposition of the radiation field has been outlined in several different

contexts 12,171. This formulation differs from Ref. [17] in that we include betatrcn oscil-

lations and finite beam emittance. " W

3

.... -2 ...-......".'.''. .. ." * p.. j,..-. ,. .. . s. " * ". . - '"L ' - •, ' '",, .' " " ' " & . "

The slowly varying complex amplitude of the radiation field is governed by

daoo()ioo(z) cosh(kK,(:-))goo(?,,-- vdz ,FaW(z)e e- (9)

where

2k e2 Czo'(1o,Yo,PXo,PNo, 0oZ)= (k+k,(z')-/ z)dz' +Ooo(i, , z)+ Ooo(Z)+ 'o

is the phase of the electron in the ponderomotive potential well, t,'o is the initial Fhase at

z =0,diko

1(")= 2"-dxo dye dpo dpyo...)W(x., yo, Pzo, Pyo, Vo)=o j 2 r f J f 0 f

is the average over all electrons in the transverse direction and one period of the pon-

deromotive potential wave, W is the initial electron distribution function suca that

< (1) >= 1, wb = (47rJe12no/mo)1/2 is the plasma frequency, n0 is the peak electron

density, F = Oblrw2 is the 1-dimensional filling factor, Ob is the area of the electron beam,

a,= eIA,,/moc2 and aoo -[ejAoo/moc 2.

EQUATION OF PHASE

The equation of phase for the electron entering the wiggler with the initial condition

(zo, yo, Pzo, Pyo, io) in the ponderomotive potential well can be written in the forra

* ¢ = -K 0 2cosh(k,(z)#)e - ' /[sine - sin 'RI, (10)

where

Ko(z) = ( w-)k.kav(z)laoo(z)I)" 2

is the synchrotron wavenumber of the electrons traveling exactly along the z-axis. The

instantaneous synchrotron wavenumber for the off-axis electrons is

Ks(ZoIyo, po,pyo,z) = K, (z) cosh(kw (z)#)exp w2+z ) •/2

4S

'~'i~ ':.>.y~c7*.*>;.;<.§... -

The resonant phase ObR is determined by the expression

I d2oo :

sin V'IR (Z 1 yo, pzo,pyo,z) =Sin Vt'Ro+ (i,,z)inRo + - r 000

K.2 dz2

+ .2Kk()1 +cos)[aw (z) (11)

where

f(UOPyo, z)= 2 kp(z')dz' + 20,,

sin P,,o(z) = T(z)/Ko(z)

is the resonant phase of electrons traveling exactly along the z-axis, and

T [)=Idkw k da2t, +w I+ a~, je OkDCldz 492 dz C -y3 m"c2 a j

is the degree of taper for the efficiency enhancement schemes, which can be achieved .:.:.

by increasing the wiggler wavenumber, decreasing the amplitude of the wiggler vector 71potential, or by applying a DC accelerating electric field. For efficiency enhancement, the

resonant phase has to be positive and less than unity.

In the betatron-synchrotron instability the resonant phase is forced to oscillate at the

wavenumber 2k. If the wavenumber of the electrons about the separatrix is = 2kv, then an

instability can occur. As electrons execute betatron oscillations, the electrons experience

a varying radiation amplitude and phase, which are contained in the second and t'ae third

terms on the right-hand side of Eq. (11). The tapering of the wiggler B. can also result in

an oscillatory driving term, i.e., the fourth term on the right-hand side of Eq. (11). This S

process is discussed in detail in Ref. [5]. If the oscillation frequency of the resonant phase ....

matches the frequency of the electrons going around the resonant phase, the synchrotron

frequency, then the phase of the electrons in the ponderomotive potential well will oscillate

with increasing amplitude, and eventually the electrons become detrapped.

- 5. .

. . . . . . . . . . . . . . . ......... .... ... .-...- .. . -".-

=ii' ii ':- " -" "' i i" -" . " i"' / " " i ° .°' i" , •°- " " ' . - - " . -i -i • " . . . - ," .. " . . " . . . . -. ." - ' - , . ," ." .' '.' '. Io . - - .. , , . , .. . . - - . , . .. . . . . , - - , . - - • - A .

The radiation amplitude variation felt by the electrons not only results in a spatially

dependent bucket size, but also in forced oscillations of the resonant phase, the second

term of Eq. (11), where

1 __2_+__

, )= - cosh(k,(z) ) exp aU,2() .-

Since 2 and cosh(kw(z) ) are both periodic functions of t), the coefficient of the second

term in Eq. (11) is also a periodic function of .

The variation in phase felt by the electrons, due to the betatron oscillations, con-

tributes the third term on the right-hand side of Eq. (11). Substituting (6) into (8), we

obtain

doz2 ' =- fo + f, cos - + f, sin -, (12)dZ2

ko (0). -3) .2.-)Io(o, ,yo, ) 2 2,, [Zi)) 2 2k()],6

f8(°~°'. (z)=- ,6() z "w2 ,(z) 0 L+ 2 ]f.,~~~ ~~ ~ ~ (yo pyz -2Z Z, +

and

- ( 2 22(Z) ( +k6 ()+ 1 ]

+;T(Z) [2ZO + 2 0

We note that each term on the right-hand side of Eq. (12) is highly dependen. on the

initial conditions as well as the axial position z. The phase variation term (1/K 2)dOoo/dz.

does not have a spatitial variation equal to 2k, because the coefficients K,, f,, f,, and fo

are functions of z. Hence, the effectiveness of the phase variation term in driing the

betatron-synchrotron instability is reduced.

The strongest effect of the resonance on the gain is not at Ko= 2k,(O), bectuse the

synchrotron wavelength associated with electrons undergoing betatron oscillation ii longer

than that associated with electrons traveling exactly on axis. This is a consequence of

6

the larger radiation field on axis. In addition, the synchrotron wavelength of the electrons

initially close to the resonant phase OR is 2ir/K,. The synchrotron wavelengtl. of the

electrons, that were initially trapped further away from the resonant phase, is lont'er than

2r/K8 . Hence, the more accurate resonant condition is

6k, > K,, > 2k3. (13)

NUMERICAL EXAMPLES

We present numerical results illustrating various properties of this instability. The

. linearly polarized wiggler amplitude is B,(0) = 3 kG, and the wavelength is t,(0) = 2.73

cm. The wiggler length is L, = 150 cm, the minimum waist is located at z = 75 cm, andthe electron beam energy is 20.8 MeV. The electron density on axis is n, = 2.5x 10I 1 cm - 3 ,

which corresponds to a plasma frequency wb of 2.8 x 1010 sec - '. Radiation wavelength is

10 jim, with a Rayleigh length z0 = 62.5 cm and spot size w0 = 0.14 cm. The betatron

wavenumber is ko = 0.03 cm- and the betatron wavelength is Lo = 2r/k9 = 21t cm. ....

A Gaussian electron distribution function is chosen:

"2W=Cexp( - exp - r

eb eb /

where C is the normalization constant, and P 0o 0.Here we present results where k, is tapered and a, is held constant. The taper of k".

is linear, i.e.,

ki.,( = k,,,(0)(1 + 6z),

where 6 = 11L,, and L, is the length the wavenumber increases by k (0). For . linear

variation of k,, sin S'Ro is not a constant. The constant 6 is chosen such that sin pRo(Z =L.)= 0.4. The parameters that will be varied are the betatron-synchrotron waveiumber

mismatch ratioKso(z = Le)

2kp(-)

and the radius of the electron beam rb.

7

-0.

" Figures 1-6 show the results obtained with p= 2.0 and reb = we. For these parameters,.. ~the second term on the right-hand side of Eq. (11) is the largest oscillatory" driving term...._:-i

For electrons with the same initial conditions (xo,yo,po) but -r ' < 7r, Figs. 1, 3, 5

are plots of y' versus r(y/O: and Figs. 2, 4, 6 are plots of i, versus z. Each curve represents

the history of an electron in the phase space from = 0 to z = L,..

Figures 1 and 2 are plots of phase for electrons traveling exactly down the a zi', i.e.,

x, = 0, y, = 0, and puo = 0. Electrons that are initially trapped remain trapped. S

Figures3 and 4 are plots of phase for electrons with initial conditions x u= , , "0,

and pv, = 0. These electrons do not execute betatron oscillations. Since they are on the

edge of the radiation beam, the bucket size is reduced, and only 4V0% of the electrons are

initially trapped, these trapped electrons remain trapped to the end of the wiggler.

Figures 5 and 6 are phase plots for electrons with initial conditions x, = 0, yo = U'0 .

and py, = 0. If these electrons did not undergo betatron oscillations, their phase space

diagrams would be identical to those in Figs. 3 and 4. We notice that 25 of the electrons

become detrapped at z c= 100 cm s- r/ko(O). Only 20% of the electrons remain trapped

at the end of the wiggler.

The numerical results confirm that the synchrotron wavelengths associated with Figs.

3-6 are much longer than those of Figs. 1-2, because the radiation amplitude felt by

the electrons on axis is larger than the the average radiation field felt by the electrons

undergoing betatron oscillations.

Figure 7 is a plot of normalized relative amplitude gain,

versus reh/W, for p = 1.4. p - 2.0, and p - 2.9. The solid curves are the results with

betatron oscillations, and the dashed curves are the results without betatron oscillations.

The results are almost identical for r~,/tI' < 0.8. There is a small reduction of the gain

when rI/wo = 1 for p = 2.0 and p = 1.4. The reduction is small because the distribution -

function associated with the electrons that take part in the betatron-sy nchrotron instability

is siall.

8

III conclusion, we identified three different sources responsible for the betatron- syn-

chrotron instability: the radiation phase front curvature, the transverse radiation ampli-

tude variation in an FEL with efficiency enhancement schemes, and the tapering of the

magnetic wiggler field amplitude. For the parameters considered in this paper, the radi-

ation amplitude variation is found to be the largest driving term. For short wigglers of

this example, i.e., L,. 2= 1.5r/kq, and reb/Uo < 0.8, the effect of betatron-syuchrotron

instability on the gain is negligible. -

Acknowledgmient

This work is sponsored by DARPA under Contract 3817. •

9 * -_

* * ~* ~ * **.. **** * . . . . . .

00

2h/',,

// 10

0j %i 7

5ir

-7r/

0 50 100 150

Axial distance z (cm)

Fig. 2. Plot of 0L versus z for electrons with initial condition x, = 0, u~=0, and Po=0

2h • ,-..

-h--

, .2

/. .7 . -- , :'- .. ..-

// / ,.

/7 /

7r 0 ( 2

--"

-2hI

40 2i 3: -

Fig. 3. Plot of , versus O /Oz for electrons with initial condition ao = u'o, yo, = , and •" -

P yo 0 .". .

12

"'"-

..-. ...... .. - . . -. , .1"' * . ., " ... ' ". " . . *" .'" 1 **" * " , " - .. * " ,43. ." .. .. , ." , .; -, .... " .. , ] , .. .y3!i" ' i ;

57r

37r'1

X /

-7r

3i13

2h

00

-2h

0 27r 37r

Fig. 5. Plot of t'versus 80/49z for electrons with initial condition z. 0, Vo w., and[PiO 0.

14

57r.

5ir

7'.

0 50 100 150

Axial distance z (CM)

Fig. 6. Plot of vt' versus z for electrons with initial condition x. 0, yo = w, and po , 0.

15

1.0

04

S0.75

-with betatron oscillations

0 no betatron oscillations

00.5 1.0

reb/WO --Fig. 7. Plot of normalized relative amplitude gain versus rethto for betatron-synclirotron

wavenumber mismatch ratio p =1.4, p 2.0, and p =2.9.

16

0

References

111 M. N. Rosenbiuth, "~Two-Dimensional Effects in FEL's, paper No. I-ARA-83-U-45

(ARA-488), Austin Research Asso., TX (1983).

121 C.-M. Tang and P. Sprangle, "Semi-Analytical Formulation of the Two-Dimensional

Pulse Propagation in the Free Electron Laser Oscillator", Free-Electron Generators of

Cohrei),tRaiation, SPIE Proc. 453, (ed. by C. A. Brau, S. F. Jacobs and M. 0.

Scully), Bellingham, WA, p.11 (1983).

13] C.-M. Tang, "Particle Dynamics Associated with a Free Electron Laser", to be pub-

lished in the Proc. of Lasers '83, held at San Francisco, CA, Dec 12-16, 1983.--p.

141 W. M. Fawley, D. Prosnitz and E. T. Scharlemaun, accepted for publication in Phys.

Rev. A.

[51 P. Sprangle and C.-M. Tang, "Betatron-Synch rot ron Detrapping in a Tapered Wiggler

Free Electron Laser", NRL Memo. Report 5445.

[61 T. 1. Smith and J. M. J. Madey, Appl. Phys. .2,195 (1982).

[7] P. Diament, Phys. Rev. A2,2537 (1971).

181 V. K. Neil, "Eniittance of Transport of Electron Beam in a Free Electron Laser", SRI

Tech. Report JSR-79-10, SRI International (1979). AD-A081-064

[91 C.-M. Tang, Proc. of the Intl. Conf. on Lasers '82, 164 (1983).

1101 P. Sprangle and C.-M. Tang, Appl. Phys. Lett. 32, 677 (1981).

1111 C.-M. Tang and P. Sprangle, Free-Electron Generators of Coherent Radiation, [Phys. t*of Quantum Electronics, Vol. 8], ed. by Jacobs, Moore, Pilloff. Sargent, Scully and

Spitzer, Addison- Wesley Pubi. Co., Reading, MA, p.627 (1982).

1121 A. Gover, H. Freund, V. L. Granatstein, J. H. McAdoo and C.-M. Tang, "Basic

Design Considerations for Free Electron Laser Driven by Electron Beams from RF

Accelerutors", Infrared and Millimeter W es, Vol. 12, ed. K. J. Button.

1131 N. M. Kroll, P. L. Morton and M. N. Rosenbiuth, IEEE J. of Quantum Elec. OE17

1436 (1981).

[141 P. Spranigle, C.-M. Tang and W. M. Manheimer, Phys. Rev. Lett. l, 1932 (1979).

115] P. Spraigle, C.-M. Tang and W. M. Manheimer, Phys. Rev. A2.I, 302 (1980).

[161 C.-M. Tang and P. Sprangle, J. Applied Phys., E2, 3148 (1981).

17

I

[171 P. Elieaume and D. A. G. Deacon, Appi. Phys. ~, 9 (1984).

Ih

I

F:4

18

-. :1,KJ . . ............- S..,..* -- ,.~

K3-8

DTI