Optical diagrams of prism spectrometers with quadrupole lenses

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INSTRUMENTS

AND METHODS

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OPTICAL DIAGRAMS OF P R I S M S P E C T R O M E T E R S W I T H Q U A D R U P O L E LENSES E. V. SHPAK, S. YA. Y A V O R and YA. G. L Y U B C H I K

A. F. Ioffe Physico-Technical Institute, USSR Academy of Sciences, Leningrad, USSR Received 3 April 1968 This paper deals with optical diagrams of prism spectrometers for charged particles employing single quadrupole lenses or the corresponding doublets as collimating and focussing lenses. The parameters of spectrometers with an astigmatic beam at the

entrance to and exit from the prism are considered. Conditions for the compensation of the third-order spherical aberration of quadrupole lens systems in prism spectrometers by means of octupoles are determined.

In charged particle prism spectrometers employing two-dimensional magnetic or electric fields as dispersion elements, one ordinarily uses a collimating and a focussing lens to produce a parallel beam incident on the prism and to focus that emerging from the prism, respectively1-5). Axially-symmetrical lenses were used for this purpose in the works cited. An exclusion is the fl-spectrometer described in 6) where axially-symmetrical lenses were replaced by doublets of magnetic quadrupole lenses, the result being an increase in transmission by several times. An advantage of the prism analyzers consists in their small geometrical aberrations when operated under conditions where both the incident and outgoing beams are parallel. Therefore it is essential that the aberrations of all other components of the optical arrangement be also small. Axially-symmetrical lenses have a thirdorder spherical aberration, its coefficient increasing sharply with increasing focal length. At the same time the linear dispersion of the instrument is proportional to the focal length of the focussing lens and therefore it cannot be chosen small. One of the means of reducing the spherical aberration of lenses consists in the replacement of axially-symmetrical lenses with quadrupole systems. Their spherical aberration can be compensated for by using octupoles which would involve some complication of the system. Additional advantages of using quadrupole lenses consist in the possibility of increasing transmission of the instrument and of reducing its overall dimensions due to a decrease of the length of its arms at a fixed focal length. Apart from this, chromatic aberration in a mass spectrometer with an achromatic prism can be completely compensated for by using achromatic quadrupole lenses7). The simplest quadrupole lens system capable of producing a three-dimensional parallel beam or of focussing it into a point is a doublet. Therefore we shall consider it in more detail. It should be noted that by slightly changing the

optical diagram of the spectrometer it becomes possible to use single quadrupoles rather than doublets as the focussing and collimating lenses. We shall come back to this point later. We shall consider the optical properties of the doublet assuming its component lenses to be thin. The validity of this approximation here is due to the fact that the lenses used in spectrometers should have a large focal length. A doublet of quadrupole lenses is shown schematically in fig. 1. In the plane y = 0 the first lens of the doublet acts as a diverging, and the second one as a converging lens. We shall denote this plane in what follows with the indices DC. In the plane x = 0 the lenses will act in the opposite sense. This plane will be denoted with the indices CD. The condition for the stigmaticity of the doublet can be written in the following way8): -

f12L2 = f l , L2 , a

2 / [ f l ,4L , a2 2 s 2 - ( a + s ) 2 ] ,

(1)

where L is the effective length of a lens, a is the distance from the object to the center of the first lens, s is the

z

J /¢c~

Z

Fig. 1. A doublet of quadrupole lenses.

97

E.V. SHPAK et al.

98

separation between the centers of the lenses, f12 being the lens excitation:

0)

f12 = +_ {2UMKM/(R2 c)} { _ e/(Zm~b)}½, fl~ = --UEKE/(R20).

(2)

The subscript M refers here to the magnetic field, E to the electric field, e,m are the charge and mass of the particle, ff the accelerating potential, e the velocity of light, u the potential at the poles and electrodes, K a constant depending on their shape, R the aperture radius. Subscript 1 refers to the first lens, and subscript 2 refers to the second lens of the doublet. The distance from the center of the second lens to the image will be denoted by g. In deriving eq. (1) we assumed a, g and s to be much greater than L1 and L2. The trajectory shown in fig. 1 corresponds to the case of g = oo. Under these conditions the focal lengths f of the lenses in the object space in the plane D C are related to the doublet characteristics in the following way: flDc = - (flZL,) - ' = -- a{s [(a + s)} ~:,

f 2 . c = (f12L2)- 1 = {(a + s)s} ½.

(3)

Here and in what follows the direction of the Z-axis is taken as positive. In the plane CD the focal lengths of the lenses reverse their signs. The focal lengths of the doublet in the object space are: 1/FDc = a - l ( 1 - - ( 1 +a/s)-~}, 1/FcD = a - t { l + ( l + a / s ) - ~ }

•

(4)

It follows from eq. (4) that always FDC > FCD. As seen from fig. 1, the principal planes of the doublet are shifted strongly with respect to its center. The distances, from the center (O) of the first lens to the principal planes of the object space, OHDc and OHcD have the following form: OHoc = a / {(1 + a/s) ~ -- 1 }, OHcD = - - a / {(a +a/s)½ + l }.

(5)

The focal lengths of the lenses of the second doublet which focucsses a parallel beam into a point can be obtained from expressions (3) by means of transition a ~ g and the replacement of subscripts 1 ~ 4 , 2 ~ 3 . Subscript 3 refers to the first lens of the second doublet, and subscript 4 refers to the second lens. The cardinal elements of the second doublet in the image space are determined by the expressions (4) and (5) if one makes the transition a ~ g , D C ~ C D and reverses the signs in all expressions. The position of the principal planes should be reckoned from the center of the second lens.

5;

Fig. 2. A prism spectrometer with a three-dimensional parallel beam of particles. Fig. 2 presents a schematical view of the spectrometer optical system: (a) top view; (b) side view; 1 - prism (,magnetic, electrostatic or their combination); 2 - collimating lens; 3 - f o c u s s i n g lens; 4 - source; 5 - entrance slit. The median plane of the prism in which the separation of charged particles takes place coincides with the horizontal plane. The source and the detector lie on a line perpendicular to this plane. To obtain greater dispersion, the doublet acting as a focussing lens should be arranged so that its plane CD coincides with the median plane of the prism, because in the doublet focussing a parallel beam into a point rcD > FDO It is expedient to arrange the doublet serving as a collimating lens in such a way that its plane D C coincides with the median plane of the prism. Now the height of the beam at its entrance into the prism will be much smaller than its width (fig. 1) which will permit a more rational use of the gap between the magnetic prism poles or between the electrodes of an electrostatic prism. Since it is desirable to have smaller magnification in the median plane, it is seen that also from this viewpoint it would be expedient to bring the plane D C of the first doublet in coincidence with the median plane

( MDc/ McD -= FcD/FDc ). By way of illustration we will present here the calculated parameters of a doublet made up of two thin lenses and will compare them with data obtained when approximating the distribution of field along the axis with rectangles. We assume the focal length of the collimating doublet in the plane DC, Foe = 47 cm. Taking the distance between the lens-centers s = 6 cm, we obtain from eq. (4) that a = 27.0 cm. F r o m expressions (3) one may calculate the focal lengths of the component lenses: f l v c = - 11.7 cm, f2DC = 14.1 cm. Assuming the lens lengths L 1 --L2 = 6 cm, we find

OPTICAL

D I A G R A M S OF P R I S M S P E C T R O M E T E R S

their excitation: f12=0.0145cm -2 and f12z=0.0118 cm -2. If one focuses a charged particle beam accelerated to ~b = 4 kV by means of electrostatic quadrupole lenses with K2 ~-1 and RE = 3 cm, the lens electrode potentials should be u~ ~-_+520V and u2 -~ _+ 420 V. The focal length of the doublet in the plane CD will be FCD = 19.0 cm. A calculation of the parameters of these lenses in the rectangular model approximation while maintaining their lengths, center-to-center separation and the position of the center yields the following results: the excitation of the lenses is f12 = 0.0183 c m - 2 , f12 = 0.0149 cm -2. These results have been obtained from the graphs of 9), assuming the distance between the source and the entrance to the first lens to be 24.0 cm. The focal lengths of such a doublet are found by the formulasS):

1IFDc

=

- fl, smh (fl, L,) cos (f12L2) +

~-f12cosh (fll Lt)sin(fl2Lz) + + fltfl2s" sinh(fl,L,)sin(fl2L2), I / F c D = fll

sin(fllL1)cosh(fl2L2)-

- flE COS(fl l L1)sinh (fl2L2) + + fllflzs'sin(fllLx)sinh(fl2L2).

(6)

They are Foc = 51.0 cm and FCD = 17.1 cm. As seen

99

from these figures, a calculation in the thin lens approximation gives a smaller focal length in the D C plane (a difference of 6%) and a larger one in the CD plane (by 11%). The excitations in this approximation are less than in the rectangular model approximation by ~ 22%. As the focal length Foc increases, the disagreement between the two approximations decreases. Therefore in preliminary calculations one may use with a sufficient accuracy the thin lens approximation. We will calculate now the gain in transmission resulting from a replacement of an axially-symmetrical collimating lens by a doublet made up of quadrupole lenses. The doublet focal length Foc will be chosen equal to the focal length of an axially-symmetrical lens. Now match the centers of the axially-symmetrical lens and of the doublet. Since the lenses are weak, one may assume in the first approximation that the principal planes of the axially-symmetrical lens coincide with its center. The beam height 2h on the vertical plane will be determined by the prism, namely in a magnetic prism by the useful part of the magnet gap, and in an electrostatic prism by the electrode separation (fig. 3). The maximum angle of acceptance er in this plane is h/Ffor an axially-symmetrical lens and % = h / F c D for a doublet. In the horizontal plane the beam width 2b is limited by the lens apertures, the maximum angle of acceptance being ctx = b/F for an axially-symmetrical lens, and ax = b/Foc = b / F f o r a doublet. Thus the solid angle of acceptance increases by a factor of {(1 +a/s)~+ 1} {(1 +a/s) ½ - 1 } -1,

..

F

,

P

I

I

xI

if one uses a doublet. However, one should bear in mind that the use of quadrupole lenses imposes a more rigid restriction on the source length. In the case of an axially-symmetrical lens the useful length of the source is of the order t ~ F(h/P) where P is the distance from the center to the entrance to the prism (fig. 3). The useful length in a doublet is approximately

t ~ FcD{h/(p+ls--OHcD)}.

IO

F3¢

i ]Hj¢

Fig. 3. Comparison of transmission of the collimating axiallysymmetrical lens and the quadrupole doublet.

Therefore to gain in transmission one has to use short sources. As already mentioned, an advantage of this system consists in a possibility of compensating for spherical aberration of the width of the linear image by comparatively simple means. One of the ways is to use two compensating octupoles in each doublet1°). The aberration in the linear image width will be compensated for separately in each doublet. However, it can be shown that in order to compensate the system as a

E.V. SHPAK et al.

100 0, a

oe

I

II

I

I

II

i

M = (gla)Mh[{s, I(a + s,)} ½-1] / rl - {se I(s 2 + I

Ii

i

(8)

i

Oe m I~

where m h is the angular magnification of the prism in the horizontal plane, equal to M h = cos 01/cos 02, 01 and 02 being the angle between the projection of the beam-velocity to the median plane and the normal to a side surface of the prism at the entrance to and exit from the prism respectively, M v the angular magnification of the prism in the vertical plane, M v =fdfn, withf~ andfH the focal lengths of the cylindrical lenses formed by the edges of the prism at the entrance to and at the exit from it.

O, I

i

tl

i

m

Oe

0~ I

I

I

#

£

r--1 r - - i

I

II

!

!

a'

i

i[

i

e

i

II

I

i

r---I ii i

I

v--iv---1 & & l

II

I

l

tt

I

i

i II

&

ac

g)}~],

ae

i I

Poc = ~(a2/sl)(a +sl) {(3n z - 2 n t + 2)(aq/Lt) + + (3n 2 - 2n2 +2)(~2/L2)Q~}-

Z

Fig. 4. Arrangement of octupoles and quadrupoles, Oa and O2 are the first and second octupoles. whole for aberration, only two octupoles will suffice. The actual situation of these octupoles is not crucial• We have considered cases where the octupoles are brought into coincidence with the corresponding quadrupoles (fig. 4). To obtain the conditions for compensation, i.e. the relationship between the parameters of the octupoles and quadrupoles, one has to write the expression for the aberration of the system as a whole• It is derived by summing up the aberration of the second doublet and that of the first doublet multiplied by the magnification of the next elements (the prism and the second doublet)• The expressions for the aberration coefficients of a doublet composed of thin lenses are given in 8). The contribution of octupoles to aberration is determined by the formulas given in ~1). In the case where the octupoles are brought in coincidence with the lenses of the first doublet (fig. 4a) the expression for the overall aberration has the form:

-~,, tl a"-~,~/~ [{(a + sl)~, }~ + (a + s,)]", SDc = -'(a21s,)(a +st) {(n~-2n1-2)(ul/LO + + (n22- 2na - 2)(~2/L2)} + + 3Yl lla 4 + 37alaa2(a + sl) z, PCDII =-- [[{(g+s2)s2}qt +(g+s2)]/ {6(g+s2)s2}] " • [(3n 2 - 2 n 3 + 2)(~3/L 3)+ + (3n 2 - 2n4 + 2) (~4/L4)Q2],

Sco,, = [E{(g + s2)s2 * +(g + s2)]/{2(g

•

• [ ( n 2 - 2n3 - 2)(xa/L3) + (n 2 - 2n4-- 2)(z4/L,)],

Q, = [ { ( a + s l ) s l } % ( a + s , ) ] / [ { ( . + s l ) s , } L ( a + s l ) ] .

Qa = [ {(g+sz)s2}½-(g+sz)]/[ {(g+sz)s2}a* +(g+s2)] •

(9) Here sl and Sa are the separations between the lenses of the first and second doublet, ~
+ y';

+ s,)

/(MhM~[{(a+sl)sl}½+Sl])]}.

+

(7)

Here M is the magnification of the system in a horizontal plane, which is

where T is a coefficient depending on the shape of the electrodes or poles of an octupole lens. The subscripts 1 or 2 for n, x, L refer to the first and second lenses of the first doublet, and 3, 4 refer to the first and second lenses of the second doublet, respectively. In order that Ax be zero for any initial angle, the coefficients at x~3 and "~' should be zero• Hence ~ 0 . Y,,,a 0

OPTICAL

DIAGRAMS

OF PRISM

SPECTROMETERS

101

s,)s, }½+ (a + s,)] 4 (a_l_s,)2a2_[{(a+s,)sl}~ +(a+s,)]4 '

r , l l = 111(a + s,)2a z - nE[{(a +

~212 =

(-/-/2 --H1)a"

(10)

(a + s,)Za a - [{(a + s1)s 1}½ + (a + sl)]" ' Ha = {(a + s,)/(6a Zs,)} [(3na2 -- 2n, + 2 ) ( z , / L , ) + (3n z - 2n2 + 2)(xz/LE)Q z ] + + (3n 3z - 2n 3 + 2)(x3/L3) + (3n 2 - 2n, + 2)(zs/Ls)QZ2

6s2(g+s2)[1 - {sl/(a + sl)}~] ` M 4 HE = {(a +s~)/(6a2s,)} [(n~--Znl --2)(xl/La)+(nZ--Zna --2)(xz/L2)] + + [(a + sl)2 / {6M~MZa Zsz(g + s2)}] [(n3z - 2n3 - 2) (x3/L3) + (n z - 2n, - 2) (xJL~)].

(ll)

For other arrangements of the octupoles their excitations are determined in the following way (in terms of the parameters of the system): r, 11 _ n , MEg Z{(a + s,) ~-- s~}" -- H a ME a2 {(g + sz) ½- s~2}4

M ~ g Z { ( a + s , ) } _ s ~ } , _ Mva z 2~,(g-k-S2) -~- - $ 2~) ,

(12)

],212 = ( / / 2 - H , ) M h M v a " 2 2(g.+_ $2)2 [1_{s1/(a_.[_$1)}4i]4. 22 ½ ~- 4 22 ~-

Mhg {(a+s,) --s~}--ZVIva {(g+s2) --s~} 4

That was the case of the octupoles coinciding with the first lens of the first doublet and with the second doublet (fig. 4b).

Mhg{(a+sl)~--s~} 2 ~ Mva{(g+s2)½-s~2} 2.

~111 = Ilx {(a + sl)½--s~}4M~--llzMZ~a 2 2 ~ 41 4 2 2 Mh{(a+sl) --sl} --Mva ~zl2 =

(11~

4

2 2

[l-{s,/(a+s,)}*] ¢ M~ {(a + s,) ~ - st}" - M2 a z

-110MhMva

(13)

4 2 2 - M v 2) , Ha)MhMv/(Mh

(14)

corresponds to fig. 4d. In the latter case

113 = 111aS /[ {(a + s,)s, }~ + a + s,] ", 17, = ll2{a/(a +s,)} z.

(15)

The excitation of the octupoles in the case shown in fig. 4e can be obtained from eqs. (10) and (11) by means of the following replacements a ~g,

s 1 ~s2,

f, ~f.,

xl/La ~ , / L 4 ,

nl ~-n4,

n2 ~ n 3 .

],,111 ~+~_~,212,

(18)

and for the case of fig. 4d:

2 / ( M 2 - M J, 2 = ( U 3 M2h - H , M O

~'212 = ( / - ] 4 - -

(17)

In particular, this condition rules out a completely symmetrical spectrometer arrangement. For the version of fig. 4c the corresponding condition has the form

Mh{(a+st)~--S~} ~ Mva,

This corresponds to the case shown in fig. 4c, and ?1/1

In some of these versions certain restrictions are imposed on the parameters of the system. In the case of fig. 4b an additional inequality should be satisfied:

t,Q1 ~ 0 2 ,

x2/L2~-743/L 3, (16)

If the octupoles coincide with the second lenses of the doublets (fig. 4f), the corresponding expressions can be derived from eq. (13) using the same procedure.

M. 4: My,

(19)

indicating that in the latter version compensation can be reached only at 01 # 02 (a nonsymmetrical operation of the prism). The limitations for the version of fig. 4f are obtained from eq. (18) using eq. (16). By way of illustration, we give here the values of y~l~ and 7212 for the abovementioned parameters of the system assuming a unity magnification of the prism and using electrostatic quadrupole lenses with rc = 1. We will consider the version where the octupoles coincide with the first lenses of the doublets (fig. 4c). Here ylll = - 3 . 0 6 x 10 -3 c m - 3 ; 72/2 =2.61 x 10 -3 c m -3. For electrostatic octupoles with RE = 3 cm, l = L and T = 1, the octupole potentials V at ~b = 4 kV will be +VI=83V, _ _ _ V 2 = - 7 0 V which is considerably below the quadrupole potentials. If we use four octupoles under the same conditions

102

E.V. SHPAK et al.

(each coinciding with a quadrupole), then Till = 1.31 x 10 -3 cm -3, and Y212 = - 1 . 4 7 × 10 -3 cm -3, so that somewhat lower excitations will be required in this case. The requirement that the charged particle beam be parallel to the Z-axis both in the horizontal and vertical plane at the entrance to and exit from the prism follows from the condition of zero aberration of the prism A O 2 : AO 2 = (COSO2m)-l[½~lZsinO2m__(Vrl/Vrll)½ "~1Sln01m]. 1 2 •

(20) Expression (20) describes the dependence of the aberration AO 2 on the angles ¢~ and ~92 between the vector of the velocity of a charged particle and the horizontal plane at the entrance to and exit from the prism, respectively, to terms containing ~2. The subscript m refers to the trajectories lying in the median plane. The relativistic potential Vr is V, = ~b[1 - {(ec~)/(2mc2)}]. The subscripts I and II correspond to the values at the entrance to and exit from the prism, accordingly. At ¢q = ~z = O, AOz = O. Consider another version of an optical arrangement where the angles ~J are not zero, i.e. an astigmatic beam of particles impinges on the prism. We will find the relation between them which would ensure A02 = 0 as before. From eq. (20) we have $22V~,sin02m = ~j2V~sin0,m.

(21)

Condition (21) can be satisfied only if the angles 02," and 0~m are of the same sign. In the case of the electrostatic and achromatic two-dimensional prisms this does not involve any additional restrictions, whereas in a magnetic prism this may result in reduced dispersion.

For an electrostatic prism, condition (21) reduces to

Such an astigmatic beam can be produced with quadrupole lenses. In the simplest case one can use single quadrupoles as the collimating and focussing lenses. Here one should match their collecting plane with the spectrometer median plane. In order that the projections of the trajectories onto the median plane remain parallel at the entrance to the prism the source should lie in the focal plane of the collimating lens. The system should be adjusted so that the beam emerging from the prism will be focused by the focussing lens into a line in its focal plane (fig. 5). In the arrangement utilizing a three-dimensional parallel beam the image of an extended source becomes warped without broadeningS). In the above arrangement with an astigmatic beam the image in the general case will become diffused at the edges of the line. The ratio of the entrance and exit angles is: ¢214~, =y~ly~* = 1

-

(dlf.)- (a* + y*lT'*)"

•[ ( l / f , ) + ( 1 / f , , ) - { d / ( f j f u ) ) ] ,

(22)

Here d is the prism width along the Z-axis, Yo and y~ being the initial values of the coordinate and angle of tilt, the asterisk referring to the imaginary image of the source formed by the collimating lens. As seen from eq. (22), for rays emerging from one point (y* = const.) but at different angles y'~ the ratio ~2/~Jl will be different and hence will be different also the aberration of the prism determined by expression (20). This results in smearing out of the linear image of a source. However, if the coefficient at (a* + Yo/Yo * ' *) in eq. (22) is zero, the image of the source will not be distorted. The conditions fl +fll = d and eq. (21) can be fulfilled simultaneously, for instance for a three-electrode electrostatic prism at f, = f,, = ½d.

Fig. 5. A prism spectrometer with an astigmatic beam of particles.

A shortcoming of the second optical arrangement lies in the need of increasing the prism aperture, its advantage being the possibility of using a smaller number of quadrupole lenses. Besides, spherical aberration of a thin quadrupole lens is considerably smaller than that of a thin axially-symmetrical lens12). If required, its aberrations can be compensated for by bringing the octupoles in coincidence with the two quadrupole lenses. From the condition of equality to zero of

O P T I C A L D I A G R A M S OF PRISM S P E C T R O M E T E R S spherical

aberration

of the

linear i m a g e w i d t h

we

obtain:

~,~l t

2

2

2

2

1

2

(MhM~(f2/fx)(~xl/L1)(3nl-2nt+2)-

- ( ~ x l / L 1 ) ( n ~ - - 2 n l - 2) + ( M ~ / M ~ ) ( x 2 / L z ) ( n Z z + 2)}" 2

2 2

•( M h M , f 2 - f l )

2 -i

,

~2/2 ---- { M ~ ( - n_l2T()xL+ /),MhM~n(,2_2n2_2.) 1

2

•( ~ x 2 / L 2 ) _ ( f 2 / f ~ ) ( i × 2 / L 2 ) ( 3 n 2

2 2

• (MhMq, f 2 - f , )

2-i

2

2

2

_ 2n 2 + 2)}. (23)

,

where

M~ = 1 -(½fl +2,)/f~-(½fl

+21 +d)/f.+

+ d(½f, + 1~1)/(f,J~O, 21 b e i n g t h e d i s t a n c e f r o m t h e c e n t e r o f t h e first lens t o t h e e n t r a n c e to t h e p r i s m .

103

References 1) V. M. Kel'man and D. L. Kaminskii, JETP 21 (1951) 555. ~) V. M. Kel'man, D. L. Kaminskii and V. A. Romanov, Izv. Akad. Nauk SSSR, Ser. fiz. 18 (1954) 148. a) V. M. Kel'man and L. N. Gall', Zh. Tekhn. Fiz. 31 (1961) 1083. 4) V. M. Kel'man and I. V. Rodnikova, Zh. Tekhn. Fiz. 32 (1962) 269 and 279. 5) V. M. Kel'man and S. Ya. Yavor, Elektronnaya optika (Electron Optics; Moscow, 1963). 6) V. V. Tuchkevich, V. A. Romanov and M. G. Totubalina, Izv. Akad. Nauk SSSR, Ser. fiz. 27 (1963) 246. 7) V. M. Kel'man and S. Ya. Yavor, Zh. Tekhn. Fiz. 31 (1961) 1439. 8) A. D. Dymnikov, T. Ya. Fishkova and S. Ya. Yavor, Radiotekhn, elektr. 12 (1967) 662. 9) H. A. Enge, Rev. Sci. Instr. 30 (1959) 248. 10) T. Ya. Fishkova, E. V. Shpak and S. Ya. Yavor, Zh. Tekhn. Fiz. 38 (1968) 375. 11) T. Ya. Fishkova and S. Ya. Yavor. Zh. Tekhn. Fiz. 38 (1968)• 686. 12) A. D. Dymnikov, T. Ya. Fishkova and S. Ya. Yavor, Zh. Tekhn. Fiz. 35 (1965) 759.