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The potential of a metal sphere in interplanetary space
THE ~~~1~ OF A 8dFiTA.LSPHE?REIN INTERPLANETARY SPACE P. G. ICURT md V. 1. MOROZ
TrzumWedby R. ltUmmws from ~E&WJWW~!+miki Zen& No. 7, pp. 78-W&1961
For the correct performance and interpretation of some experiments which can be carried out in interpIa.netary space on space rockets it is necessary to have an idea of the potential of the container carrying the instrumentation. An attempt is made here to solve &is proMem to a first approximation, considering only the more important factors. The potential U of a metal body in internee space can be found from the condition of equating to zero the total current to the body: 4 -i- r, = 1, + I,, + 1, i- 43
(0
where I, is the electron current of the interplanetary plasma; 5 is the electron current occurring in the radiation belts *; 1, is the plasma ion current (protons); I,, is the proton **radiation” current; Je is the photoelectric current; 1’ is the secondaxy electron current which may occur under the influence of “radiation” electrons and protons. Containers with instrumentation employed on Soviet space rockets had an approximately spherical shape and we win solve equation (1) for a spherical body. In all the further calculations we will take the radius of the sphere as r = 65 cm. We will evaluate separately the terms of equation (1) each of which generahy speaking is a function of U. Then, employing equation (1) we will fhtd U. A similar problem has been studied by K, I, Gringauz and M. Kh. bin for artificial earth satellites disregarding ah the terms in equation (I) other than I9 and & This is permissible for fairly low altitudes where the ion and electron concentrations are large (II*= n, > lo” particles.cm-8), as a result of which the photocurrent and radiation electrons have only a slight infiuence on the potential of the artificial satelhte. Similar simpli6cations are not permissible when dealing with the potential of a space rocket. We wih first calculate the potential U of a metal sphere in the absence of movement and magnetic field and we wilI then estimate the influence of these factors on IX EVALXJATION OF THE Pv With U = 0 the
FROM THE SUREACZ OF THE CON%XINER
photoelectron flux from unit surface is obviously eqnal to N, =
2 k, dv cm-s~9,
P. CL KURT and V. 1. MOROZ
260
For tiding the quantity I$, in the shortwave range of the spectrum (A c 2000 A), usewillbemadeof the data(*), obtained from rocket ~v~ti~tions, For d > 2000 A the energy ~s~bution in the solar sp@rum is given, for example in the survey(a). The qua yield of pure me&Is, excluding alkali metals, in the range 1~ 2000 A falls below 10410-s (4). Surface ~tion ~811,however, produce an increase in k,. In the work(s) with the aid of rocket exp&ments data was obtained on the quantum yield of tungsten ~~es~~~~<~A. Atthesame~ej;LIthisnungeofthes~~~sre found values near to k, for dif&&entmetals if the surfacas are clean. Accordmg to the work@)the quantum yield for ;Z= 584 A and 740 A is equal to @B-0*14, falling near to L, (1215 A) to 042. Table 1 was drawn up on the basis of these data. TABLE1 4 F
Aha
KdA&, a-% ~-1
6 x 10’ 4XfW 3 x l@
n
3oooAL>L,
8 x 10 8 x 10’ 5 x 1.0’
Total fluxF&J, = 1.4 x lB*
Obviously the maximum contribution to the photocurrent can be attributed to LQ emission. The range 2 < La provides considerably less, whereas the mn&r of phow
)t:' 86 a
0
20
40 u,
FoRm#ALz.PumA
60
80
100
tf s3fmmlm‘AND
N,(nr#
ljhtowrmt
as a bction of pots&al (totalcurrunt to tlmbody); %&ctron ixmmt Z, as 8 function ~~~~forn~l~.~~; 3-Z~~a~functionofUforn~10~.~4; in~onof lhlcs12 cb%im v,, = +lSVandtheIixml*3-U~,-+6V. electrons
from the range R > L, can vary as a function of the purity of the container sur&c, N&rally Table 1 contains data for the pure metal. For further cakulations current density &, = AI, e = 24 x we c4m take Nar = 14 x 10”’cm-s see photon 109 A.cm-s).’ For the total photocurrcn t from the container surhacethe value I@= 7+&e
THE-OFAMETAL.SPHERElNlNlXRPUNETARYSPACE
261
is taken, disregarding the rclationehip of the quantum yield to the angle of dcsecnt. With hmrca&g pocitiva potc&al of the container the photoeurrcnt apparently diminishes whilst at U m 6 V a “‘out4f” of photoclcctrons knocked out by the L, quanta occurs leading to a reduction in the photoourmn t by 1 order. The approximate relationship of the photomur& to the positive potential is shown in Fig. 1. Rece and Rena@ employing a rocket spectrograph obscrvcd the He11 jz 303 A line. At an altitude 212 km its intensity was approximately 25 per cent of the La intensity. The eonecpts introduecd in the work(s) in faVOUr of this high extra-atmospheric intensity of HcII 1303 A (five tiqxs grcatcr thanthe L, intensity), are not convincing. However, even if this relationship is taken as true, the photocurrent doe8 not exceed kc = lo-8 A cn.9, this agreeing with our evaluation. We will further cakulatc the variation in the container potential with time in the presence of photoeurrent in empty space. Obviously,
UC’
t s
co G dt,
where C is the capacitance of a sphere with radius r(C = r in the absence of plasma). Substituting the numerical values we obtain U = 2 x 10i4jie dt, if icpis expressed in A em-*, and Uin volts. During the period t - lad seconds, Uattains +6 V, increasing to +lOO V after 1O-s scoond8. Further growth in the potential will proceed extremely slowly due to the weakness of the weak flux of the Roentgen quanta ;Z - 1 A, as the result of which the potential reaches approximately +2 kV over a period in the order of days. RADLiTION ELEKTRON AND PROTON CURRENT Some invcstigatirshave proposed
that the results of measurements carried out with the aid of cosmic ray counters in the outer radiation belt maximum, point to the existence in this zone of a wry strong flux (up to 1oU cm-* se-i) “soft” electrons with energies 20-30 kcV(7*s)*. This interpretation cannot be regarded as completely definite@~g). However, if it is true then radiation electrons must play an important part in forming the container potential, when it is in the outer belt. Data is completely lacking regarding the soft proton component. However if the proton concentration nr,, does not exceed the electron concentration n, (or exceeds it by not more than 10 times), then it can be disregarded in caleulating the currents at the container surfacct, since the speed of proton is dG9 times smaller than the speed of electrons of equal energy (m, and m, are the electron and proton maaSe8 respeetivcly). On the other hand there are serious grounds for proposing that there must be very few high-cncrgy protons in the outer radiation belt (duo to charge capture-and-loss with neutral atoms of hydrogen and oxygen, sharply rcdueing the growth period of radiation protons in th0 aarth’8 magllctic trap). In the following we will assume I,.> I,=. The radiation electron current density OD N(E) dE is the total flux (in cm-s se&) of radiation electrons 4. = N,,e, where N, = s0 of the ftux of soft clcctrons (10-B keV) was carried out only at relatively low to la00 kal’l”. ~indced~truaonlyw~tbepotmtialv?qntmhigh. Ifancgativepotentialinthcorderof (whrhanooavIt~plasmadenslty~gnallaadtbenanscvaal”radiation”~~; see Tabk 21,“5, the radiation ekctron current I,, can diminish, becoming comparable with I,.. * Direct Ikmmmmnt
262
P.a. IWRT alld
v. I. MOROZ
fromthe hemisphere. No =
+J, - mj,,where J, is the flux across a sphere with section I cm”; ie is the flux across 1 cm* of a solid angle 1 star. If the integral spc&rum of electrons ofthe outer belt represents a stepped function N(>E) N P*, then according to the work (‘3, y d&m only slightly from 5. According to Van Allen and Frank@),on tho 3rd March 1959 the electron flux reached a value N, = 25 x lofo cm-s.sec-l, if the maximum measured counting rate is determined by electrons with energies in the order of 20 keV (more correctly by roentgen emission, excited in the screen layer by these electrons); there is an “off-scale” section whore with this ~te~~~tion No > 25 x 1W cm-s.se&. Complete ionization measurements in the NaI crystal during the Bight of the first Soviet space rocket on 2nd January 1959, explained in a similar manner, yield N, N loZ”cm-*/se@). From the data of Van Allen and Frank, for 16th December (“Pioneer IWrs)) No = 5 x Wcm-*/MC, if the counting rate observed is interpreted as in the work@). The obser~tions~s) were carried out after a long period of intense geomagnetic disturbances and the remainder in a relatively quiescent period. In the outer radiation belt maximum aud in higher zones a majorixing evaluation of the total number of radiation electrons can be obtained employing the condition r4) us
J Exn(E)dE<‘~, 0
(3)
where x(E) dE is the radiation electron inanition in the energy interval dE; W is the earth’s magnetic field strength. lt can be shown that the evaluation of No, employing this condition, does not depend closely on the form of the energy spectrum. A coarser hypothesis is that the integral speztrum N(> E)= klE+’ continues to the energy &, at which %(E) dE $ = (lPj8~). For E < E, we take n(E) = 0. Assuming (JP/&r) = lo-8 erg.cm~(altitude h w 25,000 km], N(>3OkeV) = 1Ogcm-* see, then we obtain E, = 18 keV and No = *N(E) a = 1.5 x 1W cm-*/~. Considering a Maxwellian distribution of radiation s SLOns with maximum in the range of some kilovolts, then with reasonable assumptions we can raise No to lou cm-*/se!c. IfNo= 1011cm-*[set the radiation electron current density i, = 1*6x lo-8 A.cm-*. The total current to the body, if the flux is isotropic (at the maximum of the belt this hypothesis is probably near the truth), is 1,. = &r*i,,. The photocurrent (if it is in accordance with our evaluation) exceeds the radiation electron current when No < SNe w 5 x lo9 cm-*/see (4) If the condition (4) is satisfied, this means that radiation electrons only slightly influence the potential, It is very probable that the magnetic traps are.substantially unsaturated in the magnetically quiescent period and the condition (4) is saMed at least in these periods. In addition there are grounds for assuming that evaluations of the soft electron flux in the radiation belts carried out on the basis of measurements employing cosmic particle counters are exaggemtedos). THE PART PLAYED BY SECONDARY EMISSION In the bombardment of the container surface with radiation ele&rons these can rise to a secondary electron emission. The secondary omission coe&cient q of normal metal and alloy constructions is appreciably less than 1 with a primary electron energy in the
THE POTIMTIAL
OF A IbiETAL t3HIERE IN INTERPLANETARY
SPACE
263
order of l&20 keV. For example, for ~~~ ?Jc 04 with an energy it3keV (maximum 3 = 097 at 300 eVm$ With q > 1 the total current I’ - 1, is positive. For a given the potential U (positive) cannot fh~~NOand any given plasma densities (even very rise, however, above a few volts, due to the secondary electron emission, since the maximurn secondary electron distribution according to energies is a few v~hs(~). ION ANR liWHXRON CW@UNTS OF INTERI’-ARY ON THEI CONTAINER BORY
I’FASMA
For ev~~~g the electron and ion currents of ~te~~e~ plasma to the spherical container body, use is made of the theory of a spherical probe in a plasma, as developed by Laugmuir aud Mott-Smith f1s*r7).The electron current to the positively charged sphetical probe and the ion current to the negatively charged probe with Maxwelhan electron speed ~s~bution (or ions respectively) according to the work@*)is
whe= r is the. radius of the probe; a is the radius of the space charge zone (‘Xangmuir” radius); U is the potential of the probe; j. = aneu is the ‘“chaotic” current density in the plasma (n is the ~on~n~~o~ 0 is the mean speed of electron or ion thermal motion); T is the temperatnre and k is the Boltzmann constant. The el&tron current to the negatively charged probe and the ion current to the positively charged probe are given by the equation I=4n6j8e-
If
-
be su~ti~~d
cu
I53I
(6)
is sufhciently large (for example, greater than 3), then equation (5) cau with sufficient accuracy by the simpler:
I = &asj* (7) The orbital motions of ions. and electrous can in this case be disregarded considering that ail the e&ctrons (or ions) reach&g the boundary of the space-charge zone reach the probe. The value a is then determhxed on the basis of the “312 law” and we obtain
wherej@) is a function of the “Laugmuir” radius a, tabulated in the workff*). For smaU PU
vahxes of -
-
9
I kT I rrS---ra
Applyiug equations (6-g), the electron and ion curreuts were c&uiated as a fimction of potential for a number of temperature and density values conceivable in interplanetary space%considering the interplanetary plasma as purely hydrogen. It was found that for
P.
aI4
a. KURT and V. I. Mt3RO2
m,> 10 paHi@mm?
and l-8 X I@ “K < T < 101“IC, a good approximation is proviM by qudans (6&f), whM for n, 4 10” partMes.cm4, T = 16L“K and for A( < 10‘ &m-s, T = 2 x 10 “K~uation (9).
4
2
0
-2
-4
-6
-8
u Fro,2. h
-IS
-10
-12
-14
-16 -16
-20
-22
v
ILLXN’iW.~
IfFoltTx6cm3n*=lfPcxw”% D BlxRMmA~oN OF THE FmmTIAL T~10’°K,1~=2.5x lO-‘Aun-‘(Z~=IOi’COSE).
an-’ w+; -5--proton cumnt Z,; 2--&w z, -I- 4; 3-&ixnm GxlrlatZ,; 4-z. + z, for N* = l(Y;O o,thmu= -2v; ifz*1occ3s& if--tatalz*~z”forN~~3xl~*cm-*~~; ifzae=o,zn= --iv; ifZ~=1~CGSE,N,=ll)ut~J~-1,thenU~-15V. Z+?,-O*tbW-
For n( = lo” partMcs.cm-s, T = 1oP“K both quations yield close results. We assumed r = 65 cm throughout. For 1.8 x 10sOK< T < 2 x 10s “K and n, = 10s particles&m-s the tbiclcness of the space charge is comparable with r even witb potentials in the order of IV, exqeding?forn, = 104 partick.cma by a few times. For larger potentials the radius of the space charge could exceed the radius of the probe by tens and hundreds of times if such small dens#ies could occur in interplanetary space. For a positive probe potential the space charge consists of electrons and for negative it consists of ions. In the absence of photocurmnt and radiation ektrons the plasma wilI charge the body (due to the difference in the ehxtron and ion speeds) to a small negative potential, qua& in those cases where the thickness of the space charge can be disregarded, to
El-#= -3*2V for T = lo’ *K. For small densities (anr< 10sparticles.cm-s) the potential is somewhat bigher (-2*1 V) on account of the substantial radius of the positive space charge with U = U,. The potential of the body U, in tbe absence of photocurrent and radiation’electrons is given in the &st line of Table 2 for difkrent values of T and n, = A~, big the reh&ionship of the electron current 1, and proton current 1, to the potential U for difktwnt values n, and T, taking the evahtations of I_ and 1, obtained above9 we solved quadon (1) graphically for differeut values of ue T and NOand found the
-14 -32 -70
~~bGhV2OkeV.
t Tk value abown
isZwxyrough
-05 -0.7 -50
-5.5 -1.1 -0.4 -1sooot -1soo -2OOOOt -6500 -#wxwlt -20000t
-2.1 -2500 -7500 --OoaOt
lo!
I@
-2oooOt -_Z{ +30 -2moot -m -2ixmt
-43
1
-43 -1lXIO
10
-iii& +4 I&) -7000 -2OOOOt -2700 -20004q -1aalo
-43 -70w ;=;
10
&, el~.an~
T=2xW%
rg -200 --loo0
-43 -85 -215 -1000
l(r
1; -86
-42.
-43 -4s -50 -85
1oL
sincetheradiationelectronspdmm is unknownin the
-2.1 -3.2 -3.2 -25 -10 -3.3 -75 -45 -3.5 --;so “-us -55 -2.4 -2.5 -1s -4 -3-l -65 -40 -3.3 -240’-120 -SO
l(P
evaluation (in absolutevalue)of thelower potentialW
lTh:tablcahowsthewtentid UineV.
-21 -70 -100
2.5 x lo-’ 2.5 x lo23 x lo-’
l& 3 x IO’ lo=
-70 -37 -0.3
-@8 -20
-2-l -250 -750 -2500 d-1.5 -150 -650 -2400
-2.1 -2mw -2amt +15 -2amq
-0-S -09
-0.8 -21~5
I&
10
1W
1w
I
l(r
1v
10°K
?l#,elm.cm-
T-
2*
n#,dedrons.cm-’
T= 1.75x 10’“K
an-%ec
e
It,
-110 -75 2.5 x: 1.0.“’ 3 x I@@ -0.2 IV.
:
amcnt A.an-’
kfadiatioil
Tm
ai
P.
a
KURT and Y. I. MUimZ
potentials for a large number of ~rnb~tio~ of these values, conceivable in interplanetary space and in the exosphere. The calculated potentials are given in Table 2. In the presence of a photocurrent with a density I. = 2.5 x 109 A.cm-s the potential of the body rises appreciably. However with plasma concentrations n, = 10 electrons.cu9 the photocurrent cannot raise the potential of the body above +4V (see 6th line in Table 2). Only at n, = 1 electr0n.cm-a is there a potential U = +lSV for T= 10P”K and U= +3OV for T = 2 X 1Db “K. If the radiation electron fly is sufficiently high it cau yield high negative potentials. Table 2 shows banes to which the body is charged for lO%m-a.sec-l < No < lw cm-*/set both in the presence and absence of photoc~ent. A graphical solution of equation (1) is given by way of example in Fig, 2. It was assumed in all the cakulations’ that the ele&ron and proton speed ~~butio~ in ~~~e~ plasma is Mowers. Negative potentials in the order of a few volts (Us < U < 0) were calculated on the assumption Ts = T,. With U c U, (large negative potentials)for the temperature shown in Table 2 the ion temperature !I‘,is understood and for U > 0 the electron temperature T*,. THE INFLUENCEOF MOTION AND MWNE~C FIELD ON THE POTENTIAL
At low altitudes (h ;c: 1000-2000km) where heavy ions of hydrogen and nitrogen predominate with relatively little hydrogen, the thermal speed of the ions is several times smaller than the speed of a&if&al earth satellites. Thus the ion current to the body (where U = 0) cau be calculated bung the ions to be stationary, so that I = Srz,ey, where S is the cross-section of the body ~~~c~r to the velocity vector, tto is the speed of the artificial satellite and n, is the conceutration (1).For space rockets at altitudes h > 30,000km, if the medium at these altitudes is attracted by the earth, there is another extreme case: qthe speed of ions, still hydrogen (for T = 104‘8 we will have t)( = 14 km/see) exceeds by several times the speed of the rocket (a~~~~ly 5 km/set) whilst the proton current I,tothebodywillbealmostthesameasforu,=O. At iutermediate altitudes (and at any altitudes, if the medium is not attracted by the earth) for calculating I, it is necessq to take account both of the thermal motion of the protons and the directioual motion of the container. For the ease where a directional drB is added to the thermal motion the currents to the probe were determined by Langmuir and Mo~-S~~ for a nmber of ~~~d~ problems(16). The stndy was not extended to a spherical probe but in the work fr6)it was shown that if the potential of a spherical collector is accelerating (U < 0 for prdtbns) then the current to the collector is appro~~ly the same & ~d~~g
the drift speed ~din~~g~e.
potential by the value AU = !!@ , 24?
where m, is the ion mass and v, is the drift speed. For m, = m, and a0 = 106cm/set the value AU # IV; consequently, I, will be only slightly greater than for u. = 0, for pratitally all cases of interest here. Hence, if n, > 3 x 108partic1es.cm-s and the potential U, calculated disregarding motion, is a small positive potential (see the 5th line of Table 2), then taking account of the motion it approwhes zero. The electron current to the body is practically independent of the motion of the rocket, since the electron speed is && times greater than the proton speed. Hence for nr = n, < 3 x 10s electrons.cm-s on the ~~a~ section of the trajectory the infhrence of the motion on the potential can be disregarded even with a stricter treatment, since the potential is here determiued by the equilibrium Ie = I,.
In tfre vi&iv
of the ear&(& d&ances up tu Z-3 %) it can be aritlcipated that the
plasma currents 1, and 1, will be markedly subject to the finthence of the earth’s maguetic field. The currents to a cylindrical and Bat probe iu the presence of a relatively powerful magnetic field (&om a few gauss to several tens of gauss) have been investigated experimentally and theoretically by G. V. Spivak and E. M. Reikhrudel (for example(r*@)). We are not aware of any works on spherical probes in magnetic fields or works which might study the behaviour of currents to probes in weak magnetic fields similar to the earth’s at high altitudes. Iu the earth’s magnetic field the plasma electrons and ions travel along spiral orbits. Larmor radii p* for electrons and pp for protons are shown in Table 3 at carried out on Soviet different altitudes assuming a dipohsr field. Magnetic rn~~rnen~ space rockets@) have shown that, at large distances, the earths field is sufliciently near to dipolar.
0
0.5
::;
E 13600
o-15
3
E 62Oflo
5” 10
E* 0908 a-004 f.boOs
6.4 25 2E 9z 7300
300 101 2.5 x IOI 8.3 x lW l-9 x IV 3.8 x 1oL 3 x fQ
It could be expected that 1, and 1, vary subsidy in calculating the magnetic field if p,, and p, c a, aud are invariable if pP and p,, s a. In practice ps > a for all conceivable concentrations (an exception may be large negative potential and A, if occurring in the radiation belts). At altitudes h -C 7,000 km the Larmor radius of electrons ps < a and the electron current at these altitudes is approximately halved due to the magnetic field, as a result of which the potential rises somewhat, i.e. approaches U = 0, if n, > 3 x lo” electronscm-s and becomes more positive if nr < 3 x 10s electrons.cm-s. In addition to the variations in the current distribution and in the mean current to the body due to distortion of the trajectories in the magnetic field outside and within the space charge zone and iudependent of whether the body is iu motion, there will also be other effects connected with the motion of the body in the maguetic field. In particular, with motion in the mag&ic field tht sur&ce of the body will cease to be ~~~ten~. Consequently with rotation, currents will occur in the body. It is not excluded that the rocket generates plasma waves in its motion. The geuerators of these flux waves may be either photoelectrons and electrons deflected from the body or the space charge itself. In the tlrst case higher fmquencies must be generated (megacycles and hundreds of kilocycles) and in the second case lower frequencies. However nothing can be said about the amplitude of the waves generated, although it could be expected that this is small, whilst the iufluence on plasma waves of the space cha,rge distribution and on the current to the body is small at least as compared with other effects occurring as the result of motion. It is proposed that in estimating the potential U there is a basis for disregarding the e&&s of motion and magnetic fiekl, in any case to a first ap~~tion~ taking intoaccount for example the cousiderable indeterminacy of the interplanetary gas temperature.
P. 0. KWRT 8nd.V. I.
268 It
MOROZ
isobtitmed in concl~on
effect on the,potential. appreciable effect.
that varia@n in diameter by several times has no practical A small difference in the shape from the spherical also has no CONCLUSIONS
1. Assuming the interplanetary gas tem@rature T = 1oL“K and the photocurrent density IO = 2.5 x 10-OA.CZII-~ (these are the more probable values) then on the illuminated ssctorofthotrajectory~econtainerpottntialmustbewit4inthtrange-2.5V c U< +4V, if n. > 10 particles.cm4. 2. The influence of the magnetic field and motion of the container causes a slight change (l-2 V) in the potential; this variation can be disregarded having in mind the indtterminacy of other factors. 3. In the zont of the outer belt on the illuminated sector of the trajectory, radiation electrons particularly do not influence the potential at least in a magnetically quiescent period. However, large negative potent@ (to some kilovolts) are not excluded if the normal concepts are true regar&g a very high concentration of soft radiation tlectrona in the outer zone &lst tht interplanttary gas in the region of the outer zone is fairly rare&d (see Table 2). In the latter case substantial negative potentials may exist even with relatively small fluzes A!, (if n, = 1 particlecm~, A$ =3 x loBcm-ssec-l,then U= -25V). K. I. Gmrw~uz and M. KE. Zusm~, UT. Rz. Na&. lb, 239 (1957) II. F~DJUN, 10th&m&n o rheMAS, Moscow(1958). F s; ’ l z. Akad. NaJr, SSSR, sun’yagco/iz.1,108 (lag). . . D T. M.- Isaims, EkccroniWt+Iim (Ekkhwye nmnozh#eli) aortrbhizdat, M&(1959). ELE. I-Umwm, K. R. Ihwm, L. A. HALL,J. Gso hy. RUT.,64,%1(19X$ M. EL Ihas, W. A. Rmms. J. Guo s. Rss., 64,1231( P959). S.N.V~,A.E!.C~UDAXOV, p. v. VANmv, Yu. I. Lu3AcfrBv,aal. Akod. &nk ASSSR,l2s# 3Q4(1959). J. VANi&at?, L. A. E&a, Nume (ihnd), .l84,219 (1959). f ximjhntupa J.v~~Au.m,7hu.h&matbr1~IC -msf&n&Rays. (lhefyhfkam&h&h huhtz)). Vol. 3, had.xm uk. SSSR., Morcow ( 1960). V.I.-LS.S~nnvsm.Yu.LGahti~andEM.SDokl. Akad.Ndr.SSSR.. l27; 78 (1959). 8. N. Vmtmv, A. E. Chm~ov, p: V. VAKULDV, Yu. I. Loo~cmw, A. 0. NIXOLUV,hk. spur.Ztmif... 5c24 0960). 3. vm AUBN, L. A.FRANK, Nature (Lo&)lB3,430 (1959). K. L Gsurmuz, V. 0. KURT,V. I. Maw, I. 5. : M. Vai Ammutt, lbbdlq dkr slacm, -,zInpsct-avid 1% artfm&E. Moocow(1958). 16. H. M. MmI. Lmcwum, Pliys.Rm., 28,727 (i926). 17. H.,M. MIYIT-W~?I.I; lbmmn~ Gen.Elm.Ra~Z7.449 (1924). 18. I. Lmmmm, K. Bkoim, Phyi Ras.,24.49 (1926).
Ft;,6,816(1936).
TrzumWedby R. ltUmmws from ~E&WJWW~!+miki Zen& No. 7, pp. 78-W&1961
For the correct performance and interpretation of some experiments which can be carried out in interpIa.netary space on space rockets it is necessary to have an idea of the potential of the container carrying the instrumentation. An attempt is made here to solve &is proMem to a first approximation, considering only the more important factors. The potential U of a metal body in internee space can be found from the condition of equating to zero the total current to the body: 4 -i- r, = 1, + I,, + 1, i- 43
(0
where I, is the electron current of the interplanetary plasma; 5 is the electron current occurring in the radiation belts *; 1, is the plasma ion current (protons); I,, is the proton **radiation” current; Je is the photoelectric current; 1’ is the secondaxy electron current which may occur under the influence of “radiation” electrons and protons. Containers with instrumentation employed on Soviet space rockets had an approximately spherical shape and we win solve equation (1) for a spherical body. In all the further calculations we will take the radius of the sphere as r = 65 cm. We will evaluate separately the terms of equation (1) each of which generahy speaking is a function of U. Then, employing equation (1) we will fhtd U. A similar problem has been studied by K, I, Gringauz and M. Kh. bin for artificial earth satellites disregarding ah the terms in equation (I) other than I9 and & This is permissible for fairly low altitudes where the ion and electron concentrations are large (II*= n, > lo” particles.cm-8), as a result of which the photocurrent and radiation electrons have only a slight infiuence on the potential of the artificial satelhte. Similar simpli6cations are not permissible when dealing with the potential of a space rocket. We wih first calculate the potential U of a metal sphere in the absence of movement and magnetic field and we wilI then estimate the influence of these factors on IX EVALXJATION OF THE Pv With U = 0 the
FROM THE SUREACZ OF THE CON%XINER
photoelectron flux from unit surface is obviously eqnal to N, =
2 k, dv cm-s~9,
P. CL KURT and V. 1. MOROZ
260
For tiding the quantity I$, in the shortwave range of the spectrum (A c 2000 A), usewillbemadeof the data(*), obtained from rocket ~v~ti~tions, For d > 2000 A the energy ~s~bution in the solar sp@rum is given, for example in the survey(a). The qua yield of pure me&Is, excluding alkali metals, in the range 1~ 2000 A falls below 10410-s (4). Surface ~tion ~811,however, produce an increase in k,. In the work(s) with the aid of rocket exp&ments data was obtained on the quantum yield of tungsten ~~es~~~~<~A. Atthesame~ej;LIthisnungeofthes~~~sre found values near to k, for dif&&entmetals if the surfacas are clean. Accordmg to the work@)the quantum yield for ;Z= 584 A and 740 A is equal to @B-0*14, falling near to L, (1215 A) to 042. Table 1 was drawn up on the basis of these data. TABLE1 4 F
Aha
KdA&, a-% ~-1
6 x 10’ 4XfW 3 x l@
n
3oooAL>L,
8 x 10 8 x 10’ 5 x 1.0’
Total fluxF&J, = 1.4 x lB*
Obviously the maximum contribution to the photocurrent can be attributed to LQ emission. The range 2 < La provides considerably less, whereas the mn&r of phow
)t:' 86 a
0
20
40 u,
FoRm#ALz.PumA
60
80
100
tf s3fmmlm‘AND
N,(nr#
ljhtowrmt
as a bction of pots&al (totalcurrunt to tlmbody); %&ctron ixmmt Z, as 8 function ~~~~forn~l~.~~; 3-Z~~a~functionofUforn~10~.~4; in~onof lhlcs12 cb%im v,, = +lSVandtheIixml*3-U~,-+6V. electrons
from the range R > L, can vary as a function of the purity of the container sur&c, N&rally Table 1 contains data for the pure metal. For further cakulations current density &, = AI, e = 24 x we c4m take Nar = 14 x 10”’cm-s see photon 109 A.cm-s).’ For the total photocurrcn t from the container surhacethe value I@= 7+&e
THE-OFAMETAL.SPHERElNlNlXRPUNETARYSPACE
261
is taken, disregarding the rclationehip of the quantum yield to the angle of dcsecnt. With hmrca&g pocitiva potc&al of the container the photoeurrcnt apparently diminishes whilst at U m 6 V a “‘out4f” of photoclcctrons knocked out by the L, quanta occurs leading to a reduction in the photoourmn t by 1 order. The approximate relationship of the photomur& to the positive potential is shown in Fig. 1. Rece and Rena@ employing a rocket spectrograph obscrvcd the He11 jz 303 A line. At an altitude 212 km its intensity was approximately 25 per cent of the La intensity. The eonecpts introduecd in the work(s) in faVOUr of this high extra-atmospheric intensity of HcII 1303 A (five tiqxs grcatcr thanthe L, intensity), are not convincing. However, even if this relationship is taken as true, the photocurrent doe8 not exceed kc = lo-8 A cn.9, this agreeing with our evaluation. We will further cakulatc the variation in the container potential with time in the presence of photoeurrent in empty space. Obviously,
UC’
t s
co G dt,
where C is the capacitance of a sphere with radius r(C = r in the absence of plasma). Substituting the numerical values we obtain U = 2 x 10i4jie dt, if icpis expressed in A em-*, and Uin volts. During the period t - lad seconds, Uattains +6 V, increasing to +lOO V after 1O-s scoond8. Further growth in the potential will proceed extremely slowly due to the weakness of the weak flux of the Roentgen quanta ;Z - 1 A, as the result of which the potential reaches approximately +2 kV over a period in the order of days. RADLiTION ELEKTRON AND PROTON CURRENT Some invcstigatirshave proposed
that the results of measurements carried out with the aid of cosmic ray counters in the outer radiation belt maximum, point to the existence in this zone of a wry strong flux (up to 1oU cm-* se-i) “soft” electrons with energies 20-30 kcV(7*s)*. This interpretation cannot be regarded as completely definite@~g). However, if it is true then radiation electrons must play an important part in forming the container potential, when it is in the outer belt. Data is completely lacking regarding the soft proton component. However if the proton concentration nr,, does not exceed the electron concentration n, (or exceeds it by not more than 10 times), then it can be disregarded in caleulating the currents at the container surfacct, since the speed of proton is dG9 times smaller than the speed of electrons of equal energy (m, and m, are the electron and proton maaSe8 respeetivcly). On the other hand there are serious grounds for proposing that there must be very few high-cncrgy protons in the outer radiation belt (duo to charge capture-and-loss with neutral atoms of hydrogen and oxygen, sharply rcdueing the growth period of radiation protons in th0 aarth’8 magllctic trap). In the following we will assume I,.> I,=. The radiation electron current density OD N(E) dE is the total flux (in cm-s se&) of radiation electrons 4. = N,,e, where N, = s0 of the ftux of soft clcctrons (10-B keV) was carried out only at relatively low to la00 kal’l”. ~indced~truaonlyw~tbepotmtialv?qntmhigh. Ifancgativepotentialinthcorderof (whrhanooavIt~plasmadenslty~gnallaadtbenanscvaal”radiation”~~; see Tabk 21,“5, the radiation ekctron current I,, can diminish, becoming comparable with I,.. * Direct Ikmmmmnt
262
P.a. IWRT alld
v. I. MOROZ
fromthe hemisphere. No =
+J, - mj,,where J, is the flux across a sphere with section I cm”; ie is the flux across 1 cm* of a solid angle 1 star. If the integral spc&rum of electrons ofthe outer belt represents a stepped function N(>E) N P*, then according to the work (‘3, y d&m only slightly from 5. According to Van Allen and Frank@),on tho 3rd March 1959 the electron flux reached a value N, = 25 x lofo cm-s.sec-l, if the maximum measured counting rate is determined by electrons with energies in the order of 20 keV (more correctly by roentgen emission, excited in the screen layer by these electrons); there is an “off-scale” section whore with this ~te~~~tion No > 25 x 1W cm-s.se&. Complete ionization measurements in the NaI crystal during the Bight of the first Soviet space rocket on 2nd January 1959, explained in a similar manner, yield N, N loZ”cm-*/se@). From the data of Van Allen and Frank, for 16th December (“Pioneer IWrs)) No = 5 x Wcm-*/MC, if the counting rate observed is interpreted as in the work@). The obser~tions~s) were carried out after a long period of intense geomagnetic disturbances and the remainder in a relatively quiescent period. In the outer radiation belt maximum aud in higher zones a majorixing evaluation of the total number of radiation electrons can be obtained employing the condition r4) us
J Exn(E)dE<‘~, 0
(3)
where x(E) dE is the radiation electron inanition in the energy interval dE; W is the earth’s magnetic field strength. lt can be shown that the evaluation of No, employing this condition, does not depend closely on the form of the energy spectrum. A coarser hypothesis is that the integral speztrum N(> E)= klE+’ continues to the energy &, at which %(E) dE $ = (lPj8~). For E < E, we take n(E) = 0. Assuming (JP/&r) = lo-8 erg.cm~(altitude h w 25,000 km], N(>3OkeV) = 1Ogcm-* see, then we obtain E, = 18 keV and No = *N(E) a = 1.5 x 1W cm-*/~. Considering a Maxwellian distribution of radiation s SLOns with maximum in the range of some kilovolts, then with reasonable assumptions we can raise No to lou cm-*/se!c. IfNo= 1011cm-*[set the radiation electron current density i, = 1*6x lo-8 A.cm-*. The total current to the body, if the flux is isotropic (at the maximum of the belt this hypothesis is probably near the truth), is 1,. = &r*i,,. The photocurrent (if it is in accordance with our evaluation) exceeds the radiation electron current when No < SNe w 5 x lo9 cm-*/see (4) If the condition (4) is satisfied, this means that radiation electrons only slightly influence the potential, It is very probable that the magnetic traps are.substantially unsaturated in the magnetically quiescent period and the condition (4) is saMed at least in these periods. In addition there are grounds for assuming that evaluations of the soft electron flux in the radiation belts carried out on the basis of measurements employing cosmic particle counters are exaggemtedos). THE PART PLAYED BY SECONDARY EMISSION In the bombardment of the container surface with radiation ele&rons these can rise to a secondary electron emission. The secondary omission coe&cient q of normal metal and alloy constructions is appreciably less than 1 with a primary electron energy in the
THE POTIMTIAL
OF A IbiETAL t3HIERE IN INTERPLANETARY
SPACE
263
order of l&20 keV. For example, for ~~~ ?Jc 04 with an energy it3keV (maximum 3 = 097 at 300 eVm$ With q > 1 the total current I’ - 1, is positive. For a given the potential U (positive) cannot fh~~NOand any given plasma densities (even very rise, however, above a few volts, due to the secondary electron emission, since the maximurn secondary electron distribution according to energies is a few v~hs(~). ION ANR liWHXRON CW@UNTS OF INTERI’-ARY ON THEI CONTAINER BORY
I’FASMA
For ev~~~g the electron and ion currents of ~te~~e~ plasma to the spherical container body, use is made of the theory of a spherical probe in a plasma, as developed by Laugmuir aud Mott-Smith f1s*r7).The electron current to the positively charged sphetical probe and the ion current to the negatively charged probe with Maxwelhan electron speed ~s~bution (or ions respectively) according to the work@*)is
whe= r is the. radius of the probe; a is the radius of the space charge zone (‘Xangmuir” radius); U is the potential of the probe; j. = aneu is the ‘“chaotic” current density in the plasma (n is the ~on~n~~o~ 0 is the mean speed of electron or ion thermal motion); T is the temperatnre and k is the Boltzmann constant. The el&tron current to the negatively charged probe and the ion current to the positively charged probe are given by the equation I=4n6j8e-
If
-
be su~ti~~d
cu
I53I
(6)
is sufhciently large (for example, greater than 3), then equation (5) cau with sufficient accuracy by the simpler:
I = &asj* (7) The orbital motions of ions. and electrous can in this case be disregarded considering that ail the e&ctrons (or ions) reach&g the boundary of the space-charge zone reach the probe. The value a is then determhxed on the basis of the “312 law” and we obtain
wherej@) is a function of the “Laugmuir” radius a, tabulated in the workff*). For smaU PU
vahxes of -
-
9
I kT I rrS---ra
Applyiug equations (6-g), the electron and ion curreuts were c&uiated as a fimction of potential for a number of temperature and density values conceivable in interplanetary space%considering the interplanetary plasma as purely hydrogen. It was found that for
P.
aI4
a. KURT and V. I. Mt3RO2
m,> 10 paHi@mm?
and l-8 X I@ “K < T < 101“IC, a good approximation is proviM by qudans (6&f), whM for n, 4 10” partMes.cm4, T = 16L“K and for A( < 10‘ &m-s, T = 2 x 10 “K~uation (9).
4
2
0
-2
-4
-6
-8
u Fro,2. h
-IS
-10
-12
-14
-16 -16
-20
-22
v
ILLXN’iW.~
IfFoltTx6cm3n*=lfPcxw”% D BlxRMmA~oN OF THE FmmTIAL T~10’°K,1~=2.5x lO-‘Aun-‘(Z~=IOi’COSE).
an-’ w+; -5--proton cumnt Z,; 2--&w z, -I- 4; 3-&ixnm GxlrlatZ,; 4-z. + z, for N* = l(Y;O o,thmu= -2v; ifz*1occ3s& if--tatalz*~z”forN~~3xl~*cm-*~~; ifzae=o,zn= --iv; ifZ~=1~CGSE,N,=ll)ut~J~-1,thenU~-15V. Z+?,-O*tbW-
For n( = lo” partMcs.cm-s, T = 1oP“K both quations yield close results. We assumed r = 65 cm throughout. For 1.8 x 10sOK< T < 2 x 10s “K and n, = 10s particles&m-s the tbiclcness of the space charge is comparable with r even witb potentials in the order of IV, exqeding?forn, = 104 partick.cma by a few times. For larger potentials the radius of the space charge could exceed the radius of the probe by tens and hundreds of times if such small dens#ies could occur in interplanetary space. For a positive probe potential the space charge consists of electrons and for negative it consists of ions. In the absence of photocurmnt and radiation ektrons the plasma wilI charge the body (due to the difference in the ehxtron and ion speeds) to a small negative potential, qua& in those cases where the thickness of the space charge can be disregarded, to
El-#= -3*2V for T = lo’ *K. For small densities (anr< 10sparticles.cm-s) the potential is somewhat bigher (-2*1 V) on account of the substantial radius of the positive space charge with U = U,. The potential of the body U, in tbe absence of photocurrent and radiation’electrons is given in the &st line of Table 2 for difkrent values of T and n, = A~, big the reh&ionship of the electron current 1, and proton current 1, to the potential U for difktwnt values n, and T, taking the evahtations of I_ and 1, obtained above9 we solved quadon (1) graphically for differeut values of ue T and NOand found the
-14 -32 -70
~~bGhV2OkeV.
t Tk value abown
isZwxyrough
-05 -0.7 -50
-5.5 -1.1 -0.4 -1sooot -1soo -2OOOOt -6500 -#wxwlt -20000t
-2.1 -2500 -7500 --OoaOt
lo!
I@
-2oooOt -_Z{ +30 -2moot -m -2ixmt
-43
1
-43 -1lXIO
10
-iii& +4 I&) -7000 -2OOOOt -2700 -20004q -1aalo
-43 -70w ;=;
10
&, el~.an~
T=2xW%
rg -200 --loo0
-43 -85 -215 -1000
l(r
1; -86
-42.
-43 -4s -50 -85
1oL
sincetheradiationelectronspdmm is unknownin the
-2.1 -3.2 -3.2 -25 -10 -3.3 -75 -45 -3.5 --;so “-us -55 -2.4 -2.5 -1s -4 -3-l -65 -40 -3.3 -240’-120 -SO
l(P
evaluation (in absolutevalue)of thelower potentialW
lTh:tablcahowsthewtentid UineV.
-21 -70 -100
2.5 x lo-’ 2.5 x lo23 x lo-’
l& 3 x IO’ lo=
-70 -37 -0.3
-@8 -20
-2-l -250 -750 -2500 d-1.5 -150 -650 -2400
-2.1 -2mw -2amt +15 -2amq
-0-S -09
-0.8 -21~5
I&
10
1W
1w
I
l(r
1v
10°K
?l#,elm.cm-
T-
2*
n#,dedrons.cm-’
T= 1.75x 10’“K
an-%ec
e
It,
-110 -75 2.5 x: 1.0.“’ 3 x I@@ -0.2 IV.
:
amcnt A.an-’
kfadiatioil
Tm
ai
P.
a
KURT and Y. I. MUimZ
potentials for a large number of ~rnb~tio~ of these values, conceivable in interplanetary space and in the exosphere. The calculated potentials are given in Table 2. In the presence of a photocurrent with a density I. = 2.5 x 109 A.cm-s the potential of the body rises appreciably. However with plasma concentrations n, = 10 electrons.cu9 the photocurrent cannot raise the potential of the body above +4V (see 6th line in Table 2). Only at n, = 1 electr0n.cm-a is there a potential U = +lSV for T= 10P”K and U= +3OV for T = 2 X 1Db “K. If the radiation electron fly is sufficiently high it cau yield high negative potentials. Table 2 shows banes to which the body is charged for lO%m-a.sec-l < No < lw cm-*/set both in the presence and absence of photoc~ent. A graphical solution of equation (1) is given by way of example in Fig, 2. It was assumed in all the cakulations’ that the ele&ron and proton speed ~~butio~ in ~~~e~ plasma is Mowers. Negative potentials in the order of a few volts (Us < U < 0) were calculated on the assumption Ts = T,. With U c U, (large negative potentials)for the temperature shown in Table 2 the ion temperature !I‘,is understood and for U > 0 the electron temperature T*,. THE INFLUENCEOF MOTION AND MWNE~C FIELD ON THE POTENTIAL
At low altitudes (h ;c: 1000-2000km) where heavy ions of hydrogen and nitrogen predominate with relatively little hydrogen, the thermal speed of the ions is several times smaller than the speed of a&if&al earth satellites. Thus the ion current to the body (where U = 0) cau be calculated bung the ions to be stationary, so that I = Srz,ey, where S is the cross-section of the body ~~~c~r to the velocity vector, tto is the speed of the artificial satellite and n, is the conceutration (1).For space rockets at altitudes h > 30,000km, if the medium at these altitudes is attracted by the earth, there is another extreme case: qthe speed of ions, still hydrogen (for T = 104‘8 we will have t)( = 14 km/see) exceeds by several times the speed of the rocket (a~~~~ly 5 km/set) whilst the proton current I,tothebodywillbealmostthesameasforu,=O. At iutermediate altitudes (and at any altitudes, if the medium is not attracted by the earth) for calculating I, it is necessq to take account both of the thermal motion of the protons and the directioual motion of the container. For the ease where a directional drB is added to the thermal motion the currents to the probe were determined by Langmuir and Mo~-S~~ for a nmber of ~~~d~ problems(16). The stndy was not extended to a spherical probe but in the work fr6)it was shown that if the potential of a spherical collector is accelerating (U < 0 for prdtbns) then the current to the collector is appro~~ly the same & ~d~~g
the drift speed ~din~~g~e.
potential by the value AU = !!@ , 24?
where m, is the ion mass and v, is the drift speed. For m, = m, and a0 = 106cm/set the value AU # IV; consequently, I, will be only slightly greater than for u. = 0, for pratitally all cases of interest here. Hence, if n, > 3 x 108partic1es.cm-s and the potential U, calculated disregarding motion, is a small positive potential (see the 5th line of Table 2), then taking account of the motion it approwhes zero. The electron current to the body is practically independent of the motion of the rocket, since the electron speed is && times greater than the proton speed. Hence for nr = n, < 3 x 10s electrons.cm-s on the ~~a~ section of the trajectory the infhrence of the motion on the potential can be disregarded even with a stricter treatment, since the potential is here determiued by the equilibrium Ie = I,.
In tfre vi&iv
of the ear&(& d&ances up tu Z-3 %) it can be aritlcipated that the
plasma currents 1, and 1, will be markedly subject to the finthence of the earth’s maguetic field. The currents to a cylindrical and Bat probe iu the presence of a relatively powerful magnetic field (&om a few gauss to several tens of gauss) have been investigated experimentally and theoretically by G. V. Spivak and E. M. Reikhrudel (for example(r*@)). We are not aware of any works on spherical probes in magnetic fields or works which might study the behaviour of currents to probes in weak magnetic fields similar to the earth’s at high altitudes. Iu the earth’s magnetic field the plasma electrons and ions travel along spiral orbits. Larmor radii p* for electrons and pp for protons are shown in Table 3 at carried out on Soviet different altitudes assuming a dipohsr field. Magnetic rn~~rnen~ space rockets@) have shown that, at large distances, the earths field is sufliciently near to dipolar.
0
0.5
::;
E 13600
o-15
3
E 62Oflo
5” 10
E* 0908 a-004 f.boOs
6.4 25 2E 9z 7300
300 101 2.5 x IOI 8.3 x lW l-9 x IV 3.8 x 1oL 3 x fQ
It could be expected that 1, and 1, vary subsidy in calculating the magnetic field if p,, and p, c a, aud are invariable if pP and p,, s a. In practice ps > a for all conceivable concentrations (an exception may be large negative potential and A, if occurring in the radiation belts). At altitudes h -C 7,000 km the Larmor radius of electrons ps < a and the electron current at these altitudes is approximately halved due to the magnetic field, as a result of which the potential rises somewhat, i.e. approaches U = 0, if n, > 3 x lo” electronscm-s and becomes more positive if nr < 3 x 10s electrons.cm-s. In addition to the variations in the current distribution and in the mean current to the body due to distortion of the trajectories in the magnetic field outside and within the space charge zone and iudependent of whether the body is iu motion, there will also be other effects connected with the motion of the body in the maguetic field. In particular, with motion in the mag&ic field tht sur&ce of the body will cease to be ~~~ten~. Consequently with rotation, currents will occur in the body. It is not excluded that the rocket generates plasma waves in its motion. The geuerators of these flux waves may be either photoelectrons and electrons deflected from the body or the space charge itself. In the tlrst case higher fmquencies must be generated (megacycles and hundreds of kilocycles) and in the second case lower frequencies. However nothing can be said about the amplitude of the waves generated, although it could be expected that this is small, whilst the iufluence on plasma waves of the space cha,rge distribution and on the current to the body is small at least as compared with other effects occurring as the result of motion. It is proposed that in estimating the potential U there is a basis for disregarding the e&&s of motion and magnetic fiekl, in any case to a first ap~~tion~ taking intoaccount for example the cousiderable indeterminacy of the interplanetary gas temperature.
P. 0. KWRT 8nd.V. I.
268 It
MOROZ
isobtitmed in concl~on
effect on the,potential. appreciable effect.
that varia@n in diameter by several times has no practical A small difference in the shape from the spherical also has no CONCLUSIONS
1. Assuming the interplanetary gas tem@rature T = 1oL“K and the photocurrent density IO = 2.5 x 10-OA.CZII-~ (these are the more probable values) then on the illuminated ssctorofthotrajectory~econtainerpottntialmustbewit4inthtrange-2.5V c U< +4V, if n. > 10 particles.cm4. 2. The influence of the magnetic field and motion of the container causes a slight change (l-2 V) in the potential; this variation can be disregarded having in mind the indtterminacy of other factors. 3. In the zont of the outer belt on the illuminated sector of the trajectory, radiation electrons particularly do not influence the potential at least in a magnetically quiescent period. However, large negative potent@ (to some kilovolts) are not excluded if the normal concepts are true regar&g a very high concentration of soft radiation tlectrona in the outer zone &lst tht interplanttary gas in the region of the outer zone is fairly rare&d (see Table 2). In the latter case substantial negative potentials may exist even with relatively small fluzes A!, (if n, = 1 particlecm~, A$ =3 x loBcm-ssec-l,then U= -25V). K. I. Gmrw~uz and M. KE. Zusm~, UT. Rz. Na&. lb, 239 (1957) II. F~DJUN, 10th&m&n o rheMAS, Moscow(1958). F s; ’ l z. Akad. NaJr, SSSR, sun’yagco/iz.1,108 (lag). . . D T. M.- Isaims, EkccroniWt+Iim (Ekkhwye nmnozh#eli) aortrbhizdat, M&(1959). ELE. I-Umwm, K. R. Ihwm, L. A. HALL,J. Gso hy. RUT.,64,%1(19X$ M. EL Ihas, W. A. Rmms. J. Guo s. Rss., 64,1231( P959). S.N.V~,A.E!.C~UDAXOV, p. v. VANmv, Yu. I. Lu3AcfrBv,aal. Akod. &nk ASSSR,l2s# 3Q4(1959). J. VANi&at?, L. A. E&a, Nume (ihnd), .l84,219 (1959). f ximjhntupa J.v~~Au.m,7hu.h&matbr1~IC -msf&n&Rays. (lhefyhfkam&h&h huhtz)). Vol. 3, had.xm uk. SSSR., Morcow ( 1960). V.I.-LS.S~nnvsm.Yu.LGahti~andEM.SDokl. Akad.Ndr.SSSR.. l27; 78 (1959). 8. N. Vmtmv, A. E. Chm~ov, p: V. VAKULDV, Yu. I. Loo~cmw, A. 0. NIXOLUV,hk. spur.Ztmif... 5c24 0960). 3. vm AUBN, L. A.FRANK, Nature (Lo&)lB3,430 (1959). K. L Gsurmuz, V. 0. KURT,V. I. Maw, I. 5. : M. Vai Ammutt, lbbdlq dkr slacm, -,zInpsct-avid 1% artfm&E. Moocow(1958). 16. H. M. MmI. Lmcwum, Pliys.Rm., 28,727 (i926). 17. H.,M. MIYIT-W~?I.I; lbmmn~ Gen.Elm.Ra~Z7.449 (1924). 18. I. Lmmmm, K. Bkoim, Phyi Ras.,24.49 (1926).
Ft;,6,816(1936).