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(PZ’8)
(EZ’8) ‘Ie;m - r/A . zrn = 10 f Zgmm : (do . . .
:suogsnba xys aqq 03 pva1 suoyp11.03 asayL
*aIflua pm+zqgu~ uv sl g pm ‘(paads uids aqq) Se = m paugap aA=y aM araqM .
(22’8)
(O&*8)
:a)nyyqns &m aivi sapom
pxulou aql pug o;L *s~oIIo3 qzy~ u! qsaxalu! ou 30 s! s!g$ Inq ‘(? 103 aqos 0) pasn
aq hmn ~2.8 l ub3 ‘UMOUT[ aPi? ‘I/A ‘J/X ‘ze “Ifl axI0 *(g)o H J/x’j/x’ze ‘To T#M
wwjsuo-3 9 ( zg)o N ry uoi$durnsse aq$ $sy$ SMOGS 92.8 uoy?nb3 -sapom px~~ou
Jno3 Pug 03 pasn aq IIW a=%Td ‘?/A P U’I! ‘f/x ‘Q ‘10 saIqySeA rno3 ayq 103 suoyxtba
hpo ssnmp aM azaH *z-g uoiq3as UI passnx!p a;[aM pus uoisuadsns qau8mx anye
s!yq oq paldnoaap hIaqalduxo:, sl UO!~OTX ppan ayq qzy% s~oys 82.8 uo!yznb3
(62’8)
‘Z!EL, “I
‘mm6m+Emz *m Z
-
:paugap aAvy a& alayfi
OET
(SE’8) LT. : p : zp = 6m : xm : mm
u! laplo ?saMoI 09 hluo uaa$l yzrea ‘sayanbag apom ~wmou moJ ayl an asay&
‘( Em ‘zm zlIio- GXmz,p+ ‘mm -) = 31
(PE’8) ‘mmfimzmn + 9PmEmxb = 0
( om)o aqq u~oys lou ahoy aM lsyl a$oN -lap10 s!yq 0% olaz 11y3 ~00~ au0 qq!~
‘(0 ( xmZII iv- ‘Xrn Z/T
D+ (mm-) = 31
(EE.8) 5imm~m;13 y pmm = 0
:?a8 a~ OS pm xapro IsaMoI ayq se ( rm)o
yo’o‘o (mm-) = n
(7X8) ‘E31mm + pw = 0
*aAoqQ uMoys S! m uo uogmba 3!$s!ra$Sm?y aq!) u! s!)ua~gao:, ay!) JO amapuadap
ay;C ‘co t m !~!rn!~ ay+ II! S)OOJ ay$ pug 0% $ua!m&ns aq 111~ !g sasodmd mo .XOJ
OrnW rmw OrnW PW - -
(E-8) * mm6mzmn + 31 mmim.a - Znf-+nG+pn=o
aaoS ‘zH 006 07 paDnpaJ s! paads ayl3: vwsuo:, auq a)nuyxx s o Tnoqv q!QM Use%
h-em shvDap Wq zHooo2: o? dn @noJq s! paads aq$ 3! maddz IqM ayq ~1030~
quasa.rd ay$ JOJ macphs mo UT paA.rasqo uaaq h[a);uyap S-%?TJ puv JJ!~M pn2~103,
ayl paIlI? s! uoy)orrr s!q,j-, ‘gg’8 -ub3 30 asnwaq LJSUO~~WJS ~souq8 s! swum JO xac+uas
IO)OJ aqq JO do? ay? $IXQ saas auo saym!ploo3 ay? 30 %uIZream ay? %mIpma~
(8E’8)
-)mmuys g = Ze
‘gmms03g = 10
:s! uo!qnIos aqS,
(U-8)
(9’2.8)
‘0 = Ze - lgmm
‘o= ” Q + Zfmm
:SQA!% pz’8 *ub3 PUP gg-8 wb3 u! $x23 s!qq %Ip pm?
!JU’S)SUO3 aru!!J %u!dmsp Q q?IM sIv!!+uauodxa paduIep .~ou am suo!$nIos aql puq
(TP.8)
“I (Zg--- = Ze - Tgmm - z$ - *
“I cTe-- = To f Zemm * z$ ” -
:amo3aq apom
(OP’8)
: (%s 03 aq-m-mv) am s)Insal aq& -JOJOJ ayq 30 mninpuad
uofs~o) 2 Bugmu hq pamseam uaaq aAy sI?lau! 30 sl)uamouI ay& *m(XI/zI) 3 mm
h.roay$ ayq 03 %mp~omv awls cz~/X~ 07 pmba aq pInoys tp!q~ ‘p.1~ = mm/m
~J!M hmanbaq UO!$W$OJ ay$ 03 Imogxodold aq o) uaas so hmanbag 14~~ ay&
‘zH 00’23 ‘zH Z’t68
(6E.8) ‘ZH !x’PP= 451rnm ‘ZH 9’!36= a Jm
:am saimanbaq panlasqo
-
(SP’8)
-Zfm+ = 10 .
6’1 6m-=Ze 0 .
(W-8)
:saA!8 MOU ~778 ‘ub3 puv $333 *ub3 1x1 S!T# %uIsn
:MO~S 0) pasn aq ~183 ,&g-8 sub3 put? 92.8 -ub3 ‘(6m)o - F
pun ‘(xm/im)o + 6m = 31 ‘(g)o - Z@Q’I/x’1/x suo!lduInsse aq? TJ$?M suogenba
paz!2aauy ag? 0% %ujum?aa wognlos 6m = 31 ayq ay@~sahu! aM Qmg
*y?“eq I!O ayl hq padmvp IIaM $1 $1 asnmaq ~uamnxl)su~
(ZP’8)
o$ ampal ~2.8 -ub3 pm gz’8 *ub3 puQ
‘($10 - Ze ‘$9
-
XIdmI ~2.8 ‘ubg u! suoy!puo:, asayL *(mm/Em + $m)o - $!
PTT
yz)uoz!~oy B dolanap o$ papual SJO)O~ ay$ paads pIoy3aly$ B aAoq2 !)ayq paJaAoX!p
lapun uo!qom ay$ Bu!zq o) Bu~dmvp ahym pp% o) hsessaDau SEM $1 OS pm smoy
u! Ipadump hIxood aq 0) apom ay!+ ?Dadxa @;UI auo ~~~$30 asnwaa ‘hvM sgt~ UT
padmzp aq c)ouuo:, apom aql OS pm hmuopqs s! JOT+OJ ayl30 do? ayl rapJo ?satioI
*paads uids ayq 0) ImroyJodozd ST hmanbag aq$ psyl panlasqo
uaaq my $1 pm ‘h.Ioay$ ayq qq~ cJuanraal%v UI ‘ZH sgl. s; ZH 006 ~a sulds ~or)o~ ayq
uayM hmanbag paA.xasqo ay;L y!o:, %I~A!I~ aqq hq ~1x2 JJO rnti 001 qnoqv paIInd ST
1070~ ayl asnwaq dn-yds Ja$J?z a+ap ayq u1 paalasqo so uo!ssaDald puoyq~t?~%
=LL ‘%9’SS = UA pm ‘uI:,g’~ A 1 ‘ZH 006. JLz = m JO3 ZH891’ - Jf$ = ZImf16tu
hDuanbaq aq$ !)e ml330 p[noys pua uo;ssaDald [t?uo~~vQn?x8 aIj$ palIP s! uogcm MO[S
(9P’8)
-$m so3 g = Ze
:are suoy+nlos ay;C
LapJo $saMOI hpo xaplSUO3 111~ aM ‘p-53 ‘%!J u! pauyap se ‘q/V uf sa!Jas JaMod e st?
s$lnsal I!ay$ dolahap hay& *aIod y?auIlarxI pa~~los~ uv 30 play aq’, uj Z@uuyds alayds
- ~~~au%?ux ay$ go pahom $1 aJtayds ay$ uayM pa$waua% s$uaIJn:, hppa MOM paMoys OTJM
pIno& saJayds aqq q’ley$ pun03 SI?M $1 paads pIoqsalq$ ay$ ahoqv l Bu!uuIds $0~ OJaM !I!
I 911
apn@Mu 30 IIaq ayl30 az23ms Zhx~~orn
ayq uo pIag Dg3aja $uazeddo m sar)vlaua% play sg& ‘p’8 ‘%~a u! ua@ sj c#) alayM
(tP’8)
40
30 JInsal aq& *alqtzlsun apom ayq ay2m aJo3alayq m3 11 *uoyom IJ~M prvmroj ayq
se uogDaJ!p sums ay!+ u! sf aDlo sgq yeyq alou 0) ye!mm s! 71 *amId ayq 30 $no dn
aIod!p aq$ qsnd 0) spua) aIod y)auZl’oux + ayl uayl fMoIaq a%my:, - E pm am%g aq?
30 amld aqq aAoqe a%.myD + v se alodip zgau%mu ay? %uguasaldaJ hq uaas aq hmxx s-e
am%g ayq 30 auqd agq 30 qno s! aDlo aqq30 uoyal!p ayJ; .aIod c)~$au%txI aq$ oq anp
(W8)
(09’8)
aXo3 ‘e amai”adxa II!M aIod!p y$au%mu sg;c
(6P.8)
yqdap ugs ayq s! a asayM ‘aue3ms
ay$ u.10~3 a ama$s!p T?. uo!%as ‘t! III hIuo SMOG $uaUn:, ay& *am%g aT# 30 auyd ay? ul
68T
(4’2.8) .
(PS.8)
(ES’8)
mm
( > %I .!A=.!4
P
yey$ OS JO$OJ aqq hq pailddns 3aMod aqq
03 Ivnba aq $snur I!O ayq o$ut %u!oZ JaMod ayL ‘swum $au%m ayl’s gz $1 WAA alayM
(7X8)
-
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(19’8)
(09'8)
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%x!oS u? p~~j aq 0) s! !)uamaAoldm! %os ‘I? LIUO poq!) Jnq ‘~~79 !$noqT? MoIaq bIp!dvl:
apw%ap 0) su!%aq oyer aslou 07 IW@S ayl !~oql) MOIJS sa!qladold as!ou &3~ ayL
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pooB ~03 ykoua a8.y aq lsnm saxre~~xdv:, %uydno:, ay& *sn!pxtl ~1070~ ay$ saxg
-
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s,aIdum aq$ plags dIIn3 03 +-toua daap aq $snuI 31 se ‘azis Jauyuo:, aldures ayq saxg
SIIJ;L *spunoJ% sys1Cyd uo uasoy:, s! azis a1dw-w aq!) QTZ 30 9s~ l Jaqd-ev sno!aard
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175
Table 9.2. Motion sensitivities for the SMIN data.
Record V R Q
SMIN33 2.4 nV/pm 34 1.0 35 1.4 37 < .9 38 < .9 39 1.0 40 < .9 41 < .9 42 < .9
1.1 nV/pm -24 pV <.l -18
.5 -19 <.l -.6 <.l -1.9 1.3 -5.4 1.7 -.8 .8 .9
2.4 .9 --
We now want to see to what extent we can account for the standard deviations
of the histograms. The amount of rotor motion inside the passband of the 200 second
average and difference filter can be calculated by integrating IkV(f)~j~ times the
square of the motion spectra given in the previous section. We find for the rms
motions av = .14 f .02pm,
OR = .30 zt .05jkm, (g-5)
ap = .03f .OlmR,
where V, R, and P mean vertical, radial, and phase. To find the contribution to
the total noise these must be multiplied by the measured motion sensitivities and
quadrature signal, which are given for each run in Table 9.2. The amplifier noise
contribution to the total noise is (8.8 nV/G)/(200 sec)‘i2 = .62 nV.
Figure 9.13 displays the conclusions. The squares are the measured standard
deviations of each histogram, with statistical errors shown. The dotted line shows
the amplifier noise level and the diamonds are the total accounted for noise, meaning
176
the amplifier noise plus the motional noise. The motion sensitivities are small
enough so that the motional noise is always less than twice the amplifier noise and
is sometimes negligible.
Figure 9.14 shows the difference between the observed noise and the accounted
for noise. Excluding SMIN39, the unexplained noise has an average value of
1.21 rt .06nV and is constant from record to record within the uncertainties. This
noise cannot be accounted for by any of the mechanisms considered so far. We
have not so far been able to identify the source of the unexplained noise, but will
consider some possibilities below.
At some rate there must be spontaneous changes of the sample charge due to
cosmic rays and natural radioactivity. If the sample charge were changing by lq,
at random times it would generate a charge noise spectrum
th = Qe ’ (2R)li2
27Tj ’
where R is the mean charge change rate. This formula is simply the time integral of
the formula for shot noise: & = (2q,1)1/2. Th e result also holds if the changes are
-Iqe, or if the changes are of both signs. Using Eqn. 9.3 above and the instrument’s
calibration of 4.7nV/qe, the 1.2 nV of unexplained noise can be accounted for if
R = 1.8 nV/hour. The frequency where the noise from charge changes and the
amplifier noise make equal contributions would be 2.7 mHz, and the spectrum would
rise as l/j below this point. This seems to be roughly the behavior in the spectra
for SMIN37, SMIN38, and SMIN41, for which the motional noise contribution is
177
( v> n
2.5
2.0
1.5
1.0
0.5
0.0
I I I I I I I I I I I I I I I I I I I I I I I I I 1 I I I 1 I I I I I I I I I I
cl cl Observed Observed 0 Explained Explained
I I
I 1 I I 1 I I I I I I I I I I 1 I , I 1 I , I I I I I I I I I I I I I I I I 1 1
34 34 36 36 38 38 40 40 42 42
SMIN #
Figure 9.13. Noise through the 200 second square average filter.
178
2.5 - I I I 1 I I I I I I l I I 1 1 I l 1 I l I 1 I 1 I
X 2.0 Unexplained -
I
SMIN #
Figure 9.14. Unexplained Noise
179
negligible.
To test the hypothesis that the unexplained noise is due to charge changes,
we can convolve the time domain data with the window of Fig. 9.8. If we set a
threshold and count the number of times the convolved data crosses the threshold,
we can hope to count the number of spontaneous charge changes. A problem arises
however, because the raw data has an unknown drift, which may be due in part to
spontaneous charge changes but is certainly not due entirely to them. If we make a
linear fit to the data and subtract it off, we would cause an unknown offset in the
convolution output if some of the drift is due to charge changes. We will instead
convolve with the window in Fig. 9.15 which is immune to a linear drift. Convolution
with this window is equivalent to making a least squares fit to the intervals on either
side of t = 0, and then measuring the differences of the y-intercepts of the fit lines
at t = 0. The bandwidth of the least squares window is 4/T instead of l/T as for
the square window. To regain some of the lost resolution we can increase T to 400
seconds, which should not result in intolerable pileup since we are looking for charge
changes that occur at an average rate of l/2000 seconds. The amplifier noise will
now make a contribution of .88nV.
We will restrict this analysis to SMIN37, SMIN38, and SMIN41, for which the
motional noise contributions are at least three times less than the amplifier noise,
and test the hypothesis that the total noise is due to amplifier noise plus spontaneous
charge changes. If we set the threshold at 30 for the amplifier noise, or f2.64 nV,
then we can expect a false rate of one per 370 opportunities. An opportunity occurs
180
Figure 9.15. Least Squares Average and Difference Window
about once per 400 seconds (since the output will be highly correlated over about
400 seconds) so we estimate a false rate of - 7 * 10e6/sec. To test the estimate a
data record of amplifier noise was convolved with the least squares window. One
count was recorded in 21000 seconds, where .15 counts were expected according to
the estimate.
Convolution with the 72100 seconds of data in SMIN37, SMIN38, and SMIN41
yielded 85 excursions above threshold, or a rate of 4.3/hour, with .50 false counts
expected. Figure 9.16 is a histogram of the peak value of each excursion above
threshold. The rate is 2.5 times too high to be due to spontaneous charge changes,
181
and the peak values do not cluster around fqe = f4.7nV. Since the rate is
high there is now considerable pileup (peaks above threshold occurring within 400
seconds of each other), so one objection that might be raised is that the background
estimate could be wrong in the region 3~400 seconds around a true fq, charge
change. This worry can be disposed of as follows. We can place an upper bound on
the true charge change rate by setting the threshold at fqe = f4.7nV, and then
doubling the number of counts obtained to account for the fact that the amplifier
noise will cause half of the charge changes to fluctuate above 4.7 nV, and half below.
We find 10 counts, or a rate of 2 . lo/20 hours = l/hour. If we now look in the
region 400 seconds before and after the 10 counts above f4.7nV, we find 11 more
counts which might be considered false. We could perhaps thus account for as
many as 2 . (10 + 11) = 42 of the counts, but this still leaves 43 unexplained.
The conclusion finally is that there could be a spontaneous charge change rate of
2*(10&&@/20hours = 1 f .3/ hour, accounting for about half of the unexplained
noise, but that there is certainly also some other noise source.
Of course some spontaneous charge changes must occur. If the cosmic ray
intensity is described by (79)
I = 1.10 l 10e2 cos’ 6’ . crnw2 = set-’ . sterad-‘, (9.7)
where 9 is the zenith angle, then the collision rate with the sample will be .25/hour.
This may cause as many as .25 charge changes per hour. Also, the sample is made
of a radioactive material. Natural indium is 95.7% In115, which p-decays with a
182
I
4.3 Counts/Hour
0.0 I I I
-5 0
nV
Figure 9.16. Peak value of each excursion above threshold. Three points are off scale at +14.14, $8.82, and +7.41nV.
183
half life of 5 - 1014 years and an end point energy of .5 MeV*. In our .73 mg sample
there will be .6 decays per hour. The mean range for the electrons is about equal
to the .2 mm sample thickness, so a large fraction of the emitted electrons will leave
the sample. A charge change rate as large as .S/hour can be accounted for by this
mechanism. The sum of these two rates is still within the l/hour rate allowed by
the analysis given above.
There are several other possible sources for the unexplained noise. A major
worry is that somehow some motion has gone undetected. Although we have some
information on each axis, it would be far preferable to continuously monitor the
sample position relative to the rotor in all three axes while data is being recorded.
This would certainly be recommended in a future instrument.
Another source of noise might be charge motion on the quartz fiber. Several
studies have been made with conventional electrometers of the surface resistance
of quartz glass (80). Unfortunately they do not provide enough information for
our purposes, since the instrument could be disturbed by rare but highly mobile
carriers. Even a single mobile ion on the quartz surface might be able to generate
the noise we see, but would be undetected in a conventional measurement of surface
resistivity. Perhaps this issue could be studied by trying samples with different fiber
diameters.
* I thank Professor Cabrera for pointing out that indium is radioactive. This
was overlooked when indium was chosen as the sample material.
184
9.5 DETECTION OF ELECTRONS
The INSR data records were made during four different runs, as shown in
Table 9.1. The intensity and duration (- .2 second) of the of the ultraviolet light
pulses was not varied during a run, but was different from run to run. Figures 9.17
and 9.18 show histograms including all of the INSR records in each of the four runs,
generated in exactly the same way as the SMIN histograms in Figs. 9.9-9.11. A
quadratic fit was subtracted off each record as before by first making a linear fit to
the slopes of each 200 second segment, and then integrating to get a quadratic fit to
the data record. The average value of each 200 second segment was computed, and
the differences of adjacent averages were histogrammed. No cuts have been made,
but three points are off scale on the 3/22/85 histogram.
The explained noise, meaning the motional noise plus the amplifier noise, is
given for each run on the histograms. The values are similar to those in Fig. 9.13
for the SMIN records. The run of 3/22/85 seems to be more noisy than the others.
This is the same run during which SMIN39 was recorded. As was mentioned in the
previous section, the instrument showed some peculiar behavior during this run,
perhaps due to dust.
All of the runs show evidence for discrete changes in the sample charge.
The charge changes are positive, showing that the photoelectrons are negatively
charged. Judged from the run of 4/19/85, the instrument’s calibration is 4.7nV/q,.
Figure 9.19 shows the number of counts in each peak in the run of 4/19/85. The
185
III1 III1
IIll IIII
IIII III1
X g?i
.
-
III1 III1
III1 III1
Illi llll’
X E%
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- ggll
-w2
8 v-4 z
‘5 -
>“a ’
a s
’ ace
d a
m
‘Z
; &
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c
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INSR
31- IN
SR35
and INSR
36 - IN
SR39
186
0 v-l
quno3
k”“l”“l”“l”“llillll’llj I
s i2
%
z E
7-4 0
0
quno3
Figure 9.18. INSR
40 - INSR
44 and INSR
45 - INSR
51
187
crosses are the data while the squares are a Poisson distribution with the same
mean as the data. This shows the Poisson statistics of the photoemission process.
188
3001 I ’ I ’ / 1”’ 1 1 I”” ‘I”_
250 - + + Data 0
+ q Fit
200 - cl 0 VI 3 150 - +
G 0 +
100 -
- c!l
50 -
43 o’l”“~““” 81 I I I I I I I i=g
0 2 4 6 0
Number of Electrons Ejected
Figure 9.19. Photoemission Statistics. Number of counts in each peak in the run of 4/19/85. The fit points are from a Poisson distribution.
189
10. Prospects for a Fractional Charge Search
Let us first ignore the motional noise and the unexplained noise and consider
whether the amplifier noise limited resolution can be made sufficient for a fractional
charge search. As the instrument stands, the amplifier noise is 8.8nV/a and the
calibration is 4.7 nV/q,. For the 200 second square average and difference procedure
the amplifier noise limited resolution is therefore
8.8 nV/&G - (200 stc)li2 ’ 4.7 nV/q. = l l3 “’
A resolution of .05 qe seems like a good goal, since then a peak at 1/3q, would
be separated from zero by 6.7 standard deviations, so a data point would have to
fluctuate by more than 3 standard deviations to mimic a fractional charge. Thus a
factor of 2.6 is needed. There are several places where it might be found:
l The total electrostatic inefficiency (which is not all understood) is 2.7.
Perhaps it can be improved.
l A factor of about 1.4 can probably be gained by cooling the JFET.
l A thorough search might turn up a quieter JFET.
l A factor of two increase in the signal frequency together with a factor of two
decrease in C’s would give a factor of 1.4 in resolution (see section 7.4).
l The averaging time can be increased.
Increasing the averaging time is a last resort, since this will slow down the
measurement and may make the motional noise harder to control. It seems very
190
likely that by some means the amplifier noise limited resolution can be reduced to
.05qe.
The unexplained noise presently contributes .25qe to the resolution, so it must
be reduced by a factor of 5. Hopefully the reader will not be too discouraged by
this. As is evident from section 9.3, nearly all of the work so far with samples
in the instrument has been aimed at reducing the motion sensitivity. Only with
the last sample was the unexplained noise clearly identified, so there has been
little opportunity to study it. A first step would be to see what effect changes in
the sample size and fiber diameter have on the unexplained noise. With the new
guarding technique it will very likely be possible to study somewhat larger samples,
and it is certainly possible to study smaller ones.
With sample motion sensitivities of 1 nV/pm, as have been achieved with
sample 0, the motional contribution at present is about equal to the amplifier noise,
and so it must be reduced by a factor of 3. If the motions are due to thermal effects
they can certainly be reduced, since the instrument could be made more compact
and from lower expansion materials. If the vertical motion is due to electronic noise
in the suspension then this can certainly also be improved. It is encouraging to note
that in the phase direction the motions are already small enough, since the .03mR
rms phase motion corresponds to .06,~m rms.
Perhaps the most serious problem that remains is maintaining the sample
container position when the sample is changed. With 1 nV/pm = .2 qe/pm motion
sensitivity, to keep the systematic error below .05q, it would be necessary to
191
reproduce the sample container position to .25pm after a sample change. This
seems difficult but possible. Actually there is no reason why the motion sensitivity
cannot be nulled more accurately than this. We have been limited to 1 nV/pm
only because during an INSR data record the sample charge is changed by several
hundred qe, which changes the motion sensitivity by - 1 nV/pm. This would not
be a problem in a real experiment since the sample container charge may always be
readjusted by photoemission after the sample is changed.
One might worry that a small change in the sample container weight would
stretch the fiber by more than .25bm. In fact for a 1 cm long 5 pm diameter fiber
a mass change of 1 mg causes an extension of only .05pm, so this does not by itself
seem very serious. Much more worrisome is the fact that our description of the
motions in terms of three translations will at some point be inadequate. When
the sample is changed, the sample container and guard might move relative to one
another, and then the relevant motion sensitivity might well be what was observed
with unguarded samples; say 4 qe/pm for small samples or 40 qe/hm for large ones.
This seems very discouraging. If stretching of the fiber is the only factor causing
relative motion of the sample and guard, then by holding the sample weights equal
to 5Opg even the 40q,/pm value could be tolerated. Unfortunately the structure
may twist or, if the fiber is not quite straight, it may flex. These problems require
careful study before the experiment c&r be attempted.
Perhaps the motion sensitivity difficulties could be greatly reduced if the sample
container were magnetically levitated. Since we don’t know how much of the motion
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