Calibration of the ISOLDE acceleration voltage using a high-precision voltage divider and applying collinear fast beam laser spectroscopy

0.84 MB·English

by  A. Krieger

Calibration of the ISOLDE acceleration voltage using a high-precision voltage
divider and applying collinear fast beam laser spectroscopy
A.Kriegera,,Ch.Gepperta,b,,R.Catherallc,F.Hochschulzd,J.Kra¨mera,R.Neugarta,S.Rosendahld,J.Schipperc,
∗
E.Sieslingc,Ch.Weinheimerd,D.T. Yordanove,andW.No¨rtersha¨usera,b
aInstitutfu¨rKernchemie,Universita¨tMainz,55128Mainz,Germany
1 bGSIHelmholtzzentrumfu¨rSchwerionenforschung,64291Darmstadt,Germany
1 cCERN,CH-1211Gene´ve23,Switzerland
0 dInstitutfu¨rKernphysik,Universita¨tMu¨nster,48149Mu¨nster,Germany
2 eMax-Planck-Institutfu¨rKernphysik,69117Heidelberg,Germany

n
a
J

3
Abstract
1

Ahigh-voltagedividerwithaccuracyattheppmlevelandcollinearlaserspectroscopywereusedtocalibratethehigh-
]
h voltageinstallationattheradioactiveionbeamfacilityISOLDEatCERN.Theaccurateknowledgeofthisvoltageis
p particularlyimportantforcollinearlaserspectroscopymeasurements.Beamvelocitymeasurementsusingfrequency-
-
m combbasedcollinearlaserspectroscopyagreewiththenewcalibration. Applyingthis,oneobtainsconsistentresults
for isotope shifts of stable magnesium isotopes measured using collinear spectroscopy and laser spectroscopy on
o
laser-cooledionsinatrap. Thelong-termstabilityandthetransientbehaviorduringrecoveryfromavoltagedropout
t
a wereinvestigatedforthedifferentpowersuppliescurrentlyappliedatISOLDE.
.
s
c Keywords: Highvoltagedivider,Collinearspectroscopy,ISOLDEfacility,Isotopeshift,Magnesium
i
s
y
h 1. Introduction past, it has been used extensively for studying nuclear
p
ground state properties of short-lived radioactive iso-
[ The accurate determination of high voltages is cru-
topes [7, 8, 9, 10, 11]. CLS utilizes the Doppler shift
1 cialforavarietyofatomic,nuclearandparticlephysics ofthefrequencyofalightwaveinthemovingframeof
v experiments. Examplesare the accelerationvoltage of an accelerated ion. Hence, a fixed-frequencylaser can
6 ion beams for collinear laser spectroscopy [1], the en-
be broughtinto resonance and tuned across the transi-
3
ergyofelectronsinanelectroncoolerappliedatstorage
tion frequencyof the ionby changingthe ionvelocity.
5
ringstonarrowthemomentumdistributionofthecircu-
2 To extract information on isotope shifts and hyperfine
. latingionbeam[2,3],orthevoltageappliedinaretar- splittings, accurate knowledge of this velocity, i.e. of
1
dation spectrometer to determine the kinetic energy of
0 theionbeamenergy,isrequired. Typically,voltagesof
electronsemitted in β decay [4, 5]. Fast-beam exper-
1 30-60kVareappliedtotheionsource. Formostinves-
−
1 iments often require precise knowledge of the kinetic tigationsof medium-massand heavy nuclei, it is suffi-
: energyorthevelocityofthebeamparticles, especially
v cienttoknowthevoltageappliedtotheionsourceand
if resonance processes are investigated. On the other
i thepotentialsatsecondaryaccelerationordeceleration
X hand,suchresonanceprocessescanbeusedtomeasure stages with a relative accuracyof the order10 4. This
−
r the ion beam velocity. In this case, sharp resonances
a isthelevelforwhichhigh-voltagedividersarecommer-
are preferred since the linewidth is one of the limiting
ciallyavailable. However,asitwillbediscussedinthe
factorsfortheaccuracythatcanbeachieved. Collinear
first section of this paper, this accuracy is by far not
laser spectroscopy (CLS) on fast ion or atomic beams sufficient for measurementson the very light elements
is a particularly clear example for both cases. In the
reachingfromhydrogentoroughlyneon.
If the frequency of an atomic resonance is well
Corresponding author at Institut fu¨r Kernchemie, Johannes
∗ known, CLS can be used (in reverse) to determine the
Gutenberg - Universita¨t Mainz, Fritz-Straßmann-Weg 2, 55128
ion velocity, hence, the kinetic energy and the voltage
Mainz,Germany.
Emailaddress:[email protected](A.Krieger) appliedtothesource. Thishasalreadybeensuggested
PreprintsubmittedtoNuclearInstrumentsandMethodsinPhysicsResearchA January14,2011
by Poulsen in 1982 [12, 13]. The latest development became increasingly sensitive and accurate. The lat-
alongtheselineswasatestapparatusformeasurements est steps in these developments where the combina-
of high voltages up to a few 100 kV, to determine and tionof CLS with anRFQ coolerandbuncher[22] and
calibrate the voltage of the electron cooler at the GSI frequency-comb-basedcollinearspectroscopy[23,24].
experimentalstorage ringESR [14]. Thelayoutofthe The scheme of our setup for CLS on an ion beam
prototype allowed measurements up to 50 kV and the is shown in Fig. 1. An ion beam at a usual beam en-
3d 4p transitionsincalciumionswereused ergy of 30-60 keV is superimposed with a laser beam
3/2,5/2 3/2
→
for probing the ion velocity. It was demonstrated that inthecollinearoranticollineardirectionusinganelec-
accuraciesintheorderof10 4canbereachedandsug- trostatic deflector. In the figure the special layout for
−
gestionsforfurtherimprovementweremade. simultaneouscollinear and anticollinearmeasurements
In this paper, we reporton the calibration of the high- withtwolasersystemsisdepicted,whereasinstandard
voltage dividers used at ISOLDE/CERN to measure CLS only a single system is applied. Photons are col-
the potential applied to the high-voltage platforms on lected in the fluorescence detection region (FDR) and
which the ion sources are mounted. There are two in- detected by photomultiplier tubes or other devices ca-
dependent units, HT1 and HT2, that can alternatively pable of single-photoncounting. Usually, the ions are
be used to provide and to measure acceleration volt- acceleratedordeceleratedintothisregion,topreventin-
agesupto60kV.Thecalibrationwasperformedusing teractionwiththelaserlightbeforetheyreachtheFDR.
a non-commercial high-precision high-voltage divider Otherwise,multipleexcitationwillinmostcasesleadto
withaccuracyintheppmrange[6],andcollinearlaser opticalpumpingintodarkstatesandhencediminishthe
spectroscopyonberylliumions. Bothapproachesgave detection sensitivity. Moreover, for two-level systems
consistentresultsandthecalibrationresolvedproblems a long interactionregion could also lead to changesin
intheearlieranalysisofisotopeshiftmeasurementson theionvelocityandthereforetoundesiredshiftsinthe
stableandradioactivemagnesiumisotopes.Theseprob- observedresonancefrequency.
lems could be traced back to differences in the mea- Acceleration of the ions leaving the hot ion source re-
suredvoltagesofHT1andHT2,whichinCLStranslate gionhastwoimportantconsequencesforCLS:First, it
intodifferentDopplershiftsoftheresonancefrequency. leadstoa strongcompressionofthemomentumdistri-
Wewillstartwithashortsummaryoftheprinciplesof butioninthelongitudinalphasespace[1]. TheDoppler
CLS and their implications for isotope shift measure- width∆ν ofanatomictransitionwithfrequencyν is
D 0
ments,andwewilldescribetestmeasurementsofabso- normally caused by the thermal distribution of kinetic
luteDopplershiftstodeterminetheionvelocity. Then, energies E = mυ2/2 of the atoms. For an ion beam
aconcisedescriptionofthehigh-accuracyhigh-voltage the width of the energy distribution δE is determined
dividerwill be givenand the resultsof two calibration bypropertiesoftheionsourcee.g.,thepotentialdistri-
campaignsare discussed in results of the long-term as butioninsidethesourceandtheionizationprocess. By
well as the transient behavior of the high-voltage sup- accelerationinanelectrostaticfieldtheenergyspread
plies.
∆E =mυ∆υ (1)
remains constant. Consequently, if the velocity υ in-
2. CollinearLaserSpectroscopy creases, the velocityspreadδυ has to decreaseaccord-
ingly. By this effect, at energies of a few 10 keV, the
CLSwas proposedbyKaufman[1] andwasrapidly Dopplerwidthinthebeamdirection
developed into a useful tool, namely for the spec-
∆ν =ν ∆υ/c (2)
troscopyofshort-livedradioactiveisotopes. Itsfirston- D 0
lineinstallationwasrealizedatanuclearresearchreac- is expected to be reduced to the order of the natural
tor [15] and soon thereafter the COLLAPS (collinear linewidth of a typical allowed dipole transition. With
laser spectroscopy) beamline at the radioactive ion υ = √2eU/mgivenby the accelerationvoltageU one
beamfacilityISOLDEwasbuilt[16]. Followedbysim- obtains
∆E
ilar andmoreadvancedexperiments(see, e.g. [17, 18, ∆ν =ν . (3)
D 0
19,20,21])collinearlaserspectroscopydevelopedinto √2eUmc2
a generaltechnique for on-line investigationsof spins, The ion source conditions also influence the total en-
electromagnetic moments and nuclear charge radii of ergyof the acceleratedbeam. This has importantcon-
short-livedisotopes. Itwascontinuouslyimprovedand sequences for high-voltage measurements and the ac-
combinedwithdifferentdetectiontechniquesand,thus, curacy in CLS: The potential applied externally to the
2
source is not necessarily identicalwith the potentialat smaller variable potentialat the fluorescence detection
whichionsarecreated. Threeionsourcesaretypically regionusedforDopplertuning. Theresultinginfluence
usedatISOLDE:surfaceionsources,theresonantion- of voltage errors is much larger in this case. We first
izationlaserionsource(RILIS)andplasmaionsources. solve the relation ν(2) = ν(1) + δν1,2 to extract a fully
0 0 IS
While for the former ones the uncertainty of the start relativisticformulafortheisotopeshiftandobtain
potentialof theionsisless than3 V, in theplasma ion
ν
sourcesitcanbe anorderofmagnitudelarger. Hence, δν1,2 = 0 m eU(1)+ eU(1)(2m c2+eU(1))
IS κ 2 1
high-voltage measurements more accurate than about
20 ppm are inappropriate and will not help to obtain nm1 (cid:16)eU(2)+ peU(1)(2m1c2+eU(1))(cid:17) (7)
−
higheraccuracy. Allmeasurementsreportedherewere
(cid:16) p (cid:17)o
performedwithionsfromRILIS. whereκ = m m c2+eU(2)+ eU(2)(2m c2+eU(2)) .
1 2 2
The second consequence of acceleration is a large Theeffectofacalibrationerrorintheisotopeshiftmea-
h p i
Dopplershiftoftheatomictransitionfrequencyaccord- surementcannoweasilybecalculatedbyreplacingU(1)
ingto andU(2),withvoltages
ν =ν γ(1 β) (4)
c 0
± U(i) =U(i) (1+k )+U(i) (1+k ), (8)
in the case of collinear excitationand anticollinearex- ′ Source Source FDR FDR
citation, respectively. Here, γ = 1 β2 is the rela-
− where i = 1,2. The unprimedvaluesare the realvolt-
tivistic time dilatation factor and β = υ/c is the ion
p ages and the primed values are the measuredvoltages,
velocity in units of the speed of light. The standard
with miscalibration factors k for the source and
procedureinCLSisasfollows: Thelaserfrequencyis Source
k for the fluorescencedetection region. In Table 1,
fixed at ν close to the Doppler-shifted resonance fre- FDR
L the results of these calculations are summarized under
quencyν and the velocityofthe ionsis changeduntil
c the following assumptions which are typical for mea-
the varyingDopplershift ofthe laser frequencybrings
surements at ISOLDE but also for CLS at other facil-
theatomictransitionintoresonancewiththelaserlight.
ities: The ISOLDE ion source potential is assumed to
Theatomicresonancesofisotopeswithmassesm and
1 be U = 50 kV and the laser frequency is chosen
m occuratdifferentvoltagesU(1)andU(2)fulfillingthe Source
2 insuch away thatthe resonancesoftwoisotopeswith
condition
massnumbersAandA+2occursymmetricallyatpost-
ν =ν(1)m1c2+eU(1)± eU(1)(2m1c2+eU(1)) (5) accelerationvoltages+UFDRand−UFDR.AtCOLLAPS
L 0 m c2 thepost-accelerationvoltageUFDRcanbeupto 10kV.
p 1 ±
Forthemeasurementthisvoltagerangedependsonthe
m c2+eU(2) eU(2)(2m c2+eU(2))
=ν(2) 2 ± 2 hyperfinestructuretobescanned.FortheISOLDEmis-
0 pm2c2 calibrationfactorweassumekSource =0.0001whichlies
withν(2) = ν(1) +δν1,2, whereδν1,2 denotestheisotope within the specified accuracy of 10−4. We further as-
shift.O0nesho0uldremISemberthateIUS (i)referstothebeam sume that UFDR is measured exactly, hence, kFDR = 0.
The resonances of both isotopes therefore appear at
energyandnotnecessarilytotheappliedionsourcepo-
measuredvoltagesU(i) =50005V U . Withthese
tential. Wewillfirstconsiderthecasethatthecomplete ′ FDR
±
conditions the approximate error formula [16] for the
acceleration voltage is measured with a miscalibrated
voltage divider. Using the approximation ν(1) ν(2), isotopeshiftbecomes
0 ≈ 0
becauseδνisusuallysmallcomparedtoν ,weobtain
0 eU U(1) U(2) (m m )
m ∆δν1,2 =ν FDR− FDR + 2− 1 k
U(2) = 2U(1). (6) IS 0 2mc2 2U m +m Source
m r  Source 1 2 
A common calibration factor1 in the voltage measure- We have calculatedthe effect for three elements th(9a)t
mentwillcanceloutonbothsides. Hence,onlyasmall have been recently investigated at ISOLDE. The most
erroroccursduetotheslightlydifferentresonancefre- crucial case is beryllium. Here, an accuracy of about
quencies which even in the case of beryllium with a 1 MHz is requiredto extractthe nuclear chargeradius
largeisotopeshiftandasmallmassislessthan1MHz oftheneutronhaloisotope11Be[23]withsufficientac-
fora10 4 voltagedeviation. However,itisstandardin curacy and it is obvious that this accuracy cannot be
−
CLS-becausemassseparatorsareused-thatthetotal reachedin thestandardapproach. Formagnesium, the
acceleration voltage is composed of the source poten- voltageaccuracyof10 4barelymeetstherequirements,
−
tial which is used to generate the fast ion beam, and a whileinthecaseofcopperthestandardvoltagedivider
3
Table1: Calculationsoftheinfluenceofhigh-voltagecalibrationsonisotopeshiftmeasurementsforlightandmediummassnuclei. Ionmasses
areusedasintegernumbers,thetransitionfrequencies refertothe2s1/2 2p1/2,the3s1/2 3p3/2,the3s1/2 3p1/2 transitioninBe+,
Mg+andCu+,respectively.δνIAS,A+2isthecompleteisotopeshiftbetweenth→etwoisotopeswithm→assnumbersA1and→A2.Thedifferentialisotope
shift∂ν/∂U(A)wascalculated accordingtoEq.(10)and∆δνA,A+2 givestheartificialisotopeshiftintroducedbya10 4 measurementerroron
IS −
the acceleration voltage. Thelast column indicates the typically required accuracy onthe isotope shiftmeasurement to extract charge radius
information.Formoredetailsseetext.
Isotopepair ν (A) δνA,A+2 ∂ν/∂U(A) ∆δνA,A+2 Requiredaccuracy
0 IS IS
(THz) (MHZ) (MHz/V) (MHz) (MHz)
9 11Be 957.22 14240.0 31.2 29.2 1
−
24 26Mg 1072.08 3220 22.5 8.5 3
−
63 65Cu 923.01 2000 11.9 1.7 5
−
is sufficient. If charge radii for two or more isotopes ions Riis and coworkers [27] used collinear and anti-
areavailablefromothertechniques,forexamplemuonic collinearsaturationspectroscopy,whichisnotsensitive
atomspectroscopy,therequirementsareslightlylessse- to an exact match of the ion velocity with the optical
vere. The systematic error caused by the voltage mis- resonance. Suchatypeofspectroscopyisalsousedfor
calibration behaves largely as the mass shift. Hence, Ives-StilwelltestsofSpecialRelativityatstoragerings
the King plot procedure used in such cases, delivers a [28, 29]. Here, the rest frame frequency is obtained
massshiftconstantthatwillresultinacorrectfieldshift fromtheobservedLambdipsusingtheproductformula
evaluation. However, for the lightest nuclei even this ofEq.(4):
approachdoesnotprovidesufficientaccuracy. ν2 =ν ν , (11)
0 c· a
In summary, CLS of light elements is difficult be-
with ν and ν being the laser frequencies at the reso-
causetheionshavealargedifferentialDopplershift a c
nance position in anticollinear and collinear geometry,
∂ν ν e mc2+eU respectively. Thisrelationisindependentofallapplied
= 0 e+ voltages but requires knowledge of the absolute laser
∂U mc2  eU(cid:16) 2mc2+e(cid:17)U  frequencies typically on the 10 9 10 10 scale. In
e·ν0p (cid:0) (cid:1) (10) the lithium experiment[27], this−wa−s pe−rformedusing
≈ √2eUmc2 iodine reference lines and the isotope shift of the two
and the observedresonancepositions are thereforeex- stableisotopes6,7Liwasextractedwithgoodaccuracy.
tremelysensitivetotheappliedvoltageandthustovolt- To avoiduncertaintiesof thevoltagemeasurementand
age fluctuations. Moreover, the mass shift in these to determine the isotope shift between 7,9,10,11Be, as
isotopes is huge compared to the tiny nuclear volume well as the absolute excitation frequencies ν for the
0
effects. Nevertheless, a few techniques were devel- 2s 2p transitions with an accuracy better
1/2 1/2,3/2
→
opedto overcomethese problemsand allowed CLS of than 2 MHz, a similar approach was used for the first
afew,particularlyinterestingcases. CLSofshort-lived time in an on-line experiment. A detailed discussion
neon isotopes including the two-proton halo candidate of the laser system and experimental setup is given in
17Newasperformedusingaspecialfeatureoftheneon [23, 24]. Summarized, as shown in Fig. 1, two dye
atomicspectrum:Twofine-structuretransitionsinneon lasers were collinearly and anticollinearly overlapped
starting from a common metastable level, which was with a beryllium ion beam. For precise frequency de-
populated in charge exchange collisions, have a split- terminationand stabilizationone laser was locked to a
ting that fits exactly to the opposite Doppler shifts in frequencycomb,thesecondonetoaniodinetransition
collinear and anticollinear excitation at a beam energy viaDoppler-freefrequencymodulationsaturationspec-
ofabout61.8keVifthelaserfrequencyissettotheav- troscopyin an iodinecell. Fromtwo second-harmonic
erage transition frequencyin the rest frame. This was generationdevices,UVlightof312nmand314nmwas
used in the neon measurements at COLLAPS to cali- coupledthroughquartzwindowsintothe collinearand
brate the beam energies and to obtain reliable isotope anticollinear directions of the ion beam, respectively.
shiftvaluesfortheneonisotopes[25,26].Inthisexperi- The observedresonancefrequenciesν and ν allowed
a c
ment,goodagreementbetweentheappliedhighvoltage us to determine the absolute transition frequencyν in
0
at ISOLDE and the beam energy was found. On Li+ the rest frame of the ion according to Eq. (11). The
4
Deflector PMT
Retardation Signal
Beamline
U
n-Doubler FDR
n-Doubler
F C
Dye Laser
M
Servo
Dye Laser
I Cell n-Comb Servo
2
10 MHz
Rb-Clock
Figure1:ExperimentalsetupforcollinearandanticollinearspectroscopyonfastBe+-ionsatISOLDE.Twofiber-coupleddyelasersseedsecond-
harmonicgeneratorringsproducingUVlightatwavelengthsof312nmand314nmrespectively.Thelaserbeamsaresuperimposedcollinearlyand
anticollinearlywiththeionbeam.ScanningoveraresonanceisachievedbyapplyingasmallstepwisevoltageUFDRtothefluorescencedetection
regionFDR.regionFDR
isotope shift was then extracted as the difference of CLS experiments using an independenthigh-precision
the absolute transition frequencies between different voltagedivider.
isotopes. Thentheinversedprocesswasusedandfrom
thenowknownvalueofν for9Beandthecollinearand
0
anticollinear signal the beam energy was determined
3. The high-voltage installation at the ISOLDE fa-
withanaccuracyatthelevelof10 5usingEq.(4).
− cility
The relative difference between the beam energy The on-line mass separator ISOLDE at CERN pro-
and the ISOLDE high-voltage readings were found duces low-energy radioactive ion beams [30] making
to be 2.0(2) 10−4 for the power supplies HT1 and use of the so called ISOL1 technique: A stack of four
− ·
6.5(4) 10−4 for HT2, corresponding to absolute synchrotrons, the Proton Synchrotron Booster (PSB),
·
values of 12(1.3)(3.0) V and 39.0(2.4)(3.0) V at the producesa pulsed 1.4 GeV proton beam. These high-
−
maximum operation voltage of 60 kV. Here the first energy protons are delivered to one of the two target
uncertaintydenotesthe purefittinguncertaintyandthe stations, inducing nuclear reactions in a thick target
secondonethesystematicuncertainty. Thissystematic to produce radioactive isotopes. The reaction prod-
uncertainty accounts for the limited knowledge about ucts are ionized, e.g. via resonant laser ionization at
the potential at which ionization takes place in the about2000 C[31,32]. Thetargetsandionsourcesare
◦
source. Both devices, including the high-voltage mountedon two platformsof positive electricalpoten-
dividers, were installed at ISOLDE in 1981 and are tial up to 60 kV. The ions are then extracted and ac-
in operation since then. More details will be given in celerated to ground potential for mass separation. For
Section3. thatpurposeeithertheGeneralPurposeSeparatorGPS
Since we found a clear discrepancy between the ortheHighResolutionSeparatorHRSmagneticsector
measured ISOLDE ion source voltages and the beam separatorcanbeused. Themassseparatedionbeamis
energy, we attributed this to a problem in the high guidedtotheexperiments.
voltage readout. Therefore, a recalibration of the
ISOLDE high-voltage divider was arranged for future
1isotopeseparationon-line
5
Thetargetandionsourceplatformisconnectedtoeither FuGpowersupply
of two units HT1 or HT2 comprising a stabilized HV
Ne thyratron
papopwleierdsuiopnplsyoaunrcdeapvootletangtieald.ivTihdeerhfiogrhthvoelrteaagdeocuitrcoufitthrye KATRIVoltagdivider atinguit
of each unitis shown in Fig. 2. Up to 2008 the accel- nc
soCir
erationvoltagewasgeneratedbytwoactivelyregulated e
R
ASTEC60kVprecisionpowersupplies. Theaccuracy R2 ASTEC
ofbothwasspecifiedto10 4. Theinternalvoltagesta- R6
−
target
bilizationfeedbackloopisbasedonaROSSvoltagedi-
vider 75-10-BDL, representedby resistors R7a/R7b in R8a R7a
Fig.2,usingascalefactor1000:1. Inordertostabilize feedback
thedevicesintemperatureto 0.1Kthepowersupplies, protons R8b R7b
±
theresonantcircuitandtheROSSvoltagedividerwere
immersedinanoilbath.
A similar ROSS voltage divider at a scale factor of
Figure2:Simplifiedschematicviewofthehighvoltagecircuitryatthe
10000:1, represented by resistor R8a/R8b and a high-
twoISOLDEHVunitsincludingaresonantcircuitusedtomodulate
precisionHP3458Adigitalmultimeter(61/2digitres- thehighvoltageappliedtothetarget.TheresistorsR7a/R7brepresent
olution,whichcorrespondstoanaccuracyof10 5)are theROSSvoltagedividerforinternalstabilizationwhereasR8a/R8b
−
used to read out the stabilized target voltage to the (framed)representthevoltagereadoutUISOLDE.
ISOLDEcontrolsystemviaGPIB.Thesedividerswere
originallyspecifiedwithanaccuracyof10 4 andasta-
− resistor R2 (=250 Ω) reduces the stabilization time to
bilityof5 10 5peryear.
· − lessthan10msafterthepulsefor 1Vfromthenom-
In 2009the formerASTEC power supply of HT1 was ±
inal voltage. At this point a voltage drop of R2I is at
replaced by a self-regulated Heinzinger power supply ·
most 500 mV. The resistor R6 (=1.5 kΩ) forms a fast
of the PNChp3p series. In this commercialdevice the
couplingoftheASTECsupplytothetarget. Note,that
applied voltage is regulated internally and specified in
the powersupplyitself is runningin a static modeand
stability to 1 10 5 over a time period of 8 hours un-
· − that only the acceleration gap receives the modulated
derconstantconditionsandinloadregulation,andfora
voltage. The figure shows also the connection to the
loadstepfromzerotothenominalvoltage,to5 10 4.
· − high-precision Karlsruher Tritium Neutrinoexperiment
ForreadouttheISOLDEcontrolsystemusesagainthe
(KATRIN)dividersusedforcalibration.
ROSS voltage divider and HP 3458A multimeter, i.e.,
resistorsR8a/R8binFig.2.
During proton beam impact, the ionization of the air
volumearoundthetargetgivesrisetoasignificantleak- 4. TheHigh-PrecisionVoltageDivider
agecurrentwhichresultsinlossofchargeontheeffec-
tive target capacitance. This voltage breakdowncould Although small voltage differences can be mea-
lead to damage of the HT supply and furthermorecan sured to the highest precision, e.g. 10 12 applying the
−
significantly slow down the regulation loop, hence the Josephson effect [34, 35], measuring high-voltages
reason of blanking the high voltage by a resonant cir- at precision levels below 10 4 becomes increasingly
−
cuit[33]. Theprincipletaskofthisresonancecircuitis difficult. To measure voltages larger than 10 kV with
to fully discharge the target capacitance prior to beam highaccuracy,voltagedividersarerequiredtodownsize
impact. The schematic is included in the upper right the voltages to a range accessible for a precise digital
part of Fig. 2: The first pole of the pulse transformer multimeter. A high-precision voltage divider, further
isconnectedtoacommercialpowersupply(FuGElek- denoted K1 [6], was developed for the Karlsruher
tronik,0-15kV),whoseoutputvoltageisafunctionof Tritium Neutrinoexperiment KATRIN [36], which is
theASTEC’soutputvoltage,controlledbyathyratron, abletodeterminevoltagesupto35kVinthesub-ppm
whichissynchronouslytriggeredwiththePSBejection regime. The KATRIN experiment measures the mass
kickers. The current supplied by the resonant circuit oftheelectronneutrinodirectlywithhighestsensitivity
dischargesthroughthecapacitanceofthetarget. Thus, in the sub-eV regime using a so-called MAC-E-Filter
ahigh-voltagepulseofupto60kVwithoppositepolar- (magnetic adiabatic collimation combined with an
itymodulatesthe targetvoltage(within30 µs) to zero, electrostatic filter). Thus high luminosity and energy
justbeforethe protonscollidewiththetarget. A small resolution are combined in order to determine the
6
Table2: CalibrationparametersoftheKarlsruherTritiumNeutrinoexperiment(KATRIN)dividersK1andK2derivedatPhysikalischTechnische
Bundesanstalt(PTB)[6]. AfirstcalibrationcampaignatPTBdemonstratedthatdividerK2showsevenhigherstabilitiesofthescalefactorwith
respecttotime,voltageandtemperature,butnotallinvestigations arefinishedyet,thereforetheK2calibrationvaluesarestillpreliminary. For
detailsseetext.
Parameter dividerK1 dividerK2
AbsolutescalefactorK asofNov2006(K1),Dec2009(K2) 3944.9597(14) 3636.2743
0
Long-termstabilityofscalefactorc := ∂K 1 6 10 7month 1
t ∂t · K · − −
TemperaturedependenceofscalefactoratT =25 C c := ∂K 1 1.7(7) 10 7K 1 1 10 7K 1
◦ T ∂T · K · − − · − −
VoltagedependenceofscalefactoratU =18.6kV c := ∂K 1 2.8(2) 10 8kV 1 1.9(2) 10 8kV 1
U ∂U · K − · − − − · − −
Quadraticvoltagedependencec := ∂2K 1 7.5(4) 10 10kV 2
UU ∂U2 · K − · − −

0
45
-2
40
-4
HT1 - U /VDEK1,K2 --11--2086 HT2 - U /VOLDEK1,K2 22330505
SOL -14 UIS 15
UI
-16 10
-18 5
-20 0
0 10000 20000 30000 40000 50000 60000 0 10000 20000 30000 40000 50000 60000
UISOLDE /V UISOLDE /V
Figure4:DiscrepancybetweenthereadoutoftheISOLDEhigh-voltagepowersuppliesHT1andHT2andthevoltagedeterminedbytheKATRIN
voltagedividersK1( upto35kV,2008)andK2( upto60kV,2009).Parabolicfunctionsarefittedtothe2009dataandlinearfunctions(dashed
• ◦
line)tothe2008data.Thelatterwasextrapolatedto65kV.Theresultofabeamenergymeasurementat60kVusingcollinearlaserspectroscopy
isshownforcomparison((cid:4)at60kV,2008).
7
nit (b)
55025 u
HT1 (a) 1V /
55020
V
e / 55015
g 12 min
a
olt 55010 100s /unit
d v
e nit
sur 54990 V /u (c)
a 1
e
m 54985
HT2

54980
11 min
54975
0 1 2 3 4 5 6 7 8 9 10
100s /unit
time / h
Figure5:(a)Long-termbehaviorofthehigh-voltageunitHT1atISOLDEequippedwiththeHeinzingerpowersupply(uppertrace,topaxis3h)
andHT2equippedwiththeASTECdevice(lowertrace,bottomaxis10h)forasetpotentialof55kVrecordedwiththeKATRINK2divider. A
shortabruptvoltagedropasitoccursatISOLDEoccasionallywasinducedonpurposeintheregionsindicatedbytheboxes,toinvestigatethe
transientbehaviorafterresettingtheHV.Thisregionisenlargedinthegraphs(b)forHT1and(c)forHT2.
energy distribution of the electrons at the end-point resistanceof184MΩ[6]. Theseresistorsarearranged
of a tritium ß-decay. The precision of this energy in a helix structure between the copper electrodes.
measurementrelyesontheppmprecisionoftheapplied Up to the forth one, each ring comprises 25 resistors.
electrostaticretardingpotential. The low voltage output is formed by the remaining
Oneyearlater,in2009,asecondhigh-precisiondivider six resistorsarrangedin each case by threeresistorsin
K2 for the KATRIN experiment was completed to parallel. Thus a scale factor of 3945:1 or 1972:1 can
measurehighvoltagesupto65kV.Bothdividerswere beprovided. Thecopperelectrodesgenerateaconstant
specified atthe PhysikalischTechnischeBundesanstalt electric field along the primary high-precision resistor
(PTB) to sub-ppm accuracy and stability. We report chain. A secondaryresistor chain of fourhigh-voltage
here on a voltage calibration of the two ISOLDE high 44 MΩ resistors (Caddock MX480) connects each
voltageunitsHT1andHT2againstthesehigh-precision pair of cooper electrodes to provide a linear potential
voltagedividers. distribution. In order to protect the primary resistors
Figure3showsapictureoftheK1divider: Acylindri- against transient overloads a capacitive chain, consist-
cal stainless steel container with a diameter of 60 cm ing of four 2.5 nF capacitors (Vishay MKT1816), is
and a height of 85 cm houses the voltage divider implementedbetween the copperelectrodes. The high
setup. The case, which shields from electromagnetic voltagetobemeasuredisfedintoasealedHVbushing
interference from outside, is flooded with N gas at locatedatthetopelectrode.
2
atmospheric pressure along the resistors for insulation The first version of the voltage divider setup K1 used
and temperature stabilization at 25 0,15 C. The in 2008 and described above, was limited to voltages
±
interiorconsistsof fivecopperringelectrodesfixedby up to 35 kV. The development of a further voltage
polyoxymethylene rods which are concurrently used divider K2 was strained to exceed K1 in disciplines
as insulators. The heart of the voltage divider is the of long-term stability and temperature stabilization
primaryresistorchain,whichconsistsof106precision behavior. Since the electric strength has already been
resistors of Bulk Metal Foil technology2 with a total increasedto 65kV (itis conceivablethatpotentialsup
to100kVcouldbemeasured,sincetheelectricstrength
of the primary resistor chain is 100 kV, but the design
2BMFisabrandofVishayIntertechnologyInc.:www.vishay.com
8
8508A digital reference multimeter. In order to avoid
driftswithin this precisionvoltmeter, a 10 V reference
potential was provided by a Fluke 732A reference
voltage source, that also had been calibrated at the
PTB.Beforeeverycalibrationmeasurement,thedigital
voltmeterwascalibratedwiththis10Vreference.
5. High-voltagemeasurements
Thefollowingsectiondescribesthecalibrationmea-
surements as well as the investigation of the transient
behavior of the power supplies. Finally, the impor-
tanceofthecalibrationisdemonstratedwitharesultof
collinear laser spectroscopy on stable magnesium iso-
topes.
5.1. Calibrationmeasurements
For calibration of the high-voltage units HT1 and
HT2 the voltage readoutof ISOLDE was comparedto
thesimultaneouslymeasuredvoltagewiththeprecision
voltagedividerK1in2008andK2in2009.Bothpower
supplies were switched on more than three hours be-
forethemeasurementstarted,tomakesurethatthermal
equilibriumwasreached. Theoutputofthepowersup-
Figure3: Theinteriorofthehigh-voltagedividerK1fromtheKarl-
sruherTritiumNeutrinoexperiment(KATRIN)experiment:106preci- plywasthenraisedstepwisefrom10kVto35kV(K1)
sionresistorswithatotalresistanceof184MΩarearrangedinahelix and to 60 kV (K2) and decreased again. After setting
structure around fivecopper ring electrodes and connects each pair
anewvoltage,thesystemwasgivenaperiodof7min-
ofcopperelectrodestoprovidealinearpotentialdistributionoverthe
primaryhigh-precisionresistorchain. Eachpairofcopperelectrodes utestothermalize,before3datapointsweretakenina
isconnectedbyahighvoltageresistor(blue)andcapacitor(green)to sequenceof30seconds.
controltheelectricalpotentialovertheprimaryresistorchainandto ThehighvoltageU isgivenbythescalefactorofthe
DIV
protectitagainstoverloads.
dividerKtimesthelow-voltagereadingU ofthedigi-
lv
talvoltmeter(DVM).Thelatteriscorrectedforanoffset
δU andagainfactorkcloseto1,whichisdetermined
lv
would have to be modified and tested), the K2 divider bythereferencevoltagesource.
is suitable to cover the full range of the acceleration
potential of the ions at ISOLDE. As both dividers U = K (U δU ) k, (12)
DIV lv lv
· − ·
are identical in concept, we mention only the major
resultinginavoltageuncertaintyof
changesinthesetupofK2: Thecopperringelectrodes
divide the setup into five (instead of four) sections,
where each section comprises34 precision resistors of ∆UDIV = ∆K 2+ ∆k 2+ ∆Ulv 2 ∆K. (13)
880kΩ. Inthelast, sixthlevelthelowvoltageoutputs UDIV s K ! k ! Ulv ! ≈ K
providedividerratiosof3636:1,1818:1and100:1.The
This simplification is allowed because the relative un-
firstoneisusedforthecalibrationsreportedhere. The
certainties of the gain factor k of the DVM and of the
secondarydividerchainconnectsthecopperelectrodes
voltagereadingU aresmallerthan10 6.
andcomprises5resistors(CaddockMX480),eachwith lv −
Thescale factorofthedividerK isderivedfromthe
36 MΩ and a 90 kΩ resistance (Caddock MS260) in
factorobtainedatthecalibrationdateK accordingto
thesixthsubsectionforthevoltageoutput. Thetertiary 0
capacitive chain consists of a series of 5 capacitors of K =K (1+c δt+c δT+c δU+c δU2) (14)
0 t T U UU
7.5nF(3capicatorsof2.5nFinparallel). · · · · ·
Both voltage dividers were specified at the PTB (see by considering its long-term drift c over a time inter-
t
Table2). ThedividedvoltageismeasuredbyaFLUKE val δt after the last calibration, its temperature and its
9
voltagedependencewithδT beingthetemperaturedif- Notethatlaserspectroscopydeterminestheionvelocity
ference to the referencetemperature of 25 C, and δU via the Doppler shift, which depends on the starting
◦
being the voltage difference to the reference voltage potentialoftheionsinsidetheionsource. Thereforea
18.6kV (see Table2). The termsc δT, c δU and smalloffsetofabout1-3Volts(systematicuncertainty)
T U
· ·
c δU2 aresmallerthan10 6, thereforethese correc- was expected corresponding to the potential gradient
uu −
·
tionsareneglectedinourvoltagemeasurements. Con- along the electrothermically heated tube in which
trary, the long-term drift of divider K1 has been de- ionization takes place [37]. Within this, both the laser
termined to be c(K1) = 6 10 7 month 1 (see Ta- andthevoltagedividermeasurementsareinreasonable
t − −
·
ble 2). Therefore the correction c δt is significant agreement.
t
·
(δt 24months)andisappliedtoourmeasuredvalues. The calibration measurements in 2009 ( ) are better
≈ ◦
For divider K2 no long-term drift has been found yet reproducedwithasecond-orderpolynomialfunction
andsinceδt = 1monthnocorrectionisapplied. Tobe
conservative we assume a total long-term drift correc-
tionuncertaintyof∆(c δt)=3 10 6forbothdividers ∆U = 2.791(23)(40) 10−4 U
t − − · ·
K1and K2. Theuncert·aintyof·thehigh-voltagedeter- +8.860(52) 10−10 U2. (17)
· ·
mination by the dividers K1 and K2 can be calculated
This yields a deviation of 13.55(16)(24)V at 60 kV.
as −
Notethatthesystematicuncertaintyofthesecondorder
∆UDIV = ∆K term in Eq. (17) is negligibly small. Since the 2009
U K calibrationagreesin the regionfrom0-30kV with the
DIV
onefrom2008,itcanbeconcludedthatasecond-order
∆K 2
0 +(∆(c δt))2 polynominalcalibrationcurveisprobablyalsovalidfor
t
≈ s K0 ! · the old data and even reduces the difference between
= 4 10 6 (15) thelaser-basedandthehigh-voltagemeasurement.
−
·
The ROSS voltage dividers used with the ASTEC
The differences between the ISOLDE HT1 and HT2 devices were specified in 1989 to an accuracy of
readout and that of the KATRIN K1 and K2 dividers 10 4 corresponding to 6 V at 60 kV. The observed
−
areplottedinFig.4asafunctionoftheappliedvoltage. discrepancy is about twice that value which might be
Eachdatapointistheaveragevalueofthreesubsequent ascribedto agingeffectsoveryears. Thefactthatboth
measurementsasdescribedabove. Thetinyerrorbars, measurements show the same deviation indicates that
mostly covered by the data points, show the standard the internal regulation circuits of both power supplies
deviation of these 3 points. Note that in 2008 the areaccurate.
calibrationcouldonlybecarriedoutupto35kVdueto The results of the investigation of the ISOLDE HT2
thelimitedoperatingrangeoftheK1divider,whilethe unit are shown in Fig. 4. The measurements taken in
2009 calibration was performed up to 60 kV directly 2008 with the KATRIN K1 divider are fitted with the
usingK2.Furthermore,afterthemeasurementsin2008 linearfunctiony=ax+b(dashedline),yielding:
theASTECpowersupplyofHT1wasreplacedwiththe
conceptionallymodernHeinzingerdevice. ∆U =+6.432(26)(40) 10 4 U 0.128(68)V, (18)
−
The linear functiony = ax between the voltage devia- · · −
tion∆U andtheISOLDEreadingU isobtainedfroma whichcorrespondstoanextrapolatedvoltagedeviation
of +38.45(22)(24) V at the acceleration voltage of
fittothe2008data( )andisgivenby
• 60 kV. In this case we had to assume a linear func-
∆U = 2.540(24)(40) 10 4 U. (16) tion with a free offset to reproduce the data points.
−
− · · Laser spectroscopy at 60 kV yielded a deviation of
The first uncertainty of the slope is the pure fitting +39.0(24)(30)V which is in excellent agreementwith
error, while the second one denotes the systematic thevalueobtainedfromthevoltagecalibration.
uncertaintyaccordingtoEq.(15). Linearextrapolation Thecalibrationresultsin2009( )werebestreproduced
◦
to an operation voltage of 60 kV thus results in a by a second-order polynomial function of the form
deviationof 15.24(15)(24)V. y=a x+a x2+b,yielding
− 1 2
This deviation can be compared to the laser-
spectroscopic beam energy measurement described in
Sec. 2 that yielded a difference of 12.0(13)(30)V at ∆U = 0.118(39)V +6.51(46)(40) 10−4 U
60 kV. This data point is also inclu−ded in Fig. 4 ((cid:4)). +−1.721(69) 10 9 U2 · ·(19)
−
· ·
10