arX

iv:0

807.

0074

v1 [

phys

ics.

atom

-ph]

1 J

ul 2

008

A novelantiproton radialdiagnostic based on octupole induced ballistic loss

G .B.Andresen,1 W .Bertsche,2 P.D.Bowe,1 C.C.Bray,3 E.Butler,2 C.L.Cesar,4 S.Chapm an,3 M .Charlton,2 J.

Fajans,3 M .C.Fujiwara,5 R.Funakoshi,6 D.R.G ill,5 J.S.Hangst,1 W .N.Hardy,7 R.S.Hayano,6 M .E.Hayden,8 A.J.

Hum phries,2 R.Hydom ako,9 M .J.Jenkins,2 L.V.J�rgensen,2 L.K urchaninov,5 R.Lam bo,4 N.M adsen,2 P.

Nolan,10 K .O lchanski,5 A.O lin,5 R.D.Page,10 A.Povilus,3 P.Pusa,10 F.Robicheaux,11 E.Sarid,12 S.SeifEl

Nasr,7 D.M .Silveira,4 J.W .Storey,5 R.I.Thom pson,9 D.P.van derW erf,2 J.S.W urtele,3 and Y.Yam azaki13

(ALPHA Collaboration)1Departm ent ofPhysics and Astronom y, Aarhus University, DK -8000 Aarhus C,Denm ark

2Departm ent ofPhysics, Swansea University, Swansea SA2 8PP,United K ingdom

3Departm ent ofPhysics,University ofCalifornia atBerkeley,Berkeley,CA 94720-7300, USA

4Instituto de F��sica,Universidade Federaldo Rio de Janeiro,Rio de Janeiro 21941-972, Brazil

5TRIUM F, 4004 W esbrook M all, Vancouver BC, Canada V6T 2A3

6Departm ent of Physics, University of Tokyo, Tokyo 113-0033, Japan

7Departm entofPhysics and Astronom y,University ofBritish Colum bia,Vancouver BC,Canada V6T 1Z4

8Departm ent ofPhysics, Sim on Fraser University, Burnaby BC,Canada V5A 1S6

9Departm ent ofPhysics and Astronom y,University ofCalgary,Calgary AB,Canada T2N 1N4

10Departm ent ofPhysics, University ofLiverpool, LiverpoolL69 7ZE,United K ingdom

11Departm ent of Physics, Auburn University, Auburn, AL 36849-5311, USA

12Departm ent ofPhysics,NRCN-Nuclear Research Center Negev,Beer Sheva,IL-84190,Israel

13Atom ic Physics Laboratory, RIK EN, Saitam a 351-0198, Japan

(D ated:Received April20,2013)

W e reportresultsfrom a noveldiagnostic thatprobestheouterradialpro�le oftrapped antipro-

ton clouds. The diagnostic allows us to determ ine the pro�le by m onitoring the tim e-history of

antiproton losses thatoccurasan octupole �eld in the antiproton con�nem entregion isincreased.

W eshow severalexam plesofhow thisdiagnostic helpsusto understand theradialdynam icsofan-

tiprotonsin norm aland nested Penning-M alm berg traps. Betterunderstanding ofthese dynam ics

m ay aid currentattem ptsto trap antihydrogen atom s.

I. IN T R O D U C T IO N

Cold antihydrogen atom s (H) were �rst produced

by the ATHENA collaboration [1],and,shortly there-

after, by ATRAP [2]at the CERN Antiproton Decel-

erator (AD) [3]in 2002. They were produced by m ix-

ing positrons(e+ )and antiprotons(p)held in Penning-

M alm berg traps.Such trapsuse a solenoidalaxialm ag-

netic �eld B z to provide radialcon�nem ent,and elec-

trostatic wells to provide axialcon�nem ent. Penning-

M alm berg trapscon�neonly charged particlesand,con-

sequently,do notcon�ne neutralH atom s.

The current generation ofexperim ents [4,5]aim s to

trap H atom sasthisislikely necessary forprecision CPT

and gravity tests. NeutralH atom s have a sm allper-

m anent m agnetic m om ent, and can be trapped in the

m agnetic m inim um ofa so-called M inim um -B trap [6].

The m agnetic m inim um can be created by two axially

separated m irror coils which create an axialm inim um ,

and a m ultipole �eld,such as an octupole [7,8],which

createsthe radialm inim um . In allcurrentschem es,the

M inim um -B and Penning-M alm berg traps m ust be co-

located becausethep’s,e+ ’s,and Hsm ustallbetrapped

in the sam e spatialregion. Thus,in cylindricalcoordi-

nates(r;�;z),the netm agnetic�eld willbe

B = B zẑ+ B w

�r

R w

� 3 h

r̂cos(4�)� �̂sin(4�)i

+ B M (r;�;z)

(1)

when using an octupole.HereR w isthetrap wallradius,

B w isthe octupole �eld atthe wall,and B M (r;z)isthe

�eld ofthe m irror coils. The m irror coils were not en-

ergized forthe data taken forthispaper;henceforth we

willsetB M = 0.

M inim um -B traps are shallow (oforder 0.7K /T per

Bohr m agneton), and experim entalists have not yet

learned to synthesize H with su�ciently low energy to

be trapped. O ne obstacle to progresshasbeen the lack

ofdetailed inform ationaboutthep cloud[10]dim ensions.

Untilrecently,onlytwotechniquesthatm easurethep ra-

dialpro�lehavebeen reported in detail.The�rst,based

on p annihilation on the background gas [11],yields a

crude [� 4m m (1�)]three-dim ensionalim age ofthe pcloud. To observe a su�cient num ber ofannihilations,

the background gaspressure m ustbe m uch higherthan

isnorm ally used when synthesizing antihydrogen atom s.

This m ay inuence the p cloud dim ensions. The sec-

ond interpolatesthe density pro�lefrom two destructive

m easurem ents[12]:the totalp num ber,and thenum ber

thatarelocated within a �xed radiussetby an aperture.

The reconstruction m akesassum ptionsaboutthe appli-

cability ofthe globaltherm alequilibrium state ofthese

plasm as[13,14],and aboutthep tem perature.W enote

that with our diagnostics (reported here and in [9]) we

haveseen m any long-lived radialpro�lesthatarenotin

globaltherm alequilibrium .

Recently we described a diagnostic that gives high

quality inform ation about the radialpro�le. The diag-

http://arxiv.org/abs/0807.0074v1

2

p catching mixing e+ recapture

main solenoid

(length indication)

inner solenoid

faraday cup/

final degrader

left mirror

octupole

right mirror helium volume

cryostatdetectors

0.00.51.01.52.02.53.0

-600 -400 -200 0 200 400 600 800 1000

Axial Position [mm]

Axia

l fie

ld [ T

]

p

e+/e-

FIG .1: (Color online) Schem atic diagram ofthe ALPHA apparatus. Particles are con�ned axially in an electrostatic well

form ed by biasing cryogenically-cooled, cylindricalelectrodes centered on the trap axis. The axialm agnetic �eld,graphed

below theschem atic,con�nesthe particlesradially.The p’swere caughtwith theinnersolenoid on,in a �eld of3T,asshown

by the blue dashed curve.The innersolenoid wasram ped o� before transferofthe p’sto the m ixing region.The experim ents

described here were done in the � 1T �eld shown by the red solid curve. The M CP/Phosphorscreen used to take im ages[9]ofthe innerregionsofthe e

�plasm asand p cloudsislocated to the rightofthe partsofthe apparatusshown here,in a �eld

of0.024T.

nosticisbased on aM CP-phosphorscreen system [9].(A

sim ilarsystem hasalso been reported by theASACUSA

collaboration [15].) Unfortunately, apertures lim it the

size ofthe p cloud thatwe can m easure with ourM CP-

phosphorsystem ;typically wecannotm easurethepro�le

beyond radiiof1:5{3:0m m ,depending on thelocalm ag-

netic �eld in which the p’sare trapped. Som e p clouds

arecom pletely im aged by thissystem ,butothersarefar

larger,and can extend alltheway outto thewallsofour

trap atradiusR w = 22:3m m . Here,using the ALPHA

collaboration trap [4],wedescribea new diagnosticthat

probestheouterradialpro�lebased on m easurem entsof

ballistic [16]lossesinduced by an octupole m agnet. Af-

tera briefdescription ofhow we load particlesinto the

trap,we describe the diagnostic. Then we discusstests

used to validate itsperform ance,and close with several

exam plesillustrating itsuse.

II. T R A P LO A D IN G C Y C LE

W e load ourtrap by accepting a pulse ofp’sfrom the

AD.Thep’sentertheapparatusfrom theleft(seeFig.1),

and are slowed in a degrading foil. They reectfrom a

repellingpotentialatthefarend ofthe\catching"region

ofthe trap,and are then captured into an electrostatic

wellby quickly erecting an electrostatic barrier,at the

nearend ofthe trap,before they can escapeback to the

degrading foil. The p’s are cooled by collisions with a

pre-existing electron (e� )plasm a [17].M ultiple p pulses

can be caughtand cooled,each adding about40,000 p’s

to the trap. Typically we use foursuch \stacks" in the

data presented here. The e� plasm a is then ejected by

fastm anipulationsoftheelectrostaticwellthatleavethe

m assive p’s behind. After cooling and e� ejection,the

p’saretransferred,via m anipulationsoftheelectrostatic

wellpotentials,to the \m ixing" region ofthe trap. The

octupolem agnet[8]weusetodeterm inethep radialpro-

�leiscentered overthisregion.Positrons,when needed,

are transferred from our Positron Accum ulator [18,19]

and recapturedin theregionindicated in Fig.1.Theyare

then transferred to the m ixing region via m anipulations

ofthe electrostaticwellpotentials.

III. D IA G N O ST IC D ESC R IP T IO N

To understand how the radialdiagnostic works,it is

helpfulto visualize the �eld linesfrom the solenoid and

octupole coils. The �eld lines originating from a cir-

cular locus ofpoints in the plane transverse to ẑ form

four-uted cylindricalsurfaces;theutesateach end are

rotated by 45� with respect to each other. An exam -

ple ofthe resulting surfaces is shown in Fig.2. Fig.3

showsan im ageofonequadrantofthe �eld lines,gener-

ated by passing e� ’sthrough the octupole and onto our

3

FIG .2: (Color online)M agnetic �eld from the octupole and

solenoid coils.Thevectorson theleftrepresentthedirections

ofthe axially-invariant �eld from these coils. The surface is

created by following the �eld lines from a radially centered

circular locus; the lines shown within the surface are �eld

lines.

M CP/Phosphorscreen [9].

Antiprotons con�ned by the electrostatic wellwithin

the octupole bounce back and forth while following the

m agnetic �eld lines [20]. Antiprotons that are on �eld

linesthatextend to the physicaltrap wallbefore reach-

ing one ofthe electrostatic walls willfollow them there

and annihilate. For a given end-to-end bounce length

L,�eld lines lying outside ofa criticalradius rc at the

trap centerwillhitthe wall,while thoselying inside the

criticalradiuswillnot.The norm alized criticalradiusis

[21,22]:

rc

R w=

1q

1+ B wB z

L

R w

: (2)

Thisrelation isdepicted in Fig.4. The longerthe trap,

and the strongerthe octupole �eld,the sm allerthe crit-

icalradius. The norm alized criticalradiusisneververy

sm allbecause the octupole �eld,which scalesasr3=R 3w,

isvery weak nearthetrap axisrelativeto itsstrength at

the wall. Thisisadvantageousforcon�nem ent[7],asa

large cloud survivesand the innercore ofthe p cloud is

notstrongly perturbed by the m ultipole �eld. However,

FIG .3: (Color online) Field lines im aged by passing a cir-

cular e�plasm a through the octupole with the octupole o�

and on. Apertures [9]form the im age boundaries and lim it

us to viewing only one quadrant ofthe octupole �eld m ap.

The distortion evident in the right-hand im age corresponds

to one ofthe utesatthe end ofthe m agnetic surface shown

in Fig.2.

FIG .4:(Coloronline)Thenorm alized criticalradius[Eq.(2)]

asa function oftheoctupolestrength B w and orbitlength L.

The alternate axes shown at the top isolate the dependence

on each param eterwhile holding the other�xed ata typical

value.

as we show below,it lim its the observable m inim um p

radiusto about7m m fora 135m m long well.Ifwe had

used a quadrupoleinstead ofan octupole,wecould have

m easured radialdistributionsto m uch sm allerradii;for

instance,to 0.24m m forequivalentparam eters. Such a

sm allcriticalradiuswould bevery usefulasa diagnostic,

butcould m akeitdi�cultto synthesizeH.

Theballisticlossofparticleson trap wallsin thepres-

ence ofa m ultipole �eld was �rst identi�ed with elec-

tronsin a quadrupolem agnet[16].Thisprocessiseasier

to study with p’sthan with e� ’s,however,becauseindi-

vidualp annihilations can be detected and localized on

the trap wallwith a position sensitivedetector.Thede-

tector[23]com prisesthree layersofsilicon cylindrically

arrayed around thetrap axisjustoutsideoftheoctupole

m agnet (see Fig.1). It is not yet fully deployed,but,

using a partialsystem consisting of10% ofthe fullsys-

tem ,weobserve(Fig.5)thatp’shitthewallattheends

ofthe electrostatic well.W e expectto observethistype

ofloss pattern as it is at the ends ofthe trap that the

accessible �eld lines extend furthest outward;we note,

however,thatannihilationstend to occuratthe endsof

the electrostatic welleven in the absence ofan octupole

�eld [11].

For the experim ents reported in Fig.6{13,annihila-

tionsweredetected by scintillatorscoupled to Avalanche

Photo Diodes(APDs).Aswith the silicon detector,the

scintillatorsarecylindricallyarrayedaroundthetrap axis

just outside ofthe octupole m agnet. Annihilations are

identi�ed by the �ring ofm orethan onescintillatorin a

4

FIG .5: (Color online) Axialpositions where the p’s hit the

trap wallunderthe inuenceoftheoctupole.The horizontal

barindicatesthe theaxialextentand position ofthe electro-

staticwellcon�ningthep’s.Thelossisgreatestneartheends

ofthe con�ning electrostatic well. The positions are deter-

m ined by aposition-sensitiveparticledetectorwhich m onitors

thep annihilation products;theverticallinesatz = � 115m mindicate the axialextentand position ofthe detector.

150ns coincidence window,and we detect annihilations

with greater than 50% e�ciency. The detector back-

ground noiseisofordera few eventspersecond.Tim ing

m odulescorrelateannihilationswith experim entalopera-

tionsand conditionssuch asthestrength oftheoctupole

�eld.

To m easure the size ofa p cloud,we �rst transfer it

into an electrostaticwellin theoctupole�eld region;the

octupole �eld isturned o� during the transfer.W e then

m easure the p kinetic energy by m onitoring the rate at

which the p’s escape as we slowly lower one endwallof

theelectrostaticwell[24].Typically we�nd thattheen-

ergy isbetween 1 and 15eV;the energy dependson the

detailsofthe transferprocessand the electrostatic well

potentials. This m easurem ent is destructive,but since

theenergy islargely setby theelectrostatics,notby the

p radialpro�le, it is su�cient to m easure this energy

once fora seriesofpro�le m easurem ents. From thisen-

ergy,wedeterm inethebouncelength L ofthep’sin the

electrostaticwell.Theuncertainty (and spread)ofthep

energy sets the uncertainty in the orbit lengths quoted

in the �gure captions. Finally,foreach p cloud thatwe

want to analyze,we slowly ram p up the octupole �eld

B w while m onitoring the losses. From the tim e history

ofthe losses,we can invert Eq.(2) to reconstruct the

radialdistribution ofp’s:

n(rc[B w (t)])=N (t)

2�rc[B w (t)]drc

dB w

dB w

dt�t

: (3)

HereB w (t)istheoctupole�eld attim et,rc[B w (t)]isthe

instantaneous criticalradius,and drc=dB w is evaluated

at the instantaneous �eld B w . The raw data from our

detectorisbinned in intervalsoftim e�t0 = 1m s;were-

bin the data into intervalsranging between �t= 0:333s

(45sand shorteroctupoleram p tim es)and 1.332s(180s

ram p tim es)to decreasethescatter.N (t)isthenum ber

ofcountsin thebin centered around t.Them apping de-

�ned by Eqs.(2) and (3)is nonlinear;points are closer

together in r at sm allradiithan at large. To further

reduce the scatter at sm allr we rebin n(r) so that the

spacing between successivepointsin r isneverlessthan

0.075m m .

IV . VA LID A T IO N T EST S

Typical data are displayed in Fig. 6, which shows

the radialpro�le oftwo otherwise identically prepared

p clouds stored in wells ofdi�erent length. Changing

the welllength should not change the radialpro�le of

identically prepared p clouds,and asexpected,them ea-

sured pro�les are alm ost identical over their com m on

range. However,as predicted by Eq.(2),changing the

welllength doeschange the m inim um radiusobservable

with the diagnostic from about 7.0m m for the 135m m

well,to 9.6m m forthe 65m m well.

Figure7com parestheradialpro�lesofidentically pre-

pared p clouds held in a at-bottom ed well, and in a

nested wellsim ilarto thoseused to synthesizeH [1].The

welllength inferred from the m easured p energies was

130m m forthenested well,which isslightly shorterthan

the135m m length inferredfortheatwell.Changingthe

wellshape should not change the radialpro�le because

theazim uthally-sym m etricelectrostaticwell�eldsdonot

induceradialtransport.Asexpected,them easured pro-

�lesare nearly identical. Thus,the diagnostic isindeed

independentofthe wellshapeso long asthe properwell

length isem ployed in the analysis.

As the octupole ram ps,outward di�usion [16,25]in-

creasesforthose p’sthatare stillwithin the criticalra-

dius;ifthisdi�usion weretoo fast,thepro�leswould be

suspect. W e have established that the di�usion is not

faston the tim e scale ofthe octupole ram p by com par-

ing (Fig.8) the radialpro�les ofidentically prepared p

cloudstaken with ram psof45 (ourstandard ram p),90,

and 180s. The di�erences between the curves are not

large.

Thediagnosticdescribed herewould havelittle utility

ifallreconstructed radialpro�leswereidentical;Figure9

showsthatradialpro�lesofp cloudsthataredi�erently

prepared can bedissim ilar.Figure9 also showsthatthe

load-to-loadreproducibilityofthep pro�lesisquitegood.

M easurem ents taken with our M CP/phosphor screen

diagnostic con�rm that the centraldensity is not sig-

ni�cantly perturbed by cycling the octupole �eld. For

instance,forparam etersidenticalto thenested wellpro-

�le shown in Fig.7,the totalnum ber ofp’s within the

M CP/phosphoraperturesvaried by lessthan 4% on two

successiveshots,one with the octupole o� and one with

itram ped up and then back down. This discrepancy is

5

FIG .6: (Color online) Com parison ofthe radialpro�les of

otherwise identicalp clouds held in wells ofdi�erentlength.

Panela) shows the electrostatic wellpotentials �(z) for the

two cases;the horizontalbars indicate the axialextent and

position ofthep orbitsbeforetheapplication oftheoctupole

�eld.Panelb)showsthetim ehistory ofthep annihilationsas

theoctupole �eld isram ped up.Panelc)showsthe resulting

radialpro�les.In allgraphs,thegreen solid curvecorresponds

to the longer well(135� 5m m ) and the red dash curve cor-respondsto the shorterwell(65� 5m m ).The m axim um B wat the end ofthe 45s ram p was 1.54T,and B z = 1:03 T.

At the inner radii,Eq.(2) predicts that the � 5m m lengthuncertainty/spread engenders a radialuncertainty ofabout

� 0:12m m at 135m m , and � 0:30m m at 65m m . Near thewall,theuncertainty predicted by Eq.(2)dim inishes,butthe

tim e binning engenders an uncertainty ofabout � 0:25m m .The errorbarsindicate the size ofthe typicalcalculated sta-

tisticalerror.Both p cloudswere collected with fourstacks.

wellwithin the shot-to-shotvariation ofourloads.This

result,taken togetherwith the resultsshown in Figs.6{

8,establish that ram ping the octupole �eld is a robust

m ethod ofobtainingtheradialpro�lethatislargelyinde-

pendentofthedetailsoftheram p speed and wellshape.

V . O B SERVA T IO N S

W ehaveused ournew diagnosticto characterizeourp

m anipulation sequences,and to study interesting physics

issues.In thissection,we outline fourofthese m easure-

m ents;allneed furtherstudy.

As described earlier,we can stack m ultiple p pulses

from the AD. Figure 10 shows the p pro�le for two,

three, and four stacks. The stacks add to each other

withoutsigni�cantly changing theradialpro�le.There-

FIG .7: (Color online) Com parison ofthe radialpro�les ob-

tained with at(green solid)and nested wellpotentials(red

dash).Thewelllengthswere 135� 5 and 130� 5m m respec-tively. The graph descriptions and allother param eters are

the sam e asin Fig.6.

FIG .8:(Coloronline)Com parison oftheradialpro�leswith

octupole ram ps of45 (green solid),90 (red short-dash),and

180s(bluelong-dash).Thewelllength in each casewas130�5m m . The graph descriptions and allother param eters are

the sam e asin Fig.6.

6

FIG .9:(Coloronline)Radialpro�lesfortwo setsofp clouds

thatwereprepared di�erently;thee� coolingplasm asused for

the two setscam e from di�erente� sources. The �gure also

shows that the load-to-load reproducibility of the p clouds

is high;the set labeled I com pares two loads,while the set

labeled IIcom paresthree.TheAD and ourapparatuscan be

quitereproducible;thetwo pro�lesin setIwerem easured 23

hoursaparton di�erentAD shifts.(Notethatthecloudswere

analyzed in di�erentshapewells,one(I)oflength 135� 5m min a at well,and the other (II) oflength 130 � 5m m in anested well.Theram p tim eforsetIIwasslightly shorterthan

for set I:36s instead of45s. However,as veri�ed in Figs.7

and 8,these di�erence should not a�ect the radialanalysis.

Finally,only twostackswereused in setII;thepro�lesforthis

set were norm alized to four stacks.) The graph descriptions

and allotherparam etersare the sam e asin Fig.6.

sults obtained when only one stack is accum ulated are

quite di�erent,however. The pro�le is com pletely con-

tained within a radius of7m m and is not visible with

thisdiagnostic.W e suspectthatthe di�erence isdue to

straggler e� ’s from the degrader accidentally captured

during the �rst (and subsequent) p injections. These

e� ’sarecaptured by thesam eelectrostaticwellm anipu-

lationsused to capturethe p’s.Aftercapture,they cool

and therm alizeviacyclotron radiation and collisions,and

join thedeliberately captured cooling e� plasm a;weob-

serve that the num ber ofe� ’s in this plasm a increases

with the num berofstacks.The stragglere� ’sare likely

em itted from thedegraderovertheentireareahitby the

p’s,and,ifthe radiusofthisarea isgreaterthan the ra-

dius ofthe deliberately injected e� plasm a,the plasm a

radius willincrease. This willincrease the size ofthe

captured p cloud [9].Itwillalso increasethe fraction of

the degraded p’s captured [9];we observe this fraction

increasing from about45% on the�rststack to over90%

FIG .10:(Coloronline)Com parison ofthe radialpro�lesfor

two (blue long-dash),three (red short-dash),and four(green

solid) stacks. The welllength was 130 � 5m m . The graphdescriptionsand allotherparam etersarethesam easin Fig.6.

on laterstacks.

The transfer process from the catching region ofour

trap to the m ixing region leaves the p’s situated in a

short wellon one side ofthe �naltrapping well. From

this short well,the p’s are injected into the �nalwell.

Norm ally,wedothisgradually,bysm oothlychangingthe

potentialsovera 1m stim eperiod.W hen wechangethe

potentialsabruptly,onatim escaleofapproxim ately3�s,

p’sareloston injection,and thep cloud’sradiusincreases

signi�cantly,as shown in Fig.11. There is no obvious

m echanism forthe im m ediate lossand cloud expansion.

Figure 12 shows the very di�erent radialpro�le ob-

tained when wedo notejectthee� ’sbeforetransferand

analysis. The antiprotons form a hollow ring around

the trap center. This type ofdistribution is com pati-

ble with the globaltherm alequilibrium ofa m ixed e� -p

plasm a,which places the p’s in a halo surrounding the

e� plasm a [26]when the particles are su�ciently cold.

However,we observed lossesduring the transferprocess

that could have preferentially hollowed the distribution

and produced theobserved pro�le.

Notethatthep’slikely coolviacollisionswith thee� ’s

during the octupole ram p.Thiswould shorten the axial

extent ofthe p orbits,and thus introduce som e uncer-

tainty into the reconstruction ofthe radialpro�les via

Eq.(3)asitintroducesvariation in L. Thisis particu-

larly true ifthe p’scoolinto the side wells,where their

orbitlength would decreaseabruptly by m orethan a fac-

tor oftwo. This e�ect would cause us to erroneously

reconstruct,via Eq.(3),som echargeto beatfalsely low

7

FIG .11:(Coloronline)Com parison oftheradialpro�lesob-

tained with agentle(green,solid)and abrupt(red short-dash)

injection into a long well. The blue dash curve in Panela)

shows the pre-injection wellstructure (the p’s start in the

leftm ostwell)and the green solid curve showsthe �nalwell,

which hasa length 135� 5m m . The graph descriptions andallotherparam etersare the sam e asin Fig.6.

radii,probably below the 7m m radiusvisible to uswith

thisdiagnostic. Thus,cooling doesnotexplain the halo

visible in Fig.12.Thisvery interesting resultneedsfur-

therstudy.

Finally,in Fig.13,weshow radialpro�lesfora m ixed

e+ -p plasm a. As the density of the e+ plasm a is in-

creased,p’sappearto be transported outward.Here,as

described in the previous paragraph,the interpretation

oftheresultsiscom plicated by cooling ofthep’s(on the

e+ in thiscase.) Cooling willagain causesom echargeto

appearatfalsely low radii,and thisvery likely causesus

to underestim ate the outward m ovem entofthe p’s.

A possible explanation of the outward m ovem ent

shown in Fig.13 is that it is the result ofthe form a-

tion ofhighly excited H thatis either 1)ionized atthe

radialedgeofthee+ plasm a by itsselfconsistentelectric

�eld,which isstrongestattheedge,or2)ionized by the

vacuum electrostaticwell�elds.Notethatthep’sfrom H

thatwasionized within thee+ plasm a radiuswould have

the opportunity to recom bine into H again,while those

atlargerradiiwould orbitunperturbed.W ith tim e,the

p’s rem aining in the e+ plasm a would be swept out to

largerradii.Unpublished sim ulationsofrealisticantihy-

drogen form ation/�eld ionization cycles,using the code

described in [27],found sim ilartransport.W edo notyet

haveany otherdirectexperim entalevidencethatthiscy-

cling isoccurring.

FIG .12:(Coloronline)Com parison oftheradialpro�leswith

and without electrons (dashed red and solid green lines,re-

spectively. The welllength was 130 � 5m m ,and the ram ptim e was180� 5s.The graph descriptionsand allotherpa-ram etersare the sam e asin Fig.6.

V I. C O N C LU SIO N S

W e have shown that we can determ ine the outer ra-

dialpro�leofp’sstored in a Penning-M alm berg trap by

m onitoring the losses induced by ram ping an octupole

m agnet. This technique com plem ents direct im aging of

theinnerradialpro�le[9],and providesm orepreciseand

reliable inform ation than earliertechniques[11,12].W e

have tested the diagnostic by varying the electrostatic

welllength and shape,and by varying the ram p tim e,

and we have used the diagnostic to study severalpro-

ceduresand m anipulationspertinentto the synthesisof

antihydrogen atom s.

This work was supported by CNPq,FINEP (Brazil),

ISF (Israel),M EXT (Japan),FNU (Denm ark),NSERC,

NRC/TRIUM F (Canada),DO E (USA),EPSRC and the

Leverhulm eTrust(UK )and HELEN/ALFA-EC.

[1]M . Am oretti, C. Am sler, G . Bonom i, A. Bouchta,

P.Bowe,C.Carraro,C.L.Cesar,M .Charlton,M .J.T.

Collier,M .D oser,etal.,Nature 419,456 (2002).

[2]G .G abrielse,N.S.Bowden,P.O xley,A.Speck,C.H.

8

FIG .13: (Color online) Com parison ofthe p radialpro�le

with di�erent density positron plasm as. The green, solid

curve shows the pro�le with no e+

,and the red short-dash

and bluelong-dash curvesshow thepro�lewith 13m illion and

25m illion e+

respectively.Thewelllength was85� 5m m ,them axim um �eld was1.20T,and theram p tim ewas20s.O nly

one stack was captured,butthe e� cooling plasm a was cre-

ated by a secondary e� source which m akes a large radius

plasm a;thus,unlike in Fig.10,p’sare visible with only one

stack. The graph descriptions and allother param eters are

the sam e asin Fig.6.

Storry,J.N.Tan,M .W essels,D .G rzonka,W .O elert,

G .Schepers,etal.,Phys.Rev.Lett.89,213401 (2002).

[3]S.M aury,Hyper�neInteractions109,43 (1997).

[4]G . Andresen, W . Bertsche, A. Boston, P. D . Bowe,

C. L. Cesar, S. Chapm an, M . Charlton, M . Chartier,

A.D eutsch,J.Fajans,etal.,Phys.Rev.Lett.98,023402

(2007).

[5]G .G abrielse,P.Larochelle,D .L.Sage,B.Levitt,W .S.

K oltham m er,I.K uljanishvili,R.M cConnell,J.W rubel,

F.M .Esser, H.G luckler, et al., Phys.Rev.Lett.98,

113002 (2007).

[6]D .E.Pritchard,Phys.Rev.Lett.51,1336 (1983).

[7]J.Fajansand A.Schm idt,Nucl.Instr.M eth.Phys.Res.

A 521,318 (2004).

[8]W .Bertsche,A.Boston,P.Bowe,C.Cesar,S.Chapm an,

M .Charlton,M .Chartier,A.D eutsch,J.Fajans,M .Fu-

jiwara,etal.,Nucl.Instr.M eth.Phys.Res.A 566,746

(2006).

[9]G . Andresen, W . Bertsche, P. D . Bowe, C. C. Bray,

E.Butler,C.L.Cesar,S.Chapm an,M .Charlton,J.Fa-

jans, M . Fujiwara, et al., Com pression of antiproton

cloudsforantihydrogen trapping,in review atPhys.Rev.

Lett.

[10]D ependingon thep density and tem perature,thep cloud

m ay be in the single particle regim e,the plasm a regim e,

or in between the two. W e will refer to it as a cloud

throughoutthispaper.

[11]M .C.Fujiwara,M .Am oretti,G .Bonom i,A.Bouchta,

P. D . Bowe, C. Carraro, C. L. Cesar, M . Charlton,

M .D oser,V.Filippini,etal.,Phys.Rev.Lett.92,65005

(2004).

[12]P. O xley, N.S.Bowden, R. Parrott, A.Speck, C. H.

Storry,J.N.Tan,M .W essels,G .G abrielse,D .G rzonka,

W .O elert,etal.,Phys.Lett.B 595,60 (2004).

[13]T.M .O ’Neiland C.F.D riscoll,Phys.Fluids 22,266

(1979).

[14]C.F.D riscoll,J.H.M alm berg,and K .S.Fine,Phys.

Rev.Lett.60,1290 (1988).

[15]Y.Yam azaki,Hyper�neInteractions138,141 (2001).

[16]J.Fajans,W .Bertsche,K .Burke,S.F.Chapm an,and

D .P.van derW erf,Phys.Rev.Lett.95,155001 (2005).

[17]G . G abrielse, X. Fei, L. A. O rozco, R. L. Tjoelker,

J.Haas, H.K alinowsky, T.A.Trainor, and W .K ells,

Phys.Rev.Lett.63,1360 (1989).

[18]T.M urphy and C.Surko,Phys.Rev.A 46,5696 (1992).

[19]L.J�rgensen,M .Collier,K .Fine,T.W atson,D .van der

W erf,and M .Charlton,M at.Sci.Forum 363-365,634

(2001).

[20]Since the m agnetic �eld is strong (> 1T),the p’s are,

apart from a slow E � B rotation around the trap axis,tightly bound to the �eld lines.

[21]J. Fajans, W . Bertsche, K . Burke, A. D eutsch, S. F.

Chapm an,K .G om bero�,D .P.van der W erf,and J.S.

W urtele,in Non-NeutralPlasm a Physics VI:W orkshop

on Non-NeutralPlasm as,edited by M .D rewsen,U.Ug-

gerh�j,and H.K nudsen (AIP,M elville,N.Y.,2006),vol.

862,p.176.

[22]J.Fajans,N.M adsen,and F.Robicheaux,Criticalloss

radius in a Penning trap subjectto m ultipole �elds,sub-

m itted to Phys.Plasm as.

[23]M .Fujiwara,in Physicswith ultra slow antiproton beam s,

edited by Y.Yam azakiand M .W ada(AIP,W ako,Japan,

2005),vol.793,p.111.

[24]M .Am oretti,C.Am sler,G .Bonom i,A.Bouchta,P.D .

Bowe,C.Canali,C.Carraro,C.L.Cesar,M .Charlton,

M .D oser,etal.,Phys.Lett.B 590,133 (2004).

[25]E. G ilson and J.Fajans, Phys.Rev.Lett.90, 015001

(2003).

[26]T.M .O ’Neil,Phys.Flu.24,1447 (1981).

[27]F.Robicheaux,Phys.Rev.A 70,022510 (2004).