6
,
D. Kawall
11
,M.Kawamura
10
, B.I.Khazin
3
, J.Kindem
9
, F.Krienen
l
, I.Kronkvist
9
, R.Larsen
2
, Y.Y.Lee
2
,
I.Logashenko
l,3
, R.McNabb
9
, W.Meng
2
, J.Mi
2
, J.P.Miller
l
, W.M.Morse
2
, D.Nikas
2
,
C.J.G.Onderwater
7
, Y.Orlov
4
, C.S.Ozben
2
, J.M.Paley
l
, C.Polly
7
, J.Pretz
11
, R.Prigl
2
, G.zuPutlitz
6
,
S.I.Redin
11
, 0.Rind
l
, B.L.Roberts
l
, N.Ryskulov
3
, S.Sedykh
7
, Y.K.Semertzidis
2
, Yu.M.Shatunov
3
,
E.P.Sichtermann
11
, E.Solodov
3
, M.Sossong
7
, A.Steinmetz
11
, L.R.Sulak
l
, C.Timmermans
9
,
A.Trofimov
l
, D.Urner
7
, P.vonWalter
6
, D.Warburton
2
, D.Winn
5
, A.Yamamoto
8
, D.Zimmerman
9


1)Department o f Physics, Boston University, Boston, MA</i>0 2215, USA
2)Brookhaven National Laboratory, Upton, NY 11973, USA
3)Budker Institute of Nuclear Physics, Novosibirsk, Russia
4)Neuman Laboratory, Cornell University ,Ithaca, NY 14853, USA
5)Fairfield University, Fairfield, CT 06430, USA
6)Physikalisches Institut der Universitat Heidelberg, 69120 Heidelberg, Germany
7)Department of Physics, University of Illinois at Urbana-Champaign, IL 61801, USA
8)KEK ,High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan
9)Department of Physics, University of Minnesota, Minneapolis, MN 55455, USA
10)Tokyo Institute of Technology, Tokyo, Japan
11)Department of Physics, Yale University, New Haven, CT 06520, USA


*

Work supported in part by US Dept of Energy, US NSF, German
Bundesminister fur Buildung unt Forschung, Russian Ministry of
Science, and US-Japan Agreement in High Energy Physics.

Abstract
A precision measurement of the anomalous g value,
a
µ
=(g<i>-</i>2)/2, for the positive muon has been made using
high intensity protons available at the Brookhaven AGS.
The result based on the 1999 data a
µ
=11659202(14)(6)x
10
10
(1.3ppm) is in good agreement with previous
measurements and has an error one third that of the
combined previous data. The current theoretical value
from the standard model is a
µ
(SM)= 11659159.6(6.7) x
10
10
(0.57 ppm) and differ by over 2.5 standard deviation
with experiment. Issues with reducing systematic errors
and enhancing the injection and storage efficiencies are
discussed.
1 INTRODUCTION
Precise muon g-2 measurements, when compared to
precise theoretical predictions of known physics, gives
insight to whether there are new physics contributions
present such as Supersymmetry or W boson substructure
to name a few. The original goal of the experiment was,
and still is, to measure the value to a precision of 0.35
parts per million (ppm) compare to previous CERN
measurement [1] of 7.3 ppm. This report is based on the
1999 data run of 1.3 ppm measurement, limited mainly
by statistics. The experiment uses the same principle as
the CERN but improved to reduce systematic errors and
to enhance the statistics.

The principle of the experiment,
previous results on earlier data, and many experimental
details have been given in earlier publications [2,3].
What we measure is the difference between muon spin
precession and cyclotron frequency
where s
and c
are the muon spin precession and
cyclotron frequencies and B is the magnetic field. In the
storage ring of uniform magnetic field, one can observe
the rotation frequency of the spin direction because the
mc
eB
c
s
a
= = Proceedings of
t
he Second Asian Particle Accelerator Conference, Beijing, China, 2001
decay positron is preferentially in the direction of the
muon spin in parity violating
µ
+

decay. By observing
positron with high enough energy to be in direction of
muon motion one can measure the rotation frequency of
the muon spin.
The muon storage ring consists of uniform magnetic
dipole guide field and focusing provided by electrostatic
quadrupoles. The quantity a
is independent of
electrostatic field at so called magic momentum of

=29.3 or p
µ
=3.094GeV/c. Therefore at this momentum
one can use electrostatic quadrupoles insteads of
magnetic gradient to focus the stored muon and avoid
corresponding uncertainty in the magnetic field
applicable to the muon population. Highly polarized
muons of 3.094 GeV/c from decay of secondary pion
beamline are injected through a superconducting
inflector [4] into a storage ring 14.2 m in diameter with
an effective circular aperture 9 cm in diameter. The
superferric storage ring[5] has a homogeneous magnetic
field of 1.45 T, which is measured by an NMR system
relative to the free proton NMR frequency [6] . A pulsed
magnetic kicker gives a 10 m-rad deflection which places
the muons into stored orbits. Positrons are detected using
24 lead/scintillating fiber electromagnetic calorimeters [7]
read out by waveform digitizers. The waveform digitizer
and NMR clocks were phase-locked to the Loran C
frequency signal. The muon of this energy has a lifetime
of 64.4
µ-sec. in the laboratory frame. And we have been
able to observe some 140 muon g-2 periods. In addition
to 375 fixed NMR probes on top and bottom of the
vacuum chamber monitoring the magnetic field
continually, the field is monitored with the travelling
NMR trolley with 17 probes inside the vacuum chamber
mapping the field distribution often while data taking.

2 STORAGE RING AND THE MAGNET

The BNL g-2 storage ring was built as a single
continuous magnet of homogeneous field of 1.45T
superferric construction (an iron magnet excited by
superconducting coils) guaranteeing azimuthal
uniformity of the field. The vertical focusing is provided
by electrostatic quadrupoles covering half the ring
circumference. The focusing lattice has four fold
symmetric structure to insure smooth batatron functions.
Size variation of the stored beam is minimal throughout
the ring as max
/

min
=1.04. The muons are stored in a
circular aperture of 9 cm diameter which is much smaller
than magnet gap to insure a good field. Two of the empty
spaces of the ring are occupied by injection inflector and
the fast injection kickers. The plan view of the ring is
shown in fig. 1. The magnet is C-shaped as dictated by
the experiment requirement that decay electrons be
observed inside the ring. The cross section of the magnet
is shown in Fig 2. The use of superconducting coils
offered the following advantages: thermal stability once
cold; relatively low power requirements; low voltage, and
hence use of a low voltage power supply; high L/R value
and hence low ripple currents; and thermal independence
of the coils and the iron. It is a goal of the experiment to
produce a magnet of about 1 ppm uniformity over the
muon storage aperture.

Fig. 1: Planview of the g-2 ring

The field, and hence its homogeneity and stability are
determined dominantly by the geometry, characteristics,
and construction tolerances of the iron.

Fig.2: Cross section view of the magnet

The NMR measurements give the additional factor of
10 improvement in knowledge of the field. The magnet is
designed as a shimmable kit. Passive iron shimming is
used to correct imperfections in the initial assembly by a
factor of two or three orders of magnitude. Iron
shimming includes adjustments to the yoke plates above
and below the magnet shown in Fig 2, insertion of iron
in the air gaps between the poles and yoke (Fig. 3), and
adjustment of edge shims on the poles. Correcting coils
on the surface of the poles permit ultimate control of
static, cyclical, and even slowly varying errors. The
surface coils can be used to correct lower multipoles to
tens of ppm, so that significant overlap shimming exists
between planned iron shimming and the surface coils.
Proceedings of
t
he Second Asian Particle Accelerator Conference, Beijing, China, 2001

Fig 3: Cross section view of magnet gap region

The air gap between each pole piece and the top and
bottom plates, respectively, of the yoke (Fig 3) serves to
decouple the storage region precision field shape from
the impact of variations within normal tolerances of yoke
piece magnetic properties and mechanical dimensions.
This decoupling of the yoke also desensitizes the impact
of major yoke perturbations, principally the large hole for
the entering beam and holes in the yoke for the coil
transfer lines. Additional steel was added adjacent to
these holes to restore the reluctance to its unperturbed
value.

Multipole(ppm)

Normal/skew

Quad -2.2(1)/2.2(1)

Sext -1.1(1)/2.5(2)

Octu -1.3(2)/1.9(2)

Decu 0.9(2)/1.0(3)




Fig 4: Two dimensional field multipole expansion of a
typical trolley measurement during 1999 data taking.
Contours are steps of 1 ppm respect to central average
field of 1.451266T. The perimeter circle indicates the
storage ring aperture.

The magnetic field B is measured and monitored by
NMR measurements of the free proton resonance
frequency p
. In addition to the 375 fixed NMR probes
mounted on the top and the bottom of the vacuum
chamber throughout the ring, seventeen NMR probes are
mounted in an array on a trolley which moves on a fixed
track inside the muon storage ring vacuum. The trolley
probes are calibrated with respect to a standard spherical
H
2
O probe to an accuracy of 0.2 ppm before and after
data-taking periods. Interpolation of the field in the
periods between trolley measurements, which are made
on average every three days, is based on the readings of
about 150 fixed NMR probes distributed