The injection kicker system for the muon g-2 experiment

Abstract

The muon g-2 experiment is designed to measure the anomalous
magnetic moment of the muon to an accuracy of 0.35 ppm by measuring the
difference between the spin precession frequency and the cyclotron
frequency of the particle in a known magnetic field. The injection
kicker is designed to deflect 3.094 GeV/c muons by an angle of 10 mrad
into a storage ring with a radius of 7.112 m. No magnetic materials can
be used in or near the beam line because of the high precision with
which the field of the main dipole magnets must be known. Eddy currents
induced in the vacuum chamber by the fast kicker pulse, and their effect
on the main dipole field must also be considered. An air core magnet
which is driven by an underdamped capacitor discharge modulator using a
spark gap switch has been designed. This design, as well as test data,
will be presented

Full text

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THE INJECTION KICKER SYSTEM FOR THE MUON G-2 EXPERIMENT1
G.C. Pappas, E.B. Forsyth, Brookhaven National Laboratory, Upton, New York 11973 USA
W. Feng, Nanjing University, Nanjing, China 210008

1 Work performed under the auspices of the U.S.D.O.E.
Abstract
The muon g-2 experiment is designed to measure the
anomalous magnetic moment of the muon to an accuracy
of 0.35 ppm by measuring the difference between the spin
precession frequency and the cyclotron frequency of the
particle in a known magnetic field. The injection kicker is
designed to deflect 3.094 GeV/c muons by an angle of 10
mrad into a storage ring with a radius of 7.112 m. No
magnetic materials can be used in or near the beam line
because of the high precision with which the field of the
main dipole magnets must be known. Eddy currents induced
in the vacuum chamber by the fast kicker pulse, and their
effect on the main dipole field must also be considered. An
air core magnet which is driven by an underdamped
capacitor discharge modulator using a spark gap switch has
been designed. This design, as well as test data, will be
presented.
I. INTRODUCTION
The muon g-2 experiment utilizes a superconducting
storage ring of 7.112 m diameter. The injection kicker
magnet is required to deflect muons of momentum 3.094
GeV/c by an angle of 10 mrad. The kicker system including
the power modulator, charging power supply, magnet, beam
chamber, and main ring dipole magnet are shown in Figure
1. The kicker system consist of three one m long air core
magnet with an aperture of 80 mm vertical by 100 mm
horizontal. A crossectional view of this magnet is shown in
Figure 2. This magnet is driven by an underdamped
capacitor discharge circuit with peak amplitude of 6500 A,
and resonant frequency of approximately 11 Mrad/s. The
power modulator switch is a 100 kV spark gap. The entire
discharge circuit is in a coaxial housing, and is shown in
Figure 3.
Several unique restrictions which apply to this kicker
system are the result of the kicker magnet being inside of
the main ring dipole magnet beam pipe. No magnetic
materials can be used in or near the beam pipe because of
the high precision which the dipole field must be known.
The high vacuum, and radiation, in the beam pipe limits
the use of plastics for electrical insulators, and mechanical
supports. Both the charging waveform, and discharge pulse
must be carefully analyzed to insure that any eddy current
fields induced in the beam vacuum chamber quickly decay
[1].
II. THE KICKER MAGNET
Three different types of kicker systems
investigated to meet the above requirements. They were, an
electrostatic kicker, a transmission line kicker and a
magnetic kicker. The basic pulsed power parameters for
each of these types of kickers are, ±400 kV pulse for the
electrostatic kicker, ±200 kV and 4000 A pulse for the
transmission line kicker, and < 100 kV and 6000A pulse for
the magnetic kicker. Placement of the kicker magnet in the
main magnet beam chamber has serious consequences for
each of these types of kickers. The limited space inside the
chamber precludes the electrostatic and transmission line
types of kickers due to electric field stresses. The magnetic
kicker induces eddy currents in the vacuum chamber which
must not contribute to the main dipole field by more than
0.1 ppm, or 21 mG. Thus, considerable effort was taken to
study the effects of eddy currents in the beam chamber
where
Figure 1. G-2 experiment main dipole magnet,
vacuum vessel, kicker magnet and modulator.
The magnet for the g-2 muon storage ring injection
kicker consists of two titanium strips of 80 mm height
separated by 100 mm. The kicker system uses three
magnets of 1 meter length each. The transient eddy current
analysis code OPERA 2D/TR was used to investigate field
distribution, eddy currents, magnetic gain, energy losses
and inductance for this magnet. The drive current for the
magnet was assumed to be a damped sinusoid,
ii e
o
=
because of the simplicity of producing such a waveform for
an inductive load. The length of the vacuum chamber, l, is
much longer than either the width w or the height h, which
in turn are each much larger than the thickness d of the
chamber walls. Thus, it is possible to consider the two
dimensional field
( )=
t
t
−α
ω
sin
HtHwt
oo
t
−∝sin .
1927
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Figure 2. Kicker magnet and vacuum Figum vessel,
with field mapping NMR probe shown.
Since the displacement currents can be ignored,
Maxwell's equations reduce to
µδ
δ
δ
δ
x
δ
δ
σ
E
x
H
H
t
E
z
y
y
= −
=
2 ,
and the diffusion equations are
δ
δ
δ
δ
x
where µ=µoµr , and σ is the conductivity. The eddy currents
in the vacuum chamber walls have been investigated for
this type of driving waveform using an iterative approach
and solving the diffusion equations.
σµδ
δ
H
σµδ
δ
E
x
E
t
H
2
t
z
2
z
yy
2
=
=
,
The conclusions drawn from this analysis are:
1. The vacuum chamber material should have a µr=1, low
conductivity and be as thin as possible for the eddy
current fields to decay quickly.
2. Decreasing the thickness improves the decay of the
steady state eddy current.
3. Increasing α improves the decay of the steady eddy
current, but also requires more drive current because of
the reduction of the kicker field. To gain a compromise
between the eddy current residual field the kicker
magnet field, and the current pulse width, ω should be
increased with α.
Figure 3. Power modulator, high voltage feedthroughs,
and charging supply.
Computer simulation wiring PE2DITR and OPRA2OITR
were used to show that appropriate choice of dimensions,
shapes, and materials for the vacuum chamber, and driving
waveform could result in the residual eddy current field
contributing less than 1 in 107 to the main dipole field at
the start of the measurement period. This analysis was
performed with several different waveshapes, and it was
found that both undershoot of the pulse and parasitic
oscillations helped to reduce the effects of induced eddy
currents. In particular, the eddy current field induced by an
underdamped current pulse with an 80 ns rise time and high
frequency parasitic oscillation decays to 12 mG after 10 µs.
Other kicker magnet parameters calculated were an
inductance of 0.21 µH/m, magnetic gain of 0.025 G/A, and
a field uniformity of ∆B/B(0,0)=25 %.
III. THE POWER MODULATOR
The pulsed power modulator to drive the above magnet
is the underdamped capacitor discharge circuit shown
schematically in Figure 4. The spark gap used is a Maxwell
Laboratories model 40264 gap, triggered with a Maxwell
Laboratories model 40168 trigger unit. The charging supply
is a command resonant supply which uses the leakage
inductance of the 85:1 step up transformer to charge the 10
nF discharge capacitor. A charge current pulse for the
charging system is shown in Figure 5. Because the charge
current flows through the magnet, eddy currents induced by
this pulse where also analyzed. Their contribution to the
main dipole field was not significant however, because of
the relatively low frequency, amplitude and long decay
time for the pulse.
Figure 4. Schematic of power modulator and charging
supply
Figure 5. Charging current, time base is 50µs/div,
amplitude is 50 A/div.
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A typical discharge pulse is shown in Figure 6. One of
the main concerns about the discharge circuit was the
choice of a switch to use. The primary objective was to
minimize circuit inductance. Thyratons were considered,
but a tube to block up to 100 kV would be a three gap tube,
and tube inductance would be on the order of several
hundred nano Henries. Multigap
problematic because of the capacitive coupling between
gaps as they break down. The tight eddy current
requirements discussed above could be exceeded by gap
coupled prepulses. Spark gap switches have inductance of
less than 50 nH in one gap up to 100 kV, but suffer from
high jitter and short life. The lifetime for the
experiment is not critical, however the jitter must be kept
to less than 5 ns. With this in mind jitter measurements
where made on the Maxwell gap and trigger unit. Figure 7
shows the gap jitter as a function of gap voltage and
pressure. Figure 8 shows the trigger generator jitter as a
function of output switch air flow and pressure.
tubes where also
G-2
Figure 6. Modulator Output Pulse. Time base is 100
ns/div, amplitude is 1000 A/div.
From this data it is clear that jitter of less than 5 ns can be
obtained by the Maxwell trigger generator and gap if proper
gas pressure and flow are maintained.
IV. CONCLUSIONS
Eddy current fields induced by the fast kicker pulse and
the slower charge pulse will decay quickly enough so as
not to distort the main dipole field for the g-2 experiment
by a factor of greater than 1 in 107. Jitter measurements
have been made on the spark gap switch and trigger unit.,
and show that the jitter requirement can be met with
Figure 7. Spark gap jitter in nano-seconds as a
function of gap voltage and pressure.
Figure 8. Trigger generator jitter in nano-seconds as a
function of pressure and flow.
careful control of the gap and trigger gap pressure and air
flow. A second gap from English Electric Valve is being
investigated. This gap offers several advantages over the
Maxwell gap, however, it has not been tested. The EEV
gap is sealed and requires no synthetic air, regulators, and
air flow controls, and is triggerable from an EEV provided
pulse transformer whose driving voltage is only several
hundred volts on the primary. A prototype modulator
magnet and vacuum vessel have been designed and are
now in fabrication. The primary area of concern now is the
insulators supporting the kicker magnet. These insulators
are now being tested for high voltage breakdown.
V. REFERENCES
[1] W.Q. Feng, and E.B. Forsyth, “Eddy Currents
Induced in a Muon Storage Ring Vacuum Chamber Due to
a Fast Kicker”, ibid.
VI. ACKNOWLEDGEMENT
The authors express their thanks to C. Pai and J. Zebuda
for their help with the design of this system, and D.
Warburton for building prototypes and taking data.
1929