Induction Inserts at the Los Alamos PSR
K.Y. Ng
Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL 60540
Abstract. Ferrite-loaded induction tuners installed in the Los Alamos Proton Storage Ring have been successful in compensating space-charge effects. However, the resistive part of the ferrite introduces unacceptable microwave instability and severe bunch lengthening. An effective cure was found by heating the ferrite cores up to
~ 130°C. An understanding of the instability and cure is presented.
INTRODUCTION
Inductive tuners were installed into the PSR to cancel
the space charge effects of the intense proton beam at
799 MeV. Each tuner consists of a stainless steel pillbox cavity closely packed with 30 Toshiba M4C21A ferrite cores, each 1.0 in thick, 5.0 in I.D. and 8.0 in O.D.
When two tuners were installed in 1997 with the intention of two-third space-charge compensation, clear
and consistent evidence was observed, including shorter
bunch length, cleaner bunch gap, and smaller rf voltage
required for stable operation. After an upgrade when 3
tuners were installed in 1999 and the beam intensity was
raised, a longitudinal instability was observed. Figure 1
shows a chopped coasting beam accumulated for 125 jus
and stored for 500 jus recorded at a wide-band wall current monitor. The ripples at the beam profile indicate
a longitudinal microwave-like instability at 72.7 MHz,
which is roughly the resonant frequency of the pill-box
cavities housing the ferrite cores. The resonance also
showed up as ripples at the rear half of a 250 ns (left) and
100 ns bunch (middle) in Fig. 2. Apparently, the instability is tolerable for the 250 ns bunch because the bunch
shape distortion is small. However, the ~ 100 ns bunch is
totally disastrous because it was lengthened to 200 ns.
CAUSE OF INSTABILITY
To incorporate loss, the relative permeability of the ferrite can be made complex: ju —> JJL'S -\- z'juf, where the subscripts denote "series". The impedance of the ferrite is
therefore
(1)
FIGURE 1. Longitudinal microwave-like instability
recorded by wall-gap monitor of a coasting beam driven at
72.7 MHz.
FIGURE 2. Instability perturbation on profiles of bunches
with full width 250 ns (left) and 100 ns (middle). Right: Upon
heating the ferrite to 130°C (see Sec. 4), the profile of the
100 ns bunch is no longer distorted.
where L denotes the inductance of the ferrite and co
the angular frequency. It is clear that JJL'S and ju" must
be frequency-dependent. The simplest circuit model is
an inductor Lp in parallel with a resistor Rp. However,
whenever ferrite is used, like the cores packed inside a
pill-box cavity, there is an accompanying capacitor Cp in
parallel. The impedance of the inductor tune can then be
represented by
where cor is roughly where ju" peaks. If we denote ju£
as the value of \i' at low frequencies and ^ the value
of JJL" at resonant frequency cor/(2n), we readily obtain
jU^ = QlJi'L. Note that Q here is the quality factor describing the ju" peak and is not the usual industrial-quoted Q.
For a space-charge dominated beam, the actual area of
beam stability in the complex Z Ij /« -plane (or the traditional U'-V' plane), where n is the revolution harmonic,
is somewhat different from the commonly quoted KeilSchnell estimation [2]. In Fig. 3, the heart- shape solid
curve 1 is the threshold for parabolic distribution in momentum spread, where the momentum gradient is discontinuous at the ends of the spread. Instability develops and
a smooth momentum gradient will result, changing the
threshold curve to that of a distribution represented by 2.
Further smoothing of the momentum gradient at the ends
of the spread to a Gaussian distribution will change the
threshold curve to 3. On the other hand, the commonly
known Keil-Schnell criterion is denoted by the circle of
unit radius in dots. This is why in many low-energy ma-
CP642, High Intensity and High Brightness Hadron Beams: 20th ICFA Advanced Beam Dynamics Workshop on
High Intensity and High Brightness Hadron Beams, edited by W. Chou, Y. Mori, D. Neuffer, and J.-F. Ostiguy
© 2002 American Institute of Physics 0-7354-0097-0/02/$ 19.00
310
wave
wave from
from one
one end
end of
of the
the ferrite
ferrite tuner
tuner via
via an
an antenna
antenna
and
receiving
it
with
an
antenna
at
the
other
end,
and receiving it with an antenna at the other end, while
while
the
the loss
loss isis recorded
recorded as
as aa function
function of
of frequency
frequency of
of the
the
wave
wave [3].
[3]. The
The results
results are
are shown
shown in
in Fig.
Fig. 44 and
andreveal
revealthat
that
the
the resonant
resonant peak
peak drops
drops by
by aa factor
factor of
of about
about 66 when
whenthe
the
ferrite
ferrite cores
cores are
are heated
heated from
from the
the room
room temperature
temperature of
of
23°C
23◦ C to
to 100°C.
100◦C. At
At the
the same
same time
timethe
theresonant
resonantfrequency
frequency
moves
moves to
to lower
lower frequencies.
frequencies.
1SI
& 2
|
-6
-4
-
2
0
2
U' (Re Zj/n)
FIGURE
FIGURE 3.
3. An
An intense
intense space-charge
space-charge beam
beam may
may have
have
impedance
at
A
outside
the
Keil-Schnell
circle
(dots)
impedance at A outside the Keil-Schnell circle (dots) but
but isis stastable
inside the
stability curve
ble inside
the stability
curve 33 for
for Gaussian
Gaussian distribution.
distribution. Ferrite
Ferrite
inserts
inserts compensating
compensating the
the space
space charge
charge completely
completely will
will lead
lead to
to aa
resistive
resistive impedance
impedance roughly
roughly at
at B,
B, which
which introduces
introduces instability.
instability.
chines
chines the
the Keil-Schnell
Keil-Schnell limit
limit has
has been
been significantly
significantly overovercome
by
a
factor
of
about
5
to
10.
come by a factor of about 5 to 10.
At
At the
the PSR,
PSR, the
the space
space charge
charge is
is almost
almost the
the only
only source
source
k
of
the
impedance,
ReZJJ/w
typically
orders
of the impedance, Re Z0 /n typically orders of
of magnimagnitude
smaller. As
tude smaller.
As an
an example,
example, if
if the
the impedance
impedance of
of the
theLos
Los
Alamos
PSR
is
at
A,
the
beam
is
within
the
microwave
Alamos PSR is at A, the beam is within the microwave
stable region
stable
region if
if the
the momentum
momentum spread
spread is
is Gaussian
Gaussian like,
like,
although it
although
it exceeds
exceeds the
the Keil-Schnell
Keil-Schnell limit.
limit. Now,
Now, ifif we
we
compensate
compensate the
the space-charge
space-charge potential-well
potential-well distortion
distortion by
by
the
the ferrite
ferrite inductance,
inductance, the
the ferrite
ferrite required
required will
will have
have an
an ininductive
ductive impedance
impedance at
at low
low frequency
frequency equal
equal to
to the
the negative
negative
value
of
the
space
charge
impedance
at
A,
for
value of the space charge impedance at A, for example,
example,
about −5.5
—5.5 units
about
units according
according to
to Fig.
Fig. 3.
3. However,
However, the
the ferferk
rite
also
has
a
resistive
impedance
or
ReZJJ/w
coming
rite also has a resistive impedance or Re Z0 /n coming
from
from /i".
µ 00 . Although
Although ReZJJ/w
Re Z0k /n is
is negligible
negligible at
at low
low frequenfrequencies
(for
example,
the
rf
frequency
of
2.796
cies (for example, the rf frequency of 2.796 MHz
MHz of
of the
the
PSR),
/(2n)
PSR), it
it reaches
reaches aa peak
peak value
value near
near co
ωrr/(2
π ) (about
(about 50
50 to
to
80 MHz
MHz for
inside
the
pill-box
con80
for the
the Toshiba
Toshiba M
M44C
C21A
inside
the
pill-box
con21A
tainer)
tainer) with
with the
the peak
peak value
value the
the same
same order
order of
of magnitude
magnitude
as
the
low-frequency
ImZ^/n.
k
as the low-frequency ImZ0 /n.
Thus
Thus the
the ferrite
ferrite will
will contribute
contribute aa resistive
resistive impedance
impedance
denoted
roughly
by
B
(~
5.5
units)
denoted roughly by B (∼ 5.5 units) when
when Q~l.
Q ∼ 1. This
This
resistive
resistive impedance
impedance of
of the
the ferrite
ferrite will
will certainly
certainly exceed
exceed
the
the threshold
threshold curve
curve of
of any
any momentum
momentum distribution
distribution and
and
we
believe
that
the
longitudinal
instability
we believe that the longitudinal instability observed
observed at
at
the
the PSR
PSR is
is aa result
result of
of this
this consideration.
consideration. In
In order
order to
to
avoid this
avoid
this instability,
instability, we
we must
must search
search for
for aa ferrite
ferrite sample
sample
having
a
small
ReZJJ/w
to
ImZJJ/w
ratio.
k
k
having a small Re Z0 /n to Im Z0 /n ratio.
FIGURE
FIGURE 4.
4. (color)
(color)As
Asthe
theferrite
ferritecores
coresare
areheated
heatedfrom
fromroom
room
temperature
temperature to
to 100°C,
100◦ C,the
theloss
lossatatthe
theresonant
resonantpeak
peakreduces
reducesby
by
almost
almost 66 times.
times. Abscissa:
Abscissa: center
center 75.0MHz,
75.0 MHz, span
span 149.4MHz.
149.4 MHz.
Ordinate:
Ordinate: 55 db/div.
db/div.
A
A measurement
measurement of
of the
the permeability
permeability of
of the
the ferrite
ferrite has
has
also
been
made
on
a
single
Toshiba
M
C
ferrite
4
21A
also been made on a single Toshiba M4 C21A ferritecore
core
as
as aa function
function of
of core
core temperature
temperature [4].
[4]. To
To provide
provide both
both aa
good
good electrical
electrical circuit
circuit path
path and
and aa uniform
uniform core
core tempertemperature,
ature, the
the core
core was
was encased
encased in
in an
an aluminum
aluminumtest
test fixture
fixture
before
being
placed
on
a
hot
plate.
The
top
half
before being placed on a hot plate. The top half of
of the
the
test
fixture
consisted
of
a
machined
aluminum
disk,
test fixture consisted of a machined aluminum disk,99in
in
in
in diameter
diameter and
and 1.25
1.25 in
in thick.
thick. The
The inner
inner section
section of
of the
the
disk
disk was
was machined
machined out
out 0.005
0.005in
in undersize
undersizetotoaccommoaccommodate
the
ferrite
core.
The
disk
was
date the ferrite core. The disk was then
then heated
heated and
and the
the
core
was
slipped
into
the
disk.
Upon
cooling,
the
core was slipped into the disk. Upon cooling, the alualuminum
minum disk
disk contracted
contractedand
andmade
made aa good
goodthermal
thermalcontact
contact
with
with one
one side
side and
and the
the outer
outer edge
edge of
of the
the ferrite
ferrite core.
core. The
The
aluminum
aluminum fixture
fixture and
and core
core were
were then
then flipped
flipped over
over onto
onto
aa flat
flat aluminum
aluminum plate
plate so
so that
that only
only the
the inner
inner edge
edge of
of the
the
core
was
exposed.
A
good
electrical
connection
between
core was exposed. A good electrical connection between
the
the aluminum
aluminum disk
disk and
and flat
flat plate
plate was
was made
made using
using strips
strips
of
adhesive
backed
copper
tape.
The
test
fixture
of adhesive backed copper tape. The test fixture was
was
placed
placed on
on aa hot
hot plate
plate and
and covered
covered with
with two
two fire
fire bricks.
bricks.
The
The test
test fixture
fixture was
was then
then heated
heated to
to 175°C
175◦ C and
and allowed
allowed
to
cool
slowly.
The
impedance
measurement
to cool slowly. The impedance measurement was
was made
made
by
by placing
placing the
the probe
probe of
of an
an HP4193A
HP4193A vector
vector impedance
impedance
meter
meter directly
directly across
across the
the inner
inner edge
edge of
of the
the ferrite
ferrite core.
core.
Impedances
were
measured
from
10
MHz
to
Impedances were measured from 10 MHz to 110
110 MHz
MHz
in
in 10
10 MHz
MHz steps
steps from
from 150°C
150◦C to
to 25°C.
25◦ C. The
The temperature
temperature
of
the
core
was
monitored
by
a
Fluke
80T-150U
of the core was monitored by a Fluke 80T-150Utempertemperature
ature probe
probe inserted
inserted into
into aa small
small hole
hole in
in the
the aluminum
aluminum
disk
disk portion
portion of
of the
thetest
test fixture.
fixture.
The
capacitor
C
p in parallel to the ferrite core was
The capacitor C p in parallel to the ferrite core was
determined by adding additional fixed 100 pf capacitors
determined by adding additional fixed 100 pf capacitors
HEATING
HEATING THE
THE FERRITE
FERRITE
Past
Past experience
experience indicates
indicates that
that when
when aa piece
piece of
of ferrite
ferrite is
is
heated
up,
ju£
will
increase
and
and
loss
at
high
frequen0
heated up, µs will increase and and loss at high frequencies
cies will
will decrease,
decrease, thus
thus having
having exactly
exactly the
the same
same properproperties we are looking for.
ties we are looking for.
A
measurement has been made by sending a sinusoidal
A measurement has been made by sending a sinusoidal
311
20
40
60
80
100
Frequency (MHz)
Frequency (MHz)
FIGURE 6. (color) Real and imaginary parts, ju£
FIGURE
µs0 and
µs00 , of
and ju",
of
the permeability of the ferrite core as functions
the
functions of frequency
frequency at
different temperatures
temperatures as
as derived
derived from
from Fermilab measurement.
different
FIGURE5.5. (color)
(color)Fermilab
Fermilabmeasurement
measurementof
ofreal
realand
andimagimagFIGURE
k /n of
inary parts
parts ofof impedance
impedance per
per revolution
revolution harmonic
harmonic ZZJJ/«
of aa
inary
0
ferritecore
coreinside
insideaasnugly
snuglyfit
fitpill
pill box
box cavity.
cavity.
ferrite
acrossthe
theinner
inneredge
edgeof
ofthe
theferrite
ferritecore
coreand
andobserving
observingthe
the
across
changeinin the
the resonant
resonant frequency
frequency of
of the
the structure
structure from
from
change
41toto28
28MHz,
MHz,aafrequency
frequency range
range in
in which
which the
the µjUs05' of
of the
the
41
ferrite
is
known
to
be
relatively
constant.
In
this manner,
manner,
ferrite is known to be relatively constant. In this
capacitanceofofCCpp==75
75pf
pfwas
waschosen
chosento
torepresent
represent the
the
aacapacitance
equivalent
parallel
capacitance
of
the
test
circuit.
There
equivalent parallel capacitance of the test circuit. There
was also
also aa residual
residual resistance
resistance of
of RRrr =
= 0.55
0.55 Ω
Q in
in the
the
was
probe
in
series
with
the
RLC
parallel
equivalent
circuit.
probe in series with the RLC parallel equivalent circuit.
This residual
residual resistance
resistance introduces
introduces aa large
large error
error at
at low
low
This
frequencies (below
(below ∼~ 10
10 Hz)
Hz) when
when the
the resistive
resistive part
part
frequencies
the RLC
RLC circuit
circuit isis small.
small. From
From the
the measurements
measurements of
of
ofof the
the input
input impedance,
impedance, RRpp and
and LLpp were
were computed.
computed. The
The
the
k
real and
and imaginary
imaginary parts
parts of
of ZZJJ/w
for one
one ferrite
ferrite core
core
real
/n for
encased inin aa cavity
cavity as
as seen
seen1by
by0 the
the beam
beam are
are shown
shown in
in
encased
Fig. 5.5. ItIt isis clear
clear that
that the
the resonant
resonant peaks
peaks of
of Re
ReZJJ/w
Fig.
Z0k /n
decreases twice
twice as
as the
the temperature
temperature increases
increases and
and the
the
decreases
resonantfrequency
frequency moves
movestowards
towardslower
lower frequencies.
frequencies. At
At
resonant
k /n increases by more than twice. If
the
same
time,
ImZJj
the same time, ImZ0 /n increases by more than twice. If
one plots
plots Re
ReZJJ
versus frequency
frequency instead,
instead, the
the decrease
decrease
one
Z0k versus
with
temperature
becomes
more
rapidly.
For
a
coasting
with temperature becomes more rapidly. For a coasting
beam,
the
area
under
a
ReZJJ
k curves represents the energy
beam, the area under a Re Z0 curves represents the energy
losstotothe
theferrite
ferriteassembly.
assembly.We
Wefind
find that
thatthis
thisloss
loss isis in
in fact
fact
loss
temperature
independent
within
10%.
temperature independent within 10%.
Thereal
realand
andimaginary
imaginaryparts
partsof
ofthe
theseries
seriespermeability
permeability
The
of
the
ferrite
core
derived
from
the
measurement
are
of the ferrite core derived from the measurement are
shown
in
Fig.
6.
It
is
interesting
to
see
that
ju"
actually
00
shown in Fig. 6. It is interesting to see that µs actually
increases with temperature. However, an increase of the
increases
the
series resistance inside the ferrite core implies a decrease
series
of the
the resistance
resistance R
Rpp in
in the
the RLC
of
RLC parallel
parallel circuit,
circuit, and
and
k
therefore
leads
to
a
decrease
in
ReZJJ/w
of
the
resonant
therefore leads to a decrease in Re Z0 /n of the resonant
peak as
as depicted
depicted in
in Fig.
Fig. 5.
5.
peak
APPLICATION TO
TO THE
THE PSR
APPLICATION
PSR
◦
When the
the induction
induction tuners
tuners at
at the
the PSR
is heated
130°,
When
PSR is
heated to
to 130
,
the
longitudinal
microwave
instability
seen
in
Fig.
the longitudinal microwave instability seen in Fig. 11
disappears. The
The profile
profile of
of the
the 100
100 ns
ns bunch
bunch now
now becomes
becomes
disappears.
as
depicted
in
the
right
plot
of
Fig.
2,
no
longer
distorted
as depicted in the right plot of Fig. 2, no longer distorted
and lengthened.
lengthened. Further
Further beam
beam
studies with
with the
1 studies
and
the heated
heated
ferrites demonstrated
demonstrated other
other benefits
benefits of
of the
ferrites
the inductor
inductor tuners
tuners
without unmanageable
unmanageable operational
operational impacts.
impacts.
without
REFERENCES
REFERENCES
1. M.A.
M.A. Plum,
Plum, et.
et. al.,
al., Phys.
Phys. Rev.
Rev. ST
STAccel.
2, 064201
1.
Accel. Beams,
Beams, 2,
064201
(1999).
(1999).
2. E.
E. Keil
Keil and
and W.
W. Schnell,
Schnell, CERN
CERN Report
Report TH-RF/69-48
2.
TH-RF/69-48
(1969); V.K.
V.K. Neil
Neil and
and A.M.
A.M. Sessler,
Sessler, Rev.
(1969);
Rev. Sci.
Sci. Instr.
Instr.
36, 429
429 (1965).
(1965). D.
D. Boussard,
Boussard, CERN
CERN Report
36,
Report Lab
Lab
II/RF/Int./75-2 (1975).
(1975).
II/RF/Int./75-2
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M.
Popovic,
private
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D.
Wildman,
private
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312