Induction inserts at the Los Alamos PSR Page: 1 of 4
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FERMILAB-Conf-02/221 September 2002
Fermilab
Induction Inserts at the Los Alamos PSR
K.Y. Ng
Fermi national Accelerator Laboratory, PO. Box 500, Batavia, IL 60540
Abstract. Ferrite-loaded induction tuners installed in the Los Alamos Proton Storage Ring have been success-
ful in compensating space-charge effects. However, the resistive part of the ferrite introduces unacceptable mi-
crowave 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 cance
the space charge effects of the intense proton beam a
799 MeV. Each tuner consists of a stainless steel pill
box cavity closely packed with 30 Toshiba M4C2lA fer
rite 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 in
tention of two-third space-charge compensation, clear
and consistent evidence was observed, including shorte
bunch length, cleaner bunch gap, and smaller rf voltag
required for stable operation. After an upgrade when
tuners were installed in 1999 and the beam intensity wa
raised, a longitudinal instability was observed. Figure 1
shows a chopped coasting beam accumulated for 125
and stored for 500 s recorded at a wide-band wall cur
rent monitor. The ripples at the beam profile indicat
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 alsc
showed up as ripples at the rear half of a 250 ns (left) and
100 ns bunch (middle) in Fig. 2. Apparently, the instabil
ity 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 fer-
rite can be made complex: -+ ' + i 4, where the sub-
scripts denote "series". The impedance of the ferrite is
therefore
Z = -i(p'+iW")oL , (1)
__ k,I
/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
e the angular frequency. It is clear that s and s' 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 C, in
- parallel. The impedance of the inductor tuner can then be
represented by
s R
OZ 1 1- iQ (C/Cr - COr/Cu) , (2)
where cor is roughly where " peaks. If we denote i
as the value of ' at low frequencies and R the value
of " at resonant frequency cor/(21c), we readily obtain
- = Qpi. Note that Q here is the quality factor describ-
ing the " 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 /n-plane (or the tradi-
tional U'-V' plane), where n is the revolution harmonic,
is somewhat different from the commonly quoted Keil-
Schnell estimation [2]. In Fig. 3, the heart-shape solid
curve 1 is the threshold for parabolic distribution in mo-
mentum spread, where the momentum gradient is discon-
tinuous 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-FIGURE 1. Longitudinal microwave-like instability
recorded by wall-gap monitor of a coasting beam driven at
72.7 MHz.1
t
rfl
I
4
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Ng, King-Yuen. Induction inserts at the Los Alamos PSR, article, September 30, 2002; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc734529/m1/1/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.