Atomic Energy, Vol. 94, No. 1, 2003
2003 Plenum Publishing Corporation
The results of an investigation of self-bunching of the U-70 proton synchrotron beam are presented. The
self-bunching arises on the top magnetic-field plateau and is caused by the interaction of the beam with the
accelerating resonators from which the rf voltage was removed. A specific feature of self-bunching is its
anomalously low threshold. It is shown that this is due to the filamentary beam structure, which appears
during drfiting of the bunches, and the threshold is determined not by the total but rather the local
momentum spread in each filament, continuously decreasing during drifting of the bunches. A novel method
used in U-70 to suppress self-bunching is described.
Self-bunching of a circulating beam is observed on the top magnetic-field plateau in the U-70 proton synchrotron.
This bunching degrades beam structure and creates serious problems for slow particle extraction. The instability appears on
the 26th harmonic of the particle revolution frequency f
, and the threshold of the instability is almost ten times lower than
the value given by the generally accepted criterion for longitudinal stability of a circulating beam :
Here Z/n is the reduced longitudinal coupling impedance of the beam with the vacuum chamber; F ~ 1–2 is a form factor
which depends on the particle momentum distribution; E
is the particle energy; β is the relativistic factor; η is the revolution
frequency dispersion; e is the electron charge; I is the average beam current; p
is the equilibrium momentum; and, ±∆p is
the total momentum spread of the particles.
The beam in U-70 is debunched by switching off the rf voltage and then shifting the characteristic frequency f
the resonators in the accelerating system by ∆f = –4.5f
. It was assumed that the equidistance of f
from two neighboring 25th
and 26th harmonics of the revolution frequency, taking account of the narrow band nature of the resonators (2∆f
will give a threshold beam intensity at least ~(1.2–1.6)·10
protons per cycle.
However, in practice it was found that self-bunching is observed at a substantially lower intensity; this is illustrated in
Fig. 1. The curves 1–4 show the distribution, along the orbit of the accelerator, of particles in a beam which initially consisted
of seven bunches with total intensity N = 2.07·10
. The bunches filled each third separatrix. The curves were obtained after the
accelerating field was switched off in intervals of 60, 250, 1000, and 1700 msec, respectively. It is evident that the parasitic struc-
ture of the beam appears already by 250 msec (curve 2); this structure subsequently forms completely and remains (3, 4).
In the present work, numerical simulation of the particle motion was used to study self-bunching. A U-70 beam with
N = 1·10
particles and ∆p/p
was studied. The total impedance of all 40 accelerating resonators is represented
by a parallel circuit with the following parameters: shunt resistance R = 320 kΩ, capacitance C = 15 pF, and Q = 160.
SELF-BUNCHING OF A CIRCULATING BEAM
IN THE U-70 PROTON SYNCHROTRON
V. A. Kalinin, A. Yu. Malovitskii,
I. I. Sulygin, and E. F. Troyanov
State Science Center of the Russian Federation – Institute of High-Energy Physics. Translated from Atomnaya
Énergiya, Vol. 94, No. 1, pp. 65–68, January, 2003.