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GSI-UPGRADE-ACC-07 GSI SCIENTIFIC REPORT 2009
Simulation and observation of the space charge induced multi-stream
instability of linac micro bunches in the SIS-18 synchrotron
S. Appel 1 , O. Boine-Frankenheim 2 , and Th. Weiland 1
1 TEMF, TU Darmstadt, Germany; 2 GSI, Darmstadt, Germany
For the upgrade of the SIS-18 synchrotron it is of importance
that the initial momentum spread of the injected
coasting beam does not exceed the limit set by the rf bucket
area. The lower limit is determined by microwave instabilities
which cause a sudden increase of the momentum
spread below a threshold momentum spread.
For a coasting Ar 18+ beam in the SIS-18 the measured momentum
spread as a function of the number of injected
turns is shown in Fig.1. The momentum spread has been
obtained from different Schottky bands.
During the transverse multi-turn injection the SIS-18 is
filled with micro bunches from the UNILAC linac at 36
MHz. For low beam intensities the micro bunches debunch
within a few turns and form a coasting beam with
a Gaussian-like momentum spread distribution. With increasing
intensity we observe a few 100 turns after injection
persistent current fluctuations and an accompanying
pseudo-Schottky spectrum.
The Schottky spectrum should be used to routinely measure
the momentum spread (see Fig.1) and revolution frequency
directly after injection. Therefore is is important to understand
the origin of the pseudo-Schottky spectrum.
In [1] it is shown that the multi-stream instability induced
by the space charge impedance leads to phase space turbulence
with strong coherent fluctuation. The dispersion
relation is
qI0η
−i
2πγβ 2mc2 Zsc
n
n 2 ω 2 0
M
M�
j=1
1
= 1, (1)
(ω − kvj)
from which the critical number of filaments results as
Mthr = 32
πUsc
where Zsc is the space charge impedance, vj the velocity
of the jth filament, Usc the space charge parameter and σ
the momentum spread.
The saturation of the instability causes persistent current
fluctuations with a broad frequency spectrum. Such a fast
transition to a broad frequency spectrum was observed in
the SIS-18 shortly after injection of N = 10 9 Ar 18+ ions
(Fig. 2) as well as in simulations. The transition occurs
exactly after Mthr filaments have been generated.
A simulation code has been developed which reproduces
the important aspects of the observed instability, like the
threshold number of filaments and the broadness of the
spectrum after saturation. The code will be used to estimate
the effect of other ring impedances on the beam momentum
and on its spread.
152
(2)
Figure 1: Rms momentum spread as a function of the
number of injected turns measured from different Schottky
bands. Approximately 10 9 Ar 18+ ions are injected per
turn. A possible reason for the obtained increase are microwave
instabilities.
Figure 2: Measured frequency spectrum from N = 10 9
Ar 18+ ions injected into SIS-18. The dashed line indicates
the duration after which the broad frequency spectrum develops
in the simulation. The solid line present the SIS-18
beam pipe cut-off frequency.
In addition the minimum momentum spread achievable in
SIS-18 as well as the characteristics of the pseudo-Schottky
noise will be analyzed using the code together with the experimental
data.
Experiments with the new SIS-18 broadband current transformer
a planed for the upcoming beam times.
References
[1] I. Hofmann, GSI Note March 1989
[2] S. Appel et al., DPG-Tagung München 2009