e. métral
DESCRIPTION
FOLLOW-UP OF THE FAST VERTICAL SINGLE- BUNCH INSTABILITY AT SPS INJECTION. E. Métral. Animation of the BBU theory ( direction of propagation solved! ) Review of Laclare’s theory (azimuthal and radial modes mq ) Animation of the TMC theory ( direction of propagation not solved! ) - PowerPoint PPT PresentationTRANSCRIPT
Elias Métral, RLC meeting, 21/10/2005
1/16
E. MétralE. Métral Animation of the BBU theory (direction of propagation solved!)
Review of Laclare’s theory (azimuthal and radial modes mq)
Animation of the TMC theory (direction of propagation not solved!)
Coupling between modes -33 and -44 (bad direction!)
Coupling between modes -24 and -35 (good direction!)
Animation of SPS measurements
With a relative (measured) chromaticity of 0.14
With a relative (measured) chromaticity of 0.54
With a relative (measured) chromaticity of 2.04
Animation of the BBU theory for the PS compared to measurements
FOLLOW-UP OF THE FAST VERTICAL SINGLE-
BUNCH INSTABILITY AT SPS INJECTION
Elias Métral, RLC meeting, 21/10/2005
2/16
BBU THEORYBBU THEORY
1st trace = turn 1 Last trace = turn 115 Every turn shown
ns7.0t
/mM10 yR
GHz1rf
1Q
BB resonatorimpedance
Elias Métral, RLC meeting, 21/10/2005
3/16
Follow-up of last RLC meeting when I said that the spectrum of
mode mq (σmq) is peaked at and extend
2 modes with same q are peaked at the same frequency (same line
density), and therefore have ~ the same sensitivity in the same
frequency range. They however correspond to entirely different
patterns in phase space…
bq
qf
2
1
1 b
LACLARE’S FORMALISM (1/6)LACLARE’S FORMALISM (1/6)
Elias Métral, RLC meeting, 21/10/2005
4/16
LACLARE’S RESULTS – LACLARE’S RESULTS – CERN 87-03, p. 315 (1/2)CERN 87-03, p. 315 (1/2)
Q
not specified
and
kmq 2
k0with
22bb
2ˆ0 b
(2/6)(2/6)
Elias Métral, RLC meeting, 21/10/2005
5/16
(3/6)(3/6)
LACLARE’S RESULTS – LACLARE’S RESULTS – CERN 87-03, p. 316 (2/2)CERN 87-03, p. 316 (2/2)
Elias Métral, RLC meeting, 21/10/2005
6/16
MY RESULTS (1/2)MY RESULTS (1/2)
f
00
S00
X00
f
02
S02
X02
f
04
S04
X04
f
11
S11
X11
S00
S02
S04
S1110 b
13.xQ
0
revfQf
(4/6)(4/6)
Elias Métral, RLC meeting, 21/10/2005
7/16
MY RESULTS (2/2)MY RESULTS (2/2)
f
13
S13
X13
f
22
S22
X22
f
24
S24
X24
f
33
S33
X33
S13
S22
S24
S33
(5/6)(5/6)
Elias Métral, RLC meeting, 21/10/2005
8/16
I have the same results as Laclare (I use his formalism…) except
for σ02 , σ11 , σ33 , where I have an opposite sign
I also have an opposite sign for X02 , X11 , X33
However, it has no effect on the signal observed at a Pick-Up
And it has also no effect in the computation of the tune shift as it
is σmq2 which enters into the formula
LACLARE’S FORMALISM (6/6)LACLARE’S FORMALISM (6/6)
Elias Métral, RLC meeting, 21/10/2005
9/16
TMC THEORY: coupling between modes -33 and -44 TMC THEORY: coupling between modes -33 and -44
1st trace = turn 1 Last trace = turn 115 Every turn shown
ns8.24 tb
turns SPS 55MOSESTMC
Elias Métral, RLC meeting, 21/10/2005
10/16
TMC THEORY: coupling between modes -24 and -35 (1/2) TMC THEORY: coupling between modes -24 and -35 (1/2)
1st trace = turn 1 Last trace = turn 115 Every turn shown
ns8.24 tb
turns SPS 55MOSESTMC
Elias Métral, RLC meeting, 21/10/2005
11/16
I asked to Elena Shaposhnikova if one can identify which (radial)
modes couple: -2? with -3? (In her paper CERN/SL/93-43 (RFS) on
MOSES’s results, it is said that if coupling of mode m is important,
radial modes up to k ~ |m| / 2 have to be considered)
If k = 1 then it is the same case as the one of the previous page
/mM10 yR
GHz1rf
1Q
BB resonatorimpedance
p102.7
mA5.010
thb
thb
N
I
mA83.0
p102.1 11
b
b
I
N
turnsSPS552TMC
sT
9.0
mA5.0thbI
mA83.0bI
TMC THEORY: coupling between modes -24 and -35 (2/2) TMC THEORY: coupling between modes -24 and -35 (2/2)
Elias Métral, RLC meeting, 21/10/2005
12/16
1st trace (in red) = turn 2 Last trace = turn 150 Every turn shown
MEASUREMENTS WITH A MEASUREMENTS WITH A CHROMATICITY OF 0.14CHROMATICITY OF 0.14
Elias Métral, RLC meeting, 21/10/2005
13/16
MEASUREMENTS WITH A MEASUREMENTS WITH A CHROMATICITY OF 0.54CHROMATICITY OF 0.54
1st trace (in red) = turn 2 Last trace = turn 150 Every turn shown
Elias Métral, RLC meeting, 21/10/2005
14/16
MEASUREMENTS WITH A MEASUREMENTS WITH A CHROMATICITY OF 2.04CHROMATICITY OF 2.04
1st trace (in red) = turn 2 Last trace = turn 150 Every turn shown
Elias Métral, RLC meeting, 21/10/2005
15/16
BBU THEORY FOR THE PS AT TRANSITION (1/2)BBU THEORY FOR THE PS AT TRANSITION (1/2)
1st trace = turn 1 Last trace = turn 90 Every turn shown
ns5.7t
/mM3 yR
MHz700rf
2Q
BB resonatorimpedance
Elias Métral, RLC meeting, 21/10/2005
16/16
, R, V signals
Time (10 ns/div)~ 700 MHz
MEASUREMENTS IN 2000MEASUREMENTS IN 2000 BBU THEORY BBU THEORY AFTER 90 TURNS (~ 200 AFTER 90 TURNS (~ 200 μμss))
BBU THEORY FOR THE PS AT TRANSITION (2/2)BBU THEORY FOR THE PS AT TRANSITION (2/2)
Seem very close except head and tail exchanged!!! Does it start only
for the maximum peak intensity, i.e. in the middle???