1) beam impedance calculation for slotted kicker and 2) three kicker option with cavities
DESCRIPTION
1) Beam Impedance calculation for slotted kicker and 2) Three kicker option with cavities. A. Gallo on behalf of the INFN Frascati Hi- Lumi LHC Broadband FBK Team* (*) D. Alesini , A. Drago , A. Gallo, F. Marcellini , M. Zobov . - PowerPoint PPT PresentationTRANSCRIPT
1) Beam Impedance calculation for slotted kicker and
2) Three kicker option with cavities
A. Gallo on behalf of the INFN Frascati Hi-Lumi LHC Broadband FBK Team*(*) D. Alesini, A. Drago, A. Gallo,
F. Marcellini, M. Zobov.
Initial impedance calculations for slotted kicker
ImaginaryReal
Impedance simulations
with GdfidL started on a
simple slotted structure
made by 2 rectangular
waveguides on both top
and bottom sides of the
beam pipe.
D. Mc. Ginnis
Slotted Kicker Impedance Calculations Comparison
GdfidL (M.Zobov, LNF INFN) Moment method (J.Cesaratto, SLAC)
ReZL
ReZT
Longitudinal
Transverse
fluxw
Lz
cj
yx
fluxw
TT P
dzecBE
PV
R
RF
_
2
0
_
2
22
Total power flux in the two waveguides
Slotted Kicker Shunt Impedance Comparison
HFSS(D.Alesini, LNF INFN)
Moment method(J.Cesaratto, SLAC)
mkLQR
Q
T /10
5
Des
ign
evol
utio
nSlotted-coaxial kicker Impedance calculation
Parameter Comparison
100052
1322
5015020805
3OK
80
Last Old
Longitudinal Impedance
024.0Im
nZl
Gaussian bunch, σz = 2 cm
25 ns
Total Power Loss
25 ns
sz = 12 cm
l
rev
b kT
NeNP2
CVkl /1006.3 10
P = 820 W for 12 cm bunch length, Nb = 144, N = 4.09x1011
Because of the device directionality, most of the power is expected to be dissipated into the dummy loads connected to the downstream ports. A precise evaluation of the delivered power partition among ports and structure walls is needed.
Transverse Wakes and Impedance (2 cm bunch length, 2 mm offset)
mk
mm 100
2200
Gaussian bunch, σz = 2 cm
25 ns
CONCLUSIONS #11. We should not expect any additional harmful multibunch effects due to
the slotted kicker since both longitudinal and transverse wakes decay in time shorter than the minimum bunch spacing of 25 ns
2. The low frequency longitudinal impedance of 0.024 is very small in comparison with the overall SPS longitudinal impedance budget (10 )
3. The longitudinal loss factor for the shortest bunch length in SPS of 12 cm is estimated to be kl = 3.06x1010 V/C . This corresponds to the total lost power of 820 W for the worst scenario (Np =4.09x1011, Nb = 144), mainly flowing out through the device downstream ports.
4. The real and imaginary parts of the total transverse impedance do not exceed 100 k/m - to be compared with ≈ 7 M/m contributed by the other SPS kickers.
2) Three kicker option with cavitiesQuestion: is a continuous, almost flat broadband frequency response strictly
necessary to kick selected bunch portions?
If not, is it possible to reduce the system bandwidth requirements?
-10 -5 0 5 10
0
0.5
1
10-2 10-1 100 1010
0.5
1 GHzf 1s
nst 16.0s
nsFWHM t 37.0
tFWHM
ff s
Gaussian frequency response Gaussian time domain pulse
A broadband system is capable to kick only a limited portion of the bunch (≈1/6 of the SPS bunch for a BW ≥ 1 GHz).
The kick is (almost) negligible on the remaining part of the bunch, and it is also zero outside the bunch at any time.
Brute bandwidth approach!
bunch21e
-10 -5 0 5 100
0.5
1
The gaussian time domain pulse can be replicated with a repetition Tp ≥ b, being b the total bunch duration (including tails).
The pulse replica will not affect the selected bunch, and the signal bandwidth becomes discrete. The amplitude of the coefficients of the Fourier expansions is modulated by a gaussian profile in frequency domain.
Lines of the Fourier expansionGaussian time domain pulse train
The same intra-bunch resolution can be obtained with a discrete spectrum. Obviously, an expansion made with pure sine-waves with constant amplitudes will kick all the bunches in the same way. To kick and control individually each bunch, each sine wave has to be multiplied by a damping term so that the individual kick will decay to a negligible value before the next bunch arrive.
bunch
10-1 100 1010
0.5
1
][nst ][GHzf
Lorentzians of the Fourier transformGaussian time domain pulse train
For practical reasons the expansion has to be limited to the few first bands. Satisfactory results could be obtained already with the first 3 lines.
0 10 200
0.5
1bunch next
bunch
10-1 100 1010
0.5
1
][nst ][GHzf
0 10 20-1
0
1
2 bunch nextbunch
][nst
Kicker #1 Kicker #2 Kicker #3Type Stripline Cavity, TM110 defl. mode Cavity, TM110 defl. mode3-dB bandwidth DC – 400 MHz 800 ± 16 MHz 1200 ± 16 MHzLength 17 cm 18 cm 12 cmFilling time 0.6 ns 10 ns 10 nsQL --- 25 38Shunt Impedance ≈ 1.5 kΩ (@ DC) ≈ 2.1 kΩ (@ 800 MHz) ≈ 3.3 kΩ (@ 1200 MHz)
0.1 0.4 1 20
1
2
3
][GHzf
][kVV
To generate the 3 deflecting harmonics, 3 different back end chains culminating into 3 different kickers can be used. Being the frequency of the 1st harmonic ≈ 400 MHz (bunch duration ≤ 2.5 ns), a compact and cost effective solution is to use a stripline extending its bandwidth from DC (bunch transverse rigid motion). For the 2nd and 3rd harmonics overloaded deflecting cavities working in the TM110 mode can be used.
TM110 cavities
17 cm stripline
55 cm striplineDeflecting voltages
delivered by striplines and TM110 single cell cavities excited with 1
kW RF power.
0.1 0.4 1 20
1
2
3
750.00 775.00 800.00 825.00 850.00Freq [MHz]
-10.00
-8.00
-6.00
-4.00
-2.00
0.00
dB(S
(1,2
))
HFSSDesign4XY Plot 1 ANSOFT
Curve Info
dB(S(1,2))Setup1 : Sw eep
1.17 1.18 1.19 1.20 1.21 1.22 1.23Freq [GHz]
-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
dB(S
(1,2
))
HFSSDesign2XY Plot 1 ANSOFT
Curve Info
dB(S(1,2))Setup1 : Sw eep
Frequency 0.8GHz 1.2 GHzQ 23 38
Vertical shunt impedance 2.1 kΩ 3.3 kΩH ≈ 100 cm ≈ 60 cm
Broadband kicker for SPS intrabunch feedback system
H
F. Marcellini (on leave of absence from INFN LNF)
Architecture of a 3-kickers intrabunch feedback system
Betatron oscillations of each bunch beamlet are tracked and 90° phase shifted by digital filters.
The resulting kick profile for each bunch is Fourier expanded.
The amplitude and phase of each harmonics are provided to the back-ends, at a clock rate equal to the bunch repetition frequency.
Example: transferring a (1,0,0,0,-1) kick profile to a selected bunch
Consider the case of a bunch divided into 5 beamlets that needs to be kicked only at its extremities, and with opposite polarities, i.e. a (1,0,0,0,-1) kick.Amplitude and phase of the first 3 harmonics of the kick profile are calculated (Fourier expansion) and, just after the passage of the preceding bunch, loaded in the back-ends.
The kick reaches the regime at the bunch passage, and since then the back ends are switched off (or loaded with the values relative to the next bunch).The kick across the bunch is smoothed by the expansion truncation, but it still acceptably reproduces a (1,0,0,0,-1) profile.
CONCLUSIONS #21. Building up the kick voltage through a Fourier - frequency domain – approach is
attractive to relax the broadband requirements to the system back-end (kickers and amplifiers);
2. The use of 3 harmonics seems sufficient to discriminate and selectively deflect small portions of the bunch (at level of 15÷20% of the entire length);
3. Kickers and amplifiers working at specific frequencies with a minimum required band of the order of 30 MHz are less critic and more efficient with respect to continuous, broadband devices. The global equalization is also simpler.
1. The broadband shunt impedance of optimized slotted kickers is comparable (or larger!) than the peak values provided by deflecting cavities and striplines;
2. The data process in the feedback architecture is more complicated and can not be just a data streaming from the BPM to the kicker.
3. The overall amount of hardware required and the beam pipe space occupancy are larger.
BUT …