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 …