Feedbacks for low emittance accelerators Alessandro Drago SuperB Meeting   30 May 2008 - 04 June 2008 La Biodola, Isola d'Elba Italy

Introduction This talk wants to discuss the question: “There is anything to do to make bunch-by-bunch feedback system compatible with low (or very low) emittance accelerators?” In my opinion the answer is YES

The starting point The starting point for a discussion about how to upgrade bunch-by-bunch feedback, in this talk is taken from two digital system designs, both originated at SLAC: I) the GBoard system proposed in the 2002/2003 by J.D.Fox and D.Teytelman and still to be implemented II) the iGp system, the engineerized version of the Gboard prototype (Gproto), implemented at DAFNE, KEK, PEP-II, ALS, Duke Univ. Note: nowadays, due to the advance of the FPGA technology, there are no more reasons to have different digital feedback design for transverse and longitudinal systems (as in PEP-II, DAFNE, KEK)

Proposed at the ICFA’03 Workshop at Alghero by J.D.Fox & D.Teytelman

Considering R&D feedback for low emittance accelerators The R&D list for an upgrade starting from iGp-like system (in the software & gateware version running at the present at DAFNE) includes: very low noise analog front end @ 3*RF maintain low cross-talk between adjacent bunches under 40 dB (better 60 dB) dual separated timing to pilot the backend power stage digital block with higher dynamic range (12/16bits) “dual gain” approach to minimize residual beam motion integrated beam-feedback model

Considering a feedback upgrade for low emittance accelerators Feedback are active system and can have strong negative impact on very low emittance beams The basic ideas of the upgrades consist in making the noise in the feedback loop as low as possible, and this means: a) Filtering at the best the external noise, i.e. coming or generated outside the feedback b) Reducing the internal noise, i.e. the noise coming from parts in the feedback system c) Reduce the crosstalk between bunch signals

1) Very low noise analog front end @ 3*RF From the rings, at revolution frequency o lower, the beam signal is much more noisy than at higher frequencies. To solve this trouble, it is possible to built a very low noise front end at 3 or 4 times RF to acquire a much more “clean” beam signal

Noise from pickup @ low frequencies (no beam!)

Longitudinal “conceptual” FE used @ PEP-II & DAFNE

ALS LFB new front end Courtesy of D.Teytelman

PEP II Transverse Feedback System The PEP TFB system takes the vector sum of 2 BPMs, delays the signal by the remainder of 1 turn and delivers a kick to the beam the next time around. Two stripline kickers, one for X and one for Y, are used. [MAC 10/26/2006 – Ron Akre ]

PEP II TFB Receiver 10/26/2006 – Ron Akre PHASE TRANSIENT Use These Phase Shifters to Remove Phase Transient PHASE TRANSIENT

1) Very low noise analog front end @ 3*RF It would be an important point to design a very low noise n*RF analog front end studying new generation components : (amplifiers, mixers, phase shifters,…) It is necessary to make tests and measurements in laboratory and on real beam signals

2) Maintain low cross-talk between adjacent bunches < 40 dB (better <60 dB) This is very important for ultra-low emittance rings but it is an important issue in general The crosstalk is a source of noise For example in DAFNE the vertical feedback crosstalk estimate is ~30 dB, probably this value is to high for low emittance beams Actions: to be evaluated

3) Separated digital timing to pilot backend power stage and kickers Typically a transverse kicker has two ports In the PEP-II scheme (seen previously) it is used a fine digital step delay for each port In DAFNE there is only a common delay for the 2 kicker ports; it is put inside the iGp to control the clock to DAC This is a much better approach because it doesn’t insert jitter in the feedback loop, it doesn’t limit the bandwidth nor attenuate the correction signal The timing control should be duplicated to delay the clock before the fast output DAC A solution is to double the fast DAC in the iGp output stage to control separately positive and negative output signal

4) Digital block with higher dynamic range (12/16bits) ? The iGp (as well the GBoard) feedback samples the input beam signal by an 8 bits analog to digital converter Do we need more bits conversion? In my opinion the answer is yes Because a small bits A-to-D conversion gives poor voltage resolution and bigger quantization noise Because the dynamic range could be not sufficient

Resuming the dynamic range in DAFNE transverse Feedback Analog Front end (AM143) dynamic range = 79.50 dB (measured) Analog Back end (ZFL500LN) dynamic range = 77.97 dB (measured) Power Amplifier (AR250250) dynamic range = 87.83 dB (measured) Digital Part (8 bits ADC) dynamic range = 48.16 dB (computed) Digital Part (7.5 bits ADC) dynamic range = 45.15 dB (computed) Note on the used formula: dyn_range = 20*log10 (Vout_max/Vout_min) in dB [if analog system] dyn_range = 20*log10 (2^adc_num_of_bit) in dB [if digital system]

The dynamic range in DAFNE feedback analog blocks is in the range 78 dB – 88 dB

ADC dynamic range versus # of bits 7.5_bit ADC_= 45.15 dB 8_bit ADC _ = 48.16 dB 10_bit ADC _= 60.20 dB 12_bit ADC _= 72.25 dB 14_bit ADC _= 84.29 dB [best value considering the analog blocks!] 15_bit ADC _= 90.31 dB 16_bit ADC = 96.33 dB 24_bit ADC = 144.49 dB Note: in general at least 0.5 bit (= 3dB) is not effective in the conversion

A factor liming the effectiveness of the ADC is the sampling clock jitter. I can suppose that a realistic value of the RMS jitter for the timing signal will be ~0.5 ps [Need to know the SuperB timing specifications] In this case (yellow trace), the ADC dynamic range should be better than 60 dB (12bits)

Recommendation on dynamic range A reasonable compromise between the present electronics technology and the specifications seems to indicate these choices: 12 bits (eventually 14 bits) for analog-to-digital conversion 16 bits for digital-to-analog conversion

5) “Dual gain” approach to minimize residual beam motion To minimize the feedback impact on a low emittance beam, the feedback gain should be held as low as possible to minimize the unfiltered residual beam motion passing through the system During injection or if necessary to control instabilities, the feedback needs all the power while in a “stable” situation the system probably needs much less gain It could be interesting to implement a “Dual gain” approach, but how it should be done?

In the digital part , the FE_signal_out is sampled by an A/D converter at rf frequency, and then demultiplexed to separate the signal of each bunch. A digital signal processor (DSP) farm is used to implement a passband filter [finite impulse response (FIR) or infinite impulse response (IIR). The number of taps, gain with sign, center frequency, filter shape, and phase response are programmable by the users.

IIR and FIR bandpass filter for each bunch For every bunch the correction signal is function only of previous input (FIR) Or the previous input / output (if IIR) values

To have a “dual gain” feedback a new FIR formula could be tested y(n,k)=G*[b(n,k) *x(n,k) +b(n-1,k) *x(n-1,k) +...+b(n-j,k) *x(n-j,k) + + b(n,k-1) *x(n,k-1) +b(n-1,k-1) *x(n-1,k-1) +...+b(n-j,k-1) *x(n-j,k-1) + + b(n,k-2) *x(n,k-2) +b(n-1,k-2) *x(n-1,k-2) +...+b(n-j,k-2) *x(n-j,k-2) + . +b(n,k-h-1)*x(n,k-h-1)+b(n-1,k-h-1)*x(n-1,k-h-1)+...+b(n-j,k-h-1)*x(n-j,k-h-1)] y = output correction value, x = input value, b = constant coefficient n = discrete time (turn), k = selected bunch, j=filter taps, h= harmonic number In the above formula, the outputs of k bunch are function not only of the k bunch previous values but also of inputs from the other bunches. In case of injection or instability the gain will rise up very fast.

“Dual gain” FIR formula analysis The first row is exactly what we use now First row coefficients can be find experimentally In the first approximation, the coefficient for the other bunches could be put at zero The other rows coefficient should be find by using a beam-feedback model with MATLAB/SIMULINK simulator In the second approximation only the first column coefficient should be identified

“Dual gain” feedback by a second FIR formula (to be tested) y(n,k) = G* [ b(n,k)*x(n,k) + b(n-1,k)*x(n-1,k) + . . . +b(n-j,k) *x(n-j,k) ] G is a dynamic function of the other bunch signals for example a simple formula can be used: G= g *{max[ x(n,k-1), x(n,k-2), .....x(n-j,k-h-1)]} g is gain from operator interface y = output correction value, x = input value, b = constant coefficient n = discrete time (turn), k = selected bunch, j=filter taps, h= harmonic number In the above formula, the outputs of k bunch are function of the k bunch previous values but the gain of the feedback depends by the inputs of the other bunches. In case of injection or instability, the gain will rise up very fast.

What do we need to implement the new FIR formulae ? Much powerful hardware A beam-feedback model to compute and manage the coefficients and test the filter behavior

2001 VIRTEX-II

Xilinx Virtex-5 performances

6) Integrated beam-feedback model In the past a beam/feedback model has been used by Teytelman & Fox to implement IIR filter, because it was the only way to find its coefficient too difficult to find experimentally To implement the “Dual Gain” FIR formula is also necessary to use a model/simulator to find the coefficients of the formula Nowadays much more powerful commercial software tools make very interesting synergy between model and real system

D. Teytelman, et al., “Design and implementation of IIR algorithms for control of longitudinal coupled-bunch instabilities” , BIW 2000, SLAC-PUB-8411, May 2000 Example of MATLAB/SIMULINK Beam/feedback model to compute IIR filter coefficients for only one bunch

Using MATLAB and SIMULINK, the real time code can be easier integrated with the simulator code !

Conclusions It is necessary to prove the effectiveness of the 6 proposed points DAFNE is a perfect test machine because has low harmonic number, low RF frequency and low number of bunches so tests on the proposal 4), 5) and 6) can be implemented easier than in other accelerators To start the experimentations we need time, a running accelerator, manpower and money !