PI laser jitter measurements Data taken on 11 th April 2013

Modifications to Previous Analysis (pilasermeasts_v1) Used Hanning window to improve frequency identification.

Hanning Window Fourier transform ideally works for signal extending to +/- infinity. Real signal is finite in time and the doesn’t necessarily include a perfect integer number of oscillations (which would allow +/- inf signal to be inferred) This leads to ‘leakage’ in the DFT, i.e. don’t get a single well defined peak at the frequency but a spread of values around the frequency. The Hann/Hanning window reduces this leakage by ‘tapering’ the original data within the original time sample.

Hanning Window Basic Example HanningElement[x_,{k_}]:= x 2 Sin[(p k)/n] 2 Hanning[X_]:= MapIndexed[HanningElement,X]/.n->Length[X] ListPlot[data=Table[1Sin[10a], {a,0,0.1*6*pi+0.05,0.01}], AspectRatio®0.3] ListPlot[Hanning[data],AspectRatio®0.3] Not sure this example demonstrates the benefits of the Hanning window clearly ListPlot[Transpose[{fscale,Abs[Fourier[data]]}], PlotRange®{{0,10},All}, Filling®Axis,FillingStyle®{Blue},AspectRatio®0.3] ListPlot[Transpose[{fscale,Abs[Fourier[Hanning[data]]]}], PlotRange®{{0,10},All}, Filling®Axis,FillingStyle®{Blue},AspectRatio®0.3]

PI laser diode Datasheet. The X-Y signals are NOT normalised

Effect of normalisation on x transients original sum- normalised ratio data corrupted before end of train in shot 4, the x data partially corrupted, causes problems in binning, need to fix

Effect of normalisation on y transients data corrupted before end of train in shot 1, no y data available original sum- normalised ratio

Transients Conclusions Normalising the X/Y signals by the sum doesn’t seem to affect the transients much – Doesn’t remove the transients in Y – Doesn’t introduce transients in X – Compare with BPM-01 shift #3205 (see later slide)

DFTs – Data on which fourier is done

DFT x charge y

DFT Hanning x charge y

Old Data for comparison/Conclusions Please remember as well as charge normalisation there are other changes – Binning of the data – Some changes in ranges of trains selected, for practical purposes Doesn’t seem to be a big difference in the DFTs in the normalised data. – Normalising hasn’t really reduced the realtive size of the 300 kHz in x and y – Seems to be some component at ~150 kHz that was also seen in BPM-01 #3205

Data (5 shots) x x charge y old data for comparison

DFT x x charge y old data for comparison

Comparison of freq spectra of BPM-01 with Photodiode (PD) Most BPM-01 data taken on #3205 (Nov ‘12) (30 shots with different conditions) – Amplitude of various x-y frequencies highly dependent on steering and solenoid – Amplitude of charge variations quite stable over all 30 shots – Transients removed by taking bunches in the 1620 bunch train. To compare with PI photodiode, also take approx the same window of data Apply Hanning window to both photodiode and BPM data Just chose one shot from the PD data and one set from the BPM data ‘at random’ to compare Wouldn’t expect the amplitude of x and y to agree between PD and BPM (for a start, the PD x and y are uncalibrated) But might expect the fractional charge variation amplitude at 300 kHz to agree But could the PD bandwidth affect (i.e. reduce) this measured amplitude ? But there are similarities in the shapes of the frequency spectrum BPM PD BPM PD

REMINDER OF BPM VARIATIONS SEEN IN 2012

Nominal Lattice FEL-like set-up. Nominal ar1q1/4 = 2.2 A 3133 AR1

3205 INJ-BPM-01 INJ-BPM-01 fast bunch electronics RAW DATA Note significant droop in all 3 observables Small transient at start of train x y charge 15 pC 21 pC 30 pC 43 pC 60 pC

BPM frequency content, 0 – 1 MHz Strong 300 kHz 100 kHz not obviously apparent Norrmalised the x,y DFT so that the amplitudes are in mm 3205 INJ-BPM-01

INJ-BPM-03 Nominal FEL set-up. ‘Typical’ 1-shot BPM train measurement 100 KHz obvious in x y very similar to sum_pickup voltage 6 Mhz present, smaller than 100 KHz ‘usual’ 300 KHz present x (mm), y (mm), sum voltage Fourier transform vertical axis amplitude^2 horizontal axis frequency in MHz Fourier transforms done after subtracting mean values 3191 INJ-BPM-03

INJ-BPM-02 Shot to Shot Variation Again, the low frequency (< 200 kHz) content does vary a bit shot-to-shot After steering to get more central y position on INJ- BPM