schottky_spectra
Revolution frequency is ~3.1 MHz
adb window starts at -0.01
4kV window starts at -0.012
3kV starts at -0.011
This plot shows the raw siganl from the FAB for the adiabatic debunch case. The FFT window is shown in red, the window starts at -0.01 seconds and is 0.0005 seconds long .
This window length/ position may not be appropriate, can adjust the window later on.
Adiabatic debunch
On the left in the above plots is the full spectra, zoomed in view is on the right
Below are plots of the strongest peaks in the spectra.
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This plot shows the raw siganl from the FAB for the 4kV abrupt debunch case. The FFT window is shown in red, the window starts at -0.012 seconds and is 0.0005 seconds long .
4kV abrupt debunch case
On the left in the above plots is the full spectra, zoomed in view is on the right
Below are plots of the strongest peaks in the spectra.
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On the left is the full spectra for both runs and the right is a zoom into 3.1 MHz
Note by SM, at 8:30 UK on 20 January.
at 56 MeV, gamma=(56+938.272)/938.272=1.0597.
slippage factor eta = alpha_p-1/gamma^2=1/(7.5+1)-1/1.0597^2=-0.773
Let read the frequency spread from the top right figure,
adb case: df/f (full) = (3.133-3.120)/((3.133+3.120)/2) = 4.2E-3, or +/-2.1E-3
4 kV abrupt case: df/f (full) = (3.138-3.114)/((3.138+3.114)/2) = 7.7E-3, or +/-3.8E-3
Therefore,
dp/p (abd) = 1/eta df/f = +/- 1/0.773 2.1E-3 = +/-2.7E-3
dp/p (4 kV) = +/- 1/0.773 3.8E-3 = +/- 5.0E-3
dp/p is proportational to V^0.25 and "adb" case rougly correspond to 0.9 kV, so that the ratio should be (4/0.9)^0.25 = 1.45, while the experimental result is 1.85 (not bad).
From David simulation with adiabatic debunching, dT (kinetic energy) = +/- 150 keV,
dp/p = 1/(1+1/gamma) dT/T = +/- 1/2 0.15/56 = +/- 1.3E-3
Measurement shows about a factor 2 larger dp/p, but still a good first result!
Below is Schottky spectra for a window of 5ms
Below is Schottky spectra for a window of 10ms
Below is Schottky spectra for a window of 10ms
Below is adb, 4kV and 3kV debunch with a 1ms window
From SM to Carl and All, at 15:00 UK on 20 January
I am very excited to see the spectrum which shows the clear difference between two beams. This is the great step forward to the March experiment. The following is my thoughts for analysis.
Uesugi-san chose h=9 and 18 peaks. It is worth looking at those higher harmonic peaks.
When you plot peaks, it should look similar frequency spread (relatively) if you scale the range of frequency axis proportional to haromonic number.
You could define averaged df/f by averaging (1/h)(df/df) for the harmonics up to some number (~20? or small when the overlap does not happen). However, this averaging may not be necessary if you define df/f clearly at a particular harmonic.
Calculate dp/p=(1/eta)(df/f) and see if those value agree with David's simulation.
As we discussed, start timing of the window could be later such as 1 ms, 5 ms or 10 ms after RF off. If dp/p=+/-2E-3, dt/t=eta dp/p=0.773 2E-3=1.5E-3. That means that after t/dt=1/1.5E-3 /2=333 turns or 0.1 ms, the head and tail of the beam meet (initial bunch length is zero). After 1 ms, the bunch legnth becomes 10 times circumference. It may be marginal to claim the beam becomes coasting if you only wait for 1 ms.
In my initial calculation, I assume that the ratio of dp/p is (4/0.9)^0.25. This is true when the RF is turned off abruptly after forming 4 kV and 0.9 kV bucket. Since the adiabatic case has another adiabatic debunching process, dp/p should be smaller. The ratio of RF bucket heigh and dp/p after debunching process is 4/pi and this factor should be included. I also assume that 0.9 kV is filled 100% with the beam.
dp/p (0.9kV)=4/pi*2.7E-3=+/-3.4E-3, dp/p (4kV)=+/-5.0E-3. Therefore the ratio=1.45, that is the same as (4/0.9)^0.25. Too good to believe!
If you have time, please calculate dp/p after abrupt RF switch off and see whether dp/p is proportional to V^0.25. Since there is several uncertainties of the absolute value of RF voltage and capturing process at injection with foil scatterling, qunatitative comparison of dp/p with simulation may be difficult. However, we are more interested in the relative value, namely whether dp/p increases during the beam stacking process and how much. Relative comparison of dp/p from adb, 0.9, 2, 3, 4 kV RF buckets give us an idea how well we can measure dp/p relatively.
I wanted to double-check the revolution frequency of the beam.
I assume that the revolution frequency of beam before and after RF-OFF is the same for 'abrupt (4kV)' case. Also I assume that the revolution frequency of beam before and after the adiabatic debunching period is the same for 'adiabatic debunch (adb)' case. Hope what I write down here is clear. The revolution frequency for both cases are the same: 3.11801MHz.
I wanted to double-check the revolution frequency of the beam.
I assume that the revolution frequency of beam before and after RF-OFF is the same for 'abrupt (4kV)' case. Also I assume that the revolution frequency of beam before and after the adiabatic debunching period is the same for 'adiabatic debunch (adb)' case. Hope what I write down here is clear. The revolution frequency for both cases are the same: 3.11801MHz.
The FFT starts from about 3.3ms from RF-OFF and the FFT window range is about 16.7ms.
The results is bellow. The sampling frequency is 250MS/s in this case.
I plot the FFT spectra with respect to the harmonics (f/f0, f0=3.1180 MHz)in the above.
We can see double peaks up to h=9. However, I cannot find the peaks at higher harmonics range easily. Yesterday, I found many strong peaks at higher harmonics region, but I think it was just a noise from RF or somewhere.
When I see the plot, it seems for me that the double peak distribution is getting asymmetry w.r.t. the centre (h=1,2,3,4,5..). This might be a noise issue? F0 has been shifted?
I am wondering if we take same data by Tora (rectungle bunch monitor), we can get data with less noise from RF?
Currently, FAB is one cell before RF cavity, therefore huge RF noise are on the FAB data. However, Tora bunch monitor is in 5cells away from RF cavity, and it has less noise from RF.
Around each harmonics, similar structures seen in the other plots can be recognised...still coasting beam is there?
I hope those figures will help to understand schottky analysis data and to give any other possibility to improve data taking (different RF patterns, kick out remaining coasting beam, 1Hz reprate etc.)
It is interesting to see the spectrum at different timing. I see the spectrum at later time, at 27 ms after RF off, is different from ones at 3.3 ms after RF off. Whether it is because of lower or almost zero intensity at later time or something different reason is the interesitng question. If the beam does not survice more than ~20 ms, the double peaks is not due to the beams from the previous cycle.
I wonder Carl could do the following. Plot the spectrum at 2 ms, (7 ms,) 12 ms, (17 ms,) 22 ms, (27 ms) after RF off. For all, the window size could be either 5 ms or 10 ms. See if df/f for adb and 4 kV cases does not change, independent of the start timing of the window. I understand that it becomes more difficult at later timing because of smaller signal. It is enough to see spectrum around only one harmonic, e.g. h=1 or around 3.1 MHz.
When the machine is available, I propose to capture the beam again at later time, 2, 7, 12, 17, 22, 27 ms after RF off. The RF pattern can be a reverse process, namely increasing voltage from zero to 0.9 kV in 1.6 ms and from 0.9 kV to 4 kV in 3.2 ms. If bunch signal appears, the beam is still there. If we can confirm that the beam does not survive after certain time period, no need to kick out.
Emi mentioned RF noise above. Is there any reason that RF noise still exists after RF turns off? All data above were taken after RF is off. I naively assume that any noise caused by RF has already gone.
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window length 5ms
Window start -1.07 ms
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window length 10ms
Window start: -1.07ms
c1: rectangular BPM (Tora), c2:RF waveform, c3:FAB (with High Pass Filter ~ a few 100kHz cutoff?)
==================File number | Description==================00000 | Main F/D magnet OFF, Corrector Magnet next to RF cavity (COR) OFF, RF burst OFF00001 | Main F ON (814A), Main D OFF, COR OFF, RF burst OFF00002 | Main F&D ON (814A), COR OFF, RF burst OFF00003 | Main F&D ON (814A), COR ON (520A), RF burst OFF00004 | Main F&D ON (814A), COR ON (520A), RF burst ON (KURNS nominal pattern)
As the harmonic of the revolution frequency increases the two peaks move apart. In Emi's plots of the schottky frequency spectrum, it appears that the left hand side peak moves further from the harmonic frequency and the right hand side stays in roughly the same place. This could indicate that the coating beam from the previous cycle is still present when the second beam is accelerated to the top energy. The second beam displaces the first beam and moves it downwards in the longitudinal phase space. The two peaks are only present in the adiabtic case so in the higher dp/p cases the beam could have been lost by the time the second beam is accelerated.
Because of the scale of each plot, it is hard to see that the left moves but the right stays. Is there any chance that the revolution frequency is slightly lower than you think? SM
E.Y: That is one possibility I think. I plot the same figure but scaled by h as you mentioned yesterday.
Also,I try to apply fitting on the first peaks for both cases at h=1 but failed if I used gaussian function. Should it be different function I should use? Even when I do not use a fitting to define RMS width or full width, it is not easy to define the peaks (distribution) on 4kV case.
Whether second peak (or first peak) is a remaining coasting beam (stacking beam?) or other reasons, the change of two peaks width in different dP/P is meaningful. It s worth to understand what the peaks mean, we have to measure beam off real-time signal as well to compare.
According to David K yesterday, if the beam energy is lower and assuming that dP/P is the same as 56MeV (?) case, we could see a larger df on schottky data as momentum compaction factor (1/k+1) is the same?
For other cases: FFT window starts at 1ms after the RF-OFF (roughly..), and its window width is about 16ms. The FFT spectrums are below. Again, I have not considered dP/P comparisons between the two.
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Schottky spectra from 2023/01/24 data where we accelerated any recaptured beam into the scraper
See 1st harmonic peak for the windows shown on the left
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See schottky spectra below for a 10 ms window. The window location is shown at the bottom
I also took an FFT of the bunched beam to confirm the revolution frequency: see thw window I took and its corresponding spectrum below
Hi Carl and Max
I think you finally got it! Double peaks disappear and the df/f is reasonable.
To plot spectrum at other harmonics, please choose the range of frequency in more sensible way. We expect df ~ a few 10 kHz at h=1. The range of frequency axis should be h * a few 10 kHz for higher harmonics. As Emi did already, it is the best to scale the range proportional to harmonic number.
I guess we have more confidence in the results by now.
I still wonder how long the beam survive. If you do Schottky scan with 1 Hz operation, can you see the same result with that with recapturing or still suffered from double peaks?
I will post this email to eLog as well.
Shinji
Hi Carl and Max (at 21:30 UK on 24 January)
I may have simplified the observations too much, but if we could conclude that we see two peaks, one from the remaining beams from a previous cycle, and the other from newly accelerated beam, we could manipulate the position (central frequency) of two peaks by RF pattern. If two AWG patters can be triggered alternatively, that is the easiest way. However, if not, we can still change the energy of remaining beams by accelerating or decelerating a little bit at the end of a cycle.
I have created 3 AWG scripts which have: 1) about 1 MeV acceleration at the end, 2) about 2 MeV acceleration at the end, 3) about 1 MeV deceleration at the end. Because of concatination of 12 segments, the total length is 65 ms.
My expectation is that Schottky signal right after adiabatic debunching at the energy of 56.056 MeV but before a bit of acceleration or deceleration will show two peaks corresponding to 56.056 MeV and 56.056+1, +2, -1 MeV. More quantitatively, dT (kinetic energy)=1 MeV corresponds to df (frequency)=20 kHz. The separation of two peaks are then 20 kHz, 40 kHz, and -20 kHz-(further sepration due to phase dispacement), respectively.
I will upload the scripts on Teams (under AWGscript/DoublePeak) and copy this email with figures on Google doc.
Shinji
tmp_12_3_3_2_30_2_3_2_2_3_2_2_0.057054_2.85.equ, Above, you can see ~1MeV acceleration at the end.
tmp_12_3_3_2_30_2_3_2_2_3_2_2_0.058058_5.70.equ, Above, you can see ~2MeV acceleration at the end.
tmp_12_3_3_2_30_2_3_2_2_3_2_2_0.055065_m2.85.equ, Above, you can see ~1MeV deceleration at the end.
The pattern has the 12 egments.
0 - 12.3321 ms, volt: 4 - 4 kV, phis: 20 - 20 deg
12.3321 - 15.5321 ms, volt: 4 - 4 kV, phis: 20 - 0 deg
15.5321 - 18.7321 ms, volt: 4 - 0.9 kV, phis: 0 - 0 deg
18;7321 - 20.3321 ms, volt: 0.9 - 0 kV, phis: 0 - 0 deg
20.3321 - 50 ms, volt: 0 - 0 kV, phis: 0 - 0 deg
50 - 51.6 ms, volt: 0 - 0.9 kV, phis: 0 - 0 deg
51.6 - 54.8 ms, volt: 0.9 - 4 kV, phis: 0 - 0deg
54.8 - 56.4 ms, volt: 4 - 4 kV, phis: 0 - 2.85 deg (to acc 1 MeV), 0 - 5.70 deg (to acc 2 MeV), or 0 - -2.85 (to dec 1 MeV)
56.4 - 58.0 ms, volt: 4 - 4 kV, phis: 2.85 - 0, 5.70 - 0, or -2.85 - 0, respectively
58.0 - 61.2 ms, volt: 4 - 0.9 kV, phis: 0 - 0 deg
61.2 - 62.8 ms, volt: 0.9 - 0 kV, phis: 0 - 0 deg
62.8 - 65 ms, volt: 0 - 0 kV, phis: 0 - 0 deg
Schottky measurement should be done between 20.3321 and 50 ms, where one beam just accelerated and the other remaining from the previous cycle but with slightly different energy should exist. It is interesting to see two peaks on Schottky scan has corresponding df.
Obviously, I do not want to say this has high priority, but please try if you have time. Scripts are ready on Teams.
Shinji
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See below, the first 6 harmonics for the data taken on the 24th. Corresponds to file numbers 44 and 46
adb window starts at t=0.0s
4kV window starts at t=-0.005s
The same for 3kV and adb, 3kV window starts at -0.01s
The same for 2kV and adb, 2kV window starts at -0.01s
The same for 0.9kV and adb, 0.9kV window starts at -0.01s
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Schottky with shaker from 26th. BEAM ON
Schottky with shaker from 26th. BEAM OFF
Schottky with shaker 10ms window starting at t = 0.0
5ms window with windows starting at -0.01s
Hi Carl and Max
I have uploaded AWG scripts in the folder named "DoublePeak10seg". I increase and decrease phase and voltage at the same time so that the total segments becomes 10 instead of 12. I also reduce the time duration of coasting beam from 30 ms to 10 ms. The total time of the programme is 38 ms. I hope those work.
As you see them, there are 5 patterns, which corresponds to deceleration or acceleration at the end of the coasting beam to separate from the newly injected beam. 5 patterns corresponds to roughly -2, -1, 0, 1, 2 MeV. In the frequency axis, it is -40, -20, 0, +20, +40 kHz with respect to the spectram to the newly injected beam. For the negative side, there must be further separation because of the phase displacement deceleration.
Hope it works.
Shinji
5 patterns are shown below: -2, -1, 0, +1, +2 MeV, respectively.
