2023-03-23

Machine Status

Machine is up-and-running again.

Vacuum is 2.4e-7 Pa (yesterday was 2.4e-7 Pa).

TORA signal is greater than around ±220 mV at injection. (Yesterday was ±300 mV, but before that was lower.)

FAB signal is larger than this.

Equipment

Yesterday, it was asked whether the extract kickers were firing and whether that might be affecting beam-1 in some way. Ishi-san has confirmed that the extract kicker is not firing. 

Measurements

Today we will start with Case 1, with RF voltage 1.18 kV when phi_s=0. 

After that, we will measure 6.985 ms acceleration case with the long-coast and short-coast cases. There will be no Schottky data in the short-coast case. Since this is the first time we've run a short-coast, we would like to run it as early as possible to identify any problems.

When the short-coast dataset is done, we will move back to doing the energy sweep. We'd like to have a dataset with Beam-2 above Beam-1, so we'll start from 7.08 ms and move down. 

All AWGScripts have 1.18 kV when phi_s = 0.

Measurement 1 - Case 1 - (1.18 kV when phi_s=0)

Measurement 2 - Two Beams - (6.985 ms with long coast)

11:15: linac down. Same issue as yesterday. restarted and seems to work. If the issue reappears change of power supply is planned (would require 1 to 2 hours).

Beam came back with no intervention. Since there is a possibility the machine will not work today, we will take 

Measurement 3 - Two Beams - (6.985 ms with short coast)

• 25 ms delay for first acquisition

• 45 + 25 = 70 ms delay for the second acquisition.

In this case, the windows from the two acquisitions will overlap and there will be close to 10 ms worth of "nothing" at the end of the 

Measurement 5 - Two Beams - (7.08 ms with long coast)

Measurement 6 - Two Beams - (7.05 ms with long coast)

We decided that given the state of the machine, we'll run a coarse energy scan.

Measurement 7 - Two Beams - (7.02 ms with long coast)

Measurement 8 - Two Beams - (6.97 ms with short coast)

Measurement 9 - Two Beams - (6.97 ms with long coast)

Measurement 10 - Two Beams - (7.00 ms with short coast)

Measurement 11 - Two Beams - (7.00 ms with long coast)

Measurement 12 - Case 4 (6.980 ms with long coast) - [CASES]

Measurement 13 - Case 2 (6.980 ms with long coast) - [CASES]

Measurement 14 - Case 3 (6.980 ms with long coast) - [CASES]

Measurement 15 - Two Beams (7.01 ms with long coast) 

Measurement 16 - Two Beams (7.005 ms with long coast) 

Investigative Data Analysis

Tomography

File 44 short recpature Tomograpghy. I adapted parts of Davids script to make these plots at starting at -0.0134 seconds in file 44. Denoting t = -0.0134 as turn 1, the plots show turn 1, 26, 51, 76 and 101.

where I_{RMS} is the "[...] RMS Schottky current per band" [1]. The power spectral density 

so really, we should be trying to estimate the power spectral density if we want the peak heights to be proportional to N.

The power spectral density is defined in terms of the discrete-time-Fourier-transform, so it can only be estimated from a finite number of samples. There are several techniques for estimating the power spectral density from a finite number of samples; the Welch method is one such technique [2, 3]. It works by splitting the finite duration sample into a finite number of chunks; since the signal is random, all chunks should have the same PSD. As each chunk will have a window applied before its spectrum is calculated, the chunks are made to overlap (so some signal from chunk 1 will also be in chunk 2, but the window will suppress it more in one chunk than the other). The PSD is estimated from each chunk, and then the results from each chunk averaged. The wikipedia page says that this is sacrificing frequency resolution for noise reduction, which can be understood because the frequency resolution will be decided by the length of each chunk.

Welch's method is implemented in Scipy [4], so we can try it easily. Using one set of data from yesterday, and chunking a single acquisition into 10 parts gives the following output. The frequency resolution has been increased from 20 Hz to 200 Hz, but this still makes around 250 samples for each peak. 

[1] - Boussard D., "Schottky Noise and Beam Transfer Function Diagnostics". Accessed 19 January 2023. http://cds.cern.ch/record/179298/files/CERN-87-03-V2.pdf

[2] - Welch, P. D. (1967), "The use of Fast Fourier Transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms" (PDF), IEEE Transactions on Audio and Electroacoustics, AU-15 (2): 70–73, Bibcode:1967ITAE...15...70W, doi:10.1109/TAU.1967.1161901

[3] - https://en.wikipedia.org/wiki/Welch%27s_method 

[4] - https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.welch.html