Ion Identification
Bob is a summer school student at IMP. He is really fascinated in precision measurements of atomic masses and lifetimes at a storage ring, so he joined the Schottky Spectroscopy Group. Before he came, he had learnt some basic knowledge about Schottky spectroscopy technique. In principle, charged ions of different species are stored in the ring——the experimental Cooler Storage Ring (CSRe), to be specific. Their periodical motions are detected by an extremely sensitive device, named Schottky resonator, in the form of sampled, digitized RF signal. Such a time-domain signal needs to be Fourier transformed into the frequency domain to easily separate all kinds of ions, since they cluster into peaks due to their common revolution frequencies. Once the revolution frequencies are measured precisely, their masses and lifetimes can be determined accordingly, which Bob does not know exactly for the moment, but will dive into this topic during his stay at IMP.
Today Bob gets an assignment from his supervisor to identify the frequency peaks in a Schottky spectrum, which is centered at 242.9 MHz and spanned over 800 kHz.
Apart from the broad bump of the background, which Bob knows as the resonance curve of the detector, he can clearly see three peaks sitting at 17 kHz, -170 kHz, and -355 kHz.
"Those must be different kinds of ions", he says, "but what are they exactly?".
From the logbook of the experiment he can reconstruct the situation back then.
It was the 58Ni19+ used as the primary beam at the kinetic energy of 394.38 MeV/u, bombarding on a 15 mm thick beryllium target.
The smashed fragments are transported by a fragment separator, filtered at the magnetic rigidity of 5.47156 Tm, and injected into the CSRe.
To get the yields of all possible ions, Bob opens a LISE++ application and simulates the production and transmission of the secondary beam according to the same experimental conditions.
Over a cup of San Pao Tai, LISE++ has generated the desired results, which Bob saves as the file 58Ni28.lpp.
To identify ions, Bob needs to correlate the calculated revolution frequencies based on the circumference of the CSRe and the fixed magnetic rigidity, with the detected locations of frequency peaks.
But that is not the full story.
One subtlety complicating the correlation is the different harmonics of Schottky bands for the same ion species, which Bob needs to take into account, since they may overlap within the same frequency window.
Fortunately Bob does not have to implement the identification algorithm from scratch.
There already exists a working code publicly hosted on GitHub at ring-exp-toolkit, as his supervisor told him earlier.
Having downloaded the repository and set up everything, Bob launches an IPython session for interactive processing.
The first two lines are pretty standard:
import ion_id as _iid
iid = _iid.IID("58Ni28.lpp", 242.9, 800)According to the example snippet in README.md, Bob learns that to instantiate the class IID he needs to provide sequentially with the name of LISE++ file, center frequency in [MHz], and span in [kHz].
Immediately after that, the code prints out 10 predicted ions with their locations in the Schottky spectrum.
center frequency 242.9 MHz
span 800 kHz
orbital length 128.8 m
Bρ 5.47156 Tm
Weight Ion Half-life Yield Rev.Freq. PeakLoc. Harmonic
2.50e+09 58Ni28 stbl 1.40e+06 1.508789 15 161
1.42e+07 56Co27 77.236 d 8.56e+03 1.507636 -171 161
4.64e+06 54Fe26 stbl 3.02e+03 1.506473 -358 161
8.18e+05 57Co27 271.70 d 5.04e+02 1.492147 320 163
7.17e+05 47V23 32.6 m 5.86e+02 1.520519 383 160
5.26e+05 45Ti22 184.8 m 4.71e+02 1.519651 244 160
4.62e+05 46Ti22 stbl 4.24e+02 1.500514 183 162
3.83e+05 43Sc21 3.891 h 3.76e+02 1.518705 93 160
2.75e+05 41Ca20 99.4 ky 2.99e+02 1.517706 -67 160
2.71e+05 55Fe26 2.744 y 1.80e+02 1.490373 31 163
The results are nothing more, nothing less, right to the point, and nicely presented in a table, except for the Weight column which Bob does not understand for now.
By scrutiny, he soon figures out that it is the product of the Yield and square of the Rev.Freq., which surely makes sense, since the Weight is directly proportional to the peak area.
Obviously all items are sorted by the Weight in a descending order.
In case the Schottky spectrum was much complex and more than 10 peaks were present, Bob could have examined more ions by explicitly telling the code
iid.update_n_peak(20)For Bob's current assignment, he is happy to work with first 10 ions. By comparing the predicted and measured peak locations, he can easily identify the three peaks (from right) as: 58Ni28+, 56Co27+, and 54Fe26+. If Bob wanted to get an even better coincidence, he could have used a measured peak location, such as the most prominent one, to calibrate the code, which essentially alters the magnetic rigidity setting of the CSRe.
iid.calibrate_peak_loc("58Ni28", 17, 161)The three arguments are the calibrating ion, peak location in [kHz], and harmonic, respectively. The resultant table are accordingly updated to
center frequency 242.9 MHz
span 800 kHz
orbital length 128.8 m
Bρ 5.47164 Tm
Weight Ion Half-life Yield Rev.Freq. PeakLoc. Harmonic
2.50e+09 58Ni28 stbl 1.40e+06 1.508801 17 161
1.42e+07 56Co27 77.236 d 8.56e+03 1.507649 -169 161
4.64e+06 54Fe26 stbl 3.02e+03 1.506486 -356 161
8.18e+05 57Co27 271.70 d 5.04e+02 1.492160 322 163
7.17e+05 47V23 32.6 m 5.86e+02 1.520532 385 160
5.26e+05 45Ti22 184.8 m 4.71e+02 1.519664 246 160
4.62e+05 46Ti22 stbl 4.24e+02 1.500526 185 162
3.83e+05 43Sc21 3.891 h 3.76e+02 1.518717 95 160
2.75e+05 41Ca20 99.4 ky 2.99e+02 1.517718 -65 160
2.71e+05 55Fe26 2.744 y 1.80e+02 1.490385 33 163
Having identified the ions in the Schottky spectrum, Bob gets more feeling about how those micro particles can be seen and distinguished inside such a giant storage ring. He thinks he is ready for more advanced tasks tomorrow!