Cryptosynchrotron: fpFCT: simulating the bunch current

2012/12/20

fpFCT: simulating the bunch current

fpFCT is an smaller name of the Filling Pattern from Fast Current Transformer. As I've said I didn't know how to simulate the signal that is in coming from the scope, and I found a solution.

This is a reused image of the scope signal from the storage ring FCT and what I found how to simulate using PySignalSimulator is:

There are only 4kpoints instead of the 40k that the scope is giving but it looks quite similar.

But how this has been set up in the PySignalSimulator properties? The initial idea was the amplitude modulation but with this what is represented looks like:

But what if the carrier wave, better than a sinusoid looks like a quadratic waveform. With this I have started to play with harmonics. The formula that likes more to be a carrier has been:

In red is plot the carrier over the modulated signal in blue. The signal that is being modulated has been omitted because is almost a sinusoid.

The formula of the carries is:

$c(t)=a_1 + a_{11}sin(2\pi w_1t)+ a_{13}sin(2\pi 3w_1t)+ a_{15}sin(2\pi 5w_1t)+ a_{17}sin(2\pi 7w_1t)+ a_{19}sin(2\pi 9w_1t)$

With parameters values:

$a_{1} = 8\\ a_{11}=10\\ a_{13}=2\\ a_{15}=0.5\\ a_{17}=0.05\\ a_{19}=0.001\\ w_{1}=0.003\\$

The formula of the modulated signal is:

$x(t)=a_{2}sin(2\pi w_{2}(t+sin(x_2)))$

With a_2 = 1; w_2=0.065. The x_2 is a value that is changing from time to time to introduce a drift in the signal in order to have a "dancing" bunches like in the scope.

Lets see the result:

Cryptosynchrotron

2012/12/20

fpFCT: simulating the bunch current

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