Touschek lifetime update

[AmarildoTopalli]

The calculation of Touschek lifetime has been updated following the work of Fu et al doi/10.1103/PhysRevAccelBeams.27.124401 (2024). In addition, the polarization dependency of Touschek lifetime has been added. The function can calculate the scattering C(s) and F(s) functions, as well as the average analyzing power, which is an important parameter used to fit the polarization of the beam.

The formula was tested agains the existing Piwinski formula and gives similar results for the tested lattices.

[gubaidulinvadim]

The formula was tested agains the existing Piwinski formula and gives similar results for the tested lattices.

You should maybe show your tests :)

[oscarxblanco]

Dear @AmarildoTopalli ,
I did a test of your function and I notice this implementation is much slower than the current one. Is there any way you could increase the speed ?
The result of the Touschek lifetime for this test seems to change very little:

current implementation: Touschek lifetime w/o harmon = 9.34 h
Amarildo implementation: Touschek lifetime w/o harmon = 9.39 h

[AmarildoTopalli]

Dear @oscarxblanco ,
I added a polarization parameter that will calculate the polarization-dependent terms only when polarization = True. By default I set polarization = False, and in this case it takes the same amout of time to run the code as the original get_lifetime function.
If the polarization-depent term is calculated, it takes twice as long to run the code, because of the additional F(s) integral.

[gubaidulinvadim]

@AmarildoTopalli Shouldn't polarisation parameter be a float? To allow calculating lifetime at a different polarisation degree?

[AmarildoTopalli]

@gubaidulinvadim What is useful for the experimentalists is the average analysing power A_avg used to fit the polarization time and equilibrium beam polarization. With that value they can calculate the lifetime of the beam with X polarization degree, without needing to run a heavy script.

[oscarxblanco]

Dear @oscarxblanco , I added a polarization parameter that will calculate the polarization-dependent terms only when polarization = True. By default I set polarization = False, and in this case it takes the same amout of time to run the code as the original get_lifetime function. If the polarization-depent term is calculated, it takes twice as long to run the code, because of the additional F(s) integral.

@AmarildoTopalli , I confirm the calculation time is now very similar.

[gubaidulinvadim]

@gubaidulinvadim What is useful for the experimentalists is the average analysing power A_avg used to fit the polarization time and equilibrium beam polarization. With that value they can calculate the lifetime of the beam with X polarization degree, without needing to run a heavy script.

I don't think it's correct to assume that the user knows how to calculate the lifetime of a polarised beam and doesn't want to just do `get_lifetime(a, b, c, polarisation=0.72)'