Closed oscarxblanco closed 4 months ago
Hi @oscarxblanco, good catch! Does this correction have a big impact on the lifetime calculation? I copied this from the matlab implement, is it there as well did you see the same issue there or is it something I introduced when translating it?
The second term in $B_2^2$ is a crossed-term (x-y) that depends on the product of energy spread, the dispersions (x and y), and the inverse of the transverse emittances.
It has an impact in lattices with vertical dispersion ($\eta_y\neq0,\eta'_y\neq0$) either due to lattice design, limits on the optics correction or transverse coupling.
However, not many lattices have vertical dispersion.
I have checked the matlab implementation and it does not have this issue. It also has the answer to an approximation that I would suggest to document also on pyat. In matlab the function TLT_IntPiw_k
uses the first term in the the modified Bessel function approximation for large numbers: $I_0 \approx \frac{\exp{x}}{\sqrt{2\pi x}}(1+\frac{1}{8x}(1+ ...))$
it is explicitly written in the comments. In pyat, the same logic is used in the function int_piwinski
but there is no explanation on why is done like that.
Ok. Thanks for this analysis. I will correct this as suggested then.
Correction proposed in #765
Fixed in #765
Dear all,
there is a missing factor 4 in function
_get_vals
of at/pyat/at/acceptance/touschek.py lines https://github.com/atcollab/at/blob/b016b779cc7bbc377a44165196e1c64a776a1d37/pyat/at/acceptance/touschek.py#L127-L129bg2i
is calculated above as $1/(2\beta^2\gamma^2)$.bg2i
is wrongly put as multiplicative factor of the whole expression.Those lines should calculate the $B^2_2$ factor in Eq. (34) on Piwinski's article titled 'The Touschek effect in Strong Focusing Storage Rings'. https://arxiv.org/abs/physics/9903034 where the second term on right hand side is not divided by 4.