Hi,
When using the IBSCATTER element for IBS simulation, under the condition of longitudinal slicing of the beam, how is the sliced bunch length statistically calculated? I checked the elegant source code and found that the sliced bunch length is given by “bLength = c_mks * tLength / sqrt(4 * PI)”. What is the basis for this bunch length calculation?
In IBS simulations, based on experience, what are the recommended or suitable numbers of beam slices and macro particles? After all, IBS IBSCATTER simulation is based on element-by-element tracking , right?
Yours Tiansk
Calculation of Sliced Beam Parameters
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michael_borland
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Re: Calculation of Sliced Beam Parameters
Tiansk,
When performing slice-based IBS, elegant calculates an equivalent rms bunch length that can be inserted into the IBS growth rate equations, which are expressed in terms of the rms bunch length.
The IBS rate is proportional to the integral of the longitudinal particle density rho(s) squared (times other integrals). For a uniform distribution of length L containing N particles, that becomes N^2/L. For a gaussian bunch, that becomes N^2/(2*sqrt(pi)*sigma).
The equivalent value of sigma to put in the gaussian-bunch equation is thus just sigma=L/2/sqrt(pi) or L/sqrt(4*pi).
--Michael
When performing slice-based IBS, elegant calculates an equivalent rms bunch length that can be inserted into the IBS growth rate equations, which are expressed in terms of the rms bunch length.
The IBS rate is proportional to the integral of the longitudinal particle density rho(s) squared (times other integrals). For a uniform distribution of length L containing N particles, that becomes N^2/L. For a gaussian bunch, that becomes N^2/(2*sqrt(pi)*sigma).
The equivalent value of sigma to put in the gaussian-bunch equation is thus just sigma=L/2/sqrt(pi) or L/sqrt(4*pi).
--Michael
Re: Calculation of Sliced Beam Parameters
Thank you for your detailed explanation. I understand the origin of the sqrt(4*PI) factor.