Set up a carbon ion beam

Source Definition
2

Dear Xiaoman,

The BEAM card is probably sufficient to achieve your desired settings: you
can specify the momentum spread, the x and y beam size, and the divergence
(equal for x and y, which is luckily your situation). Note:

  • The beam spread is expected as a momentum (p ) spread and not
    as a kinetic energy (T) spread. The relationship is

    dp = (T+m)/sqrt(T*(T+2m)) dT

    Flair offers you the function dT2dp(T,dT,m) to convert from dT to dp
    (see section F3.6 of the Flair manual).

  • Select Gaussian profiles for momentum, size, and divergence spreads.
    All spreads are then interpreted as the full width at half maximum of
    the Gaussian [note that FWHM=2sqrt(2ln(2))*sigma]. The conversion
    can be done via the “fwhm” variable in Flair.

Regarding your emittance wishes: Let x’ be the angle of the initial
particle direction with respect to the x axis. In the x-x’ plane, a setup
using a (FWHM) divergence fwhm * θx = 1.17741 mrad, and a (FWHM)
beam size fwhm * σx=1.05967 cm (beam size input is in cm in FLUKA
like all lengths) would populate a 2D Gaussian distribution with your
desired beam size σx and beam divergence θx. A measure of the
(normalized) emittance would be

εx / pi = σx * θx = 2.25 mm mrad    (essentially your desired 2.22 mm mrad)

Likewise in y-y’ space:

εy / pi = σy * θy = 2.30 mm mrad    (essentially your desired 2.37 mm mrad)

If this fits your needs, make sure you are satisfied with the sampled
primaries before proceeding.

Cesc