# Set up a carbon ion beam

Dear fluka experts,
I want to set up a carbon ion beam in flair, and the beam characteritics are Relative energy dispersion (ΔEk/Ek=2.3*10^-4)，Beam spot size (σx,σy)=(4.5mm,4.6mm), Beam lateral emissivity (εx, εy)=(2.22mm mrad, 2.37mm mrad), Beam divergence (θx, θy)=(0.5mrad, 0.5mrad). I want to know how I can set by using beam card or user routine. Thanks in advance!

Best regards,

Xiaoman

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

Dear Cesc,
Thanks for your kindly help! I set the value in the beam card in Flair

, and I don’t assure the correctness for them. Could you help me check the value? Thanks in advance!
Best regards,
Xiaoman

Dear Cesc,
Thanks for your kindly help! I have got it.
Best regards,
Xiaoman