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This notebook was created by Sergey Tomin (sergey.tomin@desy.de). June 2022

11. Slotted Foil

Mutible scattering through small angles​

The Review of Particle Physics" https://pdg.lbl.gov

"... it is sufficient for many applications to use a Gaussian approximation for the central 98% of the projected angular distribution, with an rms width given by:"

θ0=13.6MeVβcpzx/X0(1+0.038ln⁡x/X0)\theta_0 = \frac{13.6 MeV}{\beta c p} z \sqrt{x/X_0}(1 + 0.038 \ln{x/X_0})

Here pp, βcβc, and zz are the momentum, velocity, and charge number of the incident particle, and x/X0x/X_0 is the thickness of the scattering medium in radiation lengths.

Radiation length:

import copy
from ocelot import *
from ocelot.gui import *
from ocelot.cpbd.physics_proc import SlottedFoil, CopyBeam
    initializing ocelot...
p_array0 = generate_parray(sigma_x=0.0001,
    sigma_px=2e-05,
    sigma_y=None,
    sigma_py=None,
    sigma_tau=0.001,
    sigma_p=0.0001,
    chirp=0.01,
    charge=5e-09,
    nparticles=200000,
    energy=1,
    tau_trunc=None,
    tws=None)

d = Drift(5)
bb_182_b1 = SBend(l=0.5, angle=0.0532325422, e2=0.0532325422, tilt=1.570796327, eid='BB.182.B1')
bb_191_b1 = SBend(l=0.5, angle=-0.0532325422, e1=-0.0532325422, tilt=1.570796327, eid='BB.191.B1')
bb_193_b1 = SBend(l=0.5, angle=-0.0532325422, e2=-0.0532325422, tilt=1.570796327, eid='BB.193.B1')
bb_202_b1 = SBend(l=0.5, angle=0.0532325422, e1=0.0532325422, tilt=1.570796327, eid='BB.202.B1')

m1 = Marker()
m2 = Marker()
m3 = Marker()
m4 = Marker()
cell = (d, bb_182_b1, d, d, bb_191_b1, d,m1, m2,m3, d, bb_193_b1, d,d, bb_202_b1, d, m4)

lat = MagneticLattice(cell)

navi = Navigator(lat)

cb1 = CopyBeam()
cb2 = CopyBeam()
cb3 = CopyBeam()

sf = SlottedFoil(dx=10,     # um
                X0=8.9,     # cm Al
                ymin=-0.01, # m lower position of the foil slot
                ymax=0.01   # m upper position of the foil slot
                )


navi.add_physics_proc(cb1, m1, m1)
navi.add_physics_proc(sf, m2, m2)
navi.add_physics_proc(cb2, m3, m3)
navi.add_physics_proc(cb3, m4, m4)

p_array = copy.deepcopy(p_array0)

_, _ = track(lat, p_array, navi)

    z = 42.0 / 42.0. Applied: CopyBeam, SlottedFoil, CopyBeam
show_e_beam(cb1.parray, figname="Init", 
            title="initial distribution in the position of the foil")
show_e_beam(cb3.parray, figname="End of chicane", 
            title="Beam distribution at the end of the chicane")


plt.figure(100)
plt.plot(cb2.parray.tau()*1000, cb2.parray.px()*1000, ".")
plt.xlabel(r"$\tau$ [mm]")
plt.ylabel(r"$p_x$ [mrad]")
plt.figure(200)
plt.plot(cb2.parray.tau()*1000, cb2.parray.py()*1000, ".")
plt.xlabel(r"$\tau$ [mm]")
plt.ylabel(r"$p_y$ [mrad]")
plt.show()

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