The beam is split into two branches, considering the variation of the critical energy across the horizontal fan and maximizing the separation between them. Figure 1 shows the angular profile of the critical energy over the total angular acceptance on the beamline Front End. Two different plateaus can be distinguished, each one with approximately 4 mrad horizontal opening angle, between -8 to -12 mrad the hard edge and between -1 to -5 mrad the soft edge. It has been decided to split the beam into two fans of 2 mrad each, with a central 5 mrad blocked. Each fan has been centered on a different plateau. The hatched zones in figure 1 correspond to the two regions selected for each branch. Branch A with a critical energy of 9.6 keV is centered on -3.5 mrad and Branch B with a critical energy of 20.6 keV is centered on -10.5 mrad.





Figure: Angular profile of the critical energy on the wide Front End.



The beamline is situated on the dipole D25 (Bending magnet 25) (see Characteristics of bending magnet sources). The electron beam characteristics at the source position at the bending magnet corresponding to the middle of the soft edge (Branch A) and the hard edge (Branch B) are listed in the following table.



  Magnetic field Critical energy electron beam parameter
Branch (T) (KeV) sx(mm) sz(mm) s'x(mrad) s'z(mrad)
A 0.39987 9.6 91 36 42 1
B 0.8504 20.6 78 36 48 1


Table I: source characteristics 


The source


The most important characteristics of the electron beam in the storage ring are displayed in table II.



Electron beam energy E = 6.04 GeV
current in 2/3 fill mode (multibunch) I = 200 mA
current in single bunch mode I = 15 mA
horizontal emittance ex = 3.8 . 10-9 m rad
vertical emittance (with 1% coupling) ez = 3.8 . 10-11 m rad
beam lifetime t � 24 h


Table II: ESRF machine characteristics



 The electron beam in the bending magnet has a very low vertical divergence, fifty times lower than the relativistic divergence limits. Therefore in order to obtain the photon source vertical parameter one can neglect the convolution between the angular extension of the electron source with the emission profile of a single electron. Figures 3 and 4 show the density distribution of the source in the vertical phase space for branches A and B respectively. This was obtained from a 5000-ray random simulation, with a gaussian space distribution and a synchrotron source depth. The relevant quantities of interest for characterizing the bending magnet radiation are the spectral flux (brightness) and the brilliance. Figure 5 shows the brightness generated by each source point (soft edge and hard edge) from the bending magnet as a function of energy and figure 6 shows the corresponding brilliance functions.



Figure 3: Vertical phase space of the source corresponding to Branch A


Figure 4: Vertical phase space of the source corresponding to branch B


Figure 5: Brightness of the bending magnet sources A (soft edge) and B (hard edge)


Figure 6: Brilliance of the bending magnet sources A (soft edge) and B (hard edge)