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Figure-8 Undulator

The radiation source for the IUVS beamline at ELETTRA is required to provide a photon flux of at least 1015 photons/s in the range 5 to 10 eV. This calls for an undulator of the maximum length compatible with available length in the straight sections of the storage ring (4.5 m), and having the maximum possible number of periods. This requirement naturally implies a very high emitted power and power density, which can be harmful to the optical elements of the beamline. For this reason an exotic insertion device, the Figure-8 undulator, has been considered as an alternative to the stardard vertical field device. The main advantage of this solution is a much reduced on-axis power density which is obtained with no penalty on the useful photon flux.

The figure-8 undulator, as originally proposed by Tanaka and Kitamura [1,2], is made of six periodic magnetic arrays: the central rows generate a vertical field with spatial period lo, while the side blocks create a horizontal field with twice that periodicity (2lo).

Figure 1: magnetic structure of the undulator

open 3D realtime f8 magnetic structure
open 3D realtime f8 trajectory

The resultant trajectory follows a figure-of-eight pattern when projected on the transverse X/Y plane. Due to the opposite helicity in any two consecutive periods, the net polarization of the emitted photons is linear at any observation angle. However, the radiation spectrum is composed of two sets of harmonics, conventionally defined by integer (i=1,2,3,etc) and half-integer (i=1/2,3/2,5/2,etc) indices and having alternatively horizontal (i=1,3,5,...) and vertical polarization direction.

Figure 2: Predicted radiation spectrum at minimum gap through a 0.6 x 0.6 mrad2 pinhole.

The angular distribution of the emitted power (see picture below) is peaked off-axis so that a suitable pinhole can filter-off most of the unwanted power, thus reducing by a large factor the heat load on optics.

Figure 3: Power density angular distribution at minimum gap

Due to the large emission angle of the fundamental compared to that of the higher-order harmonics (which carry most of the energy) this is achieved with no significant reduction on the useful photon flux, as can be seen in the next graph where the spectral intensity produced by an equivalent conventional undulator is shown for comparison [3].

Figure 4: Predicted radiation spectrum of a conventional undulator through a 0.6 x 0.6 mrad2 pinhole.

Main Figure-8 undulator parameters

magnetic material NdFeB (Br=1.28 T)
period length (mm) 140
number of periods 32
minimum gap (mm) 19
Bxo, Byo (T) at minimum gap 0.13, 0.72
Deflection parameters Kx, Ky 3.4, 9.4
Total power (W) at minimum gap, 2 GeV, 400 mA 2500
Power (W) transmitted by a pinhole (0.6 x 0.6 mrad2) at minimum gap, 2 GeV, 400 mA 20


[1] T. Tanaka, H. Kitamura, "Figure-8 undulator as an insertion device with linear polarization and low on-axis power density", Nucl. Instr. and Meth. in Phys. Res. A 364 (1995) 368.

[2] T. Tanaka, H. Kitamura, "Analysis of Figure-8-Undulator Radiation", J. Synchrotron Rad. 3 (1996)  47.

[3] B. Diviacco et al. : "New Insertion Devices for ELETTRA", proc. 2001 Particle Accelerator Conference.

Last Updated on Friday, 06 July 2012 14:38