A 160 µm thick silicon crystalline undulator with ten sinusoidal periods of 334 µm, made with patterned silicon-nitride stressor films. The method is covered by patent application WO 2026/078554.
Research › Accelerators and colliders
Crystalline undulators
Hard photons from periodically bent crystals
A crystal with periodically bent planes makes channeled particles wiggle with a sub-millimetre period and emit hard photons.
The physics.
In a magnetic undulator a row of alternating magnets makes a relativistic electron or positron wiggle, and it radiates in a narrow band of energies. For small deflections the photon energy on axis is
Eγ ≈ 2γ2 hc / λu
where γ is the Lorentz factor of the particle and λu the period. Magnetic undulators cannot have periods shorter than a few centimetres.
In a crystal whose planes are bent along a sine wave, a channeled particle follows the planes and oscillates with their period, which can be a fraction of a millimetre. A period a hundred times shorter gives photons a hundred times harder from the same beam: with λu = 334 µm the formula gives about 30 keV for 1 GeV electrons and a few MeV at 10 GeV, from a crystal a few millimetres long.
The deformation has to be large compared with the 0.19 nm spacing of silicon (110) planes, with an amplitude above about 1 nm, yet gentle enough that the particles stay channeled, and it has to be uniform through the whole crystal, so that every channel oscillates in step.
We bend crystals periodically without damaging the lattice. Stripes of silicon nitride, deposited under tension and patterned on the surface, impose a sinusoidal deformation through the thickness; finite-element simulations choose the thickness and the period so that the shape is uniform and higher harmonics are small. Earlier undulators were made by grooving the surface and by ion implantation.
What we have shown.
A crystal with periodically bent planes makes channeled particles oscillate with a sub-millimetre period, so it can emit photons far harder than a magnetic undulator. Using patterned tensile films we produced the first damage-free sinusoidal crystals: the latest is 160 µm thick with ten 334 µm periods. The method is covered by patent application WO 2026/078554.
Planar channeling observed in a periodically bent crystal, made by grooving and tested with protons at the CERN SPS.
Radiation of 12.6 GeV electrons in a strongly bent silicon crystal: volume reflection strongly enhances the emission of low-energy photons.
Read first.
- Design of a crystalline undulator based on patterning by tensile Si₃N₄ strips on a Si crystalGuidi V., Lanzoni L., Mazzolari A., Martinelli G., Tralli A. · Applied Physics Letters 90 (2007)
- Experimental evidence of planar channeling in a periodically bent crystalBagli E., Bandiera L., Bellucci V. … Guidi V., Mazzolari A. et al. · European Physical Journal C 74 (2014)
- Silicon crystalline undulator prototypes: Manufacturing and X-ray characterizationCamattari R., Bandiera L., Tikhomirov V. … Romagnoni M., Sytov A., Mazzolari A. et al. · Physical Review Accelerators and Beams 22 (2019)
- From simulation to fabrication: Realizing silicon crystalline undulators with silicon nitride stressor layer patterningMalagutti L., Bandiera L., Bonafè F. … Fedeli P., Guidi V., Paternò G. et al. · Nucl. Instrum. Methods A 1076 (2025)
- Ion implantation for manufacturing bent and periodically bent crystalsBellucci V., Camattari R., Guidi V. … Mazzolari A., Paternò G. et al. · Applied Physics Letters 107 (2015)
- Photon emission by volume reflected electrons in bent crystalsNielsen C.F., Uggerhøj U.I., Holtzapple R. … Bandiera L., Guidi V., Mazzolari A. et al. · Physical Review Accelerators and Beams 22 (2019)