Crystal LabFerrara · UniFe & INFN

Research › Accelerators and colliders

Beam steering

Bent crystals for particle accelerators

A few millimetres of bent silicon deflect TeV protons, the work of a magnetic field of hundreds of tesla.

The physics.

Planar channeling and volume reflection in a bent crystalA bent crystal is drawn as curved atomic planes. One particle enters parallel to the planes, oscillates between two of them and leaves deflected by the bending angle. A second particle enters at a larger angle, meets a plane tangentially inside the crystal and is reflected to the opposite side by a small angle. θ beam channeling: deflected by θ = L/R volume reflection bent crystal: atomic planes, length L, bending radius R not to scale
Planar channeling (blue) and volume reflection (orange) in a bent crystal. Angles are greatly exaggerated.

Atoms in a crystal sit in planes. A pos­i­tive­ly charged par­ti­cle that enters almost par­al­lel to a plane does not feel the atoms one by one but their av­er­aged elec­tric field: between two neighbour­ing planes this is a po­ten­tial well, about 20 eV deep in silicon. If the par­ti­cle’s trans­verse energy is lower than the well, it stays trapped and os­cil­lates between the planes as it travels. This is planar channel­ing.

Trap­ping works only within a small angle, Lindhard’s crit­i­cal angle

θc = √(2U0 / pv)

about 10 µrad for 400 GeV protons in silicon and 2.5 µrad at 6.5 TeV. A crystal must there­fore be aligned with the beam to a few micro­radians.

If the crystal is bent, chan­neled par­ti­cles follow the cur­va­ture of the planes and leave de­flect­ed by its bending angle, θ = L/R, what­ev­er their energy. Near the planes the field reaches about 6 × 1011 V/m (5.7 GV/cm in silicon (110)): for an ultra­relativistic par­ti­cle this acts like a mag­net­ic field of almost 2000 T, inside a few mil­li­me­tres of silicon. The bending radius must stay above the crit­i­cal radius

Rc = pv / (e Emax)

about 0.7 m at 400 GeV and 11 m at 6.5 TeV.

Par­ti­cles that arrive outside the crit­i­cal angle can still be de­flect­ed. Where their direc­tion becomes tangent to the curved planes they are re­flect­ed, by about one and a half crit­i­cal angles, towards the outside of the bend: volume reflec­tion. It accepts in­com­ing angles over a range as wide as the bending angle, so the crystal is far easier to align.

All of this depends on the crystal. A damaged surface or a dis­tort­ed lattice makes par­ti­cles leave the channel (dechannel­ing). Our crys­tals are shaped by an­iso­trop­ic chem­i­cal etching, which leaves flat, atomi­cally sharp sur­faces, and their miscut, bending and torsion are mea­sured by X-ray diffrac­tion and in­ter­fer­om­e­try before every beam test. In CRYSTAL BOND we also bend crys­tals by bonding them to shaped sub­strates: for TWOCRYST a crystal bent by anodic bonding was tested with high-energy hadrons for the first time.

What we have shown.

Our chemi­cally shaped silicon crys­tals, free of the surface damage left by me­chan­i­cal cutting, made channel­ing a working tool at CERN. In 2015 they gave the first observa­tion of channel­ing of 6.5 TeV protons in the LHC; since the 2023 lead-ion run, crystal collima­tion is in opera­tion, at least five times better than the stan­dard system. In 2025 TWOCRYST chan­neled protons through two crys­tals in se­quence up to 2 TeV; the ALADDIN experi­ment on dipole moments will use our crys­tals. Our crys­tals also shadow the extrac­tion septum of Fermilab's Mu2e and, at MAMI and SLAC, gave the first steer­ing of neg­a­tive par­ti­cles.

> 95%

Efficiency of volume reflection of 400 GeV protons in a bent silicon crystal at the CERN SPS, over a wide range of crystal orientations.

Physical Review Letters 98 (2007)

6.5 TeV

First observation of channeling at the LHC, in 2015: beam losses in the aligned crystal fell by a factor of about 24 compared with its amorphous orientation.

Physics Letters B 758 (2016)

2 TeV

TWOCRYST channeled protons through two crystals in sequence. The same scheme, with our crystals, will be used by the ALADDIN experiment to measure the dipole moments of charmed baryons.

Read first.

  1. Shaping of silicon crystals for channelling experiments through anisotropic chemical etchingBaricordi S., Guidi V., Mazzolari A., Vincenzi D., Ferroni M. · Journal of Physics D: Applied Physics 41 (2008)
  2. High-efficiency volume reflection of an ultrarelativistic proton beam with a bent silicon crystalScandale W., Still D.A., Carnera A. … Guidi V., Mazzolari A. et al. · Physical Review Letters 98 (2007)
  3. Observation of channeling for 6500 GeV/c protons in the crystal assisted collimation setup for LHCScandale W., Arduini G., Butcher M. … Bandiera L., Guidi V., Mazzolari A. et al. · Physics Letters B 758 (2016)
  4. Crystal collimation of heavy-ion beams at the Large Hadron ColliderRedaelli S., Aberle O., Abramov A. … Bandiera L., Guidi V., Mazzolari A. et al. · Physical Review Accelerators and Beams 28 (2025)
  5. Performance of short and long bent crystals for the TWOCRYST experiment at the Large Hadron ColliderBandiera L., Cai R., Carsi S. … Guidi V., Malagutti L., Mazzolari A. et al. · European Physical Journal C 85 (2025)
  6. Observation of Fine Structure in Channeling of Particles in Bent CrystalsMazzolari A., Backe H., Bandiera L. … Guidi V., Malagutti L., Paternò G. et al. · Physical Review Letters 135 (2025)

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