Bending with channeling        updated October 25, 2007  D. Carrigan carrigan@fnal.gov (subject line must be sensible)

Channeling Formulary

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Introduction

A properly aligned, bent single crystal is capable of deflecting a high energy beam of positively charged particles through a relatively large angle. In this process channeled particles traveling near a plane or axial channeling direction follow the gradually bending crystal. Crystal septa have several limitations in acceptance. Only particles within the critical angle for channeling are accepted. The planer critical angle is five microradians at 800 GeV for the (110) plane in silicon and is inversely proportional to the square root of the momentum at relativistic energies. On the other hand particle beams in experimental areas at accelerators tend to have angular divergences on the orderof several hundred microradians. Thus the angular acceptance of a crystal in the direction of bend is typically 0.025. Likewise, the spatial acceptance in the direction of the bend is limited by the thickness of the crystal which is in turn set by the requirement that the crystal bend without breaking. Crystals up to several mm thick have been used. This should be contrasted to external beam spots which range from 3 to10 mm. Perpendicular to the bend the acceptance is good since the crystal can be quite wide and a substantial fraction of the particles captured in a plane will be bent. I explored some possible application of bent crystals in 1980 [Carrigan, Fermilab Pub 80/45 (1985)].

Anomalous losses at points of high curvature

In 1983  we discovered that anomalous losses of particles occurred halfway trhough the deflection for crystals bent with so-called three point jigs [Baker et al., Phys. Lett. 137B, 129 (1984)]. These losses were traced to distortions of the crystals at the bending point. They provided some of the first experimental information on bending dechanneling and led to the introduction of four point benders and other more sophisticated bending arrangements.

 

Replacement of a magnet septum by a bent crystal

In the early eighties we used a bent crystal to replace six meters of magnetic septum in the old M-Bottom beam in the Fermilab Meson area [Baker, et al., NIM A234, 602 (1985)]. The deflection power of the crystal was substantially higher so that the beam energy could be raised from 225 GeV to 400 GeV. (In fact this energy level was beyond the normal capacity of the beam line shielding so that it was only possible to operate for a short test.)

Deflection of an 800 GeV beam using channeling

In the mid eighties we used a crystal as a beam septum and attenuator in the NE beam at Fermilab. The septum operated at 800 GeV, the highest energy at which channeling has been observed. In NE the crystal replaced a pair of dipoles downstream of E711, a high intensity counter experiment, and upstream of a low intensity emulsion spectrometer experiment, E653. By using the attenuation properties of the crystal it was possible to carry out activities in E653 while the high intensity experiment was in operation.[Baker at al., NIM A248, 301 (1986)]


Distribution over bend

Anomalous losses

The figure on the left shows the losses on a three point bender for increasingly higher beam energies. The x axis is the angular deflection from the incident beam. At 12 GeV  there is almost no loss on the center pin. By 60 GeV there is a noticeable loss at the center pin and by 180 GeV very few of the particles survive past the center pin. Notice that for the 60 GeV case there is more dechanneling before the center pin. After the pin only a very clean beam with a narrow angular ditribution has survived so there is less dechanneling. More particles are transmitted at 60 GeV than at 12 GeV because the incident beam angular distribution is smaller.

Four point bender

The bender on the right was devised to soften the bend at lessen the stress at the bend points. This approach was quite successful.

Pencil beam at 800 GeV

The figure on the lower right shows the 800 GeV beam distribution at the experiment . Notice that the beam is extremely narrow in the x distribution (lower set) because  only particles inside the channeling critical angle were transmitted. This demonstrates an important feature of channeling, the possibility of making pencil beams.

Three point bender
Beam profile at 800 GeV