Volume channeling effects  updated Apr 14, 2016  (carrigan@fnal.gov - subject line must be sensible)

Channeling Formulary

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Two volume channeling effects in whole arc of crystal bend:

Volume reflection

Particle reflects off plane at some place in passage through a curved crystal. Deflection order of ψc

Volume capture

Particle scatters into channel with lower transverse energy and remains there. Continues to end of bend.

Recent results

The Scandale group has recently produced very comprehensive information on volume reflection and volume capture working in the CERN H4/H8 beam complex. One remarkable innovation has been the development of multiple crystal arrays to combine volume reflection from a number of crystals.

The effects are summarized in table below*

volume channeling

Accelerator collimation effects at BNL (Fliller) and Fermilab (Still)


volume
                reflection, capture

Were there volume channeling effects in the Tevatron extraction experiment?



Volume reflection (top)

Volume reflection was discovered in simulations by Taratin and Vorobiev in the eighties [Phys. Lett A, 119, 425 (1987) for English language version]. In essence particles reflect off of planes when they are nearly parallel and are deflected on the order of a critical angle away from the bend. The process will occur anywhere along the whole arc of the bend. It can be cumulative for many passes.

Since the expected deflection is O(θc) the deflection will go as 1/(pβ)1/2. R does not appear but θc for a bent crystal will be a function of R. As a result the effect will diminish more slowly than volume capture as the energy increases.

This is why many expect the whole arc effect seen at RHIC and the Tevatron is due to volume reflection.

Useful to understand p, R scaling since we are extrapolating to LHC

Volume capture (top)

"Volume capture" is the putative process whereby particles outside a channel in a bent crystal diffuse into the channel. It was first investigated at PNPI by Samsonov, Sumbaev and their colleagues at 1 GeV. Volume capture should deflect in the direction of the bend.  This diffusion process is an analog of dechanneling where the particles diffuse in to the channel. The process occurs over the whole arc of the bend. Deflections can range up to the whole arc of the bend.

In their book Biryukov, Chesnokov, and Kotov (Crystal channeling -) give a formula (BCK 5.27) for the transition probability to diffuse into the channel as:
formula
Thus as the energy goes up, volume capture goes down relative to volume reflection. As R gets smaller (tighter bend) it also decreases. Biryukov, et al., have shown that this relation holds true for 70 GeV protons and is characteristically small compared to ordinary bent crystal channeling (Fig. 3.30 in BCK)