Channeling formulary   updated Apr 8, 2016  (carrigan@fnal.gov - subject line must be sensible)

Please let me know of errors  and omissions!

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Channeling formulas

This is expanded from my contribution to the second edition of A. Chao and M. Tigner, eds   The Handbook of Accelerator Physics, World Scientific, Singapore (2002)

The BCK annotations below refer to V.M. Biryukov, V.I. Kotov, Yu.A. Chesnokov, Crystal Channeling and its Application at High Energy Accelerators, Springer (1997), the standard reference in this field.

Review information
Critical angle
Bent crystal chan
Dechanneling
Bending transmission
Negative particle chan
Extraction
Collimation
Focusing
Spin precession
Cooling
Acceleration
Radiation damage
Channeling radiation
Dark matter & chan
Review information

useful channeling reviews are available:

S.P. Moller, NIM A361 (1995) 403
R.A. Carrigan, Jr. and J. Ellison, Relativistic Channeling, Plenum (1987)

recent developments and a formula collection can be found in

H. Andersen, R. Carrigan, E. Uggerhoj eds., NIM B119 (1996)

N. Doble et al, NIM B119 (1996) 181

H. Andersen, S. Bellucci, V. Biryukov eds., NIM B234 (2005)

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web sites summarizing channeling work at IHEP and Fermilab:
IHEP channeling (Serpukhov)

Fermilab channeling         


Critical angle

ca
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Fermilab conventional channeling bibiliography
BCK section 1.3

Bent crystal channeling

bcc
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Fermilab conventional channeling bibliography
BCK chapter 2

Dechanneling

dechan

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Fermilab dechanneling bibliography
BCK section 1.4
Negative particle channeling
negative

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H. Backe, P. Kunz, W. Lauth, and A. Rueda, NIM B266, 3835 (2008)

Negative particle ansatz
Volume reflection
vol ref

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Bending transmission - external beams
  bend tran
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Fermilab conventional channeling bibliography
Fermilab bending info
BCK chapter 2
Extraction
extract
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Fermilab extraction bibliography
Fermilab extraction info
BCK chapter 4
Collimation
collimation
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Fermilab collimation
More on Fermilab collimation
M. Maslov, N. Mokhov, I. Yazynin, SSCL-484 (1991).

Focusing

focusing
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BCK section 5.6

Spin precession

spin precession

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Fermilab channeling spin precession bibliography
Fermilab channeling spin precession info
BCK section 6.2

Cooling

cooling

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Fermilab high bunch charge channeling bibliography

Z. Huang, P. Chen, R. Ruth, PRL 74, 1759 (1995)

Acceleration

acceleration

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Fermilab exotic accelerator info

Radiation damage

radiation damage

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Fermilab radiation damage bibliography
BCK section 2.5.4
crystal after exposure in 28 GeV beam at Brookhaven (scale 1/16 inch/div)
beam damaged crystal

Channeling radiation


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See M.A. Kumakhov, R. Wedell, Radiation of Relativistic Light Particles During Interaction with Single Crystals, Spektrum Physics (1991)

 Fermilab channeling radiation bibliography

BCK section  6.3.2

Dark matter and channeling

   Dark matter detection in solids typically involves the study of energy loss of particles in the 10 - 100 Kev regime. In 2010 interest developed in the possibility that channeling might explain the DAMA effect, the observation of a daily variation in a putative dark matter signal. DAMA conjectures that channeling effects could give rise to the variation as a single crystal presents different orientations to a purported dark matter wind over the day.
Those familiar with high energy channeling would ordinarily dismiss this idea out of hand because channeling critical angles are small so that channeling effects occur for only a small solid angle fraction of crystal orientations. However, for low energy the channeling critical angle becomes much larger so that the actual situation needs detailed study.
Borzognia, et al. have made a critical examination of this process. They examine channeling in the sub MeV range using Lindhard. Interestingly they rediscover a minimum energy for channeling and negligible quantal effects. They go on to determine a total geometric channeling fraction. They find channeling fractions on the order of only a percent, seemingly too small to reproduce the DAMA effect.     
      

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DAMA EPJC 53 205(2008)
Sekiya, et al., PL B571 132 (2003)
Bozorgnia, et al.(2010)
   and others