# Presentation: 004102

## Volume Reflection Simulations

** ****using Yazynin’s Channeling Code **
**and Application to Possible e- Experiment**
- Bob Noble
- SLAC
- October 29, 2008

- 1

- Special thanks to Igor Yazynin (IHEP) for kindly responding to questions and
- generously sharing his code. Thanks to Walter Scandale (CERN) for information
- on volume reflection and capture.

## Yazynin Code includes processes:

**Basic approx:** Code replaces details of particle orbits with Monte Carlo fits based on distribution fcns and analytic formulas for trajectories over long distances (not on scale of betatron motion in bent crystal). It applies probabilities to dechanneling, volume capture, volume reflection, amorphous transport, Coulomb and nucl scattering angles, energy loss, etc. Both proton and electron versions of code exist.

- multiple scattering
- channeling
- volume capture
- de-channeling
*volume reflection*

- ch

- dech

- 2

**This is a “decision-tree” code, not full Monte Carlo.**

## Example: 400 GeV protons,  Si(110),  

**crystal R = 10 m,  length=1mm**

**“****Angular Profile”**
-  change in  particle angle
-  relative to input angle
-  which is induced by crystal

**“****Rotation**
**Angle”-**
- crystal
- orientation
- rel. to beam
- input
- direction

- Rotation angle

- Usual expt plot
-  (other than sign)

- dech

- VC

- ch

- VR

- a

- a

- 3

- 0   degr

- Max rot angle= xtal thickness/R=0.1 mrad

## Example: Code runs 7000 protons (400 GeV), as pencil beam at R (horiz coord, not a radius) =0.01 mm, Z (vert) =1 mm with Z’=0, and R’ uniformly spread over [-0.05, +0.125] mrad. Transports each proton through 1 mm long, curved (10m) Si crystal.

- Output phase space R’-R

- ch

- VR

- input

- a2

- a1

- 4

- vc

- dech

- VR Angular Profile Plot

- VR

- ch

- a2

- a1

- dech

- vc

- R

- R’

## We exercised the p and e- codes over a large range of energies,  curvature

- radii, crystal thickness (primarily Si) to understand limitations and compare to
- other work and data where available. Code was originally written for use with
- multi-hundred GeV - TeV protons, so some approximations are not expected to be
- valid in all regimes.
- What we found and modified in our test version of the code:
- 1. VC particles channeled orders of magnitude deeper than physically reasonable.
- Changed the VC dechanneling formula to same as for normally channeled particles.
- 2. Added a bremsstrahlung energy loss term ~ E to the electron code.
- 3. Modified the multiple scattering formula to include log(z/Zrad) term so MS is
- correctly reduced for thin crystals (still need to add plural scatt. for ultra-thin).
- 4. At low energy and large x=Rcrys/Rcrit, code’s VC probability > 1 (intended for
- proton E>100 GeV, x<30). Modified VC probability following Taratin and Scandale’s
- potential well capture probability (~E-1.5), and used an exponential form to keep P<1.
- 5. Prior to VC at a plane deep in the crystal, code applied no MS, resulting in too
- narrow of angle spread for these particles. We added MS, and when angle increase
- is too large, we set capture probability to zero.

- 5

## Taratin and Scandale’s potential-well capture probability, NIM B262 (2007) 340 (modified from an argument of Biryukov & Chesnokov)

- Uo

- Exc

- +

- +

- Long-life
- channeling
-  orbits

- Si

- Fast VC
- orbits

- Volume capture (VC) results from MS-induced energy transitions of order U0 – Exc from above barrier to top-levels of potential.

- KE= 1⁄2 (E0 /c2) v2 = 1⁄2 E0 θ2
- d (KE)/ dz = 1⁄2 E0 dθNms2/dz
- Capture length  LN ≈ (U0 – Exc) / d (KE)/ dz

- VC probability in curved crystal ≈
- Distance that particle angle is within θc 0 of plane / Capture length
-  P ≈ Rθc 0 / LN    (P<<1)

- To insure P<1 for all regimes in code, we replace this by the usual decay rate form
- P = 1- exp(- Rθc0 / LN )

- * For thin crystal where s < Rθc 0 , include correction s / (s+ Rθc 0 )

- 6

## Code VR:  θrefl = -1.5 θc 0 (1- 1.67 (Rcrit / R)) ~ E-1/2

- θc 0 ~ E-1/2      Rcrit ~ E     Ldech ~ E

-    (6.4E-3 mrad)       (2 m)      (0.49m)

- 980 GeV protons

- 5mm Si, R=28.5m

- 0.175 mrad

- vc

- VR

- chan

- dech

- a1

- a2

- rms=2.78E-3 mrad

- rms=2.84E-3 mrad   (θms ~ E-1)

- rms=2.9E-3 mrad
- (MS+VR)

- -9.2E-3 mrad

- VR rms = 1.7 θc 0 Rcrit / R ~ E1/2   (MS  ~ 1/E)

- 7

## Code VR:  θrefl = -1.5 θc 0 (1- 1.67 (Rcrit / R))

- Code VR:  θrefl = -1.5 θc 0 (1- 1.67 (Rcrit / R))

- θc 0 ~ E-1/2       Rcrit ~ E       Ldech ~ E

- (3.4E-3 mrad)      (7.3 m)       (1.75m)

- 3500 GeV protons

- 5mm Si, R=28.5m

- 0.175 mrad

- vc

- VR

- chan

- dech

- a1

- a2

- rms=7.8E-4 mrad

- rms=8.0E-4 mrad

- rms=1.7E-3 mrad

- -3.1E-3 mrad

- VR rms = 1.7 θc 0 Rcrit / R

- 8

## Code VR:  θrefl = -1.5 θc 0 (0.1972 R/Rcrit -0.1472)

- Code VR:  θrefl = -1.5 θc 0 (0.1972 R/Rcrit -0.1472)

- θc 0  ~ E-1/2      Rcrit ~ E      Ldech ~ E

- (2.4E-3 mrad)    (14.6 m)     (3.5 m)

- 7000 GeV protons

- 5mm Si, R=28.5m

- 0.175 mrad

- vc

- VR

- chan

- dech

- a1

- a2

- rms=3.9E-4 mrad

- rms=3.9E-4 mrad

- rms=1.8E-3 mrad
- (VR rms dom)

- -9.3E-4 mrad

- VR rms = 0.714 θc 0 sin(0.4713 R/Rcrit+0.85)

- 9

## θc 0  ~ E-1/2      Rcrit ~ E      Ldech ~ E

- θc 0  ~ E-1/2      Rcrit ~ E      Ldech ~ E

- (2.4E-3 mrad)    (14.6 m)     (3.5 m)

- 7000 GeV protons

- 5mm Si, R=98.5m

- 0.051 mrad

- vc

- VR

- chan

- dech

- a1

- a2

- rms=3.9E-4 mrad

- rms=3.9E-4 mrad

- rms=7.2E-4 mrad

- -2.9E-3 mrad

- Code VR:  θrefl = -1.5 θc 0 (1- 1.67 (Rcrit / R))

- VR rms = 1.7 θc 0 Rcrit / R

- 10

## θc 0  ~ E-1/2      Rcrit ~ E      Ldech ~ E

- θc 0  ~ E-1/2      Rcrit ~ E      Ldech ~ E

-  (0.02 mrad)      (0.21 m)     (3 mm)

- 100 GeV electrons

- 1mm Si, R=10 m

- 0.1 mrad

- vc

- VR

- chan

- a1

- a2

- rms=1.2E-2 mrad

- rms=1.2E-2 mrad

- rms=1.2E-2 mrad
- (MS dominates)

- -1.4E-2 mrad

- Code VR:  θrefl = -0.8 θc 0 (1- 2.55 (Rcrit / R))

- VR rms = 1.8 θc 0 Rcrit / R  (negligible)

- 11

- 2 θc 0

## θc 0  ~ E-1/2      Rcrit ~ E      Ldech ~ E

- θc 0  ~ E-1/2      Rcrit ~ E      Ldech ~ E

-  (0.037 mrad)   (0.063 m)   (0.9 mm)

- 30 GeV electrons

- 1mm Si, R=10 m

- vc

- VR

- dechan

- a1

- a2

- rms=3.9E-2 mrad

- rms=3.8E-2 mrad

- rms=3.8E-2 mrad

- -2.5E-2 mrad

- Code VR:  θrefl = -0.8 θc 0 (1- 2.55 (Rcrit / R))

- VR rms = 1.8 θc 0 Rcrit / R  (negligible)

- 12

- 2 θc 0

## θc 0  ~ E-1/2      Rcrit ~ E      Ldech ~ E

- θc 0  ~ E-1/2      Rcrit ~ E      Ldech ~ E

-  (0.34 mrad)   (0.76 mm)   (0.01 mm)

- 360 MeV electrons

- 0.1mm Si, R=10 cm

- VR & VC
- dech

- dechan

- a1

- a2

- rms=0.87  mrad

- rms=0.85  mrad

- rms=0.77 mrad

- -0.19 mrad

- Code VR:  θrefl = -0.8 θc 0 (1- 2.55 (Rcrit / R))

- VR rms = 1.8 θc 0 Rcrit / R  (negligible)

- 13

- SLAC
- NLCTA

- εn ~ 10 μm
- 10 μm spot,
- 1 mrad

- 2 θc 0

## Summary

- 1. We made several improvements to Yazynin’s code for VR/VC probabilities,
- dechanneling of VC particles, multiple scattering, and e- energy loss, which
- extend applicable range of R, E, crystal thickness for both p and e.
- 2. The coded formulas for VR angle and rms values still need to be confirmed
- and generalized (current version from Monte Carlo fits over restricted energy range).
- Basically the code gives VR ~ θc 0 (with Rcrit / R correction) , VR rms ~ θc 0 Rcrit / R ,
- θMS~1/E.
- 3. At LHC energies (θc 0 ~2 μrad), crystal curvature radius needs to be many tens
- of meters to reduce VR rms spread < μrad and obtain good VR angular separation
- (~ 2-3 μrad). This reduces VR angular acceptance (~thickness/R), but it is
- still tens of micro-radians.
- 4. For an e- experiment at 360 MeV, MS ( ~ 1/E) dominates the rms spreads,
- and the VR  deflection tends to get lost in this spread, even for 100 micron
- thick Si. De-channeled particles tend to escape in same direction as VR
- deflection, adding to the apparent population of “deflected” particles. VR deflection
- ~ 0.2 mrad which is slightly less than θc 0 , and rms spread is nearly 4 times this.

- 14

## Extra slides

## Code VR:  θrefl = 1.5 θc0 (1- 1.67 (Rcrit/R))

- Code VR:  θrefl = 1.5 θc0 (1- 1.67 (Rcrit/R))

- θc0 ~ E-1/2       Rcrit ~ E       Ldech ~ E

- (0.01 mrad)     (0.835m)      (0.2m)

## N_cry=1

- N_cry=2

- N_cry=2

- Profile plots

- Phase space plots

- in

- in