# Presentation: 004110

## POSSIBILITY OF USING CRYSTALLINE TARGETS FOR COLLIMATION SYSTEM IN TEVATRON

**I.A Yazynin**** **
** ****(****A. Apyan)**
**IHEP, FNAL, CERN **

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- Fermilab Dec 6, 2007

## Layout of collimation system and principles of estimation the efficiency.  
One and two stage collimation
Channeling effect  (thickness, position, alignment)
Volume reflection effect
Multichanneling effect
Comparison efficiency of systems
Conclusion 

**One and two stage collimation**
**Channeling effect  (thickness, position, alignment)**
**Volume reflection effect**
**Multichanneling effect**
**Comparison efficiency of systems**
**Conclusion **

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**Outline**

- Fermilab Dec 6, 2007

## Layout of system and principles of estimation efficiency

**Simulation for estimation of efficiency --- Structure of system, limitation for transfer amplitudes, 6D matrix of last ring.**
**Limitation for amplitude defined by beam parameters and size of chambers.**
**For beam pipe can be used the full amplitude:   **
**Main sources of losses:  target and secondary collimators**:

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**Inefficiency – part of protons lost in the ring after interaction with the system.**

- Fermilab Dec 6, 2007

## Inefficiency from secondary collimators

**For impact parameter, dx>1mm, beam losses are negligible and for design systems with crystals the main part of deflected beam must have the impact parameter bigger than 1mm.    **
**At the equilibrium density D=1p/mm losses will be I****eq****=0.0083**
**Were considered all 4 edges of secondary collimators: right, left, up, down**
**Here is presented impact protons at right edge.     **

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- Fermilab Dec 6, 2007

**Notes:**
Fig.1:  Inefficiency versus impact parameter.
Fig.2:  Distribution protons at SC with some impact parameters.

## One stage collimation

**At the small value of beam diffusion the inefficiency of one stage system (only secondary collimators) will be I****acc****=6-7%. **
**That value agree with previous consideration of inefficiency at small impact parameters**

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- Fermilab Dec 6, 2007

**Notes:**
Fig.1: Inefficiency versus the diffusion velocity of the beam halo.
Fig.2: Distribution protons at SC at some diffusion velocities of beam.
In that and another simulations used size of circling beam Rbeam=8.3σ 

## Two stage collimation

**Minimum beam losses will be when (half) gap in the range , r****_sc****=5-7mm**
**For circulating beam all losses are defined by two sources: **
**    ****primary collimator (PC) (or target) and secondary collimators (SC).**
**Estimation formula for losses **
**Coefficients may defined by simulation of localization process with use the absolute secondary collimators. **

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**Efficiency versus gap of the secondary collimator (E03).**

- Fermilab Dec 6, 2007

**Notes:**
Absolute collimator catches all particles. 

## Distribution of protons at SC

**High density of protons at right and left edges of secondary collimator with small gap.**
**Asymmetry in radial plain is explained by existence the none zero dispersion at SC. Protons after interaction with PC has momentum P< P****0**** .  **
**At big gap there are more p inelastically interacted with PC and range angle for outgoing p will wider that will increase the losses (that can see at previous slide).        **

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- Fermilab Dec 6, 2007

## The choice of crystal thickness 

**Optimum thickness of crystal l****c****=1.5-2mm and inefficiency is ~ 0.035%.**
**At lc=5mm losses increase in 1.5 time.**
**Main change of losses defined by part of protons inelastically interacted (diffraction part) with the crystal (Icry, green curve)**
**The density (D, blue) at edge of SC is negligibly changed  ~ 0.03%.  **

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- Fermilab Dec 6, 2007

**Notes:**
Fig.1: Inefficiency versus the thickness of crystal.
Fig.2: Distribution protons at SC.
In that and another simulations used size of Gap the SC R=+-6mm=11.2σ
This consider old place of crystal installation and minimum inefficiency will be ~0.035% 

## Inefficiency versus alignment

**Maximum influence occur on the short crystal (l****c****=1.5mm). The level of losses less than 5% in angular range (-160 - 0) **
**At the large angle of alignment > 40 and < -180 ****μrad ****the crystal works as an amorphous target and losses increase up to 60%.**

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**For thin crystal the angular acceptance is wider with good efficiency due to the smaller losses at in crystal (dashed green curve).**

**Volume reflection occur at the left side from zero point where the beam losses are smaller.**

- Fermilab Dec 6, 2007

**Notes:**
Old variant installation

## New variant installation of crystal 

**Crystal install at place of PC, that allows to reduce the deviation angle of beam by the crystal from 150 up to 90 ****μ****rad.**
**Reduction of a component of losses due to the  inelastic interactions of protons with the crystal. Density of losses on edge of SC depends on the matrix element M****12**** as D~1/M****12****.**
**The reduction of density:**
**As a results the losses decrease in 3 time, up to 0.01%, that in 100 time smaller then for usual collimation.**

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- Fermilab Dec 6, 2007

**Notes:**
Where volume reflection occur (-100 - -5mcrad) the main losses defined by 2 part – density p at SC (blue dashed curve).  

## Influence of amorphous layer 

**Density of protons at the edge of SC (D****abs****) is increasing slowly with the thickness of amorphous layer. **
**Increasing losses in the main defined by growing inelastically interaction of protons with crystal (I****cry****). **
**    ****Part of this losses shown by red pointed line (I****abs****).**
**    ****Difference between red lines I****acc**** – I****abs**** is losses from SC.**
**    ****All losses may be defined as:  Iacc=Icry x c****1**** + D****abs**** x c****2****,  c****1****~0.01, c****2****~0.8.**

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- Fermilab Dec 6, 2007

## Volume Reflection Effect

**12 crystals, Si(110) with Rc=10m and full L=20mm, were used for simulation .**
**Crystalline target was installed in place PC, R****beam****=8****σ****, and R(SC)=11.3****σ**** **

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**Angular acceptance for VR is rather big ~ 100 ****μrad**** (-220—120) (see blue line).**
**Inefficiency ~ 0.13% that at 8 time smaller than for usual collimation.**

- Fermilab Dec 6, 2007

## Protons Distribution at SC

**At angular alignment ****α**** = -290 ****μrad**** multichanneling effect.**
**At range of angles from -230 to -130 ****μrad**** we see pure volume reflection effect.**
**At the angles >-120 the target work how amorphous.**

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- Fermilab Dec 6, 2007

## Simulation for one turn

**Simulation of one turn process of interaction protons with target and considering distribution of protons at place of SC.**
**Left figure represent VR plus multichanneling effects (1,2) and pure multichanneling (3)**
**Right figure represent pure VR effect (1,2). Target works as an amorphous (-100 ****μ****rad, the angle of beam envelope = -210 ****μ****rad) at large angles.**

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- Fermilab Dec 6, 2007

## Using of multichanneling effect

**Three crystals Si(110), Rc=10m were used for simulation**
**Angular acceptance is bigger than for 1 crystal in 1.5 time**
**Beam losses are 2 times larger.  **
**Multichanneling is effective for one interaction of beam. **

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- Fermilab Dec 6, 2007

## Amplitude distribution of losses

**1 – One stage collimation**
**2 – Two stage collimation**
**3 – Volume reflection**
**4 – Channeling**

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**Protons with A>35mm will be lost during the some periods. **

- Fermilab Dec 6, 2007

## CONCLUSIONS

**Volume reflection effect decreases losses in ten time.**
**Very large range of angle alignment with good efficiency ~100 ****μrad****. **
**Channeling effect decreases the losses in accelerator more than hundred times. **
**The range of angle alignment with good efficiency will be ~15 ****μrad**

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- Fermilab Dec 6, 2007