I.A.Yazynin, A.I. Drozhdin, A.Apyan

4th Crystal Channeling Workshop

CERN, March 27, 2009

Simulations for new goniometer and crystals

Outline• Principles of estimation the efficiency • Layout of collimation system • Optimization of crystal (at channeling):AlignmentCurve radiusLength MiscutAmorphous layer• Using of volume reflection effect• Comparison efficiency of systems• Simulation of full accelerator• Conclusion

Principles of estimation the system efficiency

• Include full transfer amplitude • Global losses – Ig (inefficiency):Number protons lost in accelerator afterinteraction with the collimation system.Amplitude of such protons bigger then

aperture• Aperture losses – Ia:Part of global losses with small transfer amplitudes near the aperture.

222yx AAA

Sources of losses

• We have two main sources:1 - crystal or primary collimator2 - secondary collimator.For estimation of losses we may use:

losses protons in target from inelastic interaction ρ - density of protons at the age of collimator• Optimization – choice parameters of crystal with

minimum losses at crystal and density on SC.

sctarg kkI 21

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Inefficiency from secondary collimators

• For impact parameter dx>1mm 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 K1~0.008

• Were considered all 4 edges of secondary collimators: right, left, up, down

• K2=0.046

Two variants of simulation

• Quick simulation: (~10^6p at 3 hour on PC)Short part of structure ~50 elements (system), amplitude limitation and 3D matrix withmomentum part. Use approximation or MC modules.Tasks: Estimation efficiency, investigationparameters, choice optimal crystals.• Full simulation:Use full structure of ring. Defined and analyze losses on elements and radiationdamage at consider work regime of accelerator.Ended estimation efficiency of system.

Primary D49, secondary EO3 collimators and bent crystal location at the Tevatron EO straight section.

January 20, 2009 A.Drozhdin, A,Apyan

Beam parameters

Aperture = 35σ, Amplitude limitation =17σ

Beam guidance

• Impact parameter =1.9 um , • rms of angle distribution = 13 urad,• Critical angle = 6.54 urad

Losses of protons versus alignment

• Optimum range of work – channeling case ~15urad, Ia~0.02%• In amorphous range Ia~1.5% • I1=l/Ln=5/450=1.1%, Namor~30, Nvr~20, Nch~0.5

Beam distribution at input E03

• 1 Optimal alignment = - 12 urad (channeling)Impact parameter for chan. part dR ~ 10 mm• 2 Volume reflection =200urad, dR ~ 5 mm

Beam distributions at E03 in horizontal plane

Amplitude distribution

Global losses: from A=20 to infinityAperture losses: from A=20 to 30 mm

Optimization from curve radius of crystal

Optimization from angle deviation of crystal

• Optimum angle deviation 200-250 urad• Impact parameter 5-6 mm

Miscut angle

• Channeling efficiency (multi turn)• Miscat(mrad) Ich%• 0 88• 1.6 86• -1.6 14

O-shape crystal

• Density at age of collimator increase in ~5 time• Losses at channeling increase in ~ 2 time

Efficiency of 1 interaction

• Pc – input efficiency of channeling• Pd – output efficiency of channeling• Optimum for 1 interaction Rc=30-40m ~15Rcrit• Optimum for multiturn Rc=10-15m ~5Rcrit

Influence of amorphous layer

• Density of protons at the edge of SC (Dabs) is increasing slowly with thickness of amorphous layer. (see fig.2 also)

• Increasing losses in the main defined by growing inelastically interaction of protons with crystal (Icry).

Part of this losses shown by red pointed line (Iabs). Difference between red lines Iacc – Iabs is losses from SC. All losses may defined: Iacc=Icry x c1 + Dabs x c2, c1~0.01, c2~0.8. At new technique the thickness of layer may make very small < 1 µm.

Vertical beam collimation

• Losses and beam distributions practically such as for collimation in horizontal plane.

• Small changes only from non equal dispersion.

Using the volume reflection effect

• Work range for VR rather big ~ 100 µrad (-220—120) (see blue line).• Inefficiency ~ 0.13% that at 8 time smaller than for usual collimation.• For simulation were used 12 crystals Si(110) with Rc=10m and full

L=20mm.• Losses from crystal(1 source)~0.07% - half of all global losses

Amplitude distribution of losses

1 – one stage collimation, 2- two stage, 3 – volume reflection, 4 – channeling.• Protons with A>35mm will be lost on the some periods, another in narrow places. In non dependence of really structure the

losses on the elements of accelerator will be proportional to the density of losses.

Initial particle population (right) and distributions on X and X’ (left) at crystal entrance for multi-turn simulations.

February 3, 2009 A.Drozhdin, A,Apyan

Three possible orientations of crystal with respect to circulating beam: with negative, zero and positive miscut angle. All calculations presented here are done for crystal without amorphous layer.

January 20, 2009 A.Drozhdin, A,Apyan

Particle position at crystal surface (top) at perfect alignment of crystal with respect to central line of accelerator for negative miscut angle of -1.6 mrad. Channeled particles, moving along the circular trajectory, leave the crystal exactly at the side surface (bottom line), but particles, passed the crystal as amorphous material along the straight trajectory, are located a little up of the side surface.

Particle angle at crystal exit (bottom). Collimators E03 and F172 are at 6 sigma.

February 25, 2009 A.Drozhdin, A,Apyan

Channeled particles Side surface

Not channeled

Particle loss at collimator E03, F172 and crystal for differend miscut angle

March 4, 2009 A.Drozhdin, A,Apyan

Particle loss at accelerator aperture excluding collimators D49, E03, F172 and crystal for differend miscut angle

March 4, 2009 A.Drozhdin, A,Apyan

CONCLUSIONS• Using of channeling effect decrease the losses in

accelerator more than hundred time. The range of angle alignment with good efficiency will be

~15 µradOptimal curvre radius~10m, angle deviation 200-300 urad.Tolerance of miscat angle <=100urad, amorphous lair ~2um.O-crystal decrease efficiency in 2 time. • Using of volume reflection effect give decrease losses in

the ten time. Optimal 12-14 strip with R~10m Very large range of angle alignment with good efficiency

~100 µrad.