CHANNELING EFFECT SIMULATION CHANNELING EFFECT SIMULATION AND ITS POSSIBLE APPLICATIONS AND ITS POSSIBLE APPLICATIONS

FOR FUTURE HIGH ENERGY FOR FUTURE HIGH ENERGY ACCELERATORSACCELERATORS

ALEXEI SYTOVALEXEI SYTOVBelarusian State University,Belarusian State University,

Research Institute for Research Institute for

Nuclear ProblemsNuclear Problems

Different effects in crystalDifferent effects in crystal

θL0

Channeling

Volume Volume reflectionreflection

Different effects in crystalDifferent effects in crystal

θL0

Channeling

Volume Volume reflectionreflection

Amorphous Amorphous scatteringscattering

0)('2

2

xUdz

xdpv

constxUpv

Ex )(2

2 z

x

Basic channeling principlesBasic channeling principles

Transverse energy conservation:

=>

=>

Condition of particle capture into the regime of channeling motion:

02 )(

2UxU

pv

z

xθL

Basic channeling principlesBasic channeling principles

pv

UL

02

=>

=>

Channeling in bent crystalChanneling in bent crystal

0)('2

2

R

pvxU

dz

xdpv

channelingchanneling

Dechanneling

Amorphous-like crystal penetration

Averaged planar potentialAveraged planar potential

channelingchanneling

Volume reflection

Straight crystal Bent crystal

Dechanneling causesDechanneling causes

Scattering on nuclei Scattering on nuclei

Dechanneling causesDechanneling causes

Dechanneling causesDechanneling causes

Scattering on nucleiScattering on nuclei

Scattering on electronsScattering on electrons

Simulation programSimulation program

Channeling simulationChanneling simulationMonte-Carlo simulation of initial incident coordinatesMonte-Carlo simulation of initial incident coordinates

and angles before the first particle pass through crystal.and angles before the first particle pass through crystal.Solving of the second-order linear differential Solving of the second-order linear differential

equation at each equation at each space step.space step.

Monte-Carlo simulation of coulomb scattering on Monte-Carlo simulation of coulomb scattering on both nucleiboth nuclei and electrons and initial angle changing at and electrons and initial angle changing at

each space step.each space step.Simulation of possibility of the inelastic nuclearSimulation of possibility of the inelastic nuclear

scattering in crystal.scattering in crystal.

0)('2

2

R

pvxU

dz

xdpv

Bent crystalBent crystalInitial coordinates and angles

x0, θx0, y0, θy0

xi+1= xi+1(xi, θxi), θxi+1 = θxi+1 (xi, θxi) yi+1= yi +dy, θyi+1 = θyi

Was a scattering?

0)('2

2

R

pvxU

dz

xdpv

Simulation by Monte-Carlo dθx, dθy;θxi+1= θxi+1 + dθx, θyi+1= θyi+1 + dθy

Was an escape from the crystal?

Yes

No

No

Final coordinates and angles

xf, θxf, yf, θyf

Yes

Simulation of channeling efficiencySimulation of channeling efficiency

Simulation of the initial coordinates and angles by Monte-Carlo

Calculation ofchannelingefficiency

Bent crystal

i>Nparticles?NoYes

Additional extension of the Additional extension of the simulation toolsimulation tool

Crystal

0 z1 z2 z3

Beam zcut

A technique to improve crystal channelingA technique to improve crystal channelingefficiency of charged particles till 99,9%efficiency of charged particles till 99,9%**

A narrow plane cut near the crystal surfaceA narrow plane cut near the crystal surfaceconsiderably increases the probability of capture intoconsiderably increases the probability of capture intothe stable channeling motion of positively chargedthe stable channeling motion of positively chargedparticles.particles.

zc*V.V.*V.V.TikhomirovTikhomirov. JINST, 2 P08006, 2007.. JINST, 2 P08006, 2007.

Phase space transformations1 2 3z=0 z=z1 z=z2

z=zc

Wit

hout

cut

x, Å x, Å

42' x, Å

θ/θc

hθ/

θch

θ/θc

h

θ/θc

h

θ/θc

h

53'

z>z1 z>z2

z=zc

*V.V.*V.V.TikhomirovTikhomirov . . JINST, 2 P08006, 2007.JINST, 2 P08006, 2007.

Wit

h cu

t

Dependence of the 7 TeV proton dechanneling Dependence of the 7 TeV proton dechanneling probability in a 1cm bent Si crystal on the r.m.s. probability in a 1cm bent Si crystal on the r.m.s.

incidence angleincidence angle**

Without cut

With cut

*V.V.*V.V.TikhomirovTikhomirov. JINST, 2 P08006, 2007.. JINST, 2 P08006, 2007.

Simulation of channeling efficiencySimulation of channeling efficiencySimulation of the initial coordinates

and angles by Monte-Carlo

xi+1= xi+1(xi, θxi), θxi+1 = θxi+1 (xi, θxi) yi+1= yi +dy, θyi+1 = θyi

No

No

Calculation ofchannelingefficiency

YesIs there the cut?

Bent crystal

Was an enter in the cut?

Motion in the cut

Yes

i>Nparticles?NoYes

Problems of the channeling effect Problems of the channeling effect for the collimationfor the collimation

Crystal collimationCrystal collimation

Absorber

The UA9 experimental layout:

experiment

simulation

UA9UA9 experiment at SPS (CERN) experiment at SPS (CERN) **Dependence of Dependence of inelasticinelastic nuclear interactionnuclear interaction number number of protonsof protons on the angular position of the crystal C1:on the angular position of the crystal C1:

*W.Scandale et al. *W.Scandale et al. Phys. Let., Phys. Let.,

B692 78-82, 2010B692 78-82, 2010..

Miscut angleMiscut angle

First crystal hitFirst crystal hit

UA9: more than UA9: more than

9090%% of particles of particles for both miscutfor both miscut

casescases

×4,5

UA9

*V. *V. TikhomirovTikhomirov, A. Sytov, arXiv:1109.5051 [physics.acc-ph];, A. Sytov, arXiv:1109.5051 [physics.acc-ph];V. V. TikhomirovTikhomirov, A. Sytov, “VANT” (57), 2012, N1, A. Sytov, “VANT” (57), 2012, N1, p. 88-92.

Probability of nuclear reactions in the crystal collimator Probability of nuclear reactions in the crystal collimator vs miscut angle at perfect crystal alignment*vs miscut angle at perfect crystal alignment*

Simulation of collimation efficiencySimulation of collimation efficiencySimulation of the initial coordinates

and angles by Monte-Carlo

No

No

Calculation ofcollimationefficiency

Yes Does particle hitthe face of the crystal?

Bent crystal

Yes

i>Nparticles?

NoYes Does particle hit the lateral surface of the crystal?

Motion in accelerator

Does particle hit the absorber?

Yes No

Calculation of probability ofinelastic nuclear

scattering in crystal

Future projectsFuture projects

Beam extraction from the Recycler Ring*Beam extraction from the Recycler Ring*

*V. Shiltsev. FNAL, No. DE-AC02-07CH11359.*V. Shiltsev. FNAL, No. DE-AC02-07CH11359.

Two (111) Si crystals in standard IHEP holdersTwo (111) Si crystals in standard IHEP holders

STRUCTSTRUCTSTRUCT

NoYesDoes particle hit

the face of the crystal?

Bent crystalNo

Does particle hit the lateralsurface of the crystal?

Yes

Calculation of probability ofinelastic nuclear scattering in crystal

X-Ray acceleratorX-Ray accelerator

Code modification for X-Ray acceleratorCode modification for X-Ray acceleratorInitial coordinates and angles

x0, θx0, y0, θy0

xi+1= xi+1(xi, zi, θxi), θxi+1 = θxi+1 (xi, zi, θxi) yi+1= yi +dy, θyi+1 = θyi, (pv/2)i+1= (pv/2)i+eEz(x,z)dz

Was a scattering?

0),()('2

2

zxeExUdz

xdpv x

Simulation by Monte-Carlo dθx, dθy;θxi+1= θxi+1 + dθx, θyi+1= θyi+1 + dθy

Was an escape from the crystal?

Yes

No

No

Final coordinates and angles

xf, θxf, yf, θyf

Yes

ConclusionsConclusionsNNumerical methodumerical methods were developed ands were developed and a program of a program of channeling simulation was createdchanneling simulation was created. . A technique of improving of crystal channeling efficiency A technique of improving of crystal channeling efficiency with cut was studied. A drastic increase of the channeling with cut was studied. A drastic increase of the channeling efficiency due to this method was showed.efficiency due to this method was showed.The dependence of The dependence of inelasticinelastic nuclear interactionnuclear interaction number number obtained at the Super Proton Synchrotron at CERN was obtained at the Super Proton Synchrotron at CERN was simulated and explained. The usual miscut angle can simulated and explained. The usual miscut angle can increase the probability of nuclear reactions with a factor increase the probability of nuclear reactions with a factor 4,5 for the UA9 case.4,5 for the UA9 case.The simulation code will be combined with STRUCT and The simulation code will be combined with STRUCT and will be used for the analysis for the experiment of the will be used for the analysis for the experiment of the crystal extraction from the Recycler Ring.crystal extraction from the Recycler Ring.Some modifications of the simulation code will allow to Some modifications of the simulation code will allow to simulate the project of X-Ray acceleratorsimulate the project of X-Ray accelerator