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
