On the possibilities of observation of
proton volume deflection from different
crystal planes in one crystal
March 26, 2009, CERN
B SU IN P
VVincenzoincenzo Guidi, A Guidi, Andreandrea Mazzolari, Mazzolari,
INFN, FerraraINFN, Ferrara
Victor TikhomirovVictor Tikhomirov
RINP, MinskRINP, Minsk
OutlineThe idea of multiple volume reflection possibility by crystal
axes in a single crystal
PNPI conditions
VR experiment simulations
MVR predictions
IHEP conditions
VR experiment simulations
MVR predictions
SPS H8 conditions
VR experiment simulations
MVR predictions
Optimal condition of MVR observation
Volume Reflection prediction
A.M.Taratin and S.A.Vorobiev, Phys. Lett. A119 (1987) 425
and
A.M.Taratin and S.A.Vorobiev, NIM B26 (1987) 512
Volume reflection by crystal axesV.V. Tikhomirov, PLB 655(2007)217
Axes form many inclined reflecting planes
-60 -40 -20 0 20 40 60
0
10
20
30
VY0
VX0
(121)(615)(615)(413)(413)(110)(321)(211)(312)(514)(101)(213)(123)(011)(154)(132)(121)(231)111(121)
Protons are reflected from many crystal plane sets of one crystal
Reflection from many crystal planes increase VR angle 4 times (LHC case)
0 5 10 15 20 25 300
4
8
12
16 high-index planes
(110)(101) (011)(312) (132)(211) (121)(321) (231)
2( ) ( )
( ) 0
2( )
2( )
( / )
( / )
2 1 1( / )
/ (
x x
x turn turn
x x turn turn
y x
X R
Y R
Rx x
px V x x sin c
R
pV x x sin
R
pV x x sin c
R
px y cos c
R
R sin sin
R sin cos
R sinR sin
)xturn
dxx
V.V. Tikhomirov, PLB 655(2007)217The approach of V.A. Maisheev, Phys. Rev. ST Accel. Beams 10:084701,2007 was used.
Both the IHEP , PNPI and CERN
experiments on VR observation
and
MVR by different crystal planes of one crystal
are simulated below considering particle scattering
by crystal axes
MVR of 1 GeV protons
-3000 -2000 -1000 0 1000 2000 30000,0
2,0x10-4
4,0x10-4
6,0x10-4
8,0x10-4
VR
1 GeV, x=160rad,
lcr=312m, =4mrad,
x0
= 2mrad, y0
= 800rad
<211> quasimosaic <111> anticlastic amorphous Si
(1/N
)dN
/d x,
rad-1
x, rad
Comparison of MVR and VR of 1 GeV protons
-2000 -1500 -1000 -500 0 500 1000 1500 20000,0
5,0x10-4
lcr=312m, =4mrad,
x0
= 2mrad, y0
= 800rad
<211> quasimosaic <111> anticlastic amorphous Si
x, rad
(1/N
)dN
/d x,
rad-1
MVR MVR
0,0
1,0x10-3
2,0x10-3
2006 experiment
1 GeV, Rb=7.8cm
lcr=30m, =385rad,
x0
=294rad, y0
= 4mrad,
amorphous Si
IHEP, 70 GeV; VR experiment and MVR
-200 -100 0 100 2000,000
0,004
MVR
(1/N
)dN
/d x,
rad-1
lcr=1.7mm =1mrad,
x0
=0.5mrad, y0
=0.2 mrad,
<211> quasimosaic <111> anticlastic amorphous Si
x, rad
x2MVR
0,000
0,004
0,008
0,012
0,016
0,020
lcr=0.72mm =423rad,
<211>
x0=211rad,
y0= 2mrad
70 GeV, Rb=1.7m,
x=15rad
0
2006 experiment
SPS experiment, 400 GeV
VR:
-50 0 500,00
0,02
0,04 400 GeV, lcr=0.86mm, =68.6rad,
x0
=35.5rad, y0
= 2mrad
(1/N
)dN
/d x,
rad-1
x, rad
VR
400 GeV; MVR simulations
-100 -50 0 50 100 150 200 2500,00
0,01
0,02
0,03
x, rad
(1/N
)dN
/d x,
rad-1
400 GeV, lcr=4mm, R
b=10m,
x0
=200mrad, y0
=75mrad
<211>, P(x<0)=84.7%
<111>, (110), 87.5% <111>, (211), 87.7% amorphous Si
x2
400 GeV, comparison of SPS VR experiment and MVR simulations
-100 -50 0 50 1000,00
0,01
0,02
0,03
0,04
400 GeV, lcr=4mm, R
b=10m,
x0
=200mrad, y0
=75mrad
<211>, <111>, l
cr=0.86mm, =68.6rad,
x0
=35.5rad, y0
= 2mrad
(1/N
)dN
/d x,
rad-1
x, rad
MVR MVR
VR, experimental
looks close to optimal one
MVR efficiency dependence on proton incidence directionE=400GeV, lcr=4mm, Rb=10m
160 180 200 220 240 26075
80
85
90
Y=80radD
(x<
0)
x, rad
40 60 80 10075
80
85
90
X=200radD
(x<
0)
y, rad
40.0/ xy
The angular deflection efficiency dependence is week
The ratio
Optimal lcr values
The optimal l values are lcr=2.5 - 4mm
2 3 4 5 687
88
89
90
91
D(
x<0)
lcr, mm
Y/
X=0.4
Rb=10m
2 3 4 5 60
10
20
30
40
50
60
70
100%
x < 0
< x>,
ra
dlcr, mm
Y/
X=0.4
Rb=10m
Optimal Rb values
The optimal Rb values are Rb=7-12m
6 8 10 12 14
84
86
88
90
92
D
(x<0
)
Y/
X=0.4
lcr=3mm
R, m6 8 10 12 14
0
10
20
30
40
50
60
70
Y/
X=0.4
lcr=3mm
R, m
< x>,
ra
d 100%
x < 0
Optimal conditions of MVR
observation at the SPS look like:
lcr = 2.5 - 4mm,
Rb= 7 - 12m,radx 200150
40.0~/ xy
VR experiment and MVR simulations,
0x
-100 -80 -60 -40 -20 00,00
0,01
0,02
0,03
0,04 400 GeV, lcr=4mm, R
b=10m,
x0
=200mrad, y0
=75mrad
(1
/N)d
N/d x,
rad-1
x, rad
MVR<211>
MVR <111>
VR SPSexperiment
Thank you for attention!
The Mir castle
