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