spatial resolution of non- invasive beam profile monitorbased on optical diffraction radiation a.p....
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SPATIAL RESOLUTION OF NON-INVASIVE BEAM PROFILE
MONITORBASED ON OPTICAL DIFFRACTION RADIATION
A.P. Potylitsyn
Tomsk Polytechnic University,
634050, pr. Lenina 2, Tomsk, Russia
e-mail: [email protected]
Advanced Beam Dynamicsc WorkshopNanobeam - 2008
May 25-30, 2008, Budker INP, Novosibirsk, Russia
Diffraction radiation approach
Impact parameter, h, – the shortest distance between the target and the particle trajectory
2
h - observation wavelength
FDRBDR
e
h
Diffraction radiation (DR) appears when a charged particle moves in the vicinity of a medium
Approach for the beam size measurements
e
0y
O D R
Assume a Gaussian beam profile
2y
2
xx
y
yx 2
aaexp
2
1,aG
2sina2
cosa4
cosh8
exp
sina2exp
4
R
dd
Wd
y02
x2x2
x2
2
2y
2
2y
2x
2
2x
20
2x
2
2x
2
2
xslitx
2
2sina2
cosa4
cosh8
exp
sina2exp
4
R
dd
Wd
y02
x2x2
x2
2
2y
2
2y
2x
2
2x
20
2
2
yslity
2
, y is the electron beam size and is its offset with respect to the slit center
xa
2x
2
yarctan
y
-6 -4 -2 0 2 4 6
0
400
800
1200
1600 b
Imin
Imax
(m)0 5 10 15 20
I min
/ I m
ax
0.00
0.02
0.04
0.06
0.08c
300nm
500nm
700nm
0
200
400
600
800
-4-2
02
4
-4-2
02In
ten
sity
(ar
b. u
nit
s)
y
x
a Beam size effect
Projection
Projected vertical polarization component
2
2
xyyx
2
yy
x
x
ddd
),,(Wd),(S
= 2500
y=0
y=30m
x – x detector angular acceptance
x
Inte
nsi
ty (
arb
. u
nit
s)
screen monitor
screen monito r
alignment laser
mirror chamber
target chamber
rotatable mirror
CCD
CCD
ICCD
beam line
to beam dump
bendingmagnet
Air Cherenkov counter
collimator
reflecting mirror
beam linealignment laserODR, OTR
lead shielding
reflecting mirror
PMT
polarizeroptical fi lter
mask chamber
bending magnetSR source
gamma rays
y-10 -5 0 5 10
Inte
nsi
ty d
evid
ed b
y O
TR
0.0
0.2
0.4
0.6
0.8
1.0
OTR
ODR
Measurements of the ODR projected vertical polarization component with PMT
y-10 -5 0 5 10
Inte
nsi
ty d
evid
ed b
y O
TR
0.0
0.2
0.4
0.6
0.8
1.0 OTR
ODR
Experiment
Theory
Optical filter 55020nm
%58I
ImaxOTR
maxODR %62
I
ImaxOTR
maxODR
Angular acceptance and beam size effect in ODR experiment
Beam size (MW2X, m)0 10 20 30 40 50
Bea
m s
ize
valu
e (
m)
0
10
20
30
40
50
MW2XMW3XODR
y
0.0 0.1 0.2 0.3 0.4
Bea
m s
ize
valu
e (
m)
0
5
10
15
20
25
30
MW2X
MW3X
Optical transition radiation (OTR) beam size monitor
OTR monitor ODR monitor
Pre-wave zone2a
We shall introduce Cartesian coordinates on the target, lens and detector using T, L, D indices and use dimensionless variables
2 2, , .T T L L D D
T T L L D D
x X x X x X
y Y y Y y Ya
2 22 21
2 2
2
,
,
exp exp4
aexp , R= , M is magnification
Dx D D
T T L LDy D D
T TT T T
T L T LT T T
D DL L
E x yconst dx dy dx dy
E x y
K x yx x yi x x y y i
y Rx y
x yi x y
M M
Model
For a rectangular lens with aperture , m L m m L mx x x y y y
One may obtain
.,,,,
sinsin
4
expexp
mDTmDTx
DT
DTm
DT
DTm
DTD
DTL
y
yL
x
xL
yyyGxxxGM
yy
M
yyy
M
xx
M
xxx
M
yyiy
M
xxixdydx
m
m
m
m
For M=1 fields on the detector surface may be written:
2 21
2 2
2 2
( , )
( , )
exp , , , , .4
DT T
x D D TT TD
y D D T T T
T Tx T D m T D m
K x yE x y xconst dx dy
E x y y x y
x yi G x x x G y y y
R
Intensity on the detector surface
2 2D Dx yI const E E
2 2m mx y
a) Normalized shape of OTR source image on the detector plane for lens aperture =100 (left curve) and = 50 (right curve) in wave zone (R = 1);
b) OTR source image in «pre-wave zone» (R = 0.001) for the same conditions and with the same normalizing factors;
c) OTR source image at the fixed lens diameter for different distances between the target and the lens (R = 0.01, = 250 - right curve; R = 0.1, = 25 - left).
OTR image from a single electron(point spread function, PSF)
mrmr
mrmr
Spatial resolution of OTR monitor is defined by the distribution maximum position
max0
3 3D
m
rr
max0 - lens acceptanceLR
a
Dimension variable: max
0
1
2 2Dr
maxDr
maxDr
max max
max
,tx x x
h y y
• For optical diffraction radiation (ODR) there are 2 dimension parameters – wavelength and impact parameter h
• Which one is defined a spatial resolution?
• To obtain an intensity of ODR on detector surface one have to integrate ODR field on the target surface:
A Very High Resolution Optical Transition Radiation Beam Profile Monitor // Ross M. et al. SLAC-PUB-9280 July 2002
10FWHM 5.8FWHM
Near-field imaging of optical diffraction radiation generated by a 7-GeV electron beam
A. H. Lumpkin, W. J. Berg, N. S. Sereno, D.W. Rule,* and C.-Y. YaoPHYSICAL REVIEW SPECIAL TOPICS - ACCELERATORS AND BEAMS 10,
022802 (2007)
E = 7 GeV = 0.8 mh = 1.25 mm
1375 200x ym m
0.2 0.15 0.1 0.05
1000
2000
3000
4000
5000
6000
7000
EyD2
m m, 100x y
m m, 50x y
m m, 25x y
y D
8Lens aperture
I
Lens aperture
PSF for ODR case (perpendicular to target edge)
h = 0.1
x = 0D
-h – ODR target edge image
arb.
uni
ts
m m, 25x y
m m, 50x y
Points - lens aperture
Lens aperture
PSF for ODR case (parallel to target edge)
Dx0.15 0.1 0.05 0.05 0.1 0.15
1000
2000
3000
4000
5000Ey
D2
0.17dy
I , arb. units
Dx0.2 0.1 0.1 0.2
500
1000
1500
2000
2500
EyD2
0.14dy
I , arb. units
h = 0.1
h = 0.1
0.2 0.1 0.1 0.2
0.2
0.4
0.6
0.8
1 2 2D Dx yI E E
2DxE
2DyE
Dx
y-PSF
x-PSF
0.05
0.06D
h
y
To simplify all calculations we shall use the approximation ,m mx y
PSF for both ODR polarized components
2
0
2
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2
0
2
2
0
2
2
1.5
1
0.5
0
0
0.2
0.4
2
0
2
Significant broadening of deep (for ) and peak (for ) is observed with increasing of impact parameter h
2DxE2D
yEDx
DyDx
Dy
0.5h 2DxE
2DyE
2D PSF for ODR case
0.4 0.2 0.2 0.4xD
0.2
0.4
0.6
0.8
1Ey
D2
0.05h 0.1h
0.2h
, arb. units
FWHM
0.6 0.4 0.2 0.2 0.4 0.6xD
0.2
0.4
0.6
0.8
1Ex
D2 , arb. units
0.05h
0.1h
0.2h
Characteristics of y-PSF and x-PSF
0.1 0.2 0.3 0.4 0.5
0.2
0.4
0.6
0.8
1
FWHMFWHM
FWHM
h
y
Almost linear dependence of FWHM and on impact parameter
Dependence on impact parameter
0.750.50.25 0.25 0.5 0.75xD
2468
101214
EyD2 , arb. units
For small offset relative to optical axes distributions remain the same
PSF dependence on particle offset
0.750.50.25 0.25 0.5 0.75xD
0.5
1
1.5
2
2.5
ExD2, arb. units
0.2 0.1 0.1 0.2
xD
0.2
0.4
0.6
0.8
1I
2DxE
2DyE
800
13700
100
50x
nm
h
800
13700
100
20x
nm
h
0.2 0.1 0.1 0.2xD
0.2
0.4
0.6
0.8
1I
2DxE
2DyE
“Smoothing” of PSF due to beam size
100 200 300 400 500XD, m
0.2
0.4
0.6
0.8
1I
50 m
20 m
, arb. units
Dependence of smoothed PSF on beam size
Developed model E = 7 GeV = 0.8 h = 100 m
Near-field imaging of optical diffraction radiation generated by a 7-GeV electron beam
A. H. Lumpkin, W. J. Berg, N. S. Sereno, D.W. Rule,* and C.-Y. Yao//
PHYSICAL REVIEW SPECIAL TOPICS - ACCELERATORS AND BEAMS 10, 022802 (2007)
400 200 200 400
XD, m
0.2
0.4
0.6
0.8
1
ExD2
50 m
20 m
, arb. units
Smoothed x-PSF for different beam sizes
600 400 200 200 400 600
xD
0.2
0.4
0.6
0.8
1
ExD2 , arb. units
50 m
20 m
80 m
Smoothed of deep for different
h = 100 m = const
20 40 60 80 100 ,
0.2
0.4
0.6
0.8
R
Ratio as a tool for beam size measurements
max min
max min
x x
x x
I IR
I I
800
13700
100
nm
h
600 400 200 200 400 600xD
0.2
0.4
0.6
0.8
1
ExD2
50h
100h
, arb. units
200h
Dependence of x-component image on impact parameter
50 const 800
13700
nm
ODR imaging of a slit
PSF – x, PSF-y for slit
Conclusion• 1.The model developed allows to obtain 2D- and 1D-distributions
of an ODR intensity on detector as well as distributions of both polarized components for beam with finite transversal sizes.
• 2.The ODR distribution from single electron (point spread function, PSF) is defined by impact parameter h only (if h>> ).
• 3.Polorized components of PSF may provide higher spatial sensitivity in contrast with total PSF.
• 4.The deep shape of polarized ODR x-component depends on a transverse beam size along target edge.
• 5.Measurements of deep ”smoothing” allows to achieve a spatial resolution (i.e. for )
• 6.For impact parameter there may be lost ~ 60% of a total ODR intensity measuring ODR X-component only.
50 H m0.2x H 0.1 / 2h 10 x m
Thanks for yourattention!