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Cherenkov Radiation (and other shocking waves).
Perhaps also the ones of the fish?
http://www.newscientist.com/lastword/answers/lwa674bubbles.htmlhttp://www.pbs.org/wgbh/nova/barrier/
Shock Waves May Confuse Birds’ Internal Compass
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The density effect in the energy loss is intimately connected to the coherent response of a medium to the passage of a relativistic particle that causes the emission of Cherenkov radiation.
b
Ze, M
-e,m
v
Calculate the electromagnetic energy flow in a cylinder of radius a around the track of the particle.
22
2
2
2
2
22 1
vcvDefine
If a is in the order of atomic dimension and |a|<<1we will then get the Fermi relation for dE/dX with the density effect.If |a|>>1 , we get (after some steps):
0 2
*
2
22
1
0 1*3
*11Re
Re
dei
c
ez
dEBcadX
dE
aa
ab
If has a positive real part the integrand will vanish rapidly at large distances all energy is deposited near the trackIfis purely imaginary the integrand is independent of a some energy escapes at infinite as radiation Cherenkov radiation and
12 1
c
vor
1
cos Cand
a
subscript 1 : along particle velocity
2, 3 : perpendicular to
we assume real as from now on
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1.E-09
1.E-07
1.E-05
1.E-03
1 100 10000
Photon energy(eV)
Re( )
-1
1.E-09
1.E-07
1.E-05
1.E-03
1-R
e( )
0.000001
0.001
1
1 100 10000
Photon energy (eV)
Imag
inar
y pa
rt o
f rel
ativ
e el
ectr
ic
perm
eabi
lity
expr
esse
d as
RA
NG
E (m
)
c
m
k
Let us consider a particle that interacts with the medium
mk
m
kThe behavior of a photon in a medium is described by the dispersion relation
02
2
k 1
cos c
Conservation of energy and momentum
W.W.M. Allison and P.R.S. Wright RD/606-2000-January 1984
Argon at normal density
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100
1000
10000
100 200 300 400 500 600 700
Wavelength (nm)
Cherenkov Photons / cm / sin2
2 eV345
Cherenkov
)(1cos n
20 sinLNN
A particle with velocityv/cin a medium with refractive index n n=n()may emit light along a conical wave front.
The angle of emission is given by
and the number of photons by
2)(
1)(
1621 sin)(106.4
12cmLN AA
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0
0.5
1
0 1 2 3 4 5 6 7
Momentum (GeV/c)
Particle mass (GeV)
cos() = 1/nm = p/m/m = [(p/p)2 + (2tg)2]½
set :n 1.28 (C6F14)
p/p2 510-4
15 mradL 1 cm1/1 -1/2 = 1/2200 - 1/1800 ( in A) with Q=20%
p
K
max = 38.6 o
min = .78
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Threshold Cherenkov Counter
Flat mirror
Photon detector
Particle with charge qvelocity
Sphericalmirror
Cherenkov gas
0
0 10 20 30 40 50
Momentum (GeV/c)
p
p
threshold AK threshold A
p threshold A
K threshold B
p threshold B
threshold B
To get a better particle identification, use more than one radiator.
A radiator : n=1.0024B radiator : n=1.0003
Positive particle identification :
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0.75
1.00
1.25
1.50
1.75
2.00
4 5 6 7 8 9
Photon energy (eV)
Relative refractive index
Poly. (Xe 862)
Poly. (Kr 471)
Poly. (Ar 297)
Poly. (Ne 65.8)
Poly. (He 34.1)
Poly. (H_2 155)
Poly. (N_2 315)
Correction Optics
Mirror
Focal Plane
Iris
PhotonDetector
Cherenkovradiator
ParallelBeam
s
c
Directional IsochronousSelfcollimating Cherenkov
(DISC)
p
p
m
m
710
Cherenkov radiatorn=f(photon energy)
r=f(n)(r)=f(resolution)
More general for an Imaging Detector
Transformation Function
200nm 150
N photonsN=f()
(n-1)*106
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The Cherenkov radiator Q
0.5 60.0 GeV/c 16.0 2.0 Kthreshold
9.3
1.4 1.0000351.00051.03Quartz HeCF4Aerogel
n
1.0014
C4F10
44 0.51.814
cmax
3.0degrees
22
sinc
Z
dLdE
dN ph
n1
cos
220
1
A
n
The particle
The light cone
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http://banzai.msi.umn.edu/leonardo/
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Cherenkov media
Focusing Mirror
Detector
e- e+
E
Proportional ChamberQuartz Plate
Photon to Electron
conversion gap
ee
e
Hey! Did I mentionTMAE toyou?! Did I?!?
0.0
0.1
0.2
0.3
0.4
0.5
150 175 200
Wavelength (nm)
TM
AE Q
uant
um E
ffici
ency
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Forward RICH
Barrel RICH
Particle Identification in DELPHI at LEP I and LEP II
2 radiators + 1 photodetector
n = 1.28C6F14 liquid
n = 1.0018
C5F12 gas
/K /K/p K/p
/h /K/p K/p
0.7 p 45 GeV/c15° 165°
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Particle Identification with the DELPHI RICHes
Liquid RICH
Gas RICH
p (GeV)Ch
ere
nkov a
ng
le (
mra
d)
From datap from K from D* from Ko
http://delphiwww.cern.ch/delfigs/export/pubdet4.htmlDELPHI, NIM A: 378(1996)57
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Yoko Ono 1994 FRANKLIN SUMMER SERIES, ID#27I forbindelse med utstillingen i BERGEN KUNSTMUSEUM, 1999
ABB.com
More beautiful pictures (which has next to nothing to do with)
Cherenkov radiation
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An exact calculation of Transition Radiation is complicatedJ. D. Jackson (bless him) and he continues:
A charged particle in uniform motion in a straight line in free space does not radiate
A charged particle moving with constant velocity can radiate if it is in a material medium and is moving with a velocity greater than the phase velocity of light in that medium (Cherenkov radiation)
There is another type of radiation, transition radiation, that is emitted when a charged particle passes suddenly from one medium to another.
If <1 no real photon can be emitted for an infinite long radiator. Due to diffraction broadening, sub-threshold emission of real photons in thin radiators.
2
1
02=plasma frequency 2 (electron density)
2
22
2
1
i
ia
If
2
21
30
2 112
aadd
Sd
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1000
10000
100000
1000000
0.0001 0.001 0.01 0.1
(rad)
d
N/d
2
The angular density of X-ray quanta from Transition radiation. = 1000p1 = 0.1 eVp2 =10 eVStep of 1 keV First from 1 to 2 keV
1-2 keV
If p2>p1 then max -1
0.001
0.01
0.1
1
10
1 10 100
(keV)
d
S/d
=103 =10
4
Total radiated power S 10-2 (eV) which is a small number
All this for a small
number?
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l1
l2
1
1 2 3 4 5 6 7 8 k k+1 2n-1 2n
Rk
Rk+1
k
k+1
P
Coherent addition in point P
n
k k
ik
k
R
eAPE
k2
1
1
0.00001
0.0001
0.001
0.01
0.1
1 10 100 1000
(keV)
dW/d
One boundary
One foil
(-1)k : The field amplitude for successive interfaces alternate in signA(k) : Amplitudek =(R/c-t) : phase factor
= 2 104
l1 = 25 ml2 = 0.2 mmpolypropylene - air
Egorytchev, V ; Saveliev, V V ;Monte Carlo simulation of transition radiation and electron identification for HERA-B ITEP-99-11. - Moscow : ITEP , 17 May 1999.
Periodic radiator for Transition Radiation.
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0
0.5
1
1.5
2
2.5
3
3.5
4
0 25 50 75 100 125 150 175 200
0.001
0.01
0.1
1
1 10 100
(keV)
Abs
orpt
ion
0.0001
0.001
0.01
0.1
1 10 100
(keV)
dW/d
0.001
0.01
0.1
1
10
10 100 1000
Energy (eV)
Tot
al I
oniz
atio
n C
ross
Sec
tion
/a 0
2
He
Ne
Ar
Kr
Xe
Productionwith multi foils
Absorptionin foils
Conversion
t=0 t=T
Pul
se H
eigh
t -electron
MIP
X radiation
Threshold
10 keV
M.L. Cerry et al., Phys. Rev. 10(1974)3594
+ saturation effect due to multi layer