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Cherenkov Radiation (and other shocking waves). Shock Waves May Confuse Birds’ Internal Compass. Perhaps also the ones of the fish?. http://www.newscientist.com/lastword/answers/lwa674bubbles.html http://www.pbs.org/wgbh/nova/barrier/. - PowerPoint PPT Presentation
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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
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
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
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
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
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 :
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
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
http://banzai.msi.umn.edu/leonardo/
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
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°
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
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
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
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?
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.
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