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/
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.
Ze, M
v
b
-e,m
Calculate the
electromagnetic energy flow
in a cylinder of radius a
around the track of the
particle.
Define
a
 
2
2
v
2

2
c
2
   
2
v
2
1 
2
  
If a is in the order of atomic dimension and |a|<<1
we will then get the Fermi relation for dE/dX with the density effect.
If |a|>>1 , we get (after some steps):

 dE 
*




ca
Re
B
 E1  d 


3

 0

 dX  b  a
subscript 1 : along particle
velocity
2, 3 : perpendicular to
  z 2e 2 
*  
1     * a 

e

 Re  
i
 1  2
d 
a 1
2 
0

c 
       


If  has a positive real part  the integrand will vanish rapidly at
large distances  all energy is deposited near the track
If  is purely imaginary  the integrand is independent of a  some
energy escapes at infinite as radiation  Cherenkov radiation
and
     1
2
or
v
1

c
  
we assume  real as from now on
and
cos C 
1
   
Let us consider a particle that interacts with the medium
m
  m
k  m

c


Conservation of
energy and
momentum
   k
The behavior of a
photon in a medium
is described by the
dispersion relation
k2

cos  c 
0
1
 
Photon energy (eV)
100
10000
0.000001
Argon at normal density
0.001
1
1.E-03
1.E-03
1.E-05
1.E-05
1.E-07
1.E-07
1.E-09
1.E-09
1
100
Photon energy(eV)
W.W.M. Allison and P.R.S. Wright RD/606-2000-January 1984
10000
1-Re( )
Re( )-1
Imaginary part of relative electric
permeability expressed as RANGE (m)
1
 
2
k
A particle with velocity 
v/c
in a medium with refractive index n
n=n()
may emit light along a conical wave front.
The angle of emission is given by
cos  
q
1
 n (  )
Cherenkov
and the number of photons by
N  N 0  L  sin 2 
N 1  2   4.6 106 
5
4

1
2 ( A )
3

 1 1( A)  L(cm)  sin 2 
2 eV
cos(q) = 1/n
m = p/
2
2
2
Dm/m = [(Dp/p) + ( tgqDq) ]½
set :
qmax = 38.6
min = .78
n
1.28 (C6F14)
-4
2
Dp/p
510
Dq
15 mrad
L
1 cm
1/1 -1/2 = 1/2200 - 1/1800 ( in A) with Q=20%
p
Particle mass (GeV)
1
K
0.5
p
0
0
1
2
3
4
5
Momentum (GeV/c)
6
7
o
Threshold Cherenkov Counter
Cherenkov gas
Particle with
charge q
velocity 
Spherical
mirror
Flat mirror
Photon detector
To get a better particle identification, use more than one radiator.
Positive particle identification :
p
p
p
p
p
K
p
p threshold B
K threshold B
p threshold B
p threshold A
K threshold A
p threshold A
0
0
10
20
30
Momentum (GeV/c)
A radiator : n=1.0024
B radiator : n=1.0003
40
50
Directional Isochronous
Selfcollimating Cherenkov
(DISC)
Correction
Optics
Mirror
Focal Plane
Iris
Photon
Detector
s
Cherenkov
radiator
D

 10 7 
Dm Dp

m
p
Parallel
Beam
c
More general for an Imaging Detector
Cherenkov radiator
n=f(photon energy)
200nm
N photons
N=f()
150
Relative refractive index
2.00
(n-1)*106
1.75
1.50
1.25
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)

Transformation
Function
1.00
0.75
4
5
6
7
8
Photon energy (eV)
r=f(,n)
D(r)=f(resolution)
9
The light cone
The Cherenkov radiator
dN ph
dLdE

Z 2
c
The particle
sin 2 
cos  
n 1 
A
0 2   2
0.5
K
threshold
2.0
1
n
9.3
16.0
60.0 GeV/c
1.0014
n
1.4
Quartz
C4F10
1.03
1.0005
Aerogel
CF4
3.0
degrees
cmax
44
1.000035
He
14
1.8
0.5
http://banzai.msi.umn.edu/leonardo/
Detector
Focusing
Mirror
Cherenkov media
e+



e
e
e
Hey! Did
I mention
TMAE to
you?!
Did I?!?
TMAE Quantum Efficiency
e-
0.5
0.4
0.3
0.2
0.1
0.0
150
175
Wavelength (nm)
200
Forward RICH
Barrel RICH
Particle Identification in DELPHI at LEP I and LEP II
n = 1.28
C6F14 liquid
0.7  p  45 GeV/c
p/K
p/K/p
K/p
15°  q  165°
n = 1.0018
C5F12 gas
p/h
2 radiators + 1 photodetector
p/K/p
K/p
Particle Identification with the DELPHI RICHes
Liquid RICH
Gas RICH
p (GeV)
From data
p from L
K from F D*
http://delphiwww.cern.ch/delfigs/export/pubdet4.html
DELPHI, NIM A: 378(1996)57
p from Ko
More beautiful pictures (which has next to nothing to do with)
Cherenkov radiation
ABB.com
Yoko Ono 1994 FRANKLIN SUMMER SERIES, ID#27
I forbindelse med utstillingen i BERGEN KUNSTMUSEUM, 1999
An exact calculation of Transition Radiation is complicated
J. 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)
If 
d S0
2  1 1 

  
dd
p  a1 a2 
2
3
i2
2
ai  2    2


1
2
0.5
I
n
t
e
n
s
i
t
y
0.4
1000
0.3
6000
0.2
11000
16000
0.1
21000
0
0.0001
26000
0.0032
(rad)
0.1024
 (eV)
If p2>p1 then max  -1
The angular density of
X-ray quanta from
Transition radiation.
 = 1000
p1 = 0.1 eV
p2 =10 eV
Step of 1 keV
First from 1 to 2 keV
1000000
p/  dN/d
2
1-2 keV
100000
10000
1000
0.0001
0.001
0.01
0.1
 (rad)
p/  dS/d
10
1
0.1
=104
=103
0.01
0.001
1
10
 (keV)
Total radiated power S  10-2  (eV)
 which is a small number
100
All this for a
small number?
1
Periodic radiator for Transition Radiation.
l1
P

Rk
Rk+1
k+1
k
1 2 3 4 5 6 7 8
k
l2
Coherent addition in point P
k+1
2n-1
2n
2n
 1k A k ei
k 1
Rk
E P   
k
(-1)k : The field amplitude for successive interfaces alternate in sign
A(k) : Amplitude
fk = (R/c-t) : phase factor
0.1
One boundary
dW/d
0.01
0.001
One foil
0.0001
0.00001
1
10
 = 2 104
l1 = 25 mm
 (keV)
l2 = 0.2 mm
polypropylene - air
100
1000
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.
0.1
Production
with multi foils
dW/d
0.01
+ saturation
effect due to
multi layer
0.001
0.0001
1
10
100
 (keV)
Absorption
in foils
Absorption
1
0.1
  10 keV
0.01
0.001
1
10
100
 (keV)
Total Ionization Cross Section /p a0
2
10
1
0.1
He
Ne
0.01
Ar
Kr
Conversion
Xe
0.001
10
100
1000
Energy (eV)
4
X radiation
3.5
d-electron
Pulse Height
3
2.5
MIP
2
1.5
Threshold
1
0.5
0
t=0
0
25
50
75
100
M.L. Cerry et al., Phys. Rev. 10(1974)3594
125
150
175
200
t=T