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