PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 29: Start reading Chap. 15 –

PHY 712 Spring 2014 -- Lecture 29 1

PHY 712 Electrodynamics10-10:50 AM MWF Olin 107

Plan for Lecture 29:

Start reading Chap. 15 –

Radiation from collisions of charged particles

1. Overview

2. X-ray tube

04/09/2014

PHY 712 Spring 2014 -- Lecture 29 204/09/2014




Generation of X-rays in a Coolidge tubehttps://www.orau.org/ptp/collection/xraytubescoolidge/coolidgeinformation.htm

https://www.orau.org/ptp/collection/xraytubescoolidge/coolidgeinformation.htm


http://www.ndt-ed.org/EducationResources/CommunityCollege/Radiography/Physics/xrays.htm

http://www.ndt-ed.org/EducationResources/CommunityCollege/Radiography/Physics/xrays.htm

PHY 712 Spring 2014 -- Lecture 29 7

Radiation during collisions

b(t) b(t+Dt)

2

/ˆ

2

22

ˆ1

ˆˆ

4

:Intensity

βr

βrrRr

dt

dedt

c

q

dd

Id crti q

2

2

22

2211

ˆ1ˆ14

:0frequency and

onpolarizatiwith radiation emitting duration ofcollision aFor

ˆˆ that Note

t

t

t

t

c

q

dd

Id

βr

β

βr

βε

ε

εβεεβεβrr

04/09/2014


Radiation during collisions -- continued

ˆ1

ˆ

4

: smallwith collision icRelativist

4

:limit icrelativist-Non

ˆ1ˆ14

:0frequency and

onpolarizatiwith radiation emitting duration ofcollision aFor

2

22

22

2

2

22

2

2

22

βr

ββrβε

β

ββββε

βr

β

βr

βε

ε

c

q

dd

Id

ttc

q

dd

Id

t

t

t

t

c

q

dd

Id



ˆ1

ˆ

4

: smallwith collision icRelativist2

22

22

βr

ββrβε

β

c

q

dd

Id

b

Db

r q

f

cos1

1

8

cos1

cos-

8

:onpolarizati or ||for )over (averaging sExpression

2

2

2

22

4

22

2

2||

2

β

β

c

q

dd

Id

c

q

dd

Id polarization in r and b plane

polarization perpendicular to r and b plane

ε

ε



2 2||

Relativistic collision at low and with small

ˆ and perpendicular to plane of and ,

ˆas a function of where cos ;

Integrating over solid angle:

2

3

d I d IdId

d d d d d

β β r β

r β

222

q

c β

y

b

Db

r q

f

x

z


b(t) b(t+Dt)

q q

Estimation of Db

Db

Δβpp 2

: transferMomentum

McttQ

232

222

2

3

2

3

2Q

cM

q

c

q

d

dI

β

mass of particle having charge q


b(t) b(t+Dt)

q q

Estimation of Db -- for the case of Rutherford scattering

Db

'cos122/'sin2

:scattering elastic Assuming

2/'sin2

12

:section-cross scattering Rutherford

M; mass has ) (charge nucleuset that targAssume

222

4

2

ppQ

pv

Zeq

d

d

Ze

Ze


Case of Rutherford scattering -- continued

Q

p(t+Dt) q

Zep(t)

q’

dQ

d

d

dd

dQ

d

pv

Zeq

d

d

'

2/'sin2

12

:section-cross scattering Rutherford

4

2

22 2

2

3

2 sin '/ 2 2 1 cos '

1 8

Q p p

d Zeq

dQ c Q


Case of Rutherford scattering -- continued

Q

p(t+Dt) q

Zep(t)

q’

QMc

q

c

Ze

Qc

ZeqQ

cM

q

dQ

d

d

dI

dQd

d

11

3

16

18

3

2

:section crossradiation alDifferenti

2

2

2

22

3

2

232

22


min

max2

2

2

222

ln1

3

16

transfermomentumover gIntegratin

continued --section crossradiation alDifferenti

max

minQ

Q

Mc

q

c

Ze

dQd

ddQ

d

dQ

Q

Comment on frequency dependence --

βrβrRr

Rr

βr

βrrRr

ˆ1''ˆ/ˆ

.1/ˆ

that assumed have wes,derivation previous In the

ˆ1

ˆˆ

4

:intensityradiation for expression Original

0

2

/ˆ

2

22

tdttctt

ctt

dt

dedt

c

q

dd

Id

t

q

q

ctti q


min

max2

2

2

222

ln1

3

16

transfermomentum of in termssection crossRadiation

continued --section crossradiation alDifferenti

max

minQ

Q

Mc

q

c

Ze

dQd

ddQ

d

dQ

Q

2min

min

max22

2 1condition

timecollision by the determined is general,In

2 'cos12 : thatNote

v

ZeqQ

Q

pQpQ

Zeq

Mv

Mc

q

c

Ze

d

d 3

2

2

2

22

ln1

3

16

process icrelativist-non classicalfor section crossRadiation

l= “fudge factor” of order unity

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PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 29: Start reading Chap. 15 –