PHYS Introduction to Synchrotron Radiation

Transcription

1 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 PHYS Introduction to Synchrotron Radiation Term: Spring 2018 Meetings: Tuesday & Thursday 13:50-15:05 Location: 213 Stuart Building Instructor: Carlo Segre Office: 136A Life Sciences Phone: segre@iit.edu Book: Web Site: Elements of Modern X-Ray Physics, 2 nd ed., J. Als-Nielsen and D. McMorrow (Wiley, 2011) segre/phys570/18s

2 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Course objectives Understand the means of production of synchrotron x-ray radiation

3 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Course objectives Understand the means of production of synchrotron x-ray radiation Understand the function of various components of a synchrotron beamline

4 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Course objectives Understand the means of production of synchrotron x-ray radiation Understand the function of various components of a synchrotron beamline Be able to perform calculations in support of a synchrotron experiment

5 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Course objectives Understand the means of production of synchrotron x-ray radiation Understand the function of various components of a synchrotron beamline Be able to perform calculations in support of a synchrotron experiment Understand the physics behind a variety of experimental techniques

6 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Course objectives Understand the means of production of synchrotron x-ray radiation Understand the function of various components of a synchrotron beamline Be able to perform calculations in support of a synchrotron experiment Understand the physics behind a variety of experimental techniques Be able to make an oral presentation of a synchrotron radiation research topic

7 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Course objectives Understand the means of production of synchrotron x-ray radiation Understand the function of various components of a synchrotron beamline Be able to perform calculations in support of a synchrotron experiment Understand the physics behind a variety of experimental techniques Be able to make an oral presentation of a synchrotron radiation research topic Be able to write a General User Proposal in the format used by the Advanced Photon Source

8 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Course syllabus Focus on applications of synchrotron radiation

9 Course syllabus Focus on applications of synchrotron radiation Homework assignments C. Segre (IIT) PHYS Spring 2018 January 09, / 20

10 Course syllabus Focus on applications of synchrotron radiation Homework assignments In-class student presentations on research topics Choose a research article which features a synchrotron technique Timetable will be posted C. Segre (IIT) PHYS Spring 2018 January 09, / 20

11 Course syllabus Focus on applications of synchrotron radiation Homework assignments In-class student presentations on research topics Choose a research article which features a synchrotron technique Timetable will be posted Final project - writing a General User Proposal Start thinking about a suitable project right away Make proposal and get approval before starting C. Segre (IIT) PHYS Spring 2018 January 09, / 20

12 Course syllabus Focus on applications of synchrotron radiation Homework assignments In-class student presentations on research topics Choose a research article which features a synchrotron technique Timetable will be posted Final project - writing a General User Proposal Start thinking about a suitable project right away Make proposal and get approval before starting C. Segre (IIT) PHYS Spring 2018 January 09, / 20

13 Course syllabus Focus on applications of synchrotron radiation Homework assignments In-class student presentations on research topics Choose a research article which features a synchrotron technique Timetable will be posted Final project - writing a General User Proposal Start thinking about a suitable project right away Make proposal and get approval before starting Visits to Advanced Photon Source (outside class, not required) All students who plan to attend will need to request badges from APS Go to the APS User Portal, and register as a new user. Use MRCAT (Sector 10) as location of experiment Use Carlo Segre as local contact State that your beamtime will be in the second week of March C. Segre (IIT) PHYS Spring 2018 January 09, / 20

14 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Course grading 33% Homework assignments

15 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Course grading 33% Homework assignments Weekly or bi-weekly

16 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Course grading 33% Homework assignments Weekly or bi-weekly Due at beginning of class

17 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Course grading 33% Homework assignments Weekly or bi-weekly Due at beginning of class May be turned in via Blackboard

18 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Course grading 33% Homework assignments Weekly or bi-weekly Due at beginning of class May be turned in via Blackboard 33% General User Proposal

19 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Course grading 33% Homework assignments Weekly or bi-weekly Due at beginning of class May be turned in via Blackboard 33% General User Proposal 33% Final Exam Presentation

20 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Course grading 33% Homework assignments Weekly or bi-weekly Due at beginning of class May be turned in via Blackboard 33% General User Proposal 33% Final Exam Presentation Grading scale A 80% to 100% B 65% to 80% C 50% to 65% E 0% to 50%

21 Topics to be covered (at a minimum) C. Segre (IIT) PHYS Spring 2018 January 09, / 20

22 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Topics to be covered (at a minimum) X-rays and their interaction with matter

23 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Topics to be covered (at a minimum) X-rays and their interaction with matter Sources of x-rays

24 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Topics to be covered (at a minimum) X-rays and their interaction with matter Sources of x-rays Refraction and reflection from interfaces

25 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Topics to be covered (at a minimum) X-rays and their interaction with matter Sources of x-rays Refraction and reflection from interfaces Kinematical diffraction

26 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Topics to be covered (at a minimum) X-rays and their interaction with matter Sources of x-rays Refraction and reflection from interfaces Kinematical diffraction Diffraction by perfect crystals

27 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Topics to be covered (at a minimum) X-rays and their interaction with matter Sources of x-rays Refraction and reflection from interfaces Kinematical diffraction Diffraction by perfect crystals Small angle scattering

28 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Topics to be covered (at a minimum) X-rays and their interaction with matter Sources of x-rays Refraction and reflection from interfaces Kinematical diffraction Diffraction by perfect crystals Small angle scattering Photoelectric absorption

29 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Topics to be covered (at a minimum) X-rays and their interaction with matter Sources of x-rays Refraction and reflection from interfaces Kinematical diffraction Diffraction by perfect crystals Small angle scattering Photoelectric absorption Resonant scattering

30 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Topics to be covered (at a minimum) X-rays and their interaction with matter Sources of x-rays Refraction and reflection from interfaces Kinematical diffraction Diffraction by perfect crystals Small angle scattering Photoelectric absorption Resonant scattering Imaging

31 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Resources for the course Orange x-ray data booklet:

32 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Resources for the course Orange x-ray data booklet: Center for X-Ray Optics web site:

33 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Resources for the course Orange x-ray data booklet: Center for X-Ray Optics web site: Hephaestus from the Demeter suite:

34 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Resources for the course Orange x-ray data booklet: Center for X-Ray Optics web site: Hephaestus from the Demeter suite: McMaster data on the Web:

35 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Resources for the course Orange x-ray data booklet: Center for X-Ray Optics web site: Hephaestus from the Demeter suite: McMaster data on the Web: X-ray Oriented Programs:

36 Today s outline - January 09, 2018 C. Segre (IIT) PHYS Spring 2018 January 09, / 20

37 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Today s outline - January 09, 2018 The big picture

38 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Today s outline - January 09, 2018 The big picture History of x-ray sources

39 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Today s outline - January 09, 2018 The big picture History of x-ray sources X-ray interactions with matter

40 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Today s outline - January 09, 2018 The big picture History of x-ray sources X-ray interactions with matter Thomson scattering

41 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Today s outline - January 09, 2018 The big picture History of x-ray sources X-ray interactions with matter Thomson scattering Atomic form factor

42 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Today s outline - January 09, 2018 The big picture History of x-ray sources X-ray interactions with matter Thomson scattering Atomic form factor Reading Assignment: Chapter ;

43 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Why synchrotron radiation? X-rays are the ideal structural probe for interatomic distances with wavelengths of 1 Å

44 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Why synchrotron radiation? X-rays are the ideal structural probe for interatomic distances with wavelengths of 1 Å Laboratory x-ray sources are extremely useful and have gotten much better in the past decades but some experiments can only be done at a synchrotron

45 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Why synchrotron radiation? X-rays are the ideal structural probe for interatomic distances with wavelengths of 1 Å Laboratory x-ray sources are extremely useful and have gotten much better in the past decades but some experiments can only be done at a synchrotron Synchrotron sources provide superior flux, brilliance, and tunability

46 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Why synchrotron radiation? X-rays are the ideal structural probe for interatomic distances with wavelengths of 1 Å Laboratory x-ray sources are extremely useful and have gotten much better in the past decades but some experiments can only be done at a synchrotron Synchrotron sources provide superior flux, brilliance, and tunability Synchrotron sources and particularly FELs produce coherent beams

47 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Why synchrotron radiation? X-rays are the ideal structural probe for interatomic distances with wavelengths of 1 Å Laboratory x-ray sources are extremely useful and have gotten much better in the past decades but some experiments can only be done at a synchrotron Synchrotron sources provide superior flux, brilliance, and tunability Synchrotron sources and particularly FELs produce coherent beams The broad range of techniques make synchrotron x-ray sources to nearly any science or engineering field

48 A bit about my research... C. Segre (IIT) PHYS Spring 2018 January 09, / 20

49 A bit about my research... SnP x Sn Li y Sn Potential (V) R (Å) a b c Lithiation 0 Delithiation Capacity (mah g -1 ) d e f (R) (Å -3 ) 0.39 In situ EXAFS-derived mechanism of highly reversible tin phosphide/graphite composite anode for Li-ion batteries, Y. Ding, Z. Li, E.V. Timofeeva, and C.U. Segre, Adv. Energy Mater (2017). C. Segre (IIT) PHYS Spring 2018 January 09, /

50 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 History of x-ray sources Free electron lasers 1895 x-rays discovered by William Röntgen Peak X-ray Brilliance Synchrotrons 10 6 X-ray tubes Year

51 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 History of x-ray sources Peak X-ray Brilliance Free electron lasers Synchrotrons 1895 x-rays discovered by William Röntgen 1 st generation synchrotrons initially used in parasitic mode (SSRL, CHESS) 10 6 X-ray tubes Year

52 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 History of x-ray sources Peak X-ray Brilliance Free electron lasers Synchrotrons 1895 x-rays discovered by William Röntgen 1 st generation synchrotrons initially used in parasitic mode (SSRL, CHESS) 2 nd generation were dedicated sources (NSLS, SRC, CAMD) 10 6 X-ray tubes Year

53 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 History of x-ray sources Peak X-ray Brilliance Free electron lasers Synchrotrons X-ray tubes Year 1895 x-rays discovered by William Röntgen 1 st generation synchrotrons initially used in parasitic mode (SSRL, CHESS) 2 nd generation were dedicated sources (NSLS, SRC, CAMD) 3 rd generation featured insertion devices (APS, ESRF, ALS)

54 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 History of x-ray sources Peak X-ray Brilliance Free electron lasers Synchrotrons X-ray tubes Year 1895 x-rays discovered by William Röntgen 1 st generation synchrotrons initially used in parasitic mode (SSRL, CHESS) 2 nd generation were dedicated sources (NSLS, SRC, CAMD) 3 rd generation featured insertion devices (APS, ESRF, ALS) 4 th generation are free electron lasers (LCLS, XFEL)

55 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 The classical x-ray The classical plane wave representation of x-rays is:

56 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 The classical x-ray The classical plane wave representation of x-rays is: E(r, t) = ˆɛE 0 e i(k r ωt)

57 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 The classical x-ray The classical plane wave representation of x-rays is: E(r, t) = ˆɛE 0 e i(k r ωt) where ˆɛ is a unit vector in the direction of the electric field

58 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 The classical x-ray The classical plane wave representation of x-rays is: E(r, t) = ˆɛE 0 e i(k r ωt) where ˆɛ is a unit vector in the direction of the electric field, k is the wavevector of the radiation along the propagation direction

59 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 The classical x-ray The classical plane wave representation of x-rays is: E(r, t) = ˆɛE 0 e i(k r ωt) where ˆɛ is a unit vector in the direction of the electric field, k is the wavevector of the radiation along the propagation direction, and ω is the angular frequency of oscillation of the radiation.

60 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 The classical x-ray The classical plane wave representation of x-rays is: E(r, t) = ˆɛE 0 e i(k r ωt) where ˆɛ is a unit vector in the direction of the electric field, k is the wavevector of the radiation along the propagation direction, and ω is the angular frequency of oscillation of the radiation. If the energy, E is in kev, the relationship among these quantities is given by:

61 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 The classical x-ray The classical plane wave representation of x-rays is: E(r, t) = ˆɛE 0 e i(k r ωt) where ˆɛ is a unit vector in the direction of the electric field, k is the wavevector of the radiation along the propagation direction, and ω is the angular frequency of oscillation of the radiation. If the energy, E is in kev, the relationship among these quantities is given by: ω = hν = E, λν = c

62 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 The classical x-ray The classical plane wave representation of x-rays is: E(r, t) = ˆɛE 0 e i(k r ωt) where ˆɛ is a unit vector in the direction of the electric field, k is the wavevector of the radiation along the propagation direction, and ω is the angular frequency of oscillation of the radiation. If the energy, E is in kev, the relationship among these quantities is given by: ω = hν = E, λν = c λ = hc/e = ( ev s)( m/s)/e = ( kev s)( Å/s)/E = Å kev/e to give units of Å

63 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Interactions of x-rays with matter For the purposes of this course, we care most about the interactions of x-rays with matter. There are four basic types of such interactions:

64 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Interactions of x-rays with matter For the purposes of this course, we care most about the interactions of x-rays with matter. There are four basic types of such interactions: 1. Elastic scattering

65 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Interactions of x-rays with matter For the purposes of this course, we care most about the interactions of x-rays with matter. There are four basic types of such interactions: 1. Elastic scattering 2. Inelastic scattering

66 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Interactions of x-rays with matter For the purposes of this course, we care most about the interactions of x-rays with matter. There are four basic types of such interactions: 1. Elastic scattering 2. Inelastic scattering 3. Absorption

67 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Interactions of x-rays with matter For the purposes of this course, we care most about the interactions of x-rays with matter. There are four basic types of such interactions: 1. Elastic scattering 2. Inelastic scattering 3. Absorption 4. Pair production

68 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Interactions of x-rays with matter For the purposes of this course, we care most about the interactions of x-rays with matter. There are four basic types of such interactions: 1. Elastic scattering 2. Inelastic scattering 3. Absorption 4. Pair production We will only discuss the first three.

69 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Elastic scattering Most of the phenomena we will discuss can be treated classically as elastic scattering of electromagnetic waves (x-rays)

70 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Elastic scattering Most of the phenomena we will discuss can be treated classically as elastic scattering of electromagnetic waves (x-rays) The typical scattering geometry is k Q k

71 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Elastic scattering Most of the phenomena we will discuss can be treated classically as elastic scattering of electromagnetic waves (x-rays) The typical scattering geometry is k Q k where an incident x-ray of wave number k

72 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Elastic scattering Most of the phenomena we will discuss can be treated classically as elastic scattering of electromagnetic waves (x-rays) The typical scattering geometry is k Q k where an incident x-ray of wave number k scatters elastically from an electron to k

73 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Elastic scattering Most of the phenomena we will discuss can be treated classically as elastic scattering of electromagnetic waves (x-rays) The typical scattering geometry is k Q k where an incident x-ray of wave number k scatters elastically from an electron to k resulting in a scattering vector Q

74 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Elastic scattering Most of the phenomena we will discuss can be treated classically as elastic scattering of electromagnetic waves (x-rays) The typical scattering geometry is k Q k where an incident x-ray of wave number k scatters elastically from an electron to k resulting in a scattering vector Q or in terms of momentum transfer: Q = k k

75 Elastic scattering Most of the phenomena we will discuss can be treated classically as elastic scattering of electromagnetic waves (x-rays) The typical scattering geometry is k Q k where an incident x-ray of wave number k scatters elastically from an electron to k resulting in a scattering vector Q or in terms of momentum transfer: Q = k k Start with the scattering from a single electron, then build up to more complexity C. Segre (IIT) PHYS Spring 2018 January 09, / 20

76 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering Assumptions: E in E rad

77 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering Assumptions: incident x-ray plane wave E in E rad

78 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering Assumptions: incident x-ray plane wave electron is a point charge E in E rad

79 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering Assumptions: incident x-ray plane wave electron is a point charge scattering is elastic E in E rad

80 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering Assumptions: incident x-ray plane wave electron is a point charge scattering is elastic scattered intensity 1/R 2 E in E rad

81 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering Assumptions: incident x-ray plane wave electron is a point charge scattering is elastic scattered intensity 1/R 2 The electron is exposed to the incident electric field E in (t ) and is accelerated E in E rad

82 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering Assumptions: incident x-ray plane wave electron is a point charge scattering is elastic scattered intensity 1/R 2 E in The electron is exposed to the incident electric field E in (t ) and is accelerated The acceleration of the electron, a x (t ), results in the radiation of a spherical wave with the same frequency E rad R

83 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering Assumptions: incident x-ray plane wave electron is a point charge scattering is elastic scattered intensity 1/R 2 E in The electron is exposed to the incident electric field E in (t ) and is accelerated The acceleration of the electron, a x (t ), results in the radiation of a spherical wave with the same frequency The observer at R sees a scattered electric field E rad (R, t) at a later time t = t + R/c E rad R

84 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering Assumptions: incident x-ray plane wave electron is a point charge scattering is elastic scattered intensity 1/R 2 E in The electron is exposed to the incident electric field E in (t ) and is accelerated The acceleration of the electron, a x (t ), results in the radiation of a spherical wave with the same frequency The observer at R sees a scattered electric field E rad (R, t) at a later time t = t + R/c E rad R Using this, calculate the elastic scattering cross-section

85 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering E rad (R, t) = e 4πɛ 0 c 2 R a x(t ) sin Ψ

86 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering E rad (R, t) = e 4πɛ 0 c 2 R a x(t ) sin Ψ where t = t R/c

87 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering E rad (R, t) = e 4πɛ 0 c 2 R a x(t ) sin Ψ where t = t R/c a x (t ) = e m E x0e iωt

88 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering E rad (R, t) = e 4πɛ 0 c 2 R a x(t ) sin Ψ where t = t R/c a x (t ) = e m E x0e iωt = e m E x0e iωt e iωr/c

89 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering E rad (R, t) = e 4πɛ 0 c 2 R a x(t ) sin Ψ where t = t R/c a x (t ) = e m E x0e iωt = e m E x0e iωt e iωr/c a x (t ) = e m E ine iωr/c

90 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering E rad (R, t) = e 4πɛ 0 c 2 R e m E ine iωr/c sin Ψ

91 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering E rad (R, t) = e e 4πɛ 0 c 2 R m E ine iωr/c sin Ψ E rad (R, t) = e2 e iωr/c E in 4πɛ 0 mc 2 sin Ψ R

92 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering E rad (R, t) = e e 4πɛ 0 c 2 R m E ine iωr/c sin Ψ E rad (R, t) = e2 e iωr/c E in 4πɛ 0 mc 2 sin Ψ but k = ω/c R

93 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering E rad (R, t) = e2 e ikr E in 4πɛ 0 mc 2 R sin Ψ = r e ikr 0 R sin Ψ

94 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Thomson scattering E rad (R, t) = e2 e ikr E in 4πɛ 0 mc 2 R sin Ψ = r e ikr 0 R e 2 r 0 = 4πɛ 0 mc 2 = Å sin Ψ

95 Scattering cross-section C. Segre (IIT) PHYS Spring 2018 January 09, / 20

96 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Detector of solid angle Ω at a distance R from electron

97 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Detector of solid angle Ω at a distance R from electron Cross-section of incoming beam is A 0

98 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Detector of solid angle Ω at a distance R from electron Cross-section of incoming beam is A 0 Φ 0 I 0 = c E in 2 A 0 ω

99 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Detector of solid angle Ω at a distance R from electron Cross-section of incoming beam is A 0 Φ 0 I 0 = c E in 2 A 0 ω I sc c(r 2 Ω) E rad 2 ω

100 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Detector of solid angle Ω at a distance R from electron Cross-section of incoming beam is A 0 Cross section of scattered beam (into detector) is R 2 Ω Φ 0 I 0 = c E in 2 A 0 ω I sc c(r 2 Ω) E rad 2 ω

101 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Detector of solid angle Ω at a distance R from electron Cross-section of incoming beam is A 0 Cross section of scattered beam (into detector) is R 2 Ω Φ 0 I 0 = c E in 2 A 0 ω I sc c(r 2 Ω) E rad 2 ω I sc = E rad 2 I 0 E in 2 R2 Ω

102 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Differential cross-section is obtained by normalizing

103 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Differential cross-section is obtained by normalizing dσ dω

104 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Differential cross-section is obtained by normalizing dσ dω = I sc Φ 0 Ω

105 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Differential cross-section is obtained by normalizing dσ dω = I sc Φ 0 Ω = I sc (I 0 /A 0 ) Ω

106 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Differential cross-section is obtained by normalizing dσ dω = I sc Φ 0 Ω = I sc (I 0 /A 0 ) Ω = E rad 2 E in 2 R2

107 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Differential cross-section is obtained by normalizing dσ dω = E rad E in I sc Φ 0 Ω = e ikr = r 0 R I sc (I 0 /A 0 ) Ω = E rad 2 E in 2 R2 ˆɛ ˆɛ

108 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Differential cross-section is obtained by normalizing dσ dω = E rad E in I sc Φ 0 Ω = e ikr = r 0 R I sc (I 0 /A 0 ) Ω = E rad 2 E in 2 R2 ˆɛ ˆɛ e ikr = r0 R cos ( π 2 Ψ)

109 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Differential cross-section is obtained by normalizing dσ dω = E rad E in I sc Φ 0 Ω = e ikr = r 0 R I sc (I 0 /A 0 ) Ω = E rad 2 E in 2 R2 ˆɛ ˆɛ e ikr = r0 R cos ( π 2 Ψ) = r0 e ikr R sin Ψ

110 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Scattering cross-section Differential cross-section is obtained by normalizing dσ dω = E rad E in I sc Φ 0 Ω = e ikr = r 0 R I sc (I 0 /A 0 ) Ω = E rad 2 E in 2 R2 = r0 2 sin 2 Ψ ˆɛ ˆɛ e ikr ( = r0 cos π R 2 Ψ) e ikr = r0 R sin Ψ

111 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Total cross-section Integrate to obtain the total Thomson scattering cross-section from an electron.

112 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Total cross-section Integrate to obtain the total Thomson scattering cross-section from an electron. σ = 8π 3 r 2 0

113 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Total cross-section Integrate to obtain the total Thomson scattering cross-section from an electron. σ = 8π 3 r 2 0 = cm 2 = barn

114 C. Segre (IIT) PHYS Spring 2018 January 09, / 20 Total cross-section Integrate to obtain the total Thomson scattering cross-section from an electron. If displacement is in vertical direction, sin Ψ term is replaced by unity and if the source is unpolarized, it is a combination. σ = 8π 3 r Polarization factor = sin 2 Ψ = cm 2 = barn 1 2 ( 1 + sin 2 Ψ )