synchrotron radiation and free electron...
TRANSCRIPT
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
Synchrotron Radiation and
Free Electron Lasers
Gwyn P. Williams
Jefferson Lab12000 Jefferson Avenue - MS 7A
Newport News, VA [email protected]
UVa April 14, 2004
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
Synchrotron Radiation and Free Electron Lasers
This lecture is aimed at teaching the physics of the productionof very bright light, from a user perspective, NOT an accelerator perspective.
It is not a rigorous presentation of the theory, although it will contain all the critical theoretical arguments and equations.
But most importantly it bridges the gap between Krafft et al’s lectures and practical calculations of light output.
See G.P. Williams, Rep. Prog. Phys. 69 310-326, 2006
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X-Ray Brightness Growth vs Time Compared with Computers
1960 1970 1980 1990 2000107
108
109
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
x1023
200 mA Diff. Limit
3rd. Gen.original design
2nd. Gen.
1st. Gen. Synch. Rad.
CDC 6600
Cray 1
Cray T90
GROWTH IN LEADING EDGECOMPUTING SPEED(Millions of operations/sec)
GROWTH IN SYNCHROTRON X-RAY SOURCE BRIGHTNESS
(Photons/sec/0.1%bw/sq.mm/mrad2)
Calendar Year
10-1
100
101
102
103
104
105
106
107
108
109
1010
1011
1012
1013
1014
1015
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How do we make light?
Light (electromagnetic waves) is made by waving an electron around.
e- light
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Radiation from Accelerated Electron - Power
electronBut dimensions of power are:
acceleration2 2 3
c
MLT L ML TT
Force Distan eTimePower
− −× =
×
=
=field
Electric field goes linearly in the electric charge and the acceleration- so intensity (power) goes like e2a2
2 22
e MLTL
−=
Now for an electric charge, force ise2/L2, so we can derive dimensions for e thus:
So e2a2 has dimensions of :ML3 T-2×L2T-4 = ML5T-6
And if we divide by c3, or L3T-3, we get ML2T-3.
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Radiation from Accelerated Electron - Power
Larmor’s Formula2 2
323e ac
Power=
Also we note that radiation is emitted in only 2 out of 3 directions, so we have a 2/3 factor, yielding:
Noting that the dimensions of power are ML2T-3, and noting That M goes like gamma, L goes like 1/gamma and T goes likegamma in the moving frame, in the rest frame the relativistic version is :
42 23
23e ac
Power γ=
N.B. Radiated energy and elapsed time transform in the same manner under Lorentz transforms 25102 −×≈
νddE J/cm-1/electron
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Theory
D.H. Tomboulian & P.L. Hartman, Phys. Rev. 102 1423 (1956)J. Schwinger, Phys. Rev. 75 1912 (1949)J.D. Jackson, Classical Electrodynamics, Wiley, NY 1975H. Winick, Synchrotron Radiation Research, Chap. 2, Plenum Press 1980.K.J. Kim AIP Proceedings 184 565 (1989).S.L. Hulbert and G.P., Williams, "Synchrotron radiation sources." In Handbook of Optics: Classical, Vision, and X-Ray Optics, 2nd ed., vol. III, chap. 32. Michael Bass, Jay M. Enoch, Eric W. Van Stryland, and William L. Wolfe (eds.). New York: McGraw-Hill, , pp. 32.1--32.20 (2001).C. A. Brau, Modern Problems in Classical Electrodynamics, Oxford University Press (2004).
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facilitytime freq. (1/time)
Inte
nsity
e2
electron(s)2 9 8
1 2t 10 Attosecondsc 10 3 10ρ∆ γγ
= = ≈× ×
cc
c c t 30 Angstromsλ ∆ω= ≈ ≈
Radiation from Accelerated Electron – SpectrumEl
e ctri
c fie
ld
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Radiation from Accelerated Electron – Emission Angle
sintan( ) (cos )r tt
θθ γ θ β=−
r is lab (receiving frame) t is transmitting frameSo θt = 900 transforms to ~1/γin the lab frame
γ = mass / rest mass
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2.nr( t )ˆi t c2 2 2
2d I e n n e dtd d 4 c
ωω βω Ω π
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
−∞
−∞= × ×∫
Synchrotron Radiation Generation - theory
Jackson, Classical Electrodynamics, Wiley, NY 1975
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where e is the charge of an electron, β is the ratio of the velocity of the particle to the speed of light, n is a unit vector and (t) is the particle position.Kim has shown that one can re-write this to give the total flux emitted in practical units, per horizontal milliradian per ampere into a 0.1% bandwidth (Dλ/ λ or DE/E), integrated over qV as:
F tot= 2.547 x 10 13 E (GeV) I (A) G1(y)where G1(y) is the Bessel function:
1 5/3( ) ( )y
G y K dη η∞
= ∫cy λλ=
03
5.59 ( )( )(cmetersA
E GeVρλ =with and
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Bessel Functions!!!
The function G1(y)
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Bessel Functions!!!
1 5/3( ) ( )y
G y K dη η∞
= ∫
can be shown to be equivalent to:
1 r=1
(0.5 )( ) 0.5 + (0.5 )2 (0.5 )y y cosh kreG y e cosh r cosh r
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
∞− −= ∑
V. Kostroun, Nucl. Instr. & Methods 172 371 (1980).
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Brightness
Brightness is sometimes called brilliance, or spectral radiance.It has units of power per unit area per unit solid angle.
ρ
ϑΗ
ϑv
svsH
ρ
ϑΗ
ϑv
svsH
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Emitted Flux as Function of Vertical Angle
222 2 216 2 2 2 2cv v V V V2/ 3F ( ) 1.325 10 E 1 K ( 1 )λθ γ θ ζ γ θ γ θ ζλ
⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠
= × + + + 21/3K (parallel perpendicular
to orbit plane
ρ
ϑΗ
ϑv
svsH
ρ
ϑΗ
ϑv
svsH
Units: photons/sec/mrad.(horiz)/mrad.(vert)/amp/0.1%bw
γ = 1957E(GeV)
32 2 2(1 )2
c vλζ γ θλ= +
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Emitted Flux as Function of Vertical Angle
-20 0 20
Pow
er p
er u
nit v
ertic
al a
ngle
Vertical angle (mradians)
Parallelto orbit plane
Perpendicularto orbit plane
10 µ 10 µ 100 µ 100 µ 1 µ 1 µ
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Synchrotron Radiation Source at JLab
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Synchrotron Radiation SourceBrightnesscomparedwith table-top
Sp e
ctr a
l Bri g
htne
ssP
h oto
ns/s
e c/m
m2/
mra
d2/ 0
. 1%
ba n
dwi d
t h
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Looking at some brightness numbers
Standard x-ray tube is a 10 keV beam of 10 mA.Power in the electron beam is 100 Watts.X-ray power is then at most ~ 1 watt.
Solid angle of emission = 4π steradiansArea of source = 1 mm2
Brightness is 1 / (4 × π × 1) = 0.08 watts/str/mm2
Synchrotron is, say 3 GeV, at 300 mA.Power in the beam is then 1000 MegawattsX-ray power is then about 10 Megawatts.Questions: What is gamma for this ring, how fast are the electrons going, and how many electrons are circulating in the ring assuming a circumference of 200 m?Solid angle of emission = 2π × 10-3 steradiansArea of source = 0.1 mm2
Brightness is 107 / (2π × 10-3 × 0.1) = 1.6 × 1010 watts/str/mm2
Ratio of synchrotron / x-ray tube = 2 × 1011
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Synchrotron Radiation and Free Electron Lasers
Up to this point we have assumed that each electron emitted independently within the bunch.
Now we are going to advance considerably into a new regime in which electrons are going to radiate coherently, meaning that their electric fields will be in phase with each other.
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How do we make light more powerful?
2e-light
42 23
2( )3
2e ac
Power γ=
e is charge on electrona is accelerationc is speed of lightγ is relativistic mass increase
4 times the power!!!
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facilitytime freq. (1/time)
Inte
nsity
e2
electron(s)2 9 8
1 2t 10 Attosecondsc 10 3 10ρ∆ γγ
= = ≈× ×
cc
c c t 30 Angstromsλ ∆ω= ≈ ≈
Radiation from Accelerated Electron – SpectrumEl
e ctri
c fie
ld
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Thomas Jefferson National Accelerator Facility
Ele c
tric
field
electron(s)
super-radiantenhancement
N
E/N
Inte
nsity
E2
Radiation from Accelerated Electrons – Spectrum
time freq. (1/time)
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Radiation from Accelerated Electrons - physics
Statistics of an electron bunch in a storage ring
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2.nr( t )ˆi t c2 2 2
2d I e n n e dtd d 4 c
ωω βω Ω π
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
−∞
−∞= × ×∫
Coherent Synchrotron Radiation Generation - theory
Jackson, Classical Electrodynamics, Wiley, NY 1975
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
where e is the charge of an electron, β is the ratio of the velocity of the particle to the speed of light, n is a unit vector and (t) is the particle position.Kim has shown that one can re-write this to give the total flux emitted in practical units, per horizontal milliradian per ampere into a 0.1% bandwidth (Dl/l or DE/E), integrated over qV as:
F tot= 2.547 x 10 13 E (GeV) I (A) G1(y)
where G1(y) is the Bessel function:
1 5/3( ) ( )y
G y K dη η∞
= ∫cy λλ=
03
5.59 ( )( )(cmetersA
E GeVρλ =with and
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Thomas Jefferson National Accelerator Facility
2/ˆi n z cf e S z dzωω⎛ ⎞ ⎛ ⎞
⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠
∞ ⋅−∞
= ∫
2.nr( t )ˆi t c2 2 22
2d I eN[1 f ( )] N f ( ) n n e dtd d 4 c
ωωω ω βω Ω π
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
⎛ ⎞⎡ ⎤⎜ ⎟⎢ ⎥ ⎜ ⎟⎢ ⎥⎣ ⎦ ⎝ ⎠
−∞
−∞= − + × × ×∫
S.L. Hulbert and G.P. Williams, Handbook of Optics: Classical, Vision, and X-Ray Optics, 2nd ed., vol. III. Bass, Michael, Enoch, Jay M., Van Stryland, Eric W. and Wolfe William L. (eds.). New York: McGraw-Hill, 32.1-32.20 (2001).S. Nodvick and D.S. Saxon, Suppression of coherent radiation by electrons in a synchrotron. Physical Review 96, 180-184 (1954).Carol J. Hirschmugl, Michael Sagurton and Gwyn P. Williams, Multiparticle Coherence Calculations for Synchrotron Radiation Emission, Physical Review A44, 1316, (1991).
Coherent Synchrotron Radiation Generation - theory
f(ω) is the form factor – the Fourier transform of the normalized longitudinal particle distribution within the bunch, S(z)
Jackson, Classical Electrodynamics, Wiley, NY 1975
REFERENCES
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Thomas Jefferson National Accelerator Facility
Synchrotron Radiation and Free Electron Lasers
We have manipulated the electrons, now let’s manipulate their radiation paths.
Instead of a single pass, let’s have an alternating series of magnets.
electron(s)
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New Undulator at Jefferson Lab
Wavelength 20 cmNumber of periods 12 ea.Gap 26 mm
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Undulator and Free Electron Laser
|NE(ω)|2
Ne-
e-
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Undulator and Free Electron Laser
C. J. Hirschmugl, M. Sagurton and G. P. Williams, Physical Review A44, 1316, (1991).
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Synchrotron Radiation SourceBrightnesscomparedwith table-topincludingundulatorsand FELs
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Synchrotron Radiation
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Thomas Jefferson National Accelerator Facility
Synchrotron Radiation
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Synchrotron Radiation - so what’s new here?
Showstopper…….3 GeV at 100 mA is 300 Megawatts!!!!!
radio-freq.cavity
Solution……..Energy Recovery
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First of a new generation of light source – The Energy Recovered Linac
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Jefferson Lab Free-electron Laser
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The JLab 10kW IR FEL and 1 kW UV FEL
Injector
Beam dump
IR wiggler
Superconducting rf linac
UV wiggler
Injector
Beam dump
IR wiggler
Superconducting rf linac
UV wiggler
Presently under commissioning
First light achieved on June 17, 2003
1000 TIMES BRIGHTER THAN ANY SUB-ps TABLE_TOP LASER
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Jefferson Lab FEL Superconducting Linac
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Superconducting Radio-Freq. Linac
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Undulator and Free Electron Laser
C. J. Hirschmugl, M. Sagurton and G. P. Williams, Physical Review A44, 1316, (1991).
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Thomas Jefferson National Accelerator Facility
R.A. Bosch, Nuclear Instr. & Methods A431 320 (1999).M. Buess, G.L. Carr, O. Chubar, J.B. Murphy, I. Schmid & G. P. Williams “Exploring New Limits in Understanding The Emission of Light from Relativistic Electrons” in preparation for Nature.O. Chubar, P. Elleaume, "Accurate And Efficient Computation Of Synchrotron Radiation In The Near Field Region", proc. of the EPAC98 Conference, 22-26 June 1998, p.1177-1179.
Coherent Synchrotron Radiation Generation - theory
REFERENCES
2
1 21 [( ) ] exp[ / )]
(1 )( ) (e e
e
ecR nn nE ec i R c dn Rω
β β ω τβ
γ β τ+∞
−
−
−
∞
−× − += −× +−∫
2nd. extra term
Need to consider the term in the velocity, or the Coulomb or near-field term, particularly when R is small and gamma is small.
Jackson, Classical Electrodynamics, Wiley, NY 1975
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Thomas Jefferson National Accelerator Facility
Brightness of IR Sources
1 10 100 1000 100001E-121E-111E-101E-91E-81E-71E-61E-51E-41E-30.010.1
110
1001000
10000
Energy (meV)
Flux
(Wat
ts/c
m-1)
Wavenumbers (cm-1)
1 10 100 1000
JLab THz
Synchrotrons
Globar
JLab FEL
Table-top sub-ps lasers
FEL proof of principle:Neil et al. Phys. Rev.Letts 84, 662 (2000)
THz proof of principle:Carr, Martin, McKinney, Neil, Jordan & WilliamsNature 420, 153 (2002)
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The THz Gap
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1 10 100 1000 10000
1E-10
1E-8
1E-6
1E-4
0.01
THz
Wat
ts/c
m-1/m
m2 /s
r
Frequency (cm-1)
2000K Black Body
0.1 1 10 100
Electronics - radios Photonics – light bulbsThe Real THz Gap
Tom Crowe, UVa
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Thomas Jefferson National Accelerator Facility
October 2002
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THz Expt and Calculation
1 10 100 10000.0
0.2
0.4
0.6
Frequency (THz)
Measured Calculated (500fs bunch length)
Wat
ts/c
m-1
Frequency (cm-1)
0.1 1 10
Diffraction losses ~ 20 Watts integrated
Carr, Martin, McKinney, Neil, Jordan & WilliamsNature 420, 153 (2002)
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THz Imaging
A tooth cavity shows up clearly in red. Teraview Ltd.
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THz Imaging
Basal cell carcinoma shows malignancy in red. Teraview Ltd.
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Terahertz computerized tomography
3cm
Turkey Bone Test Object
Ferguson et. al. Phys. Med. Biol. 47 3735 (2002)
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Terahertz Imaging
Clery, Science 297 763 (2002)
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Introduction
High power* THz light is critical for communications, imaging and remote sensing.
Jefferson Lab operates a 100 Watt average, Megawatt peak power broadband THz source.
Implementation of the above has become possible only recently with advances in the laboratory, particularly
combining modern ultra-fast lasers with superconductivity and relativity.
We have established a user facility which is equipped for spectroscopy and imaging proof of principle experiments
in this new arena.
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JLab Terahertz Beam Extraction and Transport
M1
M2M3
diamondwindow
Shutter/viewer &camera
M1V1
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Terahertz Beamline Schematic with Optical Ray-tracing
M1
-4x10-2 m
-2
0
2
4
Ver
tical
Pos
ition
-40mm -20 0 20 40
Horizontal Position
200x200mm
-3x10-2 m
-2
-1
0
1
2
3
Ver
tical
Pos
ition
-30mm -20 -10 0 10 20 30
Horizontal Position60x60mm
F2
-1.0x10-1 m
-0.5
0.0
0.5
1.0
Ver
tical
Pos
ition
-100mm -50 0 50 100
Horizontal Position
200x200mm
M2
-1.0x10-1 m
-0.5
0.0
0.5
1.0
Ver
tical
Pos
ition
-100mm -50 0 50 100
Horizontal Position200x200mm
M4 F3
-3x10-2 m
-2
-1
0
1
2
3
Ver
tical
Pos
ition
-30mm -20 -10 0 10 20 30
Horizontal Position60x60mm
THz Generation
THz To UserFacility
Optical calculations by Oleg Chubar, Paul Dumas
FundingUS Army NVL
Fundingstart 7/2003
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JLab power permits large area imaging ~ m2
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Optical transport output in User Lab Real time image from IR Demo
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Coherent Synchrotron Radiation Effect of Pulse Length
1 10 100 10001E-10
1E-9
1E-8
1E-7
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
100
1000
10000
100000
Frequency (THz)
Wat
ts/c
m-1
Frequency (cm-1)
100 MHz 100 pC 150 x 150 mr
0.1 ps 0.3 ps 1.0 ps
0.1 1 10
840 W540 W54 W
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FWHM
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Coherent Synchrotron Radiation Effect of Pulse Charge
1 10 100 10001E-10
1E-9
1E-8
1E-7
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
100
1000
10000
100000
Frequency (THz)
Wat
ts/c
m-1
Frequency (cm-1)
100 MHz 100 fs FWHM 150 x 150 mr
10 pC 100 pC 1000 pC
0.1 1 10
Total power = 800 W
Total power = 80 kW
Total power = 8 W
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Applications – proof of principle expts.
2. Military/Commercial(b) Remote Sensing, high
spatial resolution, with active imaging
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10 meters
2m
10.2meters
30cm
0.3cm of a 10cm radius spherewill be normal to the beam,which is 0.1%.
Calculations using antenna coupled bolometer sensitivitiesIndicate that about 100 W is required for this application
Clery, Science 297 763 (2002)
Passive Image
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FEL Team at JLab
This work supported by the Office of Naval Research, the Joint Technology Office, the Commonwealth of Virginia, the Air Force Research Laboratory, Army Night Vision Lab, and by DOE Contract DE-AC05-84ER40150.
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Addendum, an Application - Protein Structure
Carboxypeptidase
α-helix
β-sheetβ-turn
extended coil
synchrotron
scattering
film
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Application to Protein Crystallography
Synchrotron Radiation Brightness is 107 / (2π × 10-3 × 0.1) = 1.6 × 1010 watts/str/mm2
How many photons can we shine on a 100 micron × 100 micron protein crystal?
Throughput (étendue) is area × angle, and let’s say we are limited by 5 milliradiansof angle.
Area × angle = 0.01 × 5 × 10-3 × 5 × 10-3 = 2.5 × 10-7 mm2 str
Flux on sample is therefore 1.6 × 1010 × 2.5 × 10-7 = 4000 watts
However to get a good diffraction pattern, we need to monochromatize the beam, to get a bandwidth of, say, 0.1%, making the power 4 watts.
Question: How many photons is this at hν = 10 keV and what is their wavelength?
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Thomas Jefferson National Accelerator Facility
Answers to Questions
Questions: What is gamma for this ring, how fast are the electrons going, and how many electrons are circulating in the ring assuming a circumference of 200 m?
Rest mass of electron is 0.5 MeV, so gamma is 3 × 109 / 0.5 × 106 = 6000
From relativity: putting in numbers: v = 0.999999986 c
Last is a trick question, but 1 ampere is 1 coulomb per second, and each electron carries a charge of 1.6 × 10-19 coulombs, and that would make 0.3 / 1.6 × 10-19 = 1.9 × 1018 electrons. However, for a 200 meter circumference ring, the circulation time is 0.66 microseconds, so each electron is used 1.5 million times. So the actual number of electrons is 1 .9 × 1018 / 1.5 × 106 = 1.2 × 1012
221
ommvc
=−
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
Answers to Questions
Question: How many photons is 4 watts at 10 keV?
1 eV is the energy required to accelerate an electron through 1 eV potential.
1 watt is 1 amp / second at 1 volt, so 1 eV is 1.6 × 10-19 joules.
If each photon carries 10 keV of energy, it carries 1.6 × 10-15 joules.
Therefore the number of photons is 4 / 1.6 × 10-15 = 2.5 × 1015 / second.
and what is their wavelength?
Energy = hν, and c = lambda ν, so hcEhcE
λλ
=
=34 8 10
156.6 10 3 10 1.24 10
1.6 10hc metersEλ
− −−
× × ×= = = ××
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
Conventional THz Sources - Auston Switch for producing THz light
Auston, D.H., Cheung, K.P., Valdmanis, J.A. and Kleinman, D.A., Phys. Rev.Letters 53 1555-1558 (1984).
2 2
3
2Larmor's Formula: Power (cgs units)3e ac
=
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
THz pulseSub-picosecondlaser pulse
Si orGaAs
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
Comparing Coherent THz Synchrotron and Conventional THz Sources
a=accelerationc=vel. of lightγ=mass/rest mass
units) (cgs Power :Formula sLarmor' 43
22
23 γ
cae
=
~100 V
fseclaserpulseGaAs
THz
64
6 6 8 2
2 6
172
100V VE 10 m10 mF 10 V e / m 10 ( 3 10 )am .5MeV / c 0.5 10
m10 sec
−= =
⋅ ×= = =
×
≅
fseclaserpulse
e- -> 40 MeV
ρ THzGaAs
2 8 217
2c ( 3 10 ) ma 10 secρ 1
if ρ 1 m
×= = ≅
=4 780 80 10 !!!!andγ = =