Synchrotron Radiation and Free Electron Lasers

Transcription

1 Synchrotron Radiation and Free Electron Lasers Gwyn P. Williams Jefferson Lab Jefferson Avenue - MS 7A Newport News, VA gwyn@mailaps.org UVa April 14, 2004

2 Synchrotron Radiation and Free Electron Lasers This lecture is aimed at teaching the physics of the production of 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 , 2006

3 X-Ray Brightness Growth vs Time Compared with Computers x ma Diff. Limit GROWTH IN SYNCHROTRON X-RAY SOURCE BRIGHTNESS (Photons/sec/0.1%bw/sq.mm/mrad 2 ) 2nd. Gen. 3rd. Gen. original design st. Gen. Synch. Rad. Cray T Cray CDC 6600 GROWTH IN LEADING EDGE COMPUTING SPEED (Millions of operations/sec) Calendar Year

4 How do we make light? Light (electromagnetic waves) is made by waving an electron around. e - light

5 Radiation from Accelerated Electron - Power Electric field goes linearly in the electric charge and the acceleration electron field - so intensity (power) goes like e 2 a 2 But dimensions of power are: Power Force Distance Time MLT 2 L = ML 2 T 3 acceleration T Now for an electric charge, force is e 2 /L 2, so we can derive dimensions for e thus: e2 = MLT 2 2 So e 2 a 2 has dimensions of :ML 3 T -2 L 2 T -4 = ML 5 T -6 And if we divide by c 3, or L 3 T -3, we get ML 2 T -3. = = L

6 Radiation from Accelerated Electron - Power Also we note that radiation is emitted in only 2 out of 3 directions, so we have a 2/3 factor, yielding: Larmor s Formula Power = 2ea 3c Noting that the dimensions of power are ML 2 T -3, and noting That M goes like gamma, L goes like 1/gamma and T goes like gamma in the moving frame, in the rest frame the relativistic version is : Power= 2ea 3c γ 4 N.B. Radiated energy and elapsed time transform in the same manner under Lorentz transforms de J/cm -1 /electron dν

7 Theory D.H. Tomboulian & P.L. Hartman, Phys. Rev (1956) J. Schwinger, Phys. Rev (1949) J.D. Jackson, Classical Electrodynamics, Wiley, NY 1975 H. Winick, Synchrotron Radiation Research, Chap. 2, Plenum Press K.J. Kim AIP Proceedings (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 (2001). C. A. Brau, Modern Problems in Classical Electrodynamics, Oxford University Press (2004).

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9 Radiation from Accelerated Electron Spectrum Electric field electron(s) t = 1 ρ 2 10 Attoseconds γ 2cγ = Intensity e 2 λ c c= ω c t 30 Angstroms c time freq. (1/time)

10 Radiation from Accelerated Electron Emission Angle sinθ tan( θr) = t γ (cos θ β) t r is lab (receiving frame) t is transmitting frame γ = mass / rest mass So θ t = 90 0 transforms to ~1/γ in the lab frame

11 Synchrotron Radiation Generation -theory Jackson, Classical Electrodynamics, Wiley, NY 1975 nr(t) ˆ. iω t c d2i e2 2 ω = nˆ β nˆ e dt dω dω 4π 2c 2 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: where G 1 (y) is the Bessel function: with y= λ λ c F tot = x E (GeV) I (A) G 1 (y) and G( y) = K ( η) dη 1 5/3 y 0 λ ( ) 5.59 ( ) c A = ρ meters E3( GeV

12 Bessel Functions!!! The function G 1 (y)

13 Bessel Functions!!! G( y) = K ( η) dη 1 5/3 y can be shown to be equivalent to: ( ) 0.5 e G y = + e cosh(0.5 r) 1 r=1 cosh r y y cosh(0.5 kr) 2 (0.5 ) V. Kostroun, Nucl. Instr. & Methods (1980).

14 Brightness Brightness is sometimes called brilliance, or spectral radiance. It has units of power per unit area per unit solid angle. s H s v ρ ϑ Η ϑ v

15 Emitted Flux as Function of Vertical Angle v v = λ c λ V 2/3 + V + V K 2 1/3 ( parallel perpendicular to orbit plane F ( θ ) E 1 γθ K ( ζ γθ 1 γθ ζ) ρ s H ϑ Η Units: photons/sec/mrad.(horiz)/mrad.(vert)/amp/0.1%bw s v ϑ v 3 λ (1 2 2) 2 2 c γθ λ v ζ = + γ = 1957E(GeV)

16 Emitted Flux as Function of Vertical Angle Power per unit vertical angle Parallel to orbit plane Perpendicular to orbit plane 10 µ 10 µ 100 µ 100 µ 1 µ 1 µ Vertical angle (mradians)

17 Synchrotron Radiation Source at JLab

18 Synchrotron Radiation Source Brightness compared with table-top Spectral Brightness Photons/sec/mm2/mrad2/0.1% bandwidth

19 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 steradians Area of source = 1 mm 2 Brightness is 1 / (4 π 1) = 0.08 watts/str/mm 2 Synchrotron is, say 3 GeV, at 300 ma. Power in the beam is then 1000 Megawatts X-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 steradians Area of source = 0.1 mm 2 Brightness is 10 7 / (2π ) = watts/str/mm 2 Ratio of synchrotron / x-ray tube =

20 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.

21 How do we make light more powerful? 2e - light Power = 2( 2e) a 3c γ 4 4 times the power!!! e is charge on electron a is acceleration c is speed of light γ is relativistic mass increase

22 Radiation from Accelerated Electron Spectrum Electric field electron(s) t = 1 ρ 2 10 Attoseconds γ 2cγ = Intensity e 2 λ c c= ω c t 30 Angstroms c time freq. (1/time)

23 Radiation from Accelerated Electrons Spectrum electron(s) Electric field E/N Intensity E 2 N super-radiant enhancement time freq. (1/time)

24 Radiation from Accelerated Electrons - physics Statistics of an electron bunch in a storage ring

25 Coherent Synchrotron Radiation Generation -theory Jackson, Classical Electrodynamics, Wiley, NY 1975 nr(t) ˆ. iω t c d2i e2 2 ω = nˆ β nˆ e dt dω dω 4π 2c 2 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: where G1(y) is the Bessel function: with y= λ λ c F tot = x E (GeV) I (A) G 1 (y) and G( y) = K ( η) dη 1 5/3 y 0 λ ( ) 5.59 ( ) c A = ρ meters E3( GeV

26 Coherent Synchrotron Radiation Generation - theory Jackson, Classical Electrodynamics, Wiley, NY 1975 nr(t) ˆ. iω t c d2i 2 e2 2 N[1 f( )] N f( ) ω = ω + ω nˆ β nˆ e dt dω dω 4π 2c 2 f(ω) is the form factor the Fourier transform of the normalized longitudinal particle distribution within the bunch, S(z) REFERENCES 2 f ω eiω nz ˆ / c S z dz = 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, (2001). S. Nodvick and D.S. Saxon, Suppression of coherent radiation by electrons in a synchrotron. Physical Review 96, (1954). Carol J. Hirschmugl, Michael Sagurton and Gwyn P. Williams, Multiparticle Coherence Calculations for Synchrotron Radiation Emission, Physical Review A44, 1316, (1991).

27 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)

28 New Undulator at Jefferson Lab Wavelength Number of periods Gap 20 cm 12 ea. 26 mm

29 Undulator and Free Electron Laser e - Ne - NE(ω) 2

30 Undulator and Free Electron Laser C. J. Hirschmugl, M. Sagurton and G. P. Williams, Physical Review A44, 1316, (1991).

31 Synchrotron Radiation Source Brightness compared with table-top including undulators and FELs

32 Synchrotron Radiation

33 Synchrotron Radiation

34 Synchrotron Radiation - so what s new here? radio-freq. cavity Showstopper. Solution.. 3 Energy GeV at Recovery 100 ma is 300 Megawatts!!!!!

35 First of a new generation of light source The Energy Recovered Linac

36 Jefferson Lab Free-electron Laser

37 The JLab 10kW IR FEL and 1 kw UV FEL Presently under commissioning First light achieved on June 17, 2003 Superconducting rf linac Injector Beam dump IR wiggler UV wiggler 1000 TIMES BRIGHTER THAN ANY SUB-ps TABLE_TOP LASER

38 Jefferson Lab FEL Superconducting Linac

39 Superconducting Radio-Freq. Linac

40 Undulator and Free Electron Laser C. J. Hirschmugl, M. Sagurton and G. P. Williams, Physical Review A44, 1316, (1991).

41 Coherent Synchrotron Radiation Generation -theory Jackson, Classical Electrodynamics, Wiley, NY E ec 1 n [( n βe) βe] cr γ ( n e) ω = + β exp[ iω( τ + R/ c)] dτ (1 nβ ) 2R REFERENCES R.A. Bosch, Nuclear Instr. & Methods A (1999). e 2 nd. 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. 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, June 1998, p

42 Flux (Watts/cm -1 ) E-3 1E-4 1E-5 1E-6 1E-7 1E-8 1E-9 1E-10 1E-11 Brightness of IR Sources Energy (mev) JLab THz Synchrotrons Globar 1E Wavenumbers (cm -1 ) JLab FEL Table-top sub-ps lasers THz proof of principle: Carr, Martin, McKinney, Neil, Jordan & Williams Nature 420, 153 (2002) FEL proof of principle: Neil et al. Phys. Rev.Letts 84, 662 (2000)

43 The THz Gap

44 The Real THz Gap Electronics - radios Photonics light bulbs THz K Black Body 1E-4 Watts/cm -1 /mm 2 /sr 1E-6 1E-8 1E Frequency (cm -1 ) Tom Crowe, UVa

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46 October 2002

47 THz Expt and Calculation Frequency (THz) Diffraction losses Measured Calculated (500fs bunch length) ~ 20 Watts integrated Watts/cm Carr, Martin, McKinney, Neil, Jordan & Williams Nature 420, 153 (2002) Frequency (cm -1 )

48 THz Imaging A tooth cavity shows up clearly in red. Teraview Ltd.

49 THz Imaging Basal cell carcinoma shows malignancy in red. Teraview Ltd.

50 Terahertz computerized tomography 3cm Turkey Bone Test Object Ferguson et. al. Phys. Med. Biol (2002)

51 Terahertz Imaging Clery, Science (2002)

52 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.

53 JLab Terahertz Beam Extraction and Transport diamond window M2 M3 Shutter/viewer & camera M1 V1 M1

54 Terahertz Beamline Schematic with Optical Ray-tracing Funding start 7/2003 Vertical Position M4 F3 Vertical Position THz To User Facility x10-1 m -100mm x200mm Horizontal Position F2 Vertical Position x10-2 m -30mm 60x60mm Horizontal Position Vertical Position M2-2 -3x10-2 m 60x60mm -30mm Horizontal Position Funding US Army NVL -1.0x10-1 m -100mm Horizontal Position 200x200mm M x200mm Vertical Position 0-2 THz Generation -4x1 0-2 m -40mm Optical calculations by Oleg Chubar, Paul Dumas Horizontal Position

55 JLab power permits large area imaging ~ m 2 Optical transport output in User Lab Real time image from IR Demo

56 Coherent Synchrotron Radiation Effect of Pulse Length Watts/cm E-3 1E-4 1E-5 1E-6 1E-7 1E-8 1E-9 Frequency (THz) MHz 100 pc 150 x 150 mr 0.1 ps 0.3 ps FWHM 1.0 ps 54 W 1E Frequency (cm -1 ) 540 W 840 W

57 Coherent Synchrotron Radiation Effect of Pulse Charge Watts/cm E-3 1E-4 1E-5 1E-6 1E-7 1E-8 1E-9 Frequency (THz) Total power = 80 kw Total power = 800 W Total power = 8 W 100 MHz 100 fs FWHM 150 x 150 mr 10 pc 100 pc 1000 pc 1E Frequency (cm -1 )

58 Applications proof of principle expts. 2. Military/Commercial (b) Remote Sensing, high spatial resolution, with active imaging 30cm Passive Image 10.2meters 2m Clery, Science (2002) 10 meters 0.3cm of a 10cm radius sphere will be normal to the beam, which is 0.1%. Calculations using antenna coupled bolometer sensitivities Indicate that about 100 W is required for this application

59 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- Operated 84ER by the Southeastern Universities Research Association for the U.S. Department of Energy

60 Addendum, an Application - Protein Structure Carboxypeptidase β-turn β-sheet synchrotron scattering extended coil α-helix film

61 Application to Protein Crystallography Synchrotron Radiation Brightness is 10 7 / (2π ) = watts/str/mm 2 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 milliradians of angle. Area angle = = mm 2 str Flux on sample is therefore = 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?

62 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 / = 6000 From relativity: m= m o putting in numbers: v = c 2 1 v 2 c Last is a trick question, but 1 ampere is 1 coulomb per second, and each electron carries a charge of coulombs, and that would make 0.3 / = 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 / =

63 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 joules. If each photon carries 10 kev of energy, it carries joules. Therefore the number of photons is 4 / = / second. and what is their wavelength? Energy = hν, and c = lambda ν, so E = hc λ λ= hc E λ = hc= = E meters

64 Conventional THz Sources - Auston Switch for producing THz light 2 2 2ea Larmor's Formula: Power = (cgs units) 3 3c Sub-picosecond laser pulse THz pulse Si or GaAs Auston, D.H., Cheung, K.P., Valdmanis, J.A. and Kleinman, D.A., Phys. Rev.Letters (1984).

65 Comparing Coherent THz Synchrotron and Conventional THz Sources Larmor's Formula : Power = 2 3e a 3 2c 2 γ 4 (cgs units) a=acceleration c=vel. of light γ=mass/rest mass ~100 V GaAs 4 10 m fsec laser pulse 100V E = = 10 6 V THz F 10 V e/m 10 (3 10 ) a = = = 2 6 m.5mev /c m 2 sec m GaAs fsec laser pulse e - -> 40 MeV ρ c (3 10 ) 17 m a = = 10 ρ 1 if ρ 1 m γ = = = sec THz and 80 10!!!! 2