Electron Linear Accelerators & Free-Electron Lasers

Transcription

1 Electron Linear Accelerators & Free-Electron Lasers Bryant Garcia Wednesday, July SASS Summer Seminar Bryant Garcia Linacs & FELs 1 of 24

2 Light Sources Why? Synchrotron Radiation discovered in 1947 at the 70 MeV GE synchrotron Originally a loss mechanism for electron synchrotrons ( On the maximal energy attainable in betatron, (1944)) Spells the doom for (circular) electron machines as energy frontier devices but... Bryant Garcia Linacs & FELs 2 of 24

3 Electron Machine Basics Why? m e = 0.511MeV /c 2 ; m p = 938MeV /c 2 ; m p /m e 1835! The beginning of the beamline: E gun 1MeV Electrons are almost immediately relativistic This affects synchrotron radiation: P s 1/m 4 Bryant Garcia Linacs & FELs 3 of 24

4 Synchrotron Radiation Basics A tough (but straightforward) EM calculation gives, dw dω = 3e 2 4πɛ 0 c γ ω ω c ω/ω c K 5/3 (x)dx ω c 3 c 2 ρ γ3, λ c = 4π 3 ρ γ 3 Wavelength spectrum peaked near λ c γ 500, ρ 10m, λ c 10 nm! (but broad!) Enables the tunable production of high energy, BRIGHT photon pulses Bryant Garcia Linacs & FELs 4 of 24

5 The Evolution of Light Sources 1st generation: Parasitic synchrotron radiation from high energy physics machines 2nd generation: Dedicated synchrotron machines for production of light 3rd generation: Evolved facilities with insertion devices, many beamlines 4th generation: Free-electron Lasers and Electron-recirculating linacs APS Bryant Garcia Linacs & FELs 5 of 24

6 The Spectral Brightness Race Bryant Garcia Linacs & FELs 6 of 24

7 The typical beamlines Bryant Garcia Linacs & FELs 7 of 24

8 The Typical X-FEL Layout Electron source (Gun) Linear accelerating sections Bunch compression Undulators (radiation generation) Bryant Garcia Linacs & FELs 8 of 24

9 The LCLS Video Bryant Garcia Linacs & FELs 9 of 24

10 In the beginning... Electron Guns Cathode emits electrons (Thermionic or Photoelectric) Typically UV Laser λ 260nm on Cu Cathode High gradient RF Field ( 100MV/m) accelerates electrons to relativistic speeds Fighting against beam space charge to preserve a pristine electron beam Bryant Garcia Linacs & FELs 10 of 24

11 The Electron Acceleration High-frequency RF accelerates the electrons in conducting cavities Matched phase velocity ensures electrons are continuously accelerated in each cell Possible superconducting (LCLS-II), or PWFA (FACET) technologies at this step Bryant Garcia Linacs & FELs 11 of 24

12 The magnetic undulator Series of alternating magnetic poles with periodicity λ u, K eb 0 k umc x(z) = K γk u cos k u z Lorentz transform to the beam rest frame: k u = γk u or λ u = λ u /γ This is larmor radiation, and has wavelength λ u In the lab frame, this radiation is blueshifted again by a factor of 2γ, so we expect lab radiation λ r λ u 2γ 2 Estimate λ r = λ u 2γ 2 ( 1 + K 2 /2 + γ 2 θ 2) Reality Bryant Garcia Linacs & FELs 12 of 24

13 Undulator Radiation The undulator radiation is then simply described as { E0 e E(t) = iωr t, N u λ u /2c < t < N u λ u /2c 0, otherwise Frequency response is found via fourier transform (T N u λ u /2c) F (ω) = E(t)e iωt dt = T T E 0 e i(ω ωr )t dt Bryant Garcia Linacs & FELs 13 of 24

14 Undulator Radiation Cont d. F (ω) = 2TE 0 sinc(t (ω ω 0 )) This spectrum has a FWHM ω = ω 0 /N u Bryant Garcia Linacs & FELs 14 of 24

15 Coherent Radiation Normally, electron radiation is incoherent, that is, the phase of each electron s emission is random. Incoherent power P N e. If the electron bunch has a size < λ r, the phases are all roughly equal Coherent emission P N 2 e for Coherent emission ( 10 9!) Bryant Garcia Linacs & FELs 15 of 24

16 Free-Electron Lasers - Oscillators We can achieve coherence through low-gain operation and a cavity, as in a traditional laser Can use low energy e beams to make Visible-Microwave radiation Requires reflective optics at the wavelengths of interest no X-rays Bryant Garcia Linacs & FELs 16 of 24

17 Free-Electron Lasers - High Gain Devices Another option is to have a very LONG undulator, and allow an instability to develop: Bryant Garcia Linacs & FELs 17 of 24

18 The FEL instability The radiated light becomes intense enough to back-react on the electron bunch The effect is to bunch the electrons up at the radiation wavelength [ Video ] The bunching more coherent emission stronger EM field more bunching Bryant Garcia Linacs & FELs 18 of 24

19 Some FEL Physics The physics of the FEL process is all (basically) controlled by a single parameter ρ: ( ) 2/3 ( ρ = 1 ) ˆKλu I 1/3 2γ 2πσ b I A P sat = ρ ( ) IEb = ρp beam e L g = λ u 4π 3ρ For reference, modern X-ray FELs have ρ , λ u cm. So L g few meters. Turns out you need 20L g to saturate very long undulators Bryant Garcia Linacs & FELs 19 of 24

20 More FEL Physics λ r 1nm ɛ < 0.1nm! This is very small! Storage rings have a natural emittance nm at best, so cannot be used for X-ray FELs linac sources Bryant Garcia Linacs & FELs 20 of 24 To maintain spatial coherence, the phase space volume of the electrons should be less than the phase space volume of the photons: ɛ electrons < ɛ photon ɛ electrons < λ r 4π

21 Beam requirements for High-Gain XFELs Require very low emittance (for transverse matching) Require high energy electrons (for low λ r ) Require high peak current I /I A (for high ρ) Bryant Garcia Linacs & FELs 21 of 24

22 SASE Operation Mode Random electron beam seeds the instability with noise Locations/size of lasing regions are stochastic Many spectral spikes, non-utilization of full electron beam Spatially but not temporally coherent radiation Bryant Garcia Linacs & FELs 22 of 24

23 Coherence Length The reason for the many spikes is that information is generally not propagated through the whole electron beam λ r = λ u 2γ 2 ( 1 + K 2 /2 ) This is also a resonance condition: Bryant Garcia Linacs & FELs 23 of 24

24 Coherence Length 2 The light slips forward by one radiation wavelength per undulator period Coherence Length: Slippage in one gain length L c λ r /πρ l beam So the individual SASE spikes never have time to fully communicate Bryant Garcia Linacs & FELs 24 of 24