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## Accelerator Physics: Synchrotron radiation

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**Accelerator Physics:Synchrotron radiation**Lecture 2 Henrik Kjeldsen – ISA**Synchrotron Radiation (SR)**• Acceleration of charged particles • Emission of EM radiation • In accelerators: Synchrotron radiation • Our goals • Effect on particle/accelerator • Characterization and use • Litterature • Chap. 2 + 8 + notes**General Electric synchrotron accelerator built in 1946, the**origin of the discovery of synchrotron radiation. The arrow indicates the evidence of arcing.**Emission of Synchrotron Radiation**• Goal • Details (e.g.): Jackson – Classical Electrodynamics • Here: Key physical elements • Acceleration of charged particles: EM radiation • Lamor: Non-relativistic, total power • Angular distribution (Hertz dipole)**Relativistic particles**• Lorenz-invariant form • Result**Linear acceleration**• Using dp/dt = dE/dx: • Energy gain: dE/dx ≈ 15 MeV/m • Ratio between energy lost and gain: • h = 5 * 10-14 (for v ≈ c) • Negligible**Circular accelerators**• Perpendicular acceleration: • Energy constant... • dp = pda → dp/dt = pw = pv/R • E ≈ pc, g = E/m0c2 • In praxis: Only SR from electrons**Energy loss per turn**• Max E in praxis: 100 GeV (for electrons)**Angular distribution I**• Similar to Hertz dipole in frame of electron • Relativistic transformation**Spectrum of SR**• Spectrum: Harmonics of frev • Characteristic/critical frequency • Divide power in ½**ASTRID2**• Horizontal emittance [nm] • ASTRID2:12.1 • ASTRID: 140 • Diffraction limit:**Storage rings for SR**• SR – unique broad spectrum! • 0th generation: Paracitic use • 1st generation: Dedicated rings for SR • 2nd generation: Smaller beams • ASTRID? • 3rd generation: Insertion devices (straight sections), small beam • ASTRID2 • 4th generation: FEL**Wigglers and undulators(Insertion devices)**• The magnetic field configuration • Technical construction • Equation of motion • Wigglers vs. Undulators • Undulator radiation • The ASTRID undulator**Magnetic field**• Potential: • Solution: • Peak field on axis:**Magnetic field on axis**Construction a) Electromagnet; b) permanet magnets; c) hybrid magnets**Insertion devices**• Single period, strong field (2T / 6T) • Wavelength shifters • Several periods • Multipole wigglers • Undulators • Requirement • no steering of beam**Example (ASTRID2):Proposed multi-pole wiggler (MPW)**• B0 = 2.0 T • l = 11.6 cm • Number of periods = 6 • K = 21.7 • Critical energy = 447 eV**Summary – multi-pole wiggler(MPW)**• Insertion device in straight section of storage ring • Shift SR spectrum towards higher energies by larger magnetic fields • Gain multiplied by number of periods**Equation of motion**Set Bx = 0, vz = 0 → coupl. eq.**Undulator/wiggler parameter: K**• K – undulator/wiggler parameter • K < 1: Undulator • Qw< 1/g • K > 1: Wiggler • Qw > 1/g • Equation of motion: s(t)**Undulator radiation I**• Coherent superposition of radiation produced from each periode • Electron motion in lab frame: • Radiation in co-moving frame (cb*): • Radiation in lab:**Undulator radiation II**• If not K << 1: Harmonics of Ww**Insertion devices: Summary**• Wiggler (K > 1, Q > 1/g) • Broad broom of radiation • Broad spectrum • Stronger mag. field: Wavelength shifter (higher energies!) • Several periods: Intensity increase • Undulator (K < 1, Q < 1/g) • Narrow cone of radiation: Very high brightness • Brightness ~ N2 • Peaked spectrum (adjustable) • Harmonics if not K<<1 • Ideal source!**Use of SR**• Advantage: broad, intense spectrum! • Examples of use: • Photoionization/absorption • e.g. hn + C+ → C++ + e- • X-ray diffraction • X-ray microscopy • ...**Optical systems for SR I**• Purpose • Select wavelength: E/DE ~ 1000 – 10000 • Focus: Spot size of 0.1∙0.1 mm2**Optical systems for SR II**• Photon energy: few eV’s to 10’s of keV • Conventional optics cannot be used • Always absorption • UV, VUV, XUV (ASTRID/ASTRID2) • Optical systems based on mirrors • X-rays • Crystal monochromators based on diffraction**Mirrors & Gratings**• Curved mirrors for focusing • Gratings for selection of wavelength • r and r’ – distances to object and image • Normally q ~ 80 – 90º • Reflectivity!**Mirrors: Geometry of surface: Plane, spherical, toriodal,**ellipsoidal, hypobolic, ... • Plane: No focusing (r’ = -r) • Spherical: simplest, but not perfect... • Tangential/meridian • Saggital • Toriodal: Rt ≠ Rs • Parabola: Perfect focusing of parallel beam • Ellipse: Perfect focusing of point source**Gratings**• kNl = sin(a)+sin(b) • NB: b < 0 • N < 2500 lines/mm • Optimization • Max eff. for k = (-)1 • Min eff. for k = 2, 3 • Typical max. eff. ≈ 0.2**Design of ‘beamlines’**• Analytically • 1st order: Matrix formalism • Higher orders: Taylor expansion • Optical Path Function Theory (OPFT) • Optical path is stationary • Only one element • Numerically • Raytracing (Shadow)**Useful equations**• Bending radius • Critical energy • Total power radiated by ring • Total power radiated by wiggler • Undulator/wiggler parameter • Undulator radiation • Grating equation • Focusing by curved mirror (targentical=meridian / saggital)