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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:

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

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)

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