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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

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Accelerator physics synchrotron radiation

Accelerator Physics:Synchrotron radiation

Lecture 2

Henrik Kjeldsen – ISA


Synchrotron radiation sr
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
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
Relativistic particles

  • Lorenz-invariant form

  • Result


Linear acceleration
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
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
Energy loss per turn

  • Max E in praxis: 100 GeV (for electrons)


Angular distribution i
Angular distribution I

  • Similar to Hertz dipole in frame of electron

    • Relativistic transformation


Spectrum of sr
Spectrum of SR

  • Spectrum: Harmonics of frev

  • Characteristic/critical frequency

  • Divide power in ½


Astrid2
ASTRID2

  • Horizontal emittance [nm]

    • ASTRID2:12.1

    • ASTRID: 140

  • Diffraction limit:


Storage rings for sr
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
Wigglers and undulators(Insertion devices)

  • The magnetic field configuration

  • Technical construction

  • Equation of motion

  • Wigglers vs. Undulators

  • Undulator radiation

  • The ASTRID undulator



Magnetic field
Magnetic field

  • Potential:

  • Solution:

  • Peak field on axis:


Magnetic field on axis

Construction

a) Electromagnet; b) permanet magnets; c) hybrid magnets


Insertion devices1
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
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
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
Equation of motion

Set Bx = 0, vz = 0

→ coupl. eq.


Undulator wiggler parameter k
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
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
Undulator radiation II

  • If not K << 1: Harmonics of Ww



Insertion devices summary
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
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
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
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
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
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


Focusing by mirrors example
Focusing by mirrors: Example ellipsoidal, hypobolic, ...


Gratings
Gratings ellipsoidal, hypobolic, ...

  • 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
Design of ‘beamlines’ ellipsoidal, hypobolic, ...

  • 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
Useful equations ellipsoidal, hypobolic, ...

  • 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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