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# Accelerator Physics: Synchrotron radiation - PowerPoint PPT Presentation

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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Lecture 2

Henrik Kjeldsen – ISA

• Acceleration of charged particles

• 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.

• 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)

• Lorenz-invariant form

• Result

• 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

• Perpendicular acceleration:

• Energy constant...

• dp = pda → dp/dt = pw = pv/R

• E ≈ pc, g = E/m0c2

• In praxis: Only SR from electrons

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

• Similar to Hertz dipole in frame of electron

• Relativistic transformation

• Spectrum: Harmonics of frev

• Characteristic/critical frequency

• Divide power in ½

• Horizontal emittance [nm]

• ASTRID2:12.1

• ASTRID: 140

• Diffraction limit:

• 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

• The ASTRID undulator

• Potential:

• Solution:

• Peak field on axis:

Construction

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

• 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

• Insertion device in straight section of storage ring

• Shift SR spectrum towards higher energies by larger magnetic fields

• Gain multiplied by number of periods

Set Bx = 0, vz = 0

→ coupl. eq.

• K – undulator/wiggler parameter

• K < 1: Undulator

• Qw< 1/g

• K > 1: Wiggler

• Qw > 1/g

• Equation of motion: s(t)

• Coherent superposition of radiation produced from each periode

• Electron motion in lab frame:

• Radiation in co-moving frame (cb*):

• If not K << 1: Harmonics of Ww

• Wiggler (K > 1, Q > 1/g)

• 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

• Harmonics if not K<<1

• Ideal source!

• Examples of use:

• Photoionization/absorption

• e.g. hn + C+ → C++ + e-

• X-ray diffraction

• X-ray microscopy

• ...

• Purpose

• Select wavelength: E/DE ~ 1000 – 10000

• Focus: Spot size of 0.1∙0.1 mm2

• 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

• 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

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

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’ ellipsoidal, hypobolic, ...

• Analytically

• 1st order: Matrix formalism

• Higher orders: Taylor expansion

• Optical Path Function Theory (OPFT)

• Optical path is stationary

• Only one element

• Numerically

Useful equations ellipsoidal, hypobolic, ...

• Critical energy

• Total power radiated by ring

• Total power radiated by wiggler

• Undulator/wiggler parameter