Introduction to synchroton radiation

Main ideas and lessons

1) Purpose of the session and inviting questions

• The speaker frames the day(s) as a “practice day”, encouraging questions early (even if you’re shy).
• The goal is to build core conceptual foundations for later lectures on:
  • synchrotron radiation
  • free electron lasers (FELs)
  • coherent imaging / coherent imaging concepts

2) Why relativistic electrons produce X-rays (Doppler + Lorentz contraction)

• An accelerated charge radiates electromagnetic waves.
• In a storage ring, electrons undergo oscillatory motion (e.g., in an undulator), producing radiation.
• Relativistic Doppler shift is crucial:
  • observed wavelengths appear shorter on-axis relative to the electron’s motion.
• The Lorentz factor (γ) becomes extremely large at X-ray facilities:
  • example given: γ ≈ 12,000 (ESRF-type conditions)
  • relativistic effects (including Lorentz contraction) make time periods appear drastically shorter in the right frame.
• Combined effect:
  • what may look like a lower-frequency oscillation in the lab can appear as X-ray frequencies on-axis due to strong relativistic effects.

3) Where X-rays fit in the electromagnetic spectrum

• The electromagnetic spectrum is reviewed:
  • visible light: ~hundreds of nanometers
  • soft X-rays: roughly hundreds of eV to a few keV (example ranges around edges used in magnetism/materials)
  • hard X-rays: higher energies (e.g., medical imaging, crystallography)
• Practical workshop segmentation:
  • the workshop focuses mostly on soft X-rays, with some hard X-ray content.

4) Tunability and element/chemical sensitivity using absorption edges

• Synchrotrons/FELs provide tunable photon energy.
• Experiments can be tuned to an absorption edge of a specific element.
• Core concept:
  • choose photon energy near an element’s absorption edge so that absorption (and thus signal dominance) changes strongly.
  • Just above an edge → strong absorption → signal dominated by that element.
  • Below the edge → less absorption → other elements contribute more.
• This idea is described as a foundation for many theses (e.g., element-specific imaging/spectroscopy).

5) Absorption edges / photoelectric effect basics (K, L, M shells)

• A photon can eject an electron from an inner shell if the photon energy exceeds the electron’s binding energy.
• The ejected electron is a photoelectron; the excess energy becomes kinetic energy.
• The atom relaxes:
  • electrons fall to lower shells,
  • additional photons or electrons may be emitted (cascades).
• Shell naming in X-ray spectroscopy:
  • n = 1 → K shell
  • n = 2 → L shell
  • n = 3 → M shell
• A convenience resource is highlighted (Hercules website) for looking up:
  • absorption edges
  • refractive index
  • atomic scattering factors, etc.

6) Undulators: producing narrowband, “laser-like” radiation

• In an undulator, magnetic fields alternate direction periodically.
• An electron experiences the Lorentz force (v × B), causing oscillatory motion.
• Because electrons are ultrarelativistic:
  • emission is strongly concentrated into a narrow forward cone (micro-radians scale).
• Finite number of periods (n) creates a finite wave train:
  • bandwidth scales approximately like 1/n
  • order-of-magnitude example given: ~1% bandwidth for n ≈ 100
• Radiation properties:
  • on-axis: shortest wavelengths (highest energy)
  • off-axis: longer wavelengths via relativistic angle-dependent Doppler effect

7) Engineering constraint: why undulator period can’t be arbitrarily small

• Why not always use shorter undulator periods for harder X-rays?
• Shorter periods require stronger magnetic fields.
• Engineering limits (magnet strength / hardware constraints) prevent arbitrarily high fields.

8) Storage rings: bending magnets vs undulators (and wigglers)

• Synchrotron storage rings contain:
  • straight sections with undulators
  • curved sections with bending magnets
• Spectral characteristics:
  • Bending magnet radiation: broad spectrum, described by a critical photon energy (E₍crit₎)
  • Undulator radiation: narrower bandwidth; harmonic structure may appear
  • Wiggler (briefly):
    • fewer periods than an undulator
    • can reach higher fields while avoiding some wall-impact issues

9) Electron beam quality upgrades (smaller emittance / better focusing)

• Upgrades aim to make the electron beam more symmetric and controllable (reduce divergence/emittance).
• Motivation:
  • in nanoscale imaging/microscopy, only a small fraction of the beam may be usable
  • upgrades reduce wasted flux and improve brightness/coherence usable by experiments
• Example strategy mentioned:
  • multi-bend achromat upgrade (splitting bending into multiple weaker kicks to reduce momentum/beam distortion)

10) How undulator photon energy/wavelength is tuned (Undulator equation)

• Conceptually, the undulator equation relates emitted wavelength to:
  • undulator period
  • γ
  • a magnetic-field parameter k
• Practical tuning method:
  • adjust undulator gap → changes magnetic field strength
  • changes k
  • emission shifts to match desired photon energies (e.g., absorption edges)
• Feedback:
  • when tuned correctly, absorption features appear/disappear in spectroscopy/imaging at expected energies.

11) Quantitative scaling for radiated power (dipole radiation + transformations)

• The method starts from a classical result:
  • accelerating charges produce radiation with known angular/power dependence in the particle’s frame (dipole-like).
• Results are then transformed back to the lab using Lorentz-transform ideas.
• Emphasized dependencies:
  • power scales strongly with γ
  • power depends on beam current
  • power depends on the undulator tuning/magnetic parameter (k) through acceleration magnitude.

12) Beamlines: selection and transport of a small fraction of radiation

• Only about ~1% of undulator radiation is captured/used at a beamline (as described).
• A monochromator narrows bandwidth further, since undulator output is often too broad.
• Practical optics constraints:
  • even with tiny emission angles (micro-radians), power density can damage early optics
  • solutions include cooling and apertures/masks
• Example beamline components:
  • monochromator elements (slits/entrances/exits; gratings/crystals depending on soft vs hard X-rays)
  • mirrors for focusing/reimaging onto the sample
• Example scale:
  • beamline length on the order of ~10 meters.

13) Coherence: why it matters and how it’s defined

• Coherence is explained via an analogy:
  • marching soldiers “in phase” represent coherent photons/electric fields
  • noise limits how far coherence persists → coherence length
• Types discussed:
  • Temporal (longitudinal) coherence: depends on bandwidth
  • Spatial (transverse) coherence: depends on source size and observation angle
• Longitudinal coherence (as stated):
  • coherence length scales like λ² / (2 Δλ)
• Spatial coherence (rule of thumb):
  • source diameter × angular spread ≈ λ/2 (with Gaussian/RMS variants discussed)
  • framed as an uncertainty/Heisenberg-like relationship.

14) Creating coherence experimentally: monochromator + pinhole, and why synchrotrons still work

• To get interference/holography, you need:
  • spatial coherence
  • temporal coherence
• Synchrotron strategy:
  • use an aperture/pinhole to select the central radiation cone
  • use a monochromator/filter to select a narrow wavelength
• Trade-off:
  • coherence selection costs intensity (usable power decreases)
• FEL advantage (conceptual preview):
  • FELs can generate very strong coherent pulses via collective electron dynamics, reducing the need for extreme intensity sacrifice from apertures.

15) Pinhole size and coherence from uncertainty reasoning

• The speaker explains how small an aperture must be to approximate coherent spherical wavefronts:
  • based on wavelength and collection angle (e.g., micro-radian central cone)
  • example pinhole sizes for X-rays come out on the order of microns
• Consequences:
  • aperture too large → “wobbly” wavefront, reduced fringe modulation, weaker holography
  • aperture sized appropriately → strong interference/holograms.

16) Transition to free electron lasers (FELs): incoherent → coherent amplification

• The talk positions FELs as more than “adding many electrons.”
• Synchrotron/undulator case:
  • electrons radiate largely incoherently (random phases)
  • power scales approximately like N × (single-electron power)
• FEL case:
  • collective effects lead to microbunching and phase alignment
  • coherent field addition yields strong enhancement:
    • shifting from ~N scaling toward ~N² behavior (field addition → power ∝ field²)
• Mechanism (qualitative):
  • start with a weak radiation field (initial noise/seed)
  • radiation modulates electron energies/trajectories
  • microbunching strengthens the field
  • produces exponential growth and eventual saturation after sufficient undulator length.

---

Methodologies / step-by-step instructions included

A) How to choose photon energy near an absorption edge (tunable edge method)

1. Pick the target element/chemical state for the experiment.
2. Identify that element’s absorption edge energy (e.g., K or L edge).
3. Select photon energy:
   • Just above the edge → strong absorption (enhances that element’s contribution).
   • Below the edge → weaker absorption (reduces that element’s dominance).
4. Run the experiment (imaging, spectroscopy, scattering).
5. Validate tuning experimentally:
   • check that expected absorption features appear/disappear at the corresponding energies.

B) How to tune an undulator to reach a desired wavelength/energy (gap tuning)

1. Determine target photon energy (often to match a sample absorption edge).
2. Adjust undulator gap:
   • decreasing the gap increases the on-axis magnetic field
   • changes the undulator parameter k
3. As k changes:
   • the emission wavelength shifts according to the undulator equation
4. Iterate:
   • measure spectrum/absorption features
   • stop when the edge-feature occurs (confirm correct tuning).

C) How to obtain usable coherence for interference/holography

• Spatial coherence:
  • use an aperture/pinhole to select the central radiation cone
  • choose pinhole size consistent with the coherence condition (source size × angle ≈ λ/2 rule-of-thumb)
• Temporal coherence:
  • use a monochromator (spectral filtering) to narrow bandwidth
• Accept intensity loss:
  • coherence selection reduces transmitted power but enables fringe visibility/interference patterns
• Perform coherence-dependent measurements:
  • diffraction/scattering with accurate wavefronts
  • transmission x-ray microscopy with diffraction-limited focusing
  • standing-wave experiments
  • off-axis holography.

---

Speakers or sources featured (as stated or clearly indicated)

Speakers

• Unnamed main lecturer (dominant speaker; no specific name provided in the subtitles)

Sources mentioned (people / works)

• Vernon von Heisenberg (uncertainty principle reference)
• Arthur (subtitles mention “arthur charlo’s article” and a Nobel Prize reference; exact first name unclear—source is an article by “Arthur” about laser light)
• David Jackson (referenced as an advanced EM/physics textbook)
• Brian Kincaid (credited with introducing the undulator tuning parameter k in the described context)
• Sven Reichi / Sven Reichey (referenced for a FEL simulation/movie illustrating microbunching evolution)
• Christine Rose Fjord (mentioned for producing coherent radiation at ALS via a thesis)
• PhD students listed by name (holography example):
  • Stefan Eisbet
  • John Looning
  • Bill Schlotter
• Additional FEL-related author names (not fully captured; only some names appear clearly in subtitles)
• Kwang-jae Kim (mentioned in relation to FEL oscillator/crystal mirror concepts)

Institutions / facilities (mentioned)

• ESRF (European Synchrotron Radiation Facility)
• Electra
• ALS (Advanced Light Source, Berkeley)
• BESSY
• Trieste
• SPring-8
• PETRA III
• MAX IV / Lund
• APS (Advanced Photon Source)