Insertion device: alternating magnets make electrons wiggle and emit coherent radiation
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K (deflection)
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λ₁ (Å) fundamental
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E₁ (keV) photon
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Coherence boost N²
Undulator vs Wiggler: The deflection parameter K = eB₀λ_u / (2πm_e c) ≈ 0.934·B₀[T]·λ_u[cm]. For K ≪ 1 (undulator): small angular deviation, radiation from each pole interferes constructively → narrow harmonics, brightness ∝ N². For K ≫ 1 (wiggler): large deflection, overlapping cones, broad spectrum like many bending magnets added, flux ∝ 2N. Fundamental wavelength: λ₁ = λ_u / (2γ²) · (1 + K²/2). At K=1 the electron trajectory half-angle equals 1/γ.