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Home/Astronomy & The Sky/Bremsstrahlung & Synchrotron Radiation Pattern

Bremsstrahlung & Synchrotron Radiation Pattern

This interactive simulator explores Bremsstrahlung & Synchrotron Radiation Pattern in Astronomy & The Sky. Polar plot of dP/dΩ for an accelerating charge: a ∥ v (linear / brems) and a ⊥ v (circular / synchrotron). Pull β = v/c toward 1 — Larmor donut collapses into a forward beam of half-angle ≈ 1/γ; ω_g, ω_c shown for given B. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: For learners comfortable with heavier math or second-level detail. Typical context: Astronomy & The Sky.

Key terms

  • bremsstrahlung
  • synchrotron
  • radiation
  • pattern
  • bremsstrahlung synchrotron
  • astronomy

Accelerating-charge radiation

Acceleration geometry

0.5
1T
1

Energy preset (electron)

Shortcuts

  • •Pull the β slider to the right and watch the donut collapse into a forward beam ~1/γ wide

Measured values

β = v/c0.9900
γ = 1/√(1−β²)7.09
beam half-angle47.07mrad
1/γ (asymptote)141.07mrad
peak/Larmor amplification1.00e+6
ω_c (synchrotron, B given)1.33e+13rad/s

How it works

Angular radiation pattern of an accelerating charge — switch between bremsstrahlung-style acceleration parallel to velocity (a ∥ v) and synchrotron-style circular motion (a ⊥ v), and watch the Larmor donut at β → 0 collapse into a forward-pointing relativistic beam of half-angle ≈ 1/γ as β → 1. The polar plot is dP/dΩ in arbitrary units; the right panel cartoons the charge in linear motion or in a circular orbit (with toy magnetic field B giving the gyrofrequency ω_g = qB/(γm) and synchrotron critical frequency ω_c ≈ (3/2)γ³ω_g — the workhorse of synchrotron light sources and astrophysical jets).

Key equations

a ∥ v: dP/dΩ ∝ sin²θ / (1 − β cosθ)⁵
a ⊥ v: dP/dΩ ∝ [1 − sin²θ/γ²(1 − β cosθ)²] / (1 − β cosθ)³
beam: Δθ ≈ 1/γ, ω_c ≈ (3/2) γ³ ω_g, ω_g = qB/(γm)