Bremsstrahlung & Synchrotron Radiation Pattern

This interactive simulator explores Bremsstrahlung & Synchrotron Radiation Pattern in Астрономия и небо. 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.

Для кого: For learners comfortable with heavier math or second-level detail. Typical context: Астрономия и небо.

Ключевые понятия

bremsstrahlung
synchrotron
radiation
pattern
bremsstrahlung synchrotron
astronomy

Accelerating-charge radiation

Acceleration geometry

β = v/c (high-resolution near 1)0.5

B (only for synchrotron numbers)1T

orbit / motion speed (animation)1

Normalize each pattern to fit (focus on shape)Log-radius (compress huge dynamic range)Overlay non-relativistic Larmor (pink dashed)Animate cartoon (right panel)

Energy preset (electron)

Горячие клавиши

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

Измеренные величины

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

Как это работает

**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).