CondX - HF Radio Wave Propagation

Interactive Educational Tool

This tool demonstrates how High Frequency (HF) radio waves (1.8-30 MHz) propagate through Earth's ionosphere to enable long-distance communication. Use the interactive visualizations below to explore how different conditions affect radio propagation.

---

Key Concepts

Ionospheric Skip Propagation:

• HF radio waves launched from Earth's surface can reflect off the ionosphere (a layer of ionized atmosphere 60-600 km altitude)
• The wave "skips" back to Earth at a distant location, enabling over-the-horizon communication
• Skip distance depends on frequency, launch angle, and ionospheric conditions

Critical Parameters:

• foF2 (critical frequency): Maximum frequency that can be reflected by the F2 layer at vertical incidence
  • Higher foF2 → ionosphere can reflect higher frequencies
  • Varies with solar activity, time of day, season (typical range: 2-25 MHz in this model)
  • Night (2-5 MHz): D-layer absent, F1 layer recombines and disappears, F2 layer at higher altitude (260-350 km) due to diffusion and winds
  • Dawn/Dusk (5-10 MHz): D-layer building, F1 layer gradually emerging, F2 transitioning between nighttime and daytime altitudes
  • Day (10-25 MHz): All layers present, F2 layer at lower altitude (250-300 km) due to photoionization near peak
• Elevation angle: Launch angle of the radio wave above the horizon
  • Low angles (5-20°) → long skip distances (2000+ km)
  • High angles (60-85°) → short skip distances (< 500 km)

---

The Physics Behind the Model

1. Refractive Index (Wave Bending & Absorption)

The complex refractive index determines both wave bending and absorption using the Appleton-Hartree equation:

where:

• $X = (\omega_p/\omega)^2$ = normalized plasma frequency (depends on electron density)
• $Z = \nu/\omega$ = normalized collision frequency (determines absorption)
• $\omega_p = 2\pi \cdot 8.98 \times 10^3 \sqrt{N_e}$ (plasma frequency from electron density $N_e$)
• $\nu(z)$ = altitude-dependent electron-neutral collision frequency

2. Snell's Law in Spherical Coordinates

This model uses spherical geometry to account for Earth's curvature. The ray parameter $b = n \cdot r \cdot \sin(\psi)$ is conserved along the ray path, where:

• $n$ = refractive index
• $r$ = radial distance from Earth's center
• $\psi$ = angle between ray and radial direction

As waves travel into regions of higher electron density, $n$ decreases. To conserve $b$, the ray bends. When $n^2 < 0$, the wave reflects back toward Earth. Skip distances are measured along the curved Earth's surface, not as straight-line distances.

3. Absorption Loss (Sen-Wyller Formula)

Radio waves lose energy through collisions. The absorption coefficient is:

Total path loss: $\text{Loss (dB)} = 8.686 \int \alpha(s) \, ds$

Key behaviors (calibrated to match real-world measurements):

• Lower frequencies (1.8-7 MHz) suffer more absorption in D-layer (∝ 1/f²)
• Mid-HF (14-21 MHz) has lowest loss for long-distance paths
• D-layer (70-90 km) causes most absorption due to high collision frequency

4. Chapman Layer Electron Density

Each ionospheric layer (D, E, F1, F2) uses the Chapman function:

where $\xi = (z - h_m)/H$ with $h_m$ = peak altitude, $H$ = scale height.

Nighttime behavior: At night (low foF2), the F1 layer recombines quickly and disappears, leaving only a single broadened F layer. The F2 peak altitude (hmF2) is higher at night (260-350 km) due to diffusion and neutral winds, while during the day it's lower (250-300 km) due to photoionization near the peak.

---

How to Use This Tool

This tool includes two models:

1D Model (Vertical Variations Only)

1. Electron Density Profile - Shows how electron density varies with altitude across the ionospheric layers (D, E, F1, F2). Note that F1 disappears at night (foF2 < 4.5 MHz), and D disappears at very low foF2.
2. Plasma Frequency Profile - Shows the plasma frequency as a function of altitude, with the foF2 reference line indicating the maximum frequency that can be reflected vertically
3. Interactive Controls - Sliders to adjust foF2 (ionospheric conditions) and elevation angle (launch angle)
4. Ray Path Visualization - Shows how radio waves at different frequencies propagate through the ionosphere
5. Signal Loss Analysis - Displays absorption loss for each frequency with color-coded signal strength

Try experimenting with the sliders to see:

• How higher foF2 allows higher frequencies to propagate
• How lower elevation angles create longer skip distances
• Why some frequencies work better than others (lower absorption loss)
• How rays at different frequencies bend differently through the ionosphere

2D Model (Horizontal Gradients)

The 2D model extends the 1D model to include horizontal ionospheric gradients that create fascinating propagation effects:

1. Ionospheric Tilts - Model horizontal foF2 variations (day/night terminator, etc.). The gradient display shows how foF2 changes along the propagation path.
2. Side View and Top View - Two visualizations showing ray paths from the side (altitude vs. distance) and from above (azimuth deflection vs. distance)
3. Off-Great-Circle Propagation - Visualize how rays bend sideways when encountering horizontal gradients, causing azimuth deflection
4. 2D Absorption Loss - See how signal strength varies through the tilted ionosphere, with bar charts showing total loss for each frequency

Try experimenting with the 2D sliders to see:

• Day/night terminator effects (15 MHz → 4 MHz over 3000 km)
• Off-great-circle propagation (sideways ray bending shown in the top view)
• How horizontal gradients affect absorption loss
• Pedersen ray behavior with high elevation angles
• How the gradient distance affects the rate of change in ionospheric conditions