University:
Santa Fe College
Course:
ETS 2527C | Electromechanical Components and Mechanisms
Academic year:

2024
Views:

201

Pages:

5
Author:

Jabin F.

Maxwell's Equations for Plasma Medium: ∇ · D = ρf ∇ · B = 0 ∇ × E = -∂B/∂t ∇ × H = Jf + ∂D/∂t Derivation of Wave Equation: ∇ × (∇ × E) = ∇(∇ · E) - ∇²E ∇ × (∇ × E) = -∂/∂t(∇ × B) ∇²E - μ₀ε₀∂²E/∂t² = μ₀∂J/∂t Assumptions: Assume J = 0 (ignoring plasma currents) ∇²E - μ₀ε₀∂²E/∂t² = 0 Wave Equation Solution: Let E = E₀e^(i(kx - ωt)) ∇²E = -k²E (k²)² - μ₀ε₀ω² = 0 k² = μ₀ε₀ω² Dynamical Electrical Conductivity: σ(ω) = iNe²/mω Wave Equation: (k*)² = μ₀ε₀ω² - μ₀Ne²/mω (k*)² = (ω²/c²) * (1 - ωₚ²/ω²) ωₚ = √(Ne²/mε₀) (plasma frequency) Limiting Cases: If frequency of wave (ω) < ωₚ: k* becomes imaginary Wave cannot propagate through plasma medium. If frequency of wave (ω) > ωₚ: k* becomes real Wave can propagate through plasma medium. Diagram: Input: Light enters vertically. After passing through mth polarizer: Light becomes horizontal. Conditions: N₂ > N₁, θ₁, θ₂, m = N, mπ/2N = π/2 Equations: θ₂ = mπ / (2N₂) θ₁ = mπ / (2N₁) I₁ = I₀ cos²θ₁ I₂ = I₀ cos²θ₂ Conclusion: If θ₁ > θ₂, then I₂ > I₁. The polarization in each case is horizontal.