Maxwell's equations in infinite medium With the before mentioned assumptions Maxwell's equations become laB V●E=0V×E+ a VoB=0 VXB-lECE c a Each cartesian component of E and B satisfy the wave equation 04/08/02 12.540Lec16
04/08/02 12.540 Lec 16 6 Maxwell’s equations in infinite medium • With the before mentioned assumptions Maxwell’s equations become: • Each cartesian component of E and B satisfy the wave equation ∇ • E = 0 ∇ × E + 1 c ∂B ∂t = 0 ∇ • B = 0 ∇ × B − µε c ∂E ∂t = 0
Wave equation Denoting one component by u we have C V--22=0 √AE The solution to the wave equation is ik.x-ior O u=e u8- wave vector E=F。kx-0B= vl XE 04/08/02 12.540Lec16
04/08/02 12.540 Lec 16 7 Wave equation • Denoting one component by u we have: • The solution to the wave equation is: ∇ 2 u − 1 v 2 ∂ 2 u ∂t 2 = 0 v = c µε u = eik.x −iωt k = ω v = µε ω c wave vector E = E 0 eik.x −iωt B = µε k × E k
Simplified propagation in ionosphere For low density plasma, we have free electrons that do not interact with each other The equation of motion of one electron in the presence of a harmonic electric field is given by m X+x+00x=-eE(x, t) Where m and e are mass and charge of electron and y is a damping force Magnetic forces are neglected 04/08/02 12.540Lec16
04/08/02 12.540 Lec 16 8 Simplified propagation in ionosphere • For low density plasma, we have free electrons that do not interact with each other. • The equation of motion of one electron in the presence of a harmonic electric field is given by: • Where m and e are mass and charge of electron and γ is a damping force. Magnetic forces are neglected. m Ý x Ý + γx Ý + ω0 2 [ x ] = − e E ( x,t )