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Firben
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Homework Statement
An electromagnetic wave with the frequency f = 1.4 GHz is propagating in the z-direction from vacuum in a plasma with the magnetic field B_0 = 0.1T z^. The plasma density is 1.0*10^17 particles/m^3. The wave is the separated into a R- and L-wave in the plasma.
Homework Equations
w_c = |q|*B/m cyclotron angular resonance
w_p = (n_0*e^2/(ε*m_e))^(1/2) plasma angular frequency
(ck/w)^2 = 1-(w_p^2*w^2)/(1-(w_c/w)) R-Wave (whistler)
(ck/w)^2 = 1-(w_p^2*w^2)/(1+(w_c/w)) L-wave
(v_ph)_R = (w/ck)_R = ((w(w-w_c))/(w^2-w*w_c-w_p^2))^(1/2)
(v_ph)_L = (w/ck)_R = ((w(w+w_c))/(w^2+w*w_c+w_p^2))^(1/2)
B_0 = 0.1T z^
f = 1.4 GHz = 8.8*10^9 rad/s
w_p = 1.78*10^10 rad/s
w_c = 1.76 * 10^10 rad/s
The Attempt at a Solution
Inserting these values into the formula for the phase velocity, i get the following
(v_ph)_R = c*0.443 = 1.329 * 10^8 m/s,
since the phase velocity is defined as w/k = v_ph. So i multiple it with c
correct value is v_ph = 6.6*10^6 m/s
(v_ph)_L = no wave, since it is imaginary
Then i want to know which polarization the wave has after z=1 m