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Find the phase velocity of the wave (Plasma Physics)

  1. Aug 3, 2017 #1
    1. The problem statement, all variables and given/known data
    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 seperated into a R- and L-wave in the plasma.

    2. Relevant 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

    3. 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
     
  2. jcsd
  3. Aug 6, 2017 #2
    Can you write it with in LaTeX?
     
  4. Aug 7, 2017 #3
    1. The problem statement, all variables and given/known data
    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 \hat z ##. The plasma density is ## 1.0*10^{17} ## ## \frac {particles} {m^3} ##. The wave is then separated into a R- and L-wave in the plasma.

    2. Relevant Equations
    ## w_c = \frac {|q|*B} m ## cyclotron angular resonance

    ## w_p = \sqrt \frac {n_0*e^2 } {ε*m_e} ## plasma angular frequency

    ## (\frac {ck} {w})^2 = 1- \frac {w_p^2/w^2} {1-(w_c/w)} ## R-Wave (whistler)
    ## (\frac {ck} {w})^2 = 1- \frac {w_p^2/w^2 } {1+(w_c/w)} ## L-wave

    Phase Velocity:

    ## (v_{ph})_R = (\frac {w} {ck})_R = \sqrt \frac {w(w-w_c) } {w^2-w*w_c-w_p^2} ##
    ## (v_{ph})_L = (\frac {w} {ck})_L = \sqrt \frac {w(w+w_c) } {w^2+w*w_c-w_p^2 } ##

    ## B_0 = 0.1T \hat 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

    3. The attempt at a solution

    Inserting these values into the formula for the phase velocity, then i got the following

    ## (v_{ph})_R = c*0.443 = 1.329 * 10^8 ##m/s,
    since the phase velocity is defined as ## \frac {w} {k} = v_{ph} ##. So i multiple it with c.
    The correct value is ## v_{ph} = 6.6*10^6 ##m/s
    ##(v_{ph})_L ## = no wave, since it is imaginary

    How can i know which polarization the wave has after z=1 m ?
     
  5. Aug 10, 2017 #4
    Why is my solution wrong ?
     
  6. Aug 17, 2017 #5
    Im still stuck, why do i get a different answer ?
     
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