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Michael Morag edited Data Analysis.tex
about 10 years ago
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\section{Data Analysis}
The measurements have been plotted in figures 3 through 5. Figure 3 shows waves launched 1.2 $\mu$s after being triggered. First waves are seen propagating towards density minimum, where the duct is located. Figure 4 shows measurements taken 2.28 $\mu$s after being triggered, were the wavefront is evident to be propagating away from duct position. The limit at which the wave will propagate towards the density maximum is when \[\omega \geq \frac{\omega_{ce}}{2}\]
where $\omega_{ce} = \frac{qB}{m_e}$. Solving for the magnetic field and plugging in frequency $f = 2\pi\omega$: \[B_{max}=\frac{4\pi m_e f}{q}\]
Plugging in $f$ = 110 MHz, then $B_{max}$ = 78.6 Gauss. Looking at figure 2, the magnetic field
meas+urements measurements next to the source (position 2) were measured to be 79.4 Gauss, above the maximum magnetic field.
Since the magnetic field an that region was higher than critical magnetic field for 110 MHz, its reasonable to assume the waves will propagate towards the density minimum where the duct is located. In figure 4, after a micro second, wave fronts are
seen traveling towards the density maximum. Magnetic fields measured
after further away from the source than position 2 are less than $B_{max}$,
presumably after entering region of lower magnetic field where $\omega$ > $\frac{\omega_{ce}}{2}$. Plotting magnetic field magnitudes for x and y, as shown in figure 5, it can be seen that the plasma is right-hand elliptically polarized. This would suggest that the wave front is not necessarily travelling parallel to the field lines, but is moving at an angle, which can be seen in figures 2 and 3.