this is for holding javascript data
Michael Morag edited Data Analysis.tex
about 10 years ago
Commit id: 7389f03565aab3329da5543a127a5674ede514fd
deletions | additions
diff --git a/Data Analysis.tex b/Data Analysis.tex
index 69a2875..e81d4d9 100644
--- a/Data Analysis.tex
+++ b/Data Analysis.tex
...
\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
meaurements meas+urements next to the source (position 2) were measured to be 79.4 Gauss, above the maximum magnetic field.
because Since the magnetic field
an that region was higher than critical magnetic field for 110
MHz. After certain amount of time, 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
travel are traveling towards
the density
maximum, maximum. Magnetic fields measured after 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.