A depiction of the diocotron motion observed in the poloidal plane (cross-sectional radius ) of a toroidal plasma. As the plasma (shaded circle) moves, its center traces a circular path (dashed circle) of mode amplitude and its motion induces corresponding movement of image charge. The movement of image charge to each electrically isolated electrode is measured across an impedance (not pictured).
The diocotron frequency is plotted as a function of charge for plasmas of two different mode amplitudes. The relationship between frequency and charge is linear at fixed mode amplitude, but the constant of proportionality is greater for plasmas with large amplitude (asterisks) than for those with small amplitudes (circles).
The frequency of the toroidal version of the diocotron vs the inverse of the magnetic field strength. This relationship is also observed in cylindrical traps.
The offset of the center of the trajectory from the geometric center of the electrodes, , as a function of the amplitude is plotted for three different plasma aspect ratios : 5 (asterisks), 14 (circles), and 25 (diamonds). Both the offset and the amplitude are normalized to the radius of the electrodes, . A negative offset refers to a shift to the inboard side of the electrodes.
A plot of the measured (solid) and simulated (dashed) signal for the top electrode (top) and bottom electrode (bottom). Unlike with cylindrical plasmas, the signals from the top and bottom electrodes are not exactly 180° out of phase for a toroidal plasma.
The diocotron frequency as a function of plasma aspect ratio . The frequency is normalized to the frequency in the cylindrical limit.
The relationship between the normalized second harmonic power and the square of the amplitude is shown for three plasmas with different total charge values. This relationship is linear and independent of the amount of charge in the plasma. The −1 and −0.1 nC cases (circles and triangles, respectively) were obtained using the spectral technique, while the −0.2 nC case (diamonds) employed the curve-fitting technique described in the text.
Evolution of the plasma parameters extracted from experimental data using the numerical technique described in the text. A fixed frequency (55 kHz) tone burst was used to excite the diocotron mode. The charge (triangle, left hand axis) decays, while the amplitude (asterisk, right hand axis) increases.
Decay of charge per unit length as a function of delay time. At each delay time, the mode is excited by a near-resonant tone burst. The values obtained by using the cylindrical theory to convert the measured frequency to charge per unit length (circles) display very little difference from the values extracted from the data by application of the numerical simulations (triangles). The solid line is an exponential fit to the latter data points and has an e-folding decay time of 2.5 s.
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