Abstract
Measurements of the image charge induced on electrodes provide the primary means of diagnosing plasmas in the Lawrence Nonneutral Torus II (LNT II) [Phys. Rev. Lett.100, 155001 (2008)]. Therefore, it is necessary to develop techniques that determine characteristics of the electron plasma from features of the induced image charge signal. This paper presents a numerical study which finds that the frequency of the image charge signal due to the toroidal version of the diocotron mode is proportional to the total trapped charge and inversely proportional to magnetic field strength, as in the cylindrical case. In the toroidal case, additional information about the motion of the plasma can be obtained by analysis of the image charge signal amplitude and shape. Finally, results from the numerical simulations are compared to experimental data from the LNT II and plasmacharacteristics are reported.
The authors would like to acknowledge the work of D. P. Ryan which served as an effective starting point for the numerical model. We also would like to thank J. Danielson for helpful discussions. This work was funded by the Department of Energy and National Science Foundation under Grant No. 0317412.
I. INTRODUCTION
II. NUMERICAL TECHNIQUES
III. SIMULATION RESULTS
A. Similarities to the cylindrical diocotron mode
B. Differences from the cylindrical diocotron mode
C. Spectral analysis technique
IV. USING SIMULATIONS TO INTERPRET EXPERIMENTAL DATA
V. CONCLUSIONS
Key Topics
 Toroidal plasma confinement
 40.0
 Magnetic fields
 15.0
 Electrodes
 10.0
 Kelvin Helmholtz instability
 9.0
 Nonneutral plasmas
 9.0
Figures
A depiction of the diocotron motion observed in the poloidal plane (crosssectional 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).
A depiction of the diocotron motion observed in the poloidal plane (crosssectional 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 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 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.
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.
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 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 curvefitting technique described in the text.
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 curvefitting 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.
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 nearresonant 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 efolding decay time of 2.5 s.
Decay of charge per unit length as a function of delay time. At each delay time, the mode is excited by a nearresonant 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 efolding decay time of 2.5 s.
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