APPENDIX
A. Signal processing
Careful processing of the signal on the four HIBP detector plates is the first step toward potential computation. The steps involved in processing of data are described in a chronological manner below.
I have made a bunch of editorial changes (commas, etc.) but have not gotten them all. You should use what I have marked as a guide and look for more to fix yourself. Also, you have used alpha and theta to indicate angles when you should use the greek letters instead. You actually used both, which is worse.
A.1 HIBP detectors
Figure 1 below shows the layout of one set of HIBP detectors. As shown, the front view is facing towards MST. The plates are numbered 1-4 to avoid ambiguity introduced by terms such as left and right. Where such terms are used, the plate numbers will be explicitly mentioned as well. Three such identical detector sets were used in HIBP experiments.
fig 1. Lay out of HIBP split plate detectors
A.2 UV subtraction
The raw signal is first subtracted of any offsets that occur before t=0 ms. This step ensures that the offsets caused by drifts in the current to voltage converters in the analyzer are compensated for. (How large are these offsets? Are they reproducible? You should show signal with just noise and offset at this point. It is confusing to have HIBP signal included. Also, just point out that there is an offset and noise in addition to the signal. Your wording is confusing.) The raw signal after this processing step but before it is processed for UV is shown in figure 2. The time period ranges from 5 to 20ms to highlight what happens before and after the plasma begins. HIBP secondary signals can be seen in the time interval from 15-20 ms. The UV noise during the sawtooth crash is also seen in the figure. (Where?) Typically the magnitude of the UV spikes during the crash ranges from 15-20 nA per plate in a clean standard discharge. The noise level increases to well over 50 nA/ plate when the plasma is very dirty. In relatively clean plasmas the secondary signal is distinguishable even before UV is subtracted.
Fig 2. Raw signal on detector plates before UV processing
The next step in signal processing is to determine the UV induced noise to be subtracted from each detector plate. Since the UV level striking each plate may not be uniform, the amount of noise subtraction had to be carefully determined. A method was thereby developed to accomplish this step correctly. (Too wordy. Just give the steps.)
This method relies on using the background noise from an unused detector set to determine the UV induced noise to be subtracted from each plate. An unused detector in this context refers to a detector whose corresponding entrance aperture has been closed. Typically the HIBP operation consists of opening two entrance slits and closing the third. In all of the experiments described in this thesis the bottom entrance aperture was closed. Closing the aperture prevents secondary signal from reaching the detector but it does not prevent UV from reaching the plates, which can reach the top detector after reflecting off the analyzer anode. An important characteristic of the UV induced noise on the detector is the fact that it is similar over the entire discharge for all three detectors. The most striking example of this are the sharp spikes in UV induced noise during the sawtooth crash. Because the amount of UV reaching the different plates are is not necessarily equal in magnitudethe same, the determination of what level of background has to be subtracted from each plate in order to process the signal correctly requires a normalization step. (Don’t talk about this, just say what the method is. If I understand it correctly, you just use the signal from the unused detector to get the shape and then adjust the amplitude to cancel the noise.) A flow chart describing this procedure is given in figure 3.
(FIGURE yet to be generated)
INSERT FIGURE 3 signal processing.
When this process is carried out correctly the final secondary signal base level on each detector plate is very close 0 nA. In “all” of the signal processed, every “millisecond” time interval was examined for the correct level of UV subtracted. Whether the process was correct or not was judged solely by examining how close the final base signal level was to 0. In almost all of the cases, the final base level on each detector plate was less than 0.05 nA. The process of utilizing one of the unused detectors for UV subtraction provides a consistent way to subtract the base level UV from each used detector plate as can be seen from figure 4.
It was precisely the need for UV subtraction that required the HIBP primary ion beam to be swept on and off the detector plates for at least one part of the cycle during the experiments. The time period when the secondary signal was swept away from the detector provided the base level signature for verifying whether the background was adequately subtracted on each plate. The final UV subtracted signal for this particular shot is shown in figure 4 below. The result of sweeping the primary beam and moving the resultant secondary on and off the detector is clear in the plots. (Don’t say that the results are clear. Just describe the results.) The signals shown are plotted for very small time duration to show the signal level and the base level. (Where is the base level?)
Figure 4. Signal on detector plates after UV subtraction.
The inclusion of this subtraction process in the program was indispensable during plasma edge biasing experiments. During these experiments, the signal levels on the HIBP detectors were completely overshadowed by the massive UV/ plasma induced noise. (Does the plasma noise get to the plates with a closed aperture? You said nothing about this.) An example of the raw signal before processing is seen in figure 5 below. During the time of biasing (15-25 ms) it was literally impossible to determine whether any signal was detected at all. A noticeable feature is the dropping of the base level upon termination of plasma biasing. (Rephrase this sentence.)
fig 5. HIBP detector signals in low current edge biased experiments
Since the HIBP secondary signal level was limited to 10-15 nA per plate, the complete masking of the actual signal by UV/plasma noise was relatively easy. (You tend to speak too generally. Just make simple, direct statements such as what the signal to noise level was.) Even if secondary signal impinged on the detector, the requirement that some fraction of the total signal land on both detector plates for potential measurements could not be examined without immediate (??) processing. The processed signal for this biased discharge is shown in figure 6.
Figure 6. HIBP secondary signal after noise subtraction
A.3 Signal characteristics and strength
In order to process data for potential, shots were carefully chosen either when signal was detected on all 4 plates of the center detector either simultaneously or when there was slight left-right displacement. This requirement was imposed to minimize the uncertainty in the lateral or out of the plane angle (alpha). Because each individual plate is 7.5 cm wide, localizing the beam at any position other than near the center of the left and right plates is very difficult. The associated uncertainty in the plasma potential, thus, becomes larger when the beam is not detected in the vicinity of the center of the detector. The history of the beam on the detector and trajectory computation provides one way to determine the maximum range of the out of the plane angle alpha.
An example of the motion of the secondary beam on the detector plates during a primary beam scan is shown in figure 7. Left and right in this context refer to combined signals on plates 1 and 3, and 2 and 4 respectively according to the naming convention described in figure 1. The beam starts off on the right detector as the primary beam is swept in a manner that moves the sample location into the core. (Maybe you should show the right-left difference too.)
Figure 7. Beam motion on detector plates in response to radial sweep
What is important to understand from the above time history is that the secondary ion beam is more or less near the center of the detector during the potential profiles obtained. The effect of the lateral motion of the beam on potential profile measurements will be discussed in appendix C.3.
Another important criteriona for potential computation is the signal strength. In most potential profile data, the sum signal level was ~ 30 nA or above. However, the important issue for potential measurements is the relative signal level on each plate. A criteriona was established whereby a minimum of 1 nA was required on the upper and lower detector plates (separately) for signal to be processed for computing potential. This additional step was taken to minimize the error in potential computation when the signal levels on the upper and lower plates have a very small signal to noise ratio. This also avoids, to a certain extent, whether the potential computed is due to signal on the detector or simply random noise.
B. The energy analyzer
The MST-HIBP energy analyzer was formerly used on the 500 keV TEXT-HIBP system. A schematic of the present analyzer is illustrated in FIGURE 8. (Can you add the trajectories to this figure?)
Figure 8. Schematic of the energy analyzer
The HIBP energy analyzer is a parallel plate electrostatic energy analyzer that uses two parallel plates to electrostatically deflect the secondary beam onto the detector. The design of this type of energy analyzer is credited to Proca and Green [ref]. A detailed technical memorandum and a paper [ref] outline the design and workings of this energy analyzer. (You should probably give the authors’ names here.) The basic principle behind the operation of the energy analyzer is rooted in the fundamental equations governing parabolic motion of a charged particle under the influence of an electrostatic force. (What useful information is contained in the previous sentence?) The equation for determining the plasma potential using the HIBP analyzer [ref] is
The quantities G and F are required to be experimentally determined and will be described next. The out of the plane angle “” is not taken into account in this equation. The first term in equation XXX is actually the beam energy of the secondary beam and is represented in terms of the geometric parameters and the detected signals.
B.1 Gain Curve
The characterization of the gain curve constitutes calibration of the energy analyzer. (Why not just say that the analyzer is calibrated by obtaining the gain curve?) The gain of the analyzer is defined as the ratio of the accelerator voltage to the analyzer voltage required for centering the calibrating ion beam vertically up-down on the upper and lower detector plates. The gain is a geometric parameter and is sensitive to the entrance angle of the incoming secondary beam at the analyzer entrance aperture.
On previous HIBP systems, the gain curve calibration has been carried out using both primary and secondary beams. In instances where the primary beam was used, the magnetic field of the plasma confinement device was used to bend the ion beam into the energy analyzer. On Stellarators and Tokamaks this could be done in the absence of plasma. This method is called “absolute calibration” because it enables a measurement of the plasma potential relative to the vacuum vessel (at ground). In some devices the analyzer gain was determined using a secondary ion beam [ref]. This type of calibration enables a measurement of the potential relative to the region of the plasma that was probed during the calibration process. When calibrated this way, the HIBP can typically scan the edge region of the plasma in order to provide a relative potential between the edge and the core of the plasma. In such cases, the edge potential can also be compared to those obtained from Langmuir probes.
The analyzer used in the MST HIBP system was calibrated a number of different times. Each calibration was performed using a singly charged Na or Cs ion beam. The analyzer was calibrated twice after the secondary beamline was attached to it. However, while in this configuration the secondary beamline was detached from the MST vacuum vessel during the calibration. The lack of ability to calibrate the analyzer in its final operational position was due to the fact that the primary beam could not be deflected into the secondary beamline in MST-vacuum only operation. Owing to the 19 degree toroidal displacement between the injection and the exit port, the only way to deflect the primary beam into the secondary beamline would be through the presence of a poloidal magnetic field. Unfortunately the MST poloidal magnetic field is entirely produced by the plasma itself. The calibration of the analyzer using the secondary ion beam was also not a valid option because of the level of reproducibility of the plasma could not be met for the purpose of calibration. The lack of uncertainty in the entrance angle of the incoming secondary beam also posed a large uncertainty on the measurement. (???)
The initial operational set-up of the HIBP system also prevented the calibration using a secondary beam. The secondary beamline was oriented in a manner that was suitable for core measurements. Comparing the HIBP potential measurements at the core simultaneously with the edge was not possible in a single radial scan. Hence, calibrating the analyzer using a secondary beam and ultimately comparing the potential to the edge was altogether not possible.
As things stood, the analyzer was ultimately calibrated with an ion gun at the base of the secondary beamline. This setup ensured that the relative angle between the secondary beamline and the analyzer was close to 30 degrees as possible during the calibration process. The angular measurements in pre-calibration as well as during the calibration were made using a digital level meter, which was accurate to 0.1 degrees. A Sodium ion beam was used for on site calibration. This was also the species of choice used in all of the experiments reported here. (How was the entrance angle changed?)