4.6 Experiments in Low Current Discharges

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4.6 Experiments in low current discharges

HIBP experiments were conducted in three different low current discharges – standard [ref], locked [ref] and negative edge biased [ref]. The objective of these measurements was to determine whether the radial electric field is correlated with plasma flow in MST. Unlike high current discharges, plasma flow velocity and HIBP measurements co-incided spatially over a region of 17-32cm (30%) of the minor radius. However, the region of a well resolvable flow velocity profile is limited to approximately 15 > r > 25 cm [ref]. The main challenge in the measurement of the electric field, as in the high current case, is the determination of the magnetic equilibrium,. Aalthough, magnetic equilibriaum haves not been as well established characterized at low currents. The lack of data from internal magnetic diagnostics (polarimeter) imposes limitations on the quality of the equilibrium obtained. However, as in high current equilibrium reconstruction (discussed in chapter 5), data from on axis magnetic field and HIBP vectors is used to reconstruct equilibrium equilibria at low currents.

4. 6.1 Summary of results at low currents

Potential profile measurements were made in the middle of a sawtooth cycle of standard low current discharges at . The profiles were averaged over a time period of 1.5 ms. The electric field is outwardly directed and has a magnitude of approximately 2 kV/m. This is smaller compared tothan the field in high current discharges by about 600 V/m. The peak potential in these discharges reached 1200 V and corresponded to an n=6 mode phase velocity range of ~27-32 km/s. The average potential profile measurements in locked discharges show that the gradient to be relatively flat. The magnitude of the potential ranges from 500-750 V. Density ranged from . The average profiles in biased discharges are also relatively flat indicating the presence of a small or no negligible electric field. The plasma potential in biased discharge ranges from 200-450 V. The density ranged from in biased discharges.

4.6.2 Summary of plasma description in low current discharges

The main MST parameters in these three discharges are summarized in table 1 below. The physical description of each discharge has already been given in chapter 3. The parameters used to determine shot to shot reproducibility is the same as that for high current discharges, i.e. : plasma current, density, field reversal parameter and n=6 mode phase rotation. The plasma current chosen for the experiments conducted lies in the range of 272-277 kA (~2% variation). The density used for comparison is between 0.6-0.8 in standard and locked discharges and between 0.9-1.1 for biased discharges. The higher density in biased discharges is a natural response to the introduction of contaminants in the plasma due to the biased electrodes. Even when the density is on the order of 0.5 xbefore biasing is applied, it rises to rather rapidly to 0.9-1.1 x upon biasing. A dramatic rise in UV accompanies the sudden increase in density. As the relative concentration of impurity species begins to increase, more radiation is emitted from the plasma [ref]. The effect of UV on sweep plate loading (discussed in chapter 3) is more pronounced in biased discharges.

One of the main differences in the three discharges is the magnitude of the n= 6 mode velocity (~ ion fluid flow velocity). While, plasma rotation is a common characteristic of standard plasma discharges, the locked discharge (as the name suggests) has no n=6 mode rotation. In spite of this fact, the plasma as whole can continue to rotate even though the n=6 mode may lock.

Standard / Biased / Locked
(kA) / 270-280 / 270-280 / 270-280
/ 0.6-1.0 / 0.6-1.0 / 0.6-0.95
/ -0.21-0.23 / -0.21-0.23 / -0.21-0.23
) / 20-40 / 0 / 0

Table 2. Experimental parameters in the three low current discharge

The experiments were conducted in plasmas characterized by the parameters listed above due to limitations of the HIBP as well as MST. The electrode-biased discharge places an upper bound for the choice of the plasma current. Since the electron temperature increases with plasma current, insertion of biased electrodes (8-10 cm in depth) inside the plasma is limited to relatively cooler edge plasmas (30 eV). On the other hand the maximum plasma current was chosen to accommodate HIBP ion beam energies as well. The HIBP ion beam quality and injected current are strong functions of the beam energy. Thus, the higher the beam energy, the easier it is to focus the beam and extract relatively large beam currents. Given these two limitations, it was determined that a 40 keV Na beam and a 270-280 kA plasma would simultaneously satisfy both criteria. In order to determine the beam energy required for HIBP probing, a scaling relationship between MST parameters (minor radius and B) and HIBP parameters (beam energy and ion charge) was used. Mathematically this is given by [ref[KC1]]:

The magnitude of the total magnetic field (Mod B) of 0.2T corresponds to plasma current of ~280 kA.

4.6.3 HIBP experimental set up and measurement techniques

The experimental techniques for potential profile measurements in low currents were very similar to that in high current experiments. The main difference stems from the scaling of HIBP beam energy, analyzer and sweep plate voltage settings to meet the requirements for low current operation. Table 2 below describes the various HIBP parameters in the three different experiments described in this section. The main difference is the energy of the primary beam and the analyzer voltage settings. The analyzer voltage setting is dictated by the value of the secondary beam (primary beam + 2e[KC2]*plasma potential) [ref]. For a fixed primary beam energy, the secondary beam is then a function of the plasma potential. The plasma potential tends to be lower in the locked discharges as well as in biased discharges. This result is consistent with the expectation of potential based on results of scaling of potential with the n=6 mode velocity in high current discharges (discussed in section [KC3]). Because of lower beam energy requirements, the sweep voltages required to steer the injected beam were also reduced by the same factor as the beam energy, namely (73 keV)/(40 keV)= 1.85. The predicted values for the deflection plate closest to MST ranged from 1.36 kV to approximately 4 kV while the values for these sweeps in actual experiments ranged from 1.5 kV to ~4 kV. The same sweep plate settings were utilized throughout the low current experiments that are compared in this section. The injected ion beam was swept throughout the discharge in order to scan the plasma minor radii.

The center detector was used to obtain signal (discussed below). Errors due to uncertainty in entrance angle were minimized using the center detector (discussed in appendix).

/ 40.2 keV
/ ~6.8 kV
Radial Sweep (P20SE) / 1.5-4 kV (-ve)/ 1 kHz
Toroidal Sweep (T10NW) / 500 V
Secondary signal level / 30-60 nA

Table 2 Typical HIBP parameters for “all” low current experiments. The sweep values are quoted for P20SE (radial) and T10NE (toroidal) plates[KC4].

4.6.4 Potential profile measurement interval

The time period of a single potential profile measurement is typically 150 s.

The need to make fast time resolved measurements is also important in lower current standard discharges because the period of a sawtooth cycle is ~5-6 ms. For comparison between the three discharge types (standard, biased and locked), potential profiles are computed for one time interval which spans ~1.5 ms starting ~ 2.5 ms after a crash (shown [KC5]in figure 19 – figure is incorrectly labeled). Because, there are no m=0 crashes in locked discharges, there is no time referencing before a crash. For this reason only one time interval is chosen in the analysis to be presented below.

Figure 19. Time domain of potential analyzed in low current standard discharge

In general the time of the application of biasing and that of the sawtooth crash did not coincide very well. While the time at which biasing can be turned on and off is specified, the time at which sawtooth occurs is determined solely by the plasma. In biased discharges there is typically one time interval where the effect of biasing is manifested completely through the slowing down of plasma rotation and zero n=6 mode rotation. The potential profile measurements are reported that satisfy these two conditions.

In all of the three cases anywhere from 10-50 data shots were analyzed for each plasma condition and many realizations were obtained in each case. The standard and locked discharges typically had 4 good realizations in the 2 ms time window. This corresponded to a sweep frequency of 1 kHz (2 realizations for each complete cycle). However, the number of good realizations was less in a biased discharge because of the loading of the radial sweep plates closest to MST.

4.6.5 Standard discharge measurements

4.6.5.1 MST Parameters

The general features of the plasma parameters are given in figure 20 below. These time traces are qualitatively the same as the traces observed in the high current cases. The frequency of the sawtooth increases in low currents as is evident from the time trace of the reversal parameter F.

Figure 20. Main parameters in a 280 kA standard discharge

4.6.5.2 Potential profiles

A typical potential profile time trace for a low current standard discharge is shown in figure 21. The plasma potential versus time is plotted from raw data and shows the effect of the swept beam on the potential measured. The rising and decaying potential trace is very similar to that obtained in the high current standard discharges. The main difference is in the average plasma potential, which is lower by almost 500 V for low currents. The peak plasma potential in this shot is 1150V in the core region. The potential as calculated from the raw data shows that a radial variation of 140-210V is observed as the injected beam is scanned across the plasma minor radii. This change in potential variation is smaller compared tothan in high current discharges (230-320 V).

Figure 21. Time trace of plasma potential, radial sweep (P20SE) and sum signal in a 280 kA standard plasma discharge.

A scatter plot of the potential versus radial sweep voltage is shown in figure 22. While there is scatter of almost 100-150 volts about the trendline, the linear trendline is qualitatively similar to the typical potential trace that is depicted in figure 22[KC6]. There are various reasons for the scatter in the data. The realizations represented in the scatter plot come from many shots. The density range for this data is 0.6-0.8 xwhile the spread in the n=6 mode velocity is 27.5-32.5 km/s. In addition to the global range of density and mode velocity for each realization, the time period of the potential profile measurement is still subject to fluctuations in density and phase velocity. The range of the plasma current in these shots is between 272-277 kA.

Figure 22. Potential versus radial sweep data plotted for multiple realizations before a sawtooth crash

The potential profile obtained from the scatter plot is shown in figure 23 below. The average potential profiles are obtained after the following processing steps:

(a)The range of sweep voltages (from figure 22) was divided into seven intervals (six points). Radial sweep voltages which were within +/-100 V of each of the six points were grouped together.

(b)The corresponding potential for each point was also grouped together

(c)An average value of the radial sweeps and potential is computed for each of the points

(d)The measurement position was computed from trajectory simulations for each of the six radial sweep values.

The number of groups chosen is limited to 6 because trajectory calculations show that the overall radial coverage is approximately 15.8 to 32 cm or a total range of 16.4 cm. Thus the average displacement between each of the sample location is in the order of 2.7cm.

The scatter in potential is also represented in figure 23. The scatter in the radial locations is computed by incorporating 100 volts in the trajectory simulation code. It was found that the net average displacement of the individual points ranged from 0.91-1.2 cm about the mean value of the radial location. The higher value corresponds to larger radial sweeps or near the outer edge of the HIBP detection band.

Figure 23. Potential profile in low current standard discharge 2 ms after a sawtooth crash. The scatter in the potential and radial location is represented at each point.

The radial electric field computed from the potential profile is shown in figure 24. The mean values of the plasma potential are used to determine the mean values of the radial electric field. The scatter in the data is not inconsistent with a zero electric field. However, the field that was determined is not zero. The general trend of the potential profile in standard rotating plasmas (from raw trace of potential in figure 21) indicates that there is a gradient in the plasma potential. No evidence has been gathered in any of the discharges that show a flat potential profile in a standard rotating plasma.

Figure 24. Electric field profile in a low current standard discharge 2 ms after a crash.

The relatively large uncertainty in the electric field can be attributed mainly to the scatter in between any two local points (separated by ~2.5 cm). While the general trend of the potential profile shows a gradient for all the realizations used in this analysis, there is a variation between these local points on a shot to shot basis. Owing to the rather dynamic behavior of the plasma in the RFP, averaging potential profiles over multiple shots is required. This tends to average over the fluctuations in the local electric field which that can give rise to negative and positive fluctuating electric fields in a single shot. While the average electric field is not negatively directed in these plasmas, the fluctuating electric field can be inwardly directed. In addition, the bumps in the potential that appear in one realization as a consequence of these fluctuations, do not appear on another realization at the same values of the radial sweeps (the end result may be similar to what has been obtained).

The characterization of the electric field at these low currents is performed on a relatively short time scale (2ms). Despite this short time scale, it is relatively difficult to assign error bars on the radial electric field measurement. In a single discharge the plasma potential profile changes in response to fluctuations in density and mode velocity and these quantities also change over the sawtooth cycle. Additionally, the measurement locations change slightly as well over the sawtooth cycle. The negative electric fields that arise in the outer radii are hence not physical, but arise out of the technique used to compute the uncertainty in electric fields (discussed in the appendix). They do not necessarily represent the actual measurement but indicate that the measurement is subject to relatively large shot to shot scatter. To improve the measurement of the radial electric field, a curve can be fitted to the single realizations in any given shot to obtain potential versus radial sweep. These smoothed single scan results could be averaged over all realizations to yield an average potential profile. However, the downside is that, the magnetic field would also have to be determined for each realization to accurately account for any change in the spatial location from one realization to another. The simplest picture of the radial electric field can be obtained from examining the average slope drawn from the scatter plot in figure 22. The average electric field is determined to be on the order of 1.5 kV/m. This value is within the range of the uncertainty for all points in the electric field profile shown in figure 20.

4.6.5.3 Influence of density and plasma rotation on scatter

In this section with the effect of changes in shot to shot variation of plasma density and mode rotation on the scatter in the potential data will be discussed. In section 4.2, it was explained that the scatter in plasma potential measurements in high current discharges could be attributed to the changes in the plasma density, the n=6 mode rotation and also to a lesser extent on the plasma current. It is found that such arguments also hold for low current standard discharges.

The potential versus radial sweep voltages from two typical single realizations are plotted in figure 25 below. The data was obtained in two different discharges. The upper trace (triangle data points) corresponds to a density of 0.5 x and a mode rotation of 32.5 km/s. The lower trace (square data points) corresponds to a density of 1.0 x and an n=6 mode phase velocity of 28 km/s. The plasma current for both cases is ~ 275 kA. This plots helps to explain why the scatter in the potential data in figure 19 may be associated with the scatter in the density and mode velocity. The range of density in data shown in figure 19 was 0.6-0.8 x and that of the n=6 mode speed was 27-32 km/s. The scatter in potential in the plot in figure 22 lies within the band defined by two individual realizations shown in figure 25.

Figure 25. Potential vs radial sweep from two radial scans at different densities. Trendlines for each case are also shown. The upper trace is for and the lower trace is for

4.6.6 Locked discharges

The HIBP experimental setup for the locked discharges was identical to that used in the standard discharge experiments. The data for locked and standard discharges were all obtained on the same day.

4.6.6.1 MST discharge

Locked discharges for these experiments were produced by introducing an external perturbation using horizontal and vertical coils. Since, deuterium plasmas do not lock as spontaneously as hydrogen plasmas in lower current, the plasmas in these experiments were forced to lock by the application of an externally applied field error. An m=0 field error was applied at the poloidal gap of the MST to impose a strong electromagnetic torque on the rotating plasma during the rise phase of the sawtooth cycle, thus, causing the n=6 mode to be locked. Typically the n=6 mode tended to rotate until 15-20 ms and then lock immediately following a sawtooth crash. An example from a locked discharge is shown in figure 23 below. The n=6 mode is seen to lock following a crash at 17 ms in this example. The larger amplitude oscillation in the plasma density is also observed to lessen after locking. The m=0 modes do not grow after locking and further sawtooth crashes do not occur. The absence of sawtoothing sawteeth is seen in the time trace of F in figure 26.