Typical operating modes of a 2-grid retarding field analyzer. Plasma forms a sheath over the Slit plate. When measuring the ion temperature, electrons are rejected from the Collector by either very negative Slit and/or Grid 2. Grid 1 is swept; only ions with enough energy to overcome the bias are incident on the Collector. When measuring the electron temperature, Grid 1 is biased very positively to reject all ions from the Collector. Grid 2 is swept; only electrons with enough energy to overcome the bias are incident on the Collector. In both scenarios, Grid 2 is always more negative than the slit or Collector to ensure that secondary electrons formed at the Collector are recollected. Ion- or electron-induced secondary electrons from Grid 2 could also contribute to the Collector current but are assumed to be negligible.
Cross section of the Alcator C-Mod tokamak with a near double-null plasma equilibrium. The red line is the last closed flux surface, the boundary between open and closed magnetic flux surfaces. (Inset) Close-up view of the RFA scanning probe which scans through the plasma from behind the limiter shadow to the last closed flux surface.
Line drawing of the retarding field analyzer probe. The “West” side is exploded while the “East” side remains assembled. Pictured is the stack assembly of electrodes and insulators which is held in the molybdenum probe head with a screw. The tungsten guard plate, held on with molybdenum nuts and bolts, protects the internal components. The electrodes are attached with wires (not pictured) to the beryllium copper plugs. The scanning probe system allows for only 4 independent electrodes, whereas the retarding field analyzer probe head has two distinct analyzers (each with 4 electrodes); the plugs allow for flexible operation of which electrodes are connected. The boron nitride sleeve is removed for clarity.
Photograph of an assembled RFA head. The wires from the internal components are coming out the left side of the probe.
Photograph of one half of a RFA head. Mica is places all around the RFA stack (over-lapping in the corners) to prevent it from arcing to the molybdenum head. The mica must also extend beyond the back of the stack (where the wires are soldered) to prevent arcing there.
Composite SEM images of a 1 mm thick tungsten Slit plate. (Left) Plasma facing side. The wedge-relief (right) reduces energy-dependent reduction in transmission of ions through the slit (Larmor radius typically ∼200 μm) while retaining enough mass to drain the plasma-deposited energy. The relief was formed by plunge-EMD eroding to ∼25 μm of the opposite face. At the bottom of this valley is a 16 μm wide laser-cut slit. The slit is narrower than the Debye length to ensure that a sheath forms across it. The slit is aligned with the local flux surface.
Composite SEM images of the low and high transmission grids. Both grids were formed by laser-cutting 25 μm thick tungsten foil. The low transmission grid can be used to attenuate the plasma flux into the probe to reduce it to below the space-charge limit. The high transmission grid (∼54% transparent) provides the bias to reject plasma electrons/ions.
Retarding field analyzer mounted on the side of a limiter. Components are identical to that of the scanning retarding field analyzer, except that it is one-sided. The tip of the analyzer is flush with the limiter surface and the slit is 1.7 mm behind. The analyzer was placed here to explore lower-hybrid interactions with the boundary plasma (the scanning analyzer is not magnetically connected to the lower-hybrid antenna). The entrance slit is aligned with the local flux surface.
Result of finite element simulation (COMSOL) of plasma heat flux incident on retarding field analyzer probe. It simulated the probe plunging into the exponential heat flux of the boundary plasma to a peak heat flux of 0.4 GW/m2. Pictured is the temperature at its peak, just after full insertion. (Left) The surface temperature of one face; the peak temperature is concentrated at the front of the probe. (Right) A slice through the middle of the slit; here it can be seen that the Guard plate reduces the plasma energy incident on the slit—preventing melting of this crucial component. At the time-scale of the scan, the Guard plate is nearly semi-infinite, a thicker plate will not improve performance. (Inset) A photo of a partially melted Guard, scanned to the LCFS; demonstrating the melt pattern expected from the simulation.
Peak surface temperatures over the scan of the guard and slit for the same finite element simulation as Figure 9 . The Guard protects the delicate slit from melting.
Diagram of the new Grid Card circuit. A high voltage ground plane is driven by a PA94 op-amp. This voltage sets the voltage on “grid” and “mirror grid.” It also can be used to bias the coaxial shields of the cables. The PA94 responds to the difference between a programed voltage and a reference voltage (which can be another probe bias, a floating probe, or ground) at its inputs. Variable gain transimpedance amplifiers measure the grid current. A “mirror” grid can be implemented to negate the displacement current due to the probe capacitance. The card outputs measurements of the high voltage (divided by 40) as well as the probe current (at both 1 and 40 times, for a larger dynamic range).
Diagram of the RFA electronic system. An analog output sends waveforms to the Grid Card and sweep power supplies. Grid 1 and Grid 2 on each side of the probe were biased and measured together. The Collectors on each side were independently biased and measured. The shields of the coaxial cables connected to the Grid Cards were biased with the center conductor to reduce displacement currents. A network of variable capacitors was connected to the mirror terminals of the Grid Cards. The network was tuned to balance out the capacitive coupling among the probe electrodes.
Collector currents of doublesided RFA from repeated scans, once in T e-mode and once in T i-mode. Bottom panel is the probe trajectory in major radius during the scan.
RFA ion temperature and fit of Eq. (2) , assuming Z = 1 (deuterium plasma).
RFA electron temperature and fit of Eq. (3) .
Lower hybrid creates transient changes to the SOL. Here the floating potential of the limiter RFA Slit plate is given for two instances: mapped to a row of LH wave guides (blue) and mapped between rows of waveguides (red). While mapped to a row of waveguides the Slit floats to a very negative value (<−0.3 kV), possibly to reject a population of non-thermal electrons. During this transient, the floating potential has oscillations on order 150 Hz. While mapped between the waveguides, no transient drop is seen.
The lower hybrid system directly modifies the SOL plasma. At the limiter RFA, directly connected to the LH waveguides, the electron temperature raises by a factor of 5 (from ∼8 eV to ∼42 eV). The spikes in T e at LH turn on corresponded to large transients, shown in the floating potential in Figure 16 . Through the steady phase, the electron population remained Maxwellian up to the noise floor of the measurement (negative bias of −110 V).
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