Page 1 - FRC Fast Ion Distribution: Effect on Equilibria
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 S. Outer Divertor
S. Inner Divertor
N. Inner Divertor
Mach Probe
N. Formation
Fast-switching coils (in vessel)
N. Outer Divertor
S. Formation
Neutral Beams
NB injection
n Ion saturation currents on each Mach probe at different radial locations
n Interpolation
3. Observation
n Observations (Mach number, flow angle, correlations)
1.5 1.0 0.5
n Probe installation
n Probe installed at z=1.84 m
n Probe has an actuator and motor system to measure the radial plasma parameters
n 55 cm maximum insertion depth of the probe.
n FRC has an outflow from CV to Divertor at probe location.
-10 -5 0FRC 5 10 Scrape-off layer Axial distance (m) Separatrix
Fig. 1.1 Schematic of the C-2W device and probe installation
n Fig 3.4 shows a correlation between magnetic field strength Bz at the wall and ion saturation current.
n The outflow from midplane to divertor clearly corresponds to Bz amplitude.
Flow profile measurement with a Mach probe in the open-field line region of C-2W
Abstract and Summary
n InTAETechnologies’currentexperimentaldevice,C-2W(alsocalled“Norman”)[1],record-breaking,advancedbeam-drivenfield-reversed configuration (FRC) plasmas are produced and sustained in steady-state utilizing variable energy neutral beams, advanced divertors, end bias electrodes, and an active plasma control system.
n Acombinationprobe(MachandTripleLangmuirprobes)hasbeeninstalledintheopen-fieldlineregiontoinvestigatetheionflowoutside the separatrix. It can measure parallel – perpendicular flows as well as electron temperature and density at the same location.
n Summaryofthisposter:
n Probe observed that the Mach number from CV to Divertor was ~0.5 and the flow angle was 5 degree . n We also confirmed that the outflow of ion is corresponding to the confinement field at the CV.
n As future work, we will investigate the relationship between Isat/flow rate and FRC performance.
[1] H. Gota et al., Nucl. Fusion 59, 112009 (2019).
1. C-2W and Probe Installation
n C-2W
n The C-2W device creates field-reversed configuration (FRC) plasmas
n FRC plasmas are produced and sustained in steady-state utilizing variable energy neutral beams, advanced divertors, end bias electrodes, and an active plasma control.
n FRC core: located within separatrix, surrounded by SOL and plasma edge
n SOL: region of open field lines, terminate on electrode plates in divertors
n Plasma edge: region of open-field lines that do not make it through mirror region, terminate on CV wall.
n C-2W typical parameters
Increased biasing voltage
n Excluded-flux radius at equilibrium time: ~0.5 m
n FRC Length at equilibrium time: ~1.55 m
n Electrode voltage increased from 2kV to 2.5 kV at 13ms.
n Current FRC produced by C-2W is able to be sustained by NBs and Electrode biasing, and its lifetime depends on the pulse duration of those power supplies.
2 3⁄4” Nipple View Port
Fig. 2.1 Circuit diagram of the probe system
2. Probe Design and Model
n Simple Model of Mach Probe
n A Mach probe is composed of two sets of probes and
each surface faces opposing direction (facing upstream and downstream).
n The ratio R between upstream and downstream ion saturation current can be characterized as a function of the Mach number:
𝑀! =𝑀"ln𝑅
n Where Mc is constant of proportionality and it can be written below:
1 = 𝐾 𝛾 + 𝑇! 𝛾 𝑀" (𝑇(!
n Where K is constant value and γ , γ are adiabatic ei
coefficient for the electron and ion.
n To explain the distribution of the ion saturation current in theta direction along probe surface, the current on each probe surface can be written below:
ln𝐽! =𝐴+𝐵𝑐𝑜𝑠𝜃+𝐶𝑐𝑜𝑠%𝜃
n Where A, B, C are constant values.
Fig. 1.2 Cross-section at the probe location
North Divertor
Fig. 1.3 Exact probe orientation on CV
Fig. 3.2 Probe signal at r=55 cm. MP2 (orange line) incorporated into probe signal.
Fig. 3.3 Comparison between different probe radial location: orange line is at r=55 cm, Blue line is at r=60 cm. This plot shows a smoothed data which applied low-pass filter.
Fig. 3.4 Comparison between magnetic field at the wall and ion saturation current.
Fig. 3.1 Output signal from each probe. Color lines show the different probe radial positions.
n Since the probe location is far from the plasma radius, we assume there is no accumulation of the fast ion effect.
0 deg
Theta Direction
Tadafumi Matsumoto1,2, Thomas Roche1, Luis Frausto1, and the TAE team
1TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610 2University of California Irvine, Irvine, CA 92697
n Probe Design
Hollow linear feed through – 21” range
n Mach number and flow direction with 4 Probes
n Electrical Circuit
n To measure the ion saturation
current, we measure the voltage across the sense resistor.
n Each sense resistor is installed on each probe in series.
n The power supply consists of two capacitors installed in parallel with
batteries and can supply bias voltage.
n During the plasma shot, the two circuits will be separated by high resistance on the battery charge line.
1. ln𝐽#⁄𝐽$ = 𝑀!⁄𝑀" sin𝜃 2. ln𝐽%⁄𝐽& = 𝑀!⁄𝑀" cos𝜃
r=55 cm
r=60 cm
r=65 cm
n n n
n n
Since one of the probes is missing data, data processing is required to estimate its current.
As we mentioned in above section, we can use cosine as fitting function of current distribution.
This equation is confirmed by Hutchinson [I.H. Hutchinson, Plasma Phys. Control. Fusion 45, 1477 (2003).] between experiment and simulation.
By adopting this equation, we can assume the ion saturation current on the missing probe (MP2).
The interpolated data matches the expected probe signal.
n n
To calculate the Mach number, we assume Ti equal Te, and convention factor K=1.64 estimated by Hutchinson. We also assume γi = γe = 1.
Fig 3.3 shows a comparison of Mach number and flows angle between different probe locations. Early in the FRC equilibrium, the Mach number is larger at 55 cm than at 60 cm, later the outside flow rate is faster than at 55 cm. This means the Mach number is correlated to the FRC’s radius.
Electron temperature measurement using triple Langmuir probe on the same probe shows there is no significant difference between those two locations. The temperature was ~50eV. This means that Mach number at those positions should be same in principal.
100 kΩ 100 Ω
Then, the net Mach number and plasma flow angle at the probe location can be rewritten as:
100 Ω
10 μF
4􏰀 μF
􏰁120􏰂 22 kΩ
10 Ω 10 μF
4􏰀 μF
22 kΩ
10 Ω
10 Ω
10 Ω
2 3⁄4 Nipple 18”OAL
2 3⁄4” Gatevalve
Mach probe
Triple Langmuir probe
AX05 Boron Nitride Φ=3/8”
Tungsten W/ PEEK Shrink Insulation
J1 Flow θ
J4 J2
Fig. 2.2 Circuit diagram of the probe system
Stainless steel wire
n n
We assume that ion saturation current is a function of theta.
By expanding number of probes from two to four, we are able to calculate not only Mach number but also plasma flow direction.
𝑀 = 𝑀 ln 𝐽 ⁄𝐽 % + ln 𝐽 ⁄𝐽 %
! " # $ % 𝜃 = tan'# ln(𝐽#⁄𝐽$)⁄ln( 𝐽%⁄𝐽& )
Radius (m)