poster v3

P e,loss
= J x ( eφ ion A
+ 3/2 T
e
)
Ion Energy Analyzer
gas puff
z
The C-2W Experiment
C-2W’s End-Loss Diagnostics
Measurements
Kinetic Scrape Off Layer Model (KSOL)
Advanced beam-driven FRC, surrounded by scrape-off layer (SOL) on open field lines [1].
Fast ion orbits extend into open field lines, so slowing down on SOL electrons sets a fundamental limit on fast ion build-up.
C-2W designed for good electron heat confinement on open field lines.
FRC
Expanding Field in Divertor
Results from Ion Energy Distribution Fit
i (E) shows that an Ambipolar potential of 4-5 Te develops to control electron losses.
Bulk ion temperatures greater than 500 eV are sustained throughout the shot.
C-2W’s Divertors are Designed to Achieve Good Electron Heat Confinement on Open Field Lines
Pyrobolometer
Sheath Voltage
1. Simple Picture: Ambipolar Confinement
Ions on open field lines free-stream to a floating wall.
Ambipolar potential, φA~4-5 Te , restrains electrons so that they are lost at the same rate as ions.
Open Field Lines
FRC
z
V = IpR
FRC
Common metric for electron heat confinement, ηe = Pe,loss / ( Jion x Te ) ~ 5-6 for the ideal case.
2. Practical Difficulties:
Cold Electrons Generated at Plasma Edge
Cold electrons from ionization of neutral gas, secondary emission, or arcing can destroy ambipolar confinement.
For free-streaming electron losses: ηe ~ (mi / me)1/2 ~ 50
TMX with edge gas boxes stabilization had ηe =100 [2], GDT calculated ηe =4.6 for recent experiments [3].
4. Expanding Field Divertors
Expanding field divertor reduces voltage drop in the sheath.
Electron back-flow into the core is suppressed by reverse mirror.
Energy Analyzer Construction
Biased Grids Repel Particles
Hot Electrons in C-2W’s High Performance Regime
High performance regime shots are Sustained in steady-state until we run out of power (up to 30 ms).
Plasma heating and ramp-up clearly observed (see H. Gota, UP10.00123).
Thomson scattering measurements show averaged core Te up to 200 eV for shot under
analysis (113248), and approaching 400 eV for the best shots (e.g. 116474).
High Te not only inside closed field lines (Te
Core) but also on open field lines in the jet (Te jet).
Hot ions that escape the central vessel are accelerated through the ambipolar potential.
Assuming E, μ are conserved, i (E) at the analyzer can be approximated with a drifting half-Maxwellian [5].
Diagnostic I-V trace is an integral moment of i (E) :
Ion Energy Fitting Function
Energy per Ion, η e
1.5 1
.5 0
SOL Mirror
FRC Core
Outer Divertor
φ(z)
References
[1] M. Binderbauer et al., AIP Conf. Proc. 1721, 030003 (2016). [2] R. F. Post, J. Nucl. Mater. 76-77, 112 (1978).
[3] D. V. Yakovlev et. al., Nucl. Fusion 58 (2018).
[4] M. Griswold et al., Rev. Sci. Instr. 89, 10J110 (2018).
[5] J. H. Foote and G. D. Porter, Plasma Phys. Control. Fusion 31, 255 (1989).
[6] S. Gupta et. al., “Vlasov Fokker Planck Study of Electron Dynamics in the Scrape Off Layer with Expander Divertor” Poster presented at the 59th Annual Meeting of the APS-DPP (October, 2017).
Abstract
In TAE Technologies’ current experimental device, C-2W (also called Norman), record breaking, advanced beam-driven field reversed configuration (FRC) plasmas are produced and sustained in steady state utilizing variable energy neutral beams (15 – 40 keV, total power up to 20 MW), advanced divertors, end bias electrodes, and an active plasma control system. In C-2W, the FRC core plasma is surrounded by a mirror- confined scrape-off layer on open field lines. An array of energy analyzers and
Measurement of Axial Plasma Losses in the C-2W High Performance Regime
CV
Formation Section
Electrodes
Jet Plasma
Outer Divertor
Fast Ion Orbits
Confinement Vessel
Inner Divertor
energy analyzer
Inner Divertor
pyrobolometer
Outer Divertor
Ie / Isat : Experiment
ηe : Simulation
φA and φsheath : Simulation
Inner Divertor
Formation Section
3. C2-W Approach:
Divertors Control Cold Electron Sources
2 million liters per second pump rate in divertors to control neutral gas.
Expanding field in the divertors mitigates arcing and secondary electron emission.
current sensor electron grid
ion grid
attenuation grid
Bulk ions from the core
E
qVgrid
core ions
φ(z)
Wall φ=φA
φ=0
Method 2: Ion vs. Electron Density
Ion and electron density at the wall can be calculated from measured ion/electron current, i (E), and Te.
Assume the electron density is lower than the ion density by a Boltzmann factor of the sheath voltage drop.
Sheath voltage can be calculated this way without a gas puff experiment.
Measurements show Debye potential ~2 Te.
Expanding Field
FRC
z
Energy Analyzer Raw Data
Ion Grid Current-Voltage Trace
R φ
3
! # = () *
" $%"& 45
1
Wall
φ=φ A
φ=0
φ(z)
sheath
A φ=0
C-2W’s open field lines end on concentric electrodes in the divertors.
These electrodes are instrumented with an array of ion energy analyzers and pyrobolometers [4].
Kinetic continuum code solves 1D,2V Vlasov-Fokker-Planck equation for electrons with open spatial boundary conditions [6]. Simulation has “clean divertor” with no ionization, secondary emission, or surface discharges.
Prescribed magnetic field, ion density profile, and net electron outflow. Solves for axial potential and electron distribution function.
springs isolate the crystal from vibration
Incident power, Q
Wall φ=φ
connection to signal cables
1
pyroelectric crystal
LiTaO3 crystal
Pyroelectric LiTaO3 crystal produces
polarization current proportional to power absorbed on surface.
Mounted on springs to suppress piezoelectric noise.
e sat e
charge neutrality in the core for a real device (future work).
mounting structure
alumina baseplate
current sensor
secondary electrons
e. grid
(x)
ion grid
atten. grid
high energy ions
low energy ions
electrons
Cold ions from gas puff
φ A
φs
Measured Ion Grid Trace
ɸ debye ~ Te
cold ions from gas puff
. 6789
" ∥
1&2
7
Ambipolar potential of the core plasma ( φA ) as well as the core ion temperature ( Ti ) can be estimated from the measurement.
8" 9/-, ×41&2
e
the open field lines to control electron losses, and that the energy lost per ion, ηe, is
+,∥ 0 1
21 ∥
$ !" = %&'
)*+,-./- − $ 1&2
)*+,-./- + 4 ×6
M. E. Griswold, P. Yushmanov, S. Gupta, and the TAE Team Tae Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610
φA
φA
Ti
Ti
E
qVgrid
ηe = Pe,loss / ( Jion x Te ) ~ 5-6 for the ideal case.
Pe,loss defined as power carried by electrons before decceleration in the sheath and pre-sheath:
bolometers mounted in the divertors of C-2W measure axial power losses as well as the electron temperature and ion energy distribution of the plasma at the termination point of the open field lines. Measurements taken in the C-2W high-performance regime show bulk ion temperatures greater than 500 eV that are sustained throughout the shot. They also indicate that a strong ambipolar potential (~4.5 T ) develops along
Method 1: Gas Puff
Gas puff 3ms before shot from center of outer divertor electrodes creates a cold ion component accelerated only in the Debye sheath.
This cold component is visible as a low energy feature in the ion energy distribution,
Debye potential is roughly 1 Te for shot #107545.
Expected Ion Grid Trace
Expanding Field
Simulated values of ηe, φA, and φsheath are similar to the measured quantities.
Prescribed I /I < 1 gives η less than the ideal 5-6, but this implies radial profile effects that would maintain
Signal / Isat i (E)
Signal / Isat i (E)
Radius (meters)
Measured value of ηe ~ 6-8 is close to the ideal level.
close to the theoretical minimum.