Achievement of Field-Reversed Configuration Plasma Sustainment via 10 MW Neutral-Beam Injection on the C-2U Device
P. 1

Field-Reversed Configurations
No Gun
Gun+NBs 2 Guns+NBs
2 Guns+ Upg’d NBs
C-2U Project Goals
§  Higher NB injection power clearly improves decay rate of diamagnetism as well as extends plasma lifetime
§  This is now called “Advanced Beam-Driven FRC” state Advanced Beam-Driven FRC State
§  FRCs last beyond time that power is supplied to all systems:
Ø In the best operating condition – FRCs are maintained for 5+ ms
Ø In longer-pulsed operations – diamagnetism reaches up to and beyond 10 ms
§  Diamagnetism maintained – showcases ability to drive current by beams
§  Electron and ion temperatures maintained (Te up to 150 eV at ~6 ms, Ti ~500 eV)
§  Total plasma pressure maintained – post transient evolution, over 60% of initial thermal particle pressure replaced by fast particle pressure
§  Features / effects of energetic fast ions:
Ø Near classical confinement
Ø “Double-humped” ne and Te profiles – indicative of substantial fast ion pressure
Ø Hollow center and steep separatrix gradients consistent with past FRC data and numerical simulations
Ø Fast-ions largely define FRC dimension – plasma length contracts to fast particle footprint and then maintained, as predicted by simulation
Core Te Evolution
Divertor Magnets OFF: Flare field 
Divertor-magnet / field configurations
The C-2U Device
S. Divertor
0.8 Electrodes 0.6
Plasma gun
0 0123456789
Time (ms)
FRC Correlates with NB Pulse Duration
HPF and Advanced Beam"Driven FRC 
Forward Looking  (recently started) 
New magnet  
system for field 
ramp & active control 
Dynamic FormaAon 
C"2U  (3)
Boundary  Control via  Edge Biasing
Wall  CondiAoning 
Neutral Beam  InjecAon 
(5) (6)
FRC Length/ Shape Control
ParAcle  Refueling
Mirnov probe data
ion cyclotron
Synergetic effect
(i) showcasing current drive, (ii) double-humped density profile, (iii) FRC dimensions largely defined by fast-ions, (iv) high temperatures overall, (v) near classical fast-ion confinement, etc.
S. Formation
-5 Scrape-o  layer Mirror plug
Con nement
NB injection
0 FRC Axial distance (m)
N. Formation
N. Divertor
Plasma gun
§  Key plasma parameters maintained until end of NB duration
§  Diamagnetism persists ~1.5–2.5 ms after NB termination due to accumulated fast ions
NB termination
*All quantities normalized
Improvements in Confinement and Transport Properties
Achievement of Field-Reversed Configuration Plasma Sustainment via 10 MW Neutral-Beam Injection on the C-2U Device
The world’s largest compact-toroid device, C-2, has been upgraded to C-2U at Tri Alpha Energy to
achieve sustainment of field-reversed configuration (FRC) plasmas by neutral-beam (NB) injection (NBI)
and edge biasing, and the C-2U experiment is characterized by the following key system upgrades:
increased total NB input power from ~4 MW (20 keV hydrogen) to 10+ MW (15 keV hydrogen) with tilted
injection angle; enhanced edge-biasing capability inside of each end-divertor for boundary/stability 0.6 control. C-2U experiments with those upgraded systems have successfully demonstrated dramatic 0.4 improvements in FRC performance. As anticipated, there are strong effects of the upgraded NB injectors
on FRC performance such as: (i) rapid and strong accumulation of fast ions (about a half of initial
thermal pressure replaced by fast-ion pressure); (ii) fast-ion footprint largely determines FRC 0.2 dimensions; (iii) double-humped electron density and temperature profiles; (iv) FRC lifetime and global 0 plasma stability scale strongly with NBI power; and (v) plasma performance correlates with NB pulse 0 duration in which diamagnetism persists several milliseconds after NB termination due to accumulated
fast ions. The key accomplishment on C-2U is sustainment of advanced beam-driven FRCs with a
macroscopically stable and hot plasma state for up to 5+ ms, limited only by hardware and stored
energy constraints such as the NBs’ pulse duration (flat-top ~8 ms) and current sourcing capability of
end-on plasma guns. Furthermore, plasma diamagnetism in the best discharges has reached record
lifetimes of over 11 ms, timescales twice as long as C-2. In this regime fast ions are well trapped and
nearly classically confined, suppressing broadband magnetic turbulence as well as enhancing fusion
reactivity via beam driven collective effects. Density fluctuations near the separatrix and in the scrape-
off layer have also been dramatically suppressed by a combination of NBI and E×B shearing via plasma-
gun edge biasing, thereby improving confinement properties. The demonstrated sustainment of beam-
driven FRCs in C-2U is an extraordinary achievement for the FRC and innovative confinement concepts
communities, and may lead to intriguing possibilities for fusion reactors.
§  C-2U is the world’s largest compact toroid device, recently upgraded from C-2, that produces high temperature, stable, long-lived FRCs.
§  Upgraded neutral-beam (NB) injection (15 keV Hydrogen, co-injection) and end-on plasma- guns mitigate FRC global instabilities and improve its performance such as confinement and transport properties.
C-2U Neutral-Beam System: Performance Maker
Neutral Beam System Specification   
Parameter  Value 
Beam energy  15 keV  Total power in neutrals  10+ MW 
# of injectors  6  Pulse duration  8 ms flat-top 
Beam radial e-fold. size   < 10 cm  Beam divergence  < 28 mrad 
Te profile by Thomson Scattering
Dependence of fast-ion pressure on NB power
ne profile by FIR/CO2 interferometer
ne profile from Q2D simulation
Fast Particle Current Density at 6 ms
§  0-D global power-balance analysis, detailing loss channel characteristics and plasma timescales, indicates:
§  Substantial improvements in equilibrium and transport parameters
§  C-2 & C-2U eras have good agreement
§  Regression gives electron energy confinement time, τE,e ~Te1.8; more heating power, better confinement
§  Very different from Bohm-type scaling (unlike tokamak scaling)
0-D power-balance analysis (methodology):
§  Measurements used to derive power flow
§  Forms of transport parameters not assumed
§  Profile effects accounted for where possible
§  Ti self-consistently found by subtracting beam pressure from total pressure
Electron energy confinement time vs. electron temperature (Te scaling)
Ion current per source 
n  Centered, angled and tangential neutral-beam injection (NBI) §  Beams aimed at mid-plane to reduce plasma shape impact
§  Simulations suggest optimized injection angle in range of 15o–25o
§  Injection in ion-diamagnetic direction to drive current
n  High current at low beam energy
§  Reduces peripheral fast-ion losses
§  Increases core heating
§  Rapidly establishes dominant fast-ion pressure
Key Approaches to C-2U Achievements
145 A 
Mirror plug
H. Gota,1 M.W. Binderbauer,1 T. Tajima,1,2 S. Putvinski,1 M. Tuszewski,1 D. Barnes,1 S. Dettrick,1 E. Garate,1 S. Korepanov,1 A. Smirnov,1 M.C. Thompson,1 E. Trask,1 X. Yang,1 L. Schmitz,3 Z. Lin,2 A.A. Ivanov,4 T. Asai,5 and the TAE Team1
1TRI ALPHA ENERGY, INC., P.O. Box 7010, Rancho Santa Margarita, CA 92688, USA 2Department of Physics and Astronomy, UCI, Irvine, CA 92697, USA 3Department of Physics and Astronomy, UCLA, Los Angeles, CA 90095, USA 4Budker Institute of Nuclear Physics, Novosibirsk, 630090, Russia 5College of Science and Technology, Nihon University, Tokyo 101-8308, Japan
Overall Progress on C-2 / C-2U Experiments and Achievement of Plasma Sustainment
IAEA-FEC2016, Kyoto, Japan, October 17-22, 2016
§  A field-reversed configuration (FRC) plasma is a highly elongated compact toroid (CT) which has a closed poloidal field with zero or small self-generated toroidal field, an axisymmetric structure with a natural divertor, and a high beta value (β~1).
§  FRC offers an ideal configuration for an economic reactor and may allow use of aneutronic fuels, such as D-3He and p-11B.
§  Tangential beam injection: large orbit ion population, increased stability, and improved transport property
Ø Paper by M. Binderbauer, AIP Conference Proceedings 1721, 030003 (2016) Effect of Neutral-Beam Injection on C-2U
Global energy confinement time in C-2/C-2U
(w/ updated 0-D power-balance analysis, see below)
Core Te Increased by Flaring Divertor Field
§  Demonstrate current drive and plasma sustainment in excess of characteristic and confinement times §  C-2U to maintain: (1) Trapped magnetic flux; (2) Plasma dimensions; and (3) Total pressure inventory §  Correlate FRC lifetime with neutral-beam pulse duration
80 60 40 20
Flare field Regular field
(1) Dynamic FRC formation
èSuitable target for NB injection
(2) Wall conditioning (Titanium gettering)
èReduce background neutrals (3) Plasma guns and Plugs
èBoundary/edge control (stabilization) (4) Neutral beam injection
èImprove stability and confinement èCurrent drive and plasma sustainment
(5) Flux conserver (external)
èFRC length/shape control (6) Particle refueling via:
èCompact-toroid (CT) injection èPellet injection
§  “Non-disruptive” fast-ion driven mode
§  Burst frequency varies with beam energy and external B field §  It can be suppressed by external field profile and ExB shearing
Plasma-guns and
biasing electrodes 
(in both inner  
and end divertors) 
1.0 0.8
*Radius normalized
FRC w/ gun (03-2011)
1.0 1.5
HPF12 (07-2012)
HPF14 (01-2014)
HPF w/ 2 guns (09-2011) #20408
C-2U (06-2015)
C-2U: Sus’d FRC (w/ ~10 MW NBI)
C-2: HPF14 (w/ ~4 MW NBI)
C-2: HPF12
Gun Only
C-2/C-2U Operating Conditions
) burst frequency (kHz)
Radius (m)
τE (ms)
Te (eV)
Plasma Radius
FRC Radius
1.0 hg20150813.tae.2b 0.5
Pinj ~1.7 MW
00 1 2 3
*Radius normalized
Pinj >10 MW
8 9
6 NBs 5 NBs 4 NBs 3 NBs 2 NBs 1 NB
§  Improving open-field-line plasmas is a key for better core FRC confinement
§  Core T increased by 20–30% with flaring e
divertor magnetic field
§  Flaring divertor magnetic field effectively increases Er/r in the edge of FRC
Divertor Magnets ON: Regular field 
Fast Particle Density at 6 ms
Beam-Driven Micro-Burst
C-2W: Next Device at 10x Stored Energy
low frequency chirps
upgraded in the next device, C-2W
2.0 2.5
3.0 3.5
C-2 C-2U
FRC only (2008) #2519
HPF w/ 1 gun (04-2011) #16758
§  C-2 experiments in 2008–2014 (over 40,000 shots):
Ø Obtained “High-Performance FRC (HPF),” summary paper by M. Binderbauer, Phys. Plasmas 22, 056110 (2015)
§  C-2U experiments started in March 2015:
Ø Obtained “Advanced Beam-Driven FRC,” in which both global energy and particle confinement times greatly
improved by FRC/system optimization as well as key sub-system upgrades including NBs in C-2U
Ø Plasma sustainment (flat top) for 5+ ms was successfully achieved in 3 months of experiment/operation
Ø Plasma (diamagnetism) lifetime reached up to 11 ms
Ø Plasma lifetime is limited only by equipment / system constraints (e.g. NBs and edge-biasing power supplies and its durations)
C-2: HPF
4 5
Time (ms)
Pinj ~5 MW 6 7
*HPF – High Performance FRC regime
Time (ms)
1.4 1.2 1.0 0.8 0.6 0.4 0.2
Density fluctuation (FIR interferometer)
C-2U has successfully demonstrated plasma sustainment for 5+ ms as well as produced
8 6
Advanced beam-driven FRCs correlate with NB duration and have the following features
energy scan
long-lived FRCs (~11 ms) by ~10 MW NB injection and plasma-gun edge biasing
0 5 10 15 20
beam energy (kV)
Magnetic fluctuation (Mirnov data)
FRC performance in C-2U is limited only by equipment constraints, which will be
B scan
Inner divertor 
New confinement vessel, skin time <3 ms 
Upgraded NB’s: 13 MW, 30 ms  
Divertor  Plasma gun 
Upgraded formation sections, 15 mWb trapped flux 
End divertor