Sean_APS2016_final.pptx

Numerical FRC Project
A Suite of TAE codes form the early cornerstones of a Numerical FRC n Formation, Equilibrium, Stability, Turbulence, Transport codes
n 1D, 2D, 3D models
n Fluid, Hybrid, Kinetic models
n Engineering and Reactor issues
n We invite your participation to form a community-wide Numerical FRC Project
How HPF Beam-Driven FRCs Work
Continuing comparison between experiment, theory, and codes in the Numerical FRC Project explain how HPF works. In broad strokes:
1. FRC Formation
n Two Compact Tori (CT) are formed by Theta-pinch, and are
accelerated to collide and merge, creating a single high Ti FRC 2. Stabilization of low order modes
n High T allows ion kinetic effects to stabilize the n=1 tilt mode. i
n End biasing and line-tying stabilize the n=1 and n=2 radial modes 3. Neutral Beam (NB) Heating
n Low order stability provides good confinement for fast ions, hence FRC is a good target for NB injection
n NB heating and current drive sustain the FRC for time > 5ms n à “HPF” High Performance Beam Driven FRC
FRC For mation
ss
ure
Monte tCranrlsopocortdceo,dwehQic1hDisanudseids tuosecadlctoulsaimteuslaotuerctheetervmolsutdiouneotof the C-2
S. A. Dettrick, D. C. Barnes, E. Belova*, F. Ceccherini, D. P. Fulton, L. Galeotti, S. Gupta, C. Laune*u*t,raHlabn.edaMmCos-2.nUQk2fieDhldohraresvebtre,seYnd.bceMoncfoighumkr,atriAkoen.deNaxgpeaeircnimsatestnht,es M[1D]..QO2Dnofri, L. Steinhauer, T. Tajima and the TAE team
more than 5 ms
The experiments show that the FRC
TRI ALPHA ENERGY, INC., P.O. Box 7010, Rancho Santa Margarita, CA 92688-7010;
Equilibrium
1. LamyRidge Multi Ion Fluid model [5] n Insulating or conducting walls
n Real coil and wall geometry
« Part of integrated modeling suite
simulations start from an initial equilibrium and transport coefficients
ABSTRACT formation of a steady s
tate
in
C
-2U,
s
ust
ai
n
ed
by
fast
ion
pre
e
s
Global Transport
and separate ion and electron temperatures, coupled with a 3D
the experiments
2. Q2D code [Onofri, CP10.00088] to the axis.
Df
transport code Q1D and is used to simulate the evolution of the C-2
between beam neutrals and the plasma.
The code includes equations for a neutral fluid. The neutrals come from ion R
and C-2U field reversed configuration experiments [1]. Q2D
n Applications
recycling at the wall with recycling coefficient R=1 and from charge exchange
2. HyEq Hybrid Equilibrium [Steinhauer, CP10.00090]
simulations start from an initial equilibrium and transport coefficients
Experimental analysis [Bolte, CP10.00076]
between beam neutrals and the plasma. The Q2D model tuned on C-2 experiments has been used to simulate
C-2, with more beam power and angled beam injection, which
The simulation starts from an initial equilibrium that matches the
ABSTRACT ABSTRACT
C-2
C-2
In C-2U the beam power has been inc The Q2D code is a 2D MHD code, which includes a neutral fluid C-2 beams are injected at an angle of 20 d
The code has been used wfor C-2 experiments and transport
and separate ion and electron temperatures, coupled with a 3D coefficient have been chosen to obtain the best agreement with In C-2U the beam power has been in
The code has been used wfor C-2 experiments and transport
Simulation Overview of High-Performance Beam-Driven Field Reversed Configurations C-2
The Q2D code is a 2D MHD code, which includes a neutral fluid Monte Carlo code, which is used to calculate source terms due to
the experiments
coefficient have been chosen to obtain the best agreement with
to the axis.
The experiments show that the FRC is Transport simulations of the C-2 and C-2U Field Reversed Configurations wit
and separate ion and electron temperatures, coupled with a 3D neutral beams. Q2D has been benchmarked against the 1D
the experiments
C-2 has 6 neutral beams with a total power of 4.2 MW
C-2 has 6 neutral beams with a total power of 4.2 MW
transport code Q1D and is used to simulate the evolution of the C-2 M. Onofri, S. Dettrick, S. Gupta, D. Barnes, T. Tajima and the TAE team
The Q2D model tuned on C-2 experim more than 5 ms
*Princeton Plasma Physics Laboratory; **University of California, Irvine
are chosen to match C-2 experimental data. C-2U is an upgrade of and C-2U field reversed configuration experiments [1]. Q2D
Resistivity 3X classical
C-2U
The Q2D model tuned on C-2 experim
C-2, with more beam power and angled beam injection, which simulations start from an initial equilibrium and transport coefficients
demonstrates plasma sustainment for 5+ ms. The simulations use are chosen to match C-2 experimental data. C-2U is an upgrade of
TRI ALPHA ENERGY, INC., P.O. Box 7010, Rancho Santa Margarita, CA 92688-7010
the same transport coefficients for C-2 and C-2U, showing the
3X classical
C-2, with more beam power and angled beam injection, which
experimental profiles
The simulation starts from an initial e
B
e
a
m
-
D
r
i
demonstrates plasma sustainment for 5+ ms. The simulations use
Classical 20 X classical
C-2U
and current drive.
the same transport coefficients for C-2 and C-2U, showing the
C-2
v
e
n
M
o
Non destructive beam-driven modes hinted at by super-thermal neutron
formation of a steady state in C-2U, sustained by fast ion pressure [1] M. Binderbauer et al., Physics of Plasmas 22, 056110 (2015)
population [Magee, CP10.00067]
Ion thermal conductivity
Exp. R
Df
R s
[1] M. Binderbauer et al., Physics of Plasmas 22, 056110 (2015) Monte Carlo code, which is used to calculate source terms due to
recycling at the wall with recycling coefficient R=1 and from charge exchange
n EPOCH PIC code simulation [Necas, CP10.00068] The Q2D code is used for simulations of C-2 and C-2U
more than 5 ms
n FQre2eD eisnae2rgDycosdoeutrhcaet solavrees tfhaesMt iHoDneaqnuaistiontrsocpouypalenddwidthf/dv > are chosen to match C-2 experimental data. C-2U is an upgrade of Resistivity
0
3X classical
20 X classical Classical
C-2U
Experiment Simulation
n Kinetic ions, fluid electrons
n FRC reconstruction from experimental diagnostics n Different modes in low and high β regions
source terms due to fast ions
The Q2D code is used for simulations of C-2 and C-2U
Reconstruction [Rath, CP10.00089]
Comparison with experimental power
Neutral beams are injected into the plasma and produce fast ions demonstratesplasmasustainmentfor5+ msQ.2TDhiessaim2DulacotiodnesthuastesolvestheMHDequationscoupledwith
Experiment
3. Bayesian Inference [Romero, TO7.00013] the same transport coefficients for C-2 and sCo-u2rUce, stehromwsindguteheto fast ions Electron thermal conductivity through charge exchange and ionization
n
balance [Trask, CP10.00064]
formation of a steady state in C-2U, sustained by fast ion pressure
experimental profiles
Simulation
Exp. Ttot Ttot
Exp. L
Separatrix reconstruction from magnetic measurements Neu tralFbaesatmiosnaorebiitnsjeacretecdailncutolatheed pulsainsgma ManodntperoCdaurlcoecfoadset ions and current drive.
C2W rampup
d
1. Q1D code [6] The code has been used wfor C-2 experiments and transport
yield; suggestive of anomalous transfer of energy from fast to thermal ion
The Q2D code is a 2D MHD code, which includes a neutral fluid and current drive.
n Theory[Nicks,CP10.00069]
neutral beams. Q2D has been benchmarked against the 1D C-2 has 6 neutral beams with a total power of 4.2 MW
beams are injected at an angle of 20 degrees from the perpendicular
coefficient have been chosen to obtain the best agreement with
Resistivity
Electron thermal conductivity
The simulation starts from an initial eq 20 X classical C-2U
Electron thermal conductivity
experimental profiles
In C-2U the beam power has been increased to 10 MW and the
Classical
Ion thermal conductivity
The code includes equations for a neutral fluid. The neutrals come from ion R Df
R « Part of integrated modeling suite s
Exp. R
rt coefficients
Ti+Te
T e
n Assumethermalplasmatranspo
Exp. RDf
The experiments show that the FRC is sustained in a steady state for
beams are injected at an angle of 20 to the axis.
Density
γ/γMHD
« LamyRidge MHD code experimental system description and input/ output conventions forms a prototypical integrated modeling suite
§ All coils, shaped walls, pulsed power circuits
§ MHD plasma model, coupled to neutral fluid model, 2D (r,z)
ne
§ §
Fully kinetic ions, fluid electrons, quasineutral, Ohm’s law FRC spin-up due to particle loss and resistive decay (S*=9)
End-shorting
n Hot FRC is formed by thermalization of fast colliding FRCs
n Tilt mode is avoided by kinetic effects & equilibrium parameter control
n Low order flute modes are mitigated by end biasing
n NB injection provides heating and current drive to sustain FRC, lifetimes
limited to electric power constraints
n Beam driven modes can account for super-thermal neutron production
n KineticMicrostabilitycodesunderdevelopmentforpredictivemodeling n TheTAEresearchprogramhasbeensuccessfultodateduetoclose
interaction between theory, experiment, and engineering groups
n Weinvitecollaborationwiththewidercommunityinthedevelopmentof

n SimulationofHighPerformanceBeamDrivenFRCshows
Transport coefficients and current drive model need adjustments for
§ «
Fully kinetic ions, fluid electrons, quasineutral, Ohm’s law
n Drift kinetic or Boltzmann electrons
n Linear Perturbative electrostatic solver:
Exp. RDf RDf
R
E xp. TCX losses on input neutral target tot
§ §
Growth rate agrees with analytic theory [4]
Nonlinear saturation of tilt leading to new FRC equilibrium [3]
End Biasing
2. HYM 3D Hybrid PIC code (E. Belova, PPPL) [3]
E/S*
In Q2D simulations, plasma shots are long but decay after 3 ms, contrary to experimental observations
Vφ
End-shorting
|Vn |2 Periodic
|Vn |2
All n
resistivity, S ~ 1500
Inner divertor
New confinement vessel, skin time <3 ms
Upgraded formation sections, 15mWbtrappedflux
End divertor
Interface to integrated modeling suite
T Exp. LDf
Df
Ls
CP10.00077]
High fast ion pressure in C-2U is likely to confinement and neutral beam current dri
time (μs) 0.06
65.5 87.8 91.4
Rs is the separatrix radius
C-2W Machine Under Construction
Macro-Stability
The code includes equations for a neutral fluid. The neutrals come from ion The plasma is coupled with a neutral fluid
Exp. R R
Kinetic Stabilization of Tilt Mode
n Rewrite of GTC specializing to FRC physics
« Equilibrium import from integrated modeling suite
balance and it is different from T +T
L
s
1. FPIC 3D Hybrid PIC code [Ceccherini, CP10.00087]
Simulation
t / t t / t
t/tA
A A
End-shorting: Periodic:
a Numerical FRC Project
[1] M.W. Binderbauer et al., Phys. Plasmas 22, 056110 (2015)
[2] S. Dettrick et al., BP12.00031, 57th APS-DPP Meeting (2015 ) [3] E. Belova et al, Physics of Plasmas 11, 2523 (2004)
[4] C. Steinhauer, Physics of Plasmas 19, 070501 (2011)
§ faster spin-up; instability of §
=
1-4
mode
stable
for high
n=1 tilt and subsequent growth of the n=2 rotational mode.
§ §
Similar to Er < 0 end biasing
CHERS measurements (Osin) Vφ~60km/s after about 300μs
show
New magnet
System for field ramp & active control
[5] L. Galeotti et al, PoP 18 082509 (2011)
[6] S. Gupta et al. Phys. Plasmas 23, 05327 (2016)
[7] D. Stotler, C. Karney, Contrib. Plasma Phys 34 (1994) 392. [8] W. Deng, Z. Lin, I. Holod, Nucl. Fus., 52 (2012) 023005
0.8
0.6
0.4 104.1 127.2 0.2
E = 3.27 E = 4.52
•
Exp. Te Te
4. DEGAS2 code [7]
n Study of Neutral H, H2, and H2+ densities due to beams [Granstedt,
0
0.1 0.2 0.3
0.4 0.5
0.6
magnetic field curvature
transport models
[1] M. Binderbauer et al., Physics of Plasmas 22, 056110 (2015)
The Ohm’s law includes the Hall term
n ComputeFRCprofileevolutionoverfull
Low order modes important in FRCs:
n N=1 tilt stabilized by kinetic effects. Control by S*/E parameter an elongated FRC.
The code The Q2D code is used for simulations of C-2 and C-2U
Fluid thermal ions, electrons, and neutrals
The plasma is coupled with a neutral fluid The Ohm’s law includes the Hall term
Experiment
to experimental observations simulation of C-2U and future devices.
Benchmark
exp(-3 E/S*)
The code has been benchmarked against the 1D code Q1D, for an elongated FRC.
radial profiles at t=1 ms
R is the excluded flux radius
Ttot is calculated from pressure
Periodic
- n=0
- n=1
- n=2
-n=3
- n=4
n
10x stored energy
Plasma-guns and biasing electrodes
(In both inner and end divertors)
Upgraded NB’s
Phase 1: 13 MW, 30 ms; Phase 2: 20 MW, 30 ms
The plasma is coupled with a neutral fluid through charge exchange and ionization
tot RDf Ttot
Fast ion orbits are calculated using a Monte Carlo code
Kinetic Microturbulence
Rs
Ti+Te Exp. Ttot
n FRC physics introduced to first principles transport code GTC Benchmark
through charge exchange and ionization
balance a
nd it is different from T +T
Q2D is a 2D code that solves the MHD equations coupled with radial profiles at t=1 ms
n N=1&N=2radialmodesstabilizedbyEndBiasing 2. ANCcode[Fulton,CP10.00074];[Lau,CP10.00075]
s
Fully kinetic fast ions by:
due to fast ion pressure and
Experiment Simulation
Df Df
source terms due to fast ions
Neutral beams are injected into the plasma and produce fast ions
magnetic field curvature
The code has been benchmarked against the 1D code Q1D, for an elongated FRC.
3. Monte Carlo code
L
n Fully kinetic or Gyrokinetic ions Fast ion orbits are calculated using a Monte Carlo code
L
s
In Q2D simulations, plasma shots are lon Transport coefficients and current drive mo
radial profiles at t=1 ms
ie due to fast ion pressure anEdxp. L
magnetic field curvature L
NB injection and fast particle transport
High fast ion pressure in C-2U is likely to a confinement and neutral beam current driv
Ion thermal conductivity
Df Exp. T
Kinetic Microturbulence Code Development R XMHD
The Ohm’s law inclBudenscthhemHaallrtekrm 1. GTC code [8]
T Re
s
recycling at the wall with recycling coefficient R=1 and from charge exchange
Ttot R Ti+Te
between beam neutrals and the plasma. has been benchmarked against the 1D code Q1D, for
s
Coupled to magnets, circuits, wall eddy currents T is• caElcxpu. lTated from pressure
Df
Fast neutrals, warm neutrals, recycling, gas bleed balance and it is different from Ti +Te
due to fast ion pressure and Warm neutral generation must be included self-consistently in global
n Goal:firstprinciplescomputationoftransportcoefficientsfor specified initial equilibrium
s
Experiment Simulation
Exp. L LDf
L
Df
HighfaSstiuonmpresmsuraeirnyC-2Uislikelytoaffect(improve)plasma confinement and neutral beam current drive.
s
Ti+Te
Exp. RDf discharge
•
Exp. T e
Df Df
Simulation
Df
tot
RDf is the excluded flux radius T
e
Df
Df
R
is the excluded flux radius Ttot is calculated from pressure
is the separatrix radius
ie
RDf
Rs is the separatrix radius
In Q2D simulations, plasma shots are long to experimental observations
« Part of integrated modeling suite Experiment
tot L
NPA, NPB, neutron diagnostics
e
simulation of C-2U and future devices.
Transport coefficients and current drive m simulation of C-2U and future devices.