An Interesting Poster to look at from the Tri Alpha Energy Team in California

Transport simulations of the C-2 and C-2U Field Reversed Configurations with the Q2D code
ABSTRACT
The Q2D code is a 2D MHD code, which includes a neutral fluid and separate ion and electron temperatures, coupled with a 3D Monte Carlo code, which is used to calculate source terms due to neutral beams. Q2D has been benchmarked against the 1D transport code Q1D and is used to simulate the evolution of the C-2 and C-2U field reversed configuration experiments [1]. Q2D simulations start from an initial equilibrium and transport coefficients are chosen to match C-2 experimental data. C-2U is an upgrade of C-2, with more beam power and angled beam injection, which demonstrates plasma sustainment for 5+ ms. The simulations use the same transport coefficients for C-2 and C-2U, showing the formation of a steady state in C-2U, sustained by fast ion pressure and current drive.
C-2
 The code has been used for C-2 experiments and transport coefficient have been chosen to obtain the best agreement with the experiments
 C-2 has 6 neutral beams with a total power of 4.2 MW
 The code includes equations for a neutral fluid. The neutrals come from ion recycling at the wall with recycling coefficient R=1 and from charge exchange between beam neutrals and the plasma.
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C-2U
In C-2U the beam power has been increased to 10 MW and the beams are injected at an angle of 20 degrees from the perpendicular to the axis.
The experiments show that the FRC is sustained in a steady state for more than 5 ms
The Q2D model tuned on C-2 experiments has been used to simulate C-2U
The simulation starts from an initial equilibrium that matches the experimental profiles
Power balance
See also poster by E.Trask
M. Onofri, S. Dettrick, S. Gupta, D. Barnes, T. Tajima and the TAE team
TRI ALPHA ENERGY, INC., P.O. Box 7010, Rancho Santa Margarita, CA 92688-7010
P Pc ~ 94kW b
~ 59kW
Ions
P
~ 68kW Paux ~ 440kW
P Pc ~ 31kWb
~ 428 kW
Resistivity
3X classical
Electron thermal conductivity
20 X classical
Ion thermal conductivity
Classical
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P ~ 136kW Sources
Pc compression
Pb beam
P Ohmic
[1]
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M. Binderbauer et al., Physics of Plasmas 22, 056110 (2015)
The Q2D code is used for simulations of C-2 and C-2U
Q2D is a 2D code that solves the MHD equations coupled with source terms due to fast ions
Neutral beams are injected into the plasma and produce fast ions through charge exchange and ionization
Fast ion orbits are calculated using a Monte Carlo code The plasma is coupled with a neutral fluid
The Ohm’s law includes the Hall term
Benchmark
The code has been benchmarked against the 1D code Q1D, for an elongated FRC.
radial profiles at t=1 ms
Exp. RDf R
R s
Experiment Simulation
e
Ttot
Exp. LDf LDf
Ls
Peq ~ 250
PN ~ 110kW
Pq ~ 780kW
3 MW of beam power are deposited into the plasma (core and SOL heating).
1 MW is absorbed by the magnetic field due to work done on fast ions by the electric field ( E  J fast ), resulting in additional plasma heating.
Conclusions
Q2D simulations can reproduce C-2 and C-2U experiments reasonably well
C-2U simulations with the same transport coefficients used for C-2 shows a faster decay than observed in experiments
The actual plasma confinement in C-2U may be better due to the different neutral beams, biasing, mirror plugs, etc.
Future comparison of Q2D modelling with C-2 and C-2U experiments will provide additional insight in the physics of plasma confinement and current drive in advanced FRCs.
E
T+T Exp. T Equilibration th,e
~ 850 J E,i ~ 0.8 ms
Electrons
Paux auxiliary
(ion temperature estimate Indicates extra heating, probably from the biasing system)
Sinks
P convection
Pq conduction Prad radiation
PRad ~ 70kW

E ~ 290 J ie tot th,iEth Eth
E,e ~ 0.31 ms DfT N
PN ~380kW
Pq ~ 840kW
Exp. RDf RDf
Rs
Exp. Ttot
Ttot
T+T ie
• Exp.T e
T e
R
Rs is the separatrix radius
Ttot is calculated from pressure
balance and it is different from T +T
due to fast ion pressure and magnetic field curvature
Exp. LDf LDf
Ls
Df
is the excluded flux radius
i e
Experiment Simulation
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In Q2D simulations, plasma shots are long but decay after 3 ms, contrary to experimental observations
High fast ion pressure in C-2U is likely to affect (improve) plasma confinement and neutral beam current drive.
Transport coefficients and current drive model need adjustments for simulation of C-2U and future devices.
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Beam
Conduction