P. 1

Experimental Inputs
Reconstrcuted Equilibrium is FRC with Dominated FAST Ions Pressure
n Converged steady state equilibrium has reversed magnetic field n Separatrix is ~40 cm, same as measured excluded flux radius
n Calculated trapped poloidal flux is ~ 6 @AB
n Fast ion pressure is over 3 times thermal plasma pressure
n Fast ion energy ~ 4kJ, agrees well with experimental values n Fast ion density ~20% of total plasma density
Reconstruction is Consistent with Other Experimental Mesurement
n Equilibrium agrees very well with the experimental measurements of shine-through and neutrons rate.
n Neutron rate is dominated by the Beam-target reactions.
n Develop Interpretative equilibrium for long lived steady state Electron temperature, % C-2W plasma "
Neutral density, !
Magnetic field
1-Dimensional Equilibrium Reconstruction for C-2W Plasma Sangeeta Gupta, Dan Barnes , Peter Yushmanov
TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610
            n with significant kinetic fast ion population
n directly using measured experimental data & profiles n consistent with other experimental observations
n provide magnetic structure.
Interpretative Approach
n 1-D analysis in mid-plane
n Availability of spatially and time resolved experimental data
n Highly elongated geometry gives quasi 1-D equilibrium
Shine-through vs Time
Neutrons rate vs Time
       Magnetic Field Profile
Total Pressure Profile
     Electron density, !"
       Experimental Inputs: n Electron density, !"(#)
n Electron temperature, %"(#)
n Ion temperature, %&(#)
n Neutral density profile, !!(#)
n Magnetic field near the wall, '( n Magnetic flux near the wall, 8(
Analysis Outputs:
n Magnetic field profile, ' #
n Magnetic flux profile, 8 #
n Fast ion density, !+ #
n Fast ion Current , -+ #
n Fast ion energy spectrum n Total temperature
     Reconstruction iterates to steady state
C-2W Peak Total Temperature is > 3 kev
n Peak total temperature is maintained during the shot n Peak total temperature exceed 3 keV
  n Inferred magnetic field iterated until calculated magnetic flux 8 = ∫#( # ' :# matches measured value 8";<
Sensitivity Studies
 Interpretative Solver with Kinetic Fast Ions
( 1 , (
n Analysis evolves from low = mirror plasma without fast beam
n Final steady state magnetic field is not affected by the ion temperature and neutral density variations as total pressure is always maintained.
 n Direct experimental data: !" # , %" # , %& # , !! # , '( n Ion density profile: ! = ! − !
ions to high = mirror plasma and steady state FRC plasma.
Peak Total Temperature vs Time
C-2W Peak Ttotal vs Peak Te
n ', # is solved using Ampere’s law
Low 9 mirror without Jfast
High 9 mirror increasing Jfast
Ti varitation: 20eV, 400 eV, 800 eV
Neutal density: 1.0 Nn, 3.0 Nn
       n !+ and -+ is calculated using Kinetic MC code with realistic beam sources
n Kinetic orbits with classical slowing down on background plasma and CX losses.
n Converging ./ = ∫12/ 34 2 52 to the experimental measurement.
    Interpretative Solver
Kinetic MC Solver
     FRC configuration in Steady state
FRC is maintained throughout the discharge
n Initial decaying FRC evolves into a Beam dominated FRC.
n 1-Dimension equilibrium is reconstructed using experimental plasma profiles, 1-D Ampere’s law, and Kinetic Monte Carlo fast ions.
n Steady state equilibrium has
n Reversed magnetic field profile through out the discharge n Dominant fast ion pressure
n Peak total temperature exceeds 3 keV
n The reconstructed equilibrium is consistent with experimental measurements of shine-through and neutrons rate.
   QRS vs Time
Magnetic Field Profile