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In TAE Technologies’ current experimental device, C-2W (also called “Norman”) [1], record breaking, advanced beam-driven field reversed configuration (FRC) plasmas are produced and sustained in steady state utilizing variable energy neutral beams, expander divertors, end bias electrodes, and an active plasma control system. The neutral gas, which is produced in divertors by neutralization of the plasma flow at the divertor target plates, may negatively affect the plasma by reducing the ion and electron temperatures through ionization and charge exchange. To minimize these effects, the divertors have a large volume and a powerful pumping system to reduce the neutral gas density to an acceptable level. The neutral gas in the divertor and its effect on the plasma flow have been studied numerically using the Q2D code. Q2D is a 2D MHD code with distinct ion and electron temperatures, and neutral gas treated as a fluid. The simulations show that the gas distribution in the divertor is substantially nonuniform, which improves the effectiveness of the pumping system and reduces the interaction of the neutrals with the plasma flow. The plasma flow compresses the neutrals near the target plates and reduces the neutral density in the rest of the plasma jet coming from the FRC. Under such conditions, the interaction of neutrals with the plasma is reduced, which allows the divertors to operate normally at higher plasma outflows than were estimated earlier.
C-2W is a Field Reversed Configuration experiment with many upgrades from the previous C-2U device, including higher neutral beam power and inner divertors . Steady state FRC plasmas are sustained for 30 ms (see poster by H. Gota)
Neutrals in divertors
n Neutrals in the divertors are created when the plasma flow is neutralized at the target plates
n Neutrals affect the plasma flow decreasing the ion and electron temperatures.
n The divertors have a pumping system to reduce the density of neutrals and their interaction with the plasma.
n The MHD code Q2D [2] is used to study the distribution of neutrals in the divertor and their interactions with the plasma
Simulation domain
Geometry of the configuration used in simulations
Pumping surfaces
Divertor target
plates Plasma flow
n The plasma flow comes from the mirror region on the right and expands in the divertor following the expanding magnetic field.
n The plasma is neutralized at the target plate on the left and creates a neutral source.
n The green walls are the pumping surfaces. Neutral model
n Neutrals have 2 components: cold (emitted from the wall) and warm (from CX with plasma and high energy tail of wall reflection)
n Cold neutrals are calculated with hydrodynamic equations
n Warm neutrals are immediately redistributed to the walls due
to their large mean free paths !"#$, !&'.
n Charge exchange of cold neutrals is an instantaneous
transfer of neutrals to the walls .
n The recycling coefficients at the pumping surface were determined by matching the pumping speed measured in the C-2W divertor filled with uniform density deuterium molecules at room temperature
Q2D simulation
§ The plasma coming from the mirror region is neutralized at the divertor target plates.
The simulation can be compared with the experiment by looking at the neutral density at the top of the divertor, where the ionization gauge is installed
South divertor North divertor
Neutral density at gauge location in simulation and experiment
The initial delay of 1 ms is present in both the simulation and the experiment. 1 ms is the time neutrals take to reach the gauge location moving with room temperature thermal speed
Q2D simulations of the neutral gas in the divertors of C-2W
Marco Onofri, P. Yushmanov, and the TAE team
TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610
        § The neutrals interact with the plasma through ionization and charge exchange
      Ion flux at the wall
Ion flux at 2 ms
  The ion flux increases near the target plate due to ionization of neutrals created at the wall
  Time evolution of the number of neutrals in divertor
The neutral density is not uniform in the divertor, the plasma flow compresses the neutrals near the target plates and the neutral density is very low in the dense plasma jet coming from the mirror.
Q2D was used to study neutrals in the divertors and their interaction with the plasma. Simulations show that the neutrals have a nonuniform distribution, which reduces the interaction with the plasma. The ratio
between the ionization rate and the ion flux is 89:; ≈ 0.3. This can be 8<=>?@>
compared with what would happen if the same neutrals were distributed uniformly. In this case 89:; ≈ 4.
The lower interaction with the plasma allows divertors to operate at higher plasma outflows.
[1] H. Gota et al., Nucl. Fusion 59, 112009 (2019)
[2] M. Onofri et al. Phys. Plasmas 24, 092518 (2017)
 Particle balance equation used for the divertor design assumes uniform density and it describes the evolution of neutrals as
2D simulation
Pumping speed
Neutral density at t=1ms
Neutral density at t=4ms
/01 62 .=2 Γ4−67
  62 2 67 = Γ4 − /01 .
P is the pumping speed of the divertor surfacesandΓ4 istheplasmaparticleflux at the target plate
This can be compared with the simulation
 Number of neutral molocules in divertor
Recycling coefficient ) $$
pumping speed
Pumping speed
Evolution of the neutrals in the divertor calculated from the simulation and from the 0D neutral model with
FG . = 2000 I .
     = 0.68 gives /01 62
 G .=− 2 67 =1500F /I