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

Simulations of edge biasing and rotation in the C-2W FRC experiment using the Q2D code
Marco Onofri, S. Dettrick, D. Barnes, P. Yushmanov, T. Tajima, D. Osin and the TAE team
TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610
Abstract
We study the effects of end shorting and electrostatic biasing in simulations of the C-2W Field Reversed Configuration experiment using the Q2D code. Q2D 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. The model includes the Hall term in Ohm’s law. We modified the boundary to impose different conditions on the radial electric field. The shorting of open field lines at the external boundary generates a toroidal magnetic field and the propagation of a torsional Alfven wave. This modifies the radial electric field along the open field lines and makes the SOL plasma rotate in the ion diamagnetic direction. The plasma rotation can also be controlled by applying a finite radial electric field at the boundary to simulate the effect of electrode biasing. We observe the penetration of this rotation across the separatrix into the closed field lines by viscosity. The effect of the neutral beams on the rotation is also investigate
C-2W
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 (see poster by H. Gota)
Q2D model
MHD code (Lamy Ridge) coupled with Monte Carlo code
Simulations of edge biasing
 Rotation can be controlled by the radial electric field at the edge  Biasing is used for stabilization
 Biasing heats the plasma
3. Neutral beams, negative biasing
Goals
Understand the effect of end shorting and biasing on plasma rotation
Effects of mirrors and divertors Effects of beams on rotation Effects of neutral gas
Rotation is affected by electric field
1 𝑒𝑛
End shorting 𝐸 =0 𝑉 =ion diamagnetic velocity 𝑟𝜃
Insteadystate𝐸 ≃0inSOL 𝑟
plasma rotates at ion diamagnetic velocity
1.
2. 3. 4.
Neutral beams affect rotation at midplane
𝑉 < 0 at midplane and 𝑉 > 0 in divertors
𝜃 𝜃
Radial current produced by neutral beams creates a 𝐉 × 𝐁 force in the ion diamagnetic direction
E=-V× B+
The toroidal velocity can be controlled by the radial electric field
biasing is simulated by applying axial current at the
Ohm’s law
J × B−𝛻𝑃 𝑒
+ 𝜂J
boundary I =1kA z
Axial current density at 𝑧 = −3 𝑚
Iz
With negative biasing SOL rotates in electron diamagnetic direction
1.b)
Negative biasing
4. Neutrals
Negative biasing, neutral beams
Neutral gas comes from wall recycling and from neutral beam charge exchange Fast ion losses due to charge exchange with neutral gas
Monte Carlo Code
NBI H (source)
CX/ionize
FRC H+
B, E, n, T , T CX ie
Lamy Ridge
No neutrals
Neutral gas reduces the number of fast ions
neutrals
Less negative rotation at midplane
1.a)
Q2D simulation of spinup due to end shorting
Simple geometry: Cylindrical vessel with conducting walls
Rotation measurements
Simulation
CX/ionize
𝜃 𝑒𝑛𝐵𝜕𝑟 𝐵 𝑧𝑧
• MHD
• realistic wall geometry
• external coils and
conductors
• neutral gas from wall
recycling and warm
neutrals
• Different ion and
electron temperatures
𝑡 = 300 𝜇𝑠
1 𝜕𝑃 𝐸
𝑉 = 𝑖 − 𝑟 = 0
Initial condition is a nonrotating equilibrium  Boundary electric field is modified
to 𝐸 = 0 𝑟
 𝐵𝜃 develops near the ends  Alfvenwavestartsfromthe
boundary
(Macnab, Phys. Plasmas, 2007, Steinhauer, Phys. Plasmas, 2002)
H
Wall (sink)
Jf, nf, energy, momentum
2.
C2W-like geometry: mirrors and divertors
Axial current
mirror
30% of current penetrates mirror
Number of particles, momentum and energy conserved between fast particles and thermal plasma
measurements in C2-W show rotation rates similar to the simulations
 Neutral beams modify the rotation caused by the biasing  Neutral gas reduces the effects of fast ions
prompt loss
shine through