SGupta_APS_082317

Vlasov Fokker Planck Study Of Electron Dynamics In Scrape Off Layer With Expander Divertor
Debye sheath ΔφD
pre-sheath Mirror drop
S. Gupta1, P. Yushmanov1 D. C. Barnes2 and the TAE TEAM
1TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610 2 Coronado Consulting, Lamy, NM 87540
Motivation
n C-2W goal is to increase electron temperature by reducing electron heat losses using expander divertor
Electron Phase Space Boundaries in Expanding Magnetic Field
Sheathboundary:𝑽𝟐∥ =𝟐𝒆 𝝓𝒍 −𝝓𝒕 −𝑽𝟐+ 𝟏 −𝑩𝒕 𝑩𝒍
Mirrorboundary:𝑽𝟐∥ =𝟐𝒆 𝝓𝒍 −𝝓𝒎 −𝑽𝟐+ 𝟏 −𝑩𝒎 𝑩𝒍
Core electrons beyond sheath boundary are lost to the walls
Confined region electrons are reflected back to the core by electrostatic barrier
Trapped region bounded between electrostatic and magnetic barrier can only be filled up by collisions.
Trapped region between the electrostatic and mirror boundary increases towards target
Normalized Distribution Function Shows Incomplete Filling Of Trapped Region
§ Source is Maxwellian and reflected back distribution is truncated
§ Trapped region never filled up due to collisions
Electron Current / Biasing Has Strong Effect On Pre- sheath Potential
n Negative biasing (Ie <Isat):
n Presence of even small electron losses leads to incomplete filling of trapped region
n Temperature anisotropy reduces pre-sheath potential
n Positive biasing (Ie >Isat):
n Large electron losses further
enhance temperature gradient and anisotropy, hence reduced pre-sheath potential.
Significant Pre-sheath Potential developed in in Low expansion region
§ Pre-sheath potential increases with magnetic expansion
§Sheath potential decreases with magnetic expansion.
§ Large potential drop occurs in the small expansion region
§C-2W divertor has magnetic expansion ration K = 30
Heat Flux And Energy Loss Per Electron Decreases With Increasing Biasing
§Heat flux decreases with increasing expansion as electrons kinetic energy is converted to potential energy.
§Energy loss per particle is reduced with low electron current/negative biasing
n FRC core is surrounded by the open field mirror system
n Electrostatic potential is naturally formed to confine electrons which otherwise will be lost faster than ions
n Magnetic expander divertor
n Develop pre-sheath potential
away from the walls
SOL Mirrors
n
n
n n
n n
§T
all collisionalities.
§T⊥< T|| except for highly collisional case where , T⊥ ≈ T||
§Axial pressure balance ensures lower pre-sheath potential due to pressure anisotropy
𝑑𝑃∥ dlnB d𝜙 𝑑𝑙+𝑃+−𝑃∥ dl+en𝑑𝑙=0
§Collisionality has no significant effect for λmfp > L, consistent with the theoretical boundary layer width 𝚫𝐕 ∝ 𝝂
n Reduce interaction with the walls and neutrals
FRC Core
φt
0
Expander Divertor
mirror
n Reduce heat loads on the walls
Z
target
3-D Particles velocity space
V⊥ Target
n KSOL (kinetic Scrape Off Layer) code helps to develop better understanding of electron confinement in expander divertor
KSOL (KINETIC SCRAPE OFF LAYER) Code
n KSOL solves drift Kinetic equation in one spatial (along the magnetic field) and 2 velocity dimension (v|| and v^ ) with full collision operator and Poisson solver
n Magnetic field expansion with specified density profile and electron current
Mirror
Energy Loss/e (η) VS Electron Current
convective transport
§Pre-sheath potential develops away from the walls in the presence of magnetic expander
§Pre-sheath potential is lower than the Boltzmann potential due to incomplete filling of trapped region
§Electron losses and ion flows significantly affects the pre- sheath potential
§Energy losses per electrons are reduced with negative biasing
§K~ 30 is adequate for C-2W design
Heat Flux Profile
V||
n Boundary Conditions: Source from
Numerical Results
Outflow
Reflection
Target/divertor plates
V||
Collisionality (𝛎* = L/ 𝛌
) Has No Effect For 𝛌 mfp
mfp
> L
n Ksol reproduces analytical solution with I = 0 i.e., no
Confinement
outflow
Confinement side
and T have axial profile for ⊥ ||
e electron losses.
n C-2W will be negatively biased
Ion Density Profile Affects Pre-sheath Potential
n Ion density ni = B/vi in ideal situation
n Ions slows down in presence of neutrals and volume ionization
n Potential is highest with ion acceleration
n Pre-sheath potential is always lower than Boltzmann potential
Summary
Axial distance
n KSOL Parameters:
n Collisionality (KSOL works for arbitrary collisionality)
n Electron current, Ie: emulates electrode biasing.
n Ion density profile : emulates neutrals/volume ionization n Magnetic expansion, K = Bm/B
n Source distribution
n Ion charge (Z) effect