Correlation of global instabilities with high-frequency fluctuations in the scrape-off layer of C-2W

Introduction
The C-2W device (aka “Norman”)[1] produces advanced beam-driven field re- versed configuration (FRC) plasmas.
• Variable energy neutral beam injection (15 keV to 40 keV, up to 20 MW) • End bias electrodes
• Active plasma control
Measuring and accounting for various power flows is important for determining confinement properties and scaling.
• For 0D analysis framework
• The fast-ion distribution is estimated using a 0D time-dependent
Fast Ion Fokker-Planck (FIFP) solver adapted from Fowler[2]
• Ion temperature is constrained by a pressure balance model[3] • Parameters are adjusted for consistency with measurements
• Error analysis is performed by varying the input measurements randomly within their respective confidence intervals and observing the variation of the resulting outputs
• The algorithm is designed to be executed after each plasma discharge
R. Clary1, E. Trask1, N. Bolte1, M. Griswold1, A. Necas1, The TAE Team
1)TAE Technologies, 19631 Pauling, Foothill Ranch, CA 92610 Norman
Data Flow
0D Power Flow Analysis on the C-2W Device
Gnd
−V Gnd
Fuel
Fuel
Fuel
Fuel
Fuel
Fuel
Gnd
−V Gnd
MDS+ Process Data HDF5
Discussion
Main Algorithm
Increase ν anom,f Power Flows
no
Ei > 0? yes
Fokker-Planck
Variance
×M
Fokker-Planck
Power Flows
Power Flows with Error
AA
Inputs & Outputs
Discussion & Next Steps
Primary Inputs
External magnetic field Total energy
Average electron density FRC geometry
Total temperature.
Particle inventory
Average electron temperature Radiated power
Fast ion injection
Fueling rate
Primary Parameters
Fast-ion anomalous loss rate Temperature gradient coefficient Ionization energy
Neutral temperature
Ohmic heating coefficient Fueling efficiency
Primary Outputs
Fast ion distribution Plasma ion population Plasma ion energy
Compression heating Ohmic heating[3]
Ion-electron equilibration[4] Convection PN,i⧵e
Conduction[4] P Charge-exchange[5] P
Shot 113334
P
Peq
PΔV
P Ω Ions
PN, Pq Pcx, Panom
Pcx
Peq
Electrons
PN, Pq, Prad Pfuel, Panom
beam
Panom
Fast ions
Peq
•
Bwall 40 Eth
ne 20
rFRC, lFRC, VFRC
Ion temperature consistent with end loss analyzer (ELA)
• Neutron rate qualitatively matches measurement. Energy dependence of
fast ion anomalous losses may explain 10× discrepancy.
• Bias system input power ∼5 MW is likely heating SOL & not captured in
this analysis.
Next Steps
T
N
Te
Prad 1.0 Sbeam (E )
tot 0 1.5
neTtot = 2μ ˙
q,i⧵e cx,i
Pfuel,e
B2wall
=−κ kTi⧵eA ⊥,i⧵e C∇ ρi
PN, Pq Panom
PN, Pq Panom
0
Ef = Pbeam−Peq,fi − Peq,fe + Pcx,f + Panom,f
= −S
= −ηfuelSfuel k(Ti + Eionize)
Pcx
Ei = PΔV,i + PΩ,i+Peq,fi − Peq,ie
+ Pq,i + PN,i + Pcx,i + Panom,i
N kT cx,i i
˙
Ee = PΔV,e + PΩ,e+Peq,fe + Peq,ie
+P+P+P +P +P q,e N,e fuel,e rad,e
n
i
[1] [2] [3] [4] [5]
H. Gota et al. Nuclear Fusion 59.11 (June 2019), p. 112009.
R.H. Fowler, J. Smith, and J.A. Rome. Computer Physics Communications 13.5 (1978), pp. 323–340.
D. J. Rej and M. Tuszewski. Physics of Fluids 27.6 (1984), p. 1514.
J. D. Huba. Washington, DC 20375: Naval Research laboratory, 2016.
R.K. Janev and J.J. Smith. Atomic and Plasma-Material Interaction Data for Fusion (Supplement to Nucl. Fusion) 4 (1993), pp. 78–79.
˙
Electron cooling from fueling Plasma anomalous losses
P
=E˙ − P
0
PΔV P Ω
Sfuel
ν anom,f
C∇ Eionize Tn C Ω ,i⧵e η fuel
= 1200 s−1 =2 =30eV =Ti
0.5
0.0 4
2 0
4 2
0 2
• • • •
• •
Account for more measurement error
Include measurements of neutral density
Include measurements of Zeff
Update FIFP code for arbitrary fast ion distribution (ramping energy), en- ergy dependent anomalous losses, & E-field
anom,e
Peq,ie
= Ni(Ti−Te)νie
an,i⧵e
i⧵e
∑x
x,i⧵e
0.0
2.5
5.0
7.5
10.0 t (ms)
12.5
15.0
17.5
20.0
= 0.25
= 0.25 6
PΔV Paux
Peq
Pbeam
Fast ions
Peq
Peq
Panom
Peq
Pcx
Peq
= CΩ,i⧵e 3 Ne − ηfuelSfuel Ni⧵e k(Ti + Te) 3 2 Ne
Peq
Ions
Peq Electrons
1 = 2 Ne Ni⧵ekTi⧵e 0
2
5 Ne − ηfuelSfl
˙
2 beam i cx,f f n 1
kT + ν
+ν Nk(T−T)
ELA 0D
Measured 0D/10
Develop model for bias electrode heating Consider 2-region 0D model
Power Balance
f(E , t) Ni Ei
P Δ V,i⧵e P Ω ,i⧵e
= FIFP Solver = Ne − Nf
= Etot −Ee −Ef
= −V˙ Ni⧵e k T i⧵e ˙
Peq
The foundational theory employed for the 0D analysis is relatively simple and uses the following assumptions
• Radial pressure balance is valid for a weakly rotating field-reversed con- figuration plasma
• All bulk ions/electrons are within ellipsoidal excluded flux surface
• Fast ion population estimated from a FIFP solver has an orbit-average
contribution to the plasma pressure
• Internal & external power flows
Pressure balance
Fast ion power balance Plasma ion power balance
Electron power balance
PΔV, PΩ Paux
PΔV, PΩ Paux
NB
NB
SOL Core
NB
NB
Outflow (MW) Inflow (MW) Energy (kJ) Neutrons (109/s) Ti (keV) Radius (cm)
SOL Core
Core SOL