Fast ion D(a) diagnostic (FIDA) on C-2W

1.
Radial electron density profile (FIR interferometer and MC + LR results)
density (0 to 2.5xx1019m—3) vs y (-0.8m to + 0.8m)
NBI
FRC Fast Ion Distribution: Effect on Equilibria
Laura Galeotti, Loren Steinhauer, Francesco Ceccherini, Sean Dettrick and the TAE team TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610
Abstract
n Neutral Beam Injection (NBI) plays a critical role in TAE’s C-2W FRC device providing plasma stability, heating and current drive. C-2W produces steady-state FRCs that are stable and contain significant current and pressure from fast ions.
n We have investigated C-2W equilibria utilizing TAE’s 2D hybrid equilibrium code (MC+LR) which combines the thermal plasma multi-fluid description of TAE’s equilibrium code1(LR) with a kinetic treatment of fast ions added with a MonteCarlo code (MC) through beam injection.
n The converged FRC equilibria from MC+LR code show good agreement with the experiments. Main features of C-2W FRC equilibria are 1) strongly peaked electron density near the separatrix, 2) broad current density profiles with a gradient scale length on the order of fast ion gyroradius, and 3) fast ion pressure comparable to or exceeding the sum of electron and thermal ion pressure. These features differ from traditional FRC equilibrium without beam ions.
n Investigation of fast ion orbits and distribution functions shows that C-2W FRC equilibria are characterized by a significant presence of Betatron orbits and associated kinetic nature such as highly anisotropic fast ion pressure tensor.
n Complementing MC+LR is Monticello, a fast, exploratory particle-pusher for individual or ensembles of ions. It employs a prescribed but flexible“Quasi- eQuilibrium (QeQ) for the fields, and yields current-density structure consistent with MC+LR.
MC+LR Code
n MC+LR is based on an iterative process between MC and LR. Fast ions are added perturbatively by the MC code through NB injection into equilibria computed by LR.
n LR solves a set of equations derived from the momentum equations for each thermal species :
n Momentum equations are projected along ∇ψ and ∇ψ×∇θ for electrons, ∇Yi and ∇Yi×∇θ for each ion thermal species (where Yi=ψ+AiMrvi,θ/(Zie)) and the toroidal direction and then coupled with Te(ψ), Ti(Yi) and ∇xE=0 to obtain two other surface functions for each thermal species and an equation to relate the three surface functions for each species
n LR computes the 2D profiles for ψ, Yi, ni, ne and φ simultaneously solving the previous equations together with
n
n
n n
n n n
LR allows boundaries of any shapes with both conducting or insulating walls In this study, insulating walls are used to model the C-2W device which does not have flux conserver during long pulse (~ 30 ms) steady-state operation.
The vacuum magnetic field is modeled using the experimental coil data (locations and currents of 12 coils)
Study results (MC+LR recostruction of shot 119701)
Deuterium plasma with 8 Hydrogen neutral beam (NB) injection
While NBI operates at 3 energy components (15, 7.5 and 5 keV), we utilized two energy components of 15 keV and 6.5 keV for simplicity with a respective current ratio of 64% and 36% (corresponding to a power ratio of ~ 80% and 20%).NB are injected at 20 degrees.
For this study the neutral background density was selected as the knob to mimic the sink term needed.
An initial FRC equilibrium is chosen based on experimental measurements such as Thomson scattering and magnetics data and NBI begins at t=0.
MC+LR results agree well with experimental results from C-2W3 as can be seen from
n Radial density profile: strong peaking of electron density outside separatrix
NBI
􏰀 Current density profile: significant fast ion current density inside FRC at the beam injection radius (i.e. impact parameter). Significant broadening of the total current profile across the separatrix and increase in magnetic field scale length. Scale lengths are on the order of fast ion gyro-radius. Double hump in the radial current profile.
􏰀 Fast ion pressure comparable to or exceeding the sum of electron and thermal ion pressure with strong fast ion pressure anisotropy
Example: flux contours from QeQ (ψ(r,z) = const). Chamber radius Rw = 0.8m & half-length Zm = 2.9m. Mid-plane of symmetry on left, end plane (mirror plane) on right
Physics tasks and interpretations:
Initial equilibrium (no fast ions)
Final equilibrium after NBI
n n
n End-loss: probability of end loss; compare to analytic end-loss criterion, effect of end mirrors
n Orbital effects: recognize orbit types
n Ensemble properties: yield moments of distribution (density, current density) ensembles; radial and axial bounce frequencies; non-adiabatic scattering; contributions of partial distributions
n Comparisons with full-fledged Monte-Carlo simulations like MC+LR QeQ + Monticello reconstruction
Properties of the QeQ “quasi equilibrium”:
Rs = 0.3m, Zs = 0.7m, Bw0 = 0.1T, ΔBm = 0.14T (mirror increment)
Beam: Wb = 15keV, dimpact = 0.22m, x0 = -0.32 to +0.32, angle γb varied
Upper frames show flux contours ψ(r,z) = const for two QeQ examples:
(L) = elliptic separatrix
(R) = racetrack separatrix
Lower frames show fast-ion current density contours jθ(r.z) = const Double- hump radial profiles and sharp turning points clearly in evidence
Discussion and Future Work
MC+LR code has been utilized to investigate C-2W FRC equilibria with NBI.
MC+LR results agree well with experimental data from C-2W matching density and magnetic field profile.
MC+LR results provide valuable insights to C-2W FRC equilibrium with significant fast ion pressure (over 50% of total pressure) and fast ion current inside FRC.
QeQ + Monticello reproduce current density structures consistent with MC+LR.
Stability investigations on MC+LR equilibria are now in progress with different methods:
1. Reduced models (test particle approach) to simulate the effects of experimentally observed fluctuation in C-2W on fast ion and thermal plasma density, current density and pressure profiles.
2. 2D/3D Particle-in-cell (PIC) codes as FPIC and HYM to validate the stability of
Experimental profiles
Profile from MC+LR
n Orbit studies of fast ion population show a dominant presence of Betatron orbits, consistent with strong pressure anisotropy
n Fast ion profile exhibits highly localized turning points located at the edge of FRC.
Monticello Code
2.
3.
Magnetics data (flux and Bz)
Flux
NBI shinethrough ~22% ( experimental value ~18%)
Bz
n Flexible: a variety of launch n conditions are allowed including “dissected” distributions
Electromagnetic host structure:
fixed but operator-flexible EM field (“quasi equilibrium”, QeQ)
n n
n n
n
n Fast: computes single ions < 1 sec. n Error checking: checks
and 250 ensembles < 1 min.
n Convenient for “partial distributions” e.g. mono-energetic.
constancy of computed Hamiltonian and canonical angular momentum
n
NBI injection leads to significant changes in density and current density profiles of FRC equilibrium.
n
n
Realistic QeQ
n Fully 2D both inside & outside FRC: realistic separatrix radius R & half-length Z . ss
n Smoothness: ψ(r,z) continuous through second derivative; smooth current jθ = - Δ*ψ/μ0r.
n Realistic magnetic flux shaping at the radial wall boundary ψwall(z) n Magnetic mirror at the ends of the confinement vessel
n Diamagnetic periphery: SOL and jet.
Flexible: adjustable QeQ
n FRC radius Rs and half-length Zs n Mirror ratio
n Diamagnetism of periphery
Findings from MC+LR equilibrium
Quasi-eQuilibrium (QeQ) is a realistic, analytic, and flexible magnetic flux structure ψ(r,z) developed to serve as the host for an ion-pusher.
r-z profiles (density, current density):
0 < r < 1.2m, -4m < z < +4m
and using the analytical profiles for
ion profiles nfast and Jfast are obtained from the MC code.
NBI
Ω (Y ),Ω (ψ) ,T (ψ) and T(Y). The fast iieeii
Initial equilibrium with no fast ions
Final equilibrium after NBI
1 L.Galeotti et al. Phys. Plasmas, 18, 082509 (2011)
2 R. Smith, Poster VP13.00010, this session
3 S. Dettrick, , Poster VP13.00016, this session
Acknowledgement
Very useful discussions with Jaeyoung Park and Herb Berk are gratefully acknowledged.
MC+LR equilibria3
References
n Fast ions are introduced by a source term through the MC code but, to maintain the equilibrium, there must be a balancing sink term. Comparison between equilibrium and experimental profiles may help to elucidate fast ion sink.
n Fully-analytic “smooth” QeQ
n Allows arbitrary accuracy
for particle pushing by a Runge-Kutta
integration scheme.