Instabilities in Beam-Plasma Waves in a Model of the Beam-Driven FRC

PIC simulation: Non-thermal distribution driven by NBI in high beta plasma
A. Necas(1), T. Tajima(1,2), S. Nicks(2), R. Magee(1), R. Clary(1), T. Roche(1), E. Granstedt(1), E. Trask(1) and the TAE Team
Experimental Observations Consistent with Modeling
df/dv
MagneJcs
1-2 G fluctuation @ the wall
Proton (beam) Energy Spectrum
Deuteron (Thermal) Energy Spectrum
References
[1] M. Binderbauer et al., Phys. Plasmas 22, 056110 (2015) [2]J.W.S.Cooketal.,PlasmaPhys.Control.Fusion53,074019(2011)
FRC Equilibrium
Beams
Midplane equilibrium profiles
Beam Particle Orbits
(1) TRI ALPHA ENERGY, INC., P.O. Box 7010, Rancho Santa Margarita, CA 92688-7010 (2) University of California, Irvine, Irvine, CA 92697
PIC code and Analytical Dispersion Relation comparison
Predicted Modes for Various Beta
Robust BUT non-destructive (vφ>>vthi) instability during beam injection
Beta=10 % -- Open field line Case
Experimental observations
Dispersion diagram [FFT(E )] - simula3on
x Analytical work
Dispersion diagram [FFT(Bz)]
LEGENDS
Alfven velocity (va)
Shear Alfven velocity (va*cos(θ)) Buchsbaum-whistler (MS)
Alfven Ion Cyclotron (AIC)
Buchsbaum resonance
• Deuteron Tail
• Beam energiza3on
Magne3c fluctua3on
Increased neutron yield
Consistent df/dv
Resonances
Non-thermonuclear Neutrons
Ti = Ttot Te
■ Buchsbaum-whistler coupling facilitated by beams in presence of two q/m ion species.
■ LeXng m =m results in the excitaJon of tb
AIC mode
■ Various resonances/modes are excited as beam slows down
2 X1 !pi
2n2 2 2
Thermal ion
Beam
Thermal electron
exp[ i]In( i)
X n=1 i
2 + 1 2n2!cb Jn(⌫)Jn 1(⌫) Jn+1(⌫) =
Injected
proton
beam
Velocity [x106 m/s]
Analy3cal dispersion, growth & resonance
Large gradients Plasma beta
increasing into the core
XX
k⇢i
Sudden anomalous growth -- simulated
Beam at satura3on
i kvb n=1 !2 n2!c2b
! n⌦
Dielectric Response Function
Beam t=0
!p2b
i = 0.5(k⇢i)2 ⌫ = kvb
!cb
(|vi vj |)|vi vj | D-D cross section
!p2e c2k2
✓ ◆ ✓
◆
■ Slow growth (γ~0.03ωcD)
■ Enhanced neutron signal t!cD
!pe 2
1+ 1+
thermonuclear (calcula3on)
⌦ce
measurement
Ion at sat.
Ion t=0
Coupling of the beam ion Bernstein Harmonic and plasma lower hybrid wave
Dispersion diagram [FFT(Bz)]
Hypothesis
@f/@v > 0 Velocity
Klimontovich two-body correlation Function (KTBCF)
Beta=70 % -- Core
■ AIC mode excited due to the presence of anisotropic (Wperp >W||) beam populaJon
LEGENDS
Alfven velocity (va)
Shear Alfven velocity (v *cos(θ))
Buchsbaum-whistler (MS) Alfven Ion Cyclotron (AIC)
Large gyro-radius
Sample the core FRC AND scrape-off layer Average out a small scale fluctuations
Interaction with neutrals
Drive velocity-space instabilities
a
Presence of proton beam is source of “free energy”
Resonance
Transfer energy from beam to deuteron
Testing Hypothesis-1D3V PIC code EPOCH[2] Configuration and Velocity Space Setup for PIC
h vi =
i6=j j
Thermal
deuteron
plasma
Experiment - NPA
Simula3on – Beta=30%
Injected beam energy
Energe3c super-thermal tail in the thermal deuteron plasma
Injected beam energy
z
Theta
Phi
y
Application of KTBCF to Electrostatic model
t!cD
Initial/final Beam and Thermal Ion Distribution for Electrostatic Case
■ Proton beam and deuteron thermal
■ Only one mode excited
■ Fast growth (γ~0.13ωcD)
■ Enhanced neutron signal t!cD
Beta=30 % -- SOL (~impact par. of Neutral ParJcle Analyzer)
Velocity space
Thermal plasma
Tes3ng the hypothesis
Use a 1D PIC code (EPOCH)
Accelerated deuterons collide with thermal (or super-thermal) deuterons
Configura3on space
Enhanced increase in neutron produc3on
Dispersion diagram [FFT(Bz)]
Sta3c Uniform Bz field
Beam ring
wave vector - k
Thermonuclear
LEGENDS
Alfven velocity (va)
Shear Alfven velocity (va*cos(θ)) Buchsbaum-whistler (MS)
Alfven Ion Cyclotron (AIC)
• • •
Magnetic • mirror • plug
• •
Fully electromagne3c 1D3V PIC code
Slab model with periodic BC
IniJal value problem (introduce beam at t=0)
Thermal plasma is Maxwellian, op3onal: anisotropy, drie
Beam is set up as a Maxwellian distribu3on, ring or slowing down distribu3on – sampling problem. Anisotropy op3onal.
Beam set up with velocity parallel and perp to B field
Par3cle interac3on via collec3ve effects ONLY
Beam proton ini3al Beam proton final Thermal deuteron ini3al Thermal deuteron final
Experiment - NPA
Simula3on – Beta=30%
Final deuteron Ini3al (Maxwellian) Ini3al
Allowk||<kperp
Broadband
IonBernsteinharmonics
AICmode
Enhancedneutronsignal
Fastgrowth~0.2ωcD
Protonbeamanddeuteronthermal Highphase
t!
cD
B 2 /B02
B 2 /B02
B 2 /B02
Normalized neutron yield
Normalized neutron yield
Normalized neutron yield
E 2 /B02
Normalized neutron yield
Normalized # of par3cles per bin
DistribuJon funcJon
R = 0.5hnei2 (Ti)Vfrc
B field [G]
!/!cD