Fast ion physics in the C-2U advanced, beam-driven FRC Richard Magee for the TAE Team 216 US-Japan Workshop on the Compact Torus August 23, 216!
High β FRC embedded in magnetic mirror is a unique fast ion environment! Tangential NBI + low B field! Ø large, machine sized orbits! High NB power + compact plasma! Ø high NB power density! Device Class NBI (MW/m 3 ) ρ/a ITER tokamak.4.5 DIII-D tokamak 1.4.3 2XIIB mirror machine 5.7 C-2U FRC 1 1 GDT mirror machine 3 1.5 2
τ (ms) 12 2 4 6 8 Dominant fast ion collisional process differs inside and outside separatrix 1 8 6 4 2 2 4 6 8 1 12 τ se τ cx τ total 2 4 6 8 r (cm) In FRC, τ se < τ cx è slowing down distribution! In SOL, τ se > τ cx è df/dv > è beam-driven modes! Fast ions sample both regions of plasma! 3
Outline n Experimental evidence of classical fast ion confinement n Experimental evidence of beam-driven modes n Interpretation 4
Outline n Experimental evidence of classical fast ion confinement n Experimental evidence of beam-driven modes n Interpretation 5
NBI sustains the FRC plasma M.W. Binderbauer et. al., AIP Conference Proceedings 1721, 33 (216) FRC lifetime well correlated with NB pulse length! Clear evidence of fast ion accumulation! 6
Fast ion lifetime is near classical limit Phys. Plasmas 22, 5611 (215) measured lifetime (ms) 5 4 3 2 1 1 2 3 4 5 classical slowing down time (ms) Fast ion lifetime inferred from decay in neutron rate after beam termination! Fast ion lifetime classical slowing down time for a range of plasma conditions 7
NBI reduces broadband magnetic turbulence spectral power (G 2 ) 1-5 1-6 MW 3 MW 9 MW ~ b 2 4 6 8 1 f (khz) n n Broadband fluctuations decrease with NB power! Plasma stabilization! Ø Resonant peak in spectrum increases with NB power! Beam-driven mode! Ø! 8
Outline n Experimental evidence of classical fast ion confinement n Experimental evidence of beam-driven modes n Interpretation 9
Strong enhancement in neutron production correlated with beam-driven mode spectral power (G 2 ) 1-5 1-6 MW 3 MW 9 MW ~ b 2 4 6 8 1 f (khz) neutron rate (s -1 ) 1 1 1 9 1 8 measured thermonuclear MW 18 19 neutronrate(s-1) 11 measured thermonuclear 3 MW 18 19 neutronrate(s-1) 11 measured thermonuclear 9 MW 1 2 3 4 t (ms) 1 2 3 4 t (ms) 1 2 3 4 t (ms) 1
Strong enhancement in neutron production correlated with beam-driven mode neutron rate (s -1 ) 1 1 1 9 1 8 measured thermonuclear MW 18 19 neutronrate(s-1) 11 measured thermonuclear 3 MW 18 19 neutronrate(s-1) 11 measured thermonuclear 9 MW 1 2 3 4 t (ms) 1 2 3 4 t (ms) 1 2 3 4 t (ms) Pure H beams into D plasma è no beam-target emission! Neutron production timescale < collisional timescale! What is the source of fusion rate enhancement?! 11
E B Neutral Particle Analyzer can make mass resolved fast ion measurement Formerly installed on TFTR! Mass discrimination! High energy resolution (39 ch. / species)! Adjustable energy range (.5-4 kev)! Courtesy: Ryan Clary 12
NPA shows high energy deuterium tail develop at t~1 ms 1 2 t (ms) 3 4 5 1 2 t (ms) 3 4 5 1 2 t (ms) 3 4 5 Pure HNBI results in fast hydrogen accumulation and slowing down! High energy deuterons (E~12 kev) appear at t~1 ms! NPA measurement from single line of sight at r=49 cm, whereas neutron signal is global! energy (kev) r φ (cm) 4 3 2 1 15 1 5 hydrogen 5 4 3 2 1-1 signal (a.u.) How does deuterium tail affect calculated neutron rate?!! energy (kev) 15 1 5 1. deuterium plasma ion energizagon 5 4 3 2 1-1 signal (a.u.) 13
! 1 2 t (ms ) 3 4 5 High energy deuterium population consistent with neutron measurement Integrate f(e) from NPA with σv, scale to measured neutron rate!! Excellent time history agreement! First observation of ion energization by a beam-driven mode in a magnetic fusion energy device! energy (kev) neutrons (a.u.) 15 1 5 1..8.6.4 deuterium measured calculated.2. 1 2 3 4 5 t (ms) Magee, Necas, Tajima, et. al., Enhanced fusion reactivity in the beam-driven FRC, Nature Physics (in preparation) 14
Outline n Experimental evidence of classical fast ion confinement n Experimental evidence of beam-driven modes n Interpretation 15
Experiment with staggered beam energies shows velocity gradient is free energy source Two cases with equal total injected power (6.8 MW) are compared!.4 P = 6.8 MW peaked all beam energies the same! flat beam energies staggered! f(v).3.2.1 peaked flat Free energy source (df/dv) reduced in the flat case.!!...5 1. 1.5 2. velocity (1 6 m/s) 16
Staggering beam energies reduces fluctuations and fusion rate Strong evidence for velocity space instability! What does theory predict?!! 17
Particle-in-cell simulation shows much stronger mode activity in SOL than in core EPOCH code used to analysis beam-plasma interaction in a simplified geometry! In the core plasma, the AIC mode has the largest growth rate! In the SOL plasma, the Ion Bernstein mode appears at multiple harmonics of the cyclotron frequency!! 18
Ion Bernstein modes create high energy tail that increases neutron rate 3x The code reproduces the tail on the plasma ion velocity distribution and the enhanced neutron production.! f(v) 1 1-1 1-2 1-3 t = µs t = 8 µs Code is an initial value problem, so the mode saturates very quickly.! See talk by A. Necas Wed. afternoon.! fusion enhancement factor 1-4 4 3 2 1..5 1. 1.5 v (1 6 m/s) 5 1 15 t (µs) 19
12 2 4 6 8 1 8 6 4 2 Putting it all together Source of free energy is velocity space gradients (staggered beam energy experiments)! y (cm) 5 15 kev 5 kev -5 Optimal plasma conditions to support beam-driven mode are in the SOL (PIC simulation)! Are there velocity gradients in the SOL? Look to 1D Fokker- Planck solver! τ (ms) 12 1 8 6 4 2-5 5 x (cm) τ se τ cx τ total 2 4 6 8 r (cm) 2
Charge exchange creates df/dv> in SOL plasma 1.2 f (v) (normalized) 1..8.6.4.2 n =1 15 m -3 (core) n =1 16 m -3 (SOL)...5 1. 1.5 2. v (1 6 m/s) Source of free energy and optimal plasma conditions to support the mode are both largest in SOL! Beam-driven mode in SOL does not destroy the plasma because v beam >>v T,i 21
Summary n Beam-driven mode accelerates plasma ions and enhances fusion rate, but does not destroy the plasma n Fast ions sample two distinct plasma regions: n FRC τ se < τ cx è slowing down distribution n SOL τ se > τ cx è df/dv > è beam-driven modes n Fast ion free energy is larger in SOL where beam-driven modes are supported Email: rmagee@trialphaenergy.com 22
Thank you!