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Observation and Suppression of a New Fast Ion Driven Micro-Burst Instability in a Field-Reversed Configuration Plasma
B.H. Deng1, E. BELOVA2, M. BEALL1, M. BINDERBAUER1, R. CLARY1, S. DETRICK1, J. DOUGLASS1, E. GARATE1, H. GOTA1, E. GRANSTEDT1, S. KOREPANOV1, R. MAGEE1, A. NECAS1, S. PUTVINSKI1, T. ROCHE1, A. SMIRNOV1, T. TAJIMA1, M. THOMPSON1, M. TUSZEWSKI1, A. VAN DRIE1, and the TAE Team
1. TRI ALPHA ENERGY, INC., P.O. Box 7010, Rancho Santa Margarita, CA 92688-7010; 2. Princeton Plasma Physics Laboratory, Princeton, NJ 08543
Abstract
Analyzing the Bursting Chirps
Micro Burst Mode Structure
Good Confinement Required for Micro Bursts
Theory and Simulation of Beam-Plasma Effects
 Early theory based on general energy principle [5] predicts that modes with phase velocity parallel to the ion ring current are destabilized resonantly – but has not been observed before.
 Recently, the importance of radial resonances in the small S*, kinetic FRCs has been demonstrated in [2], where the resonance condition is derived
analytically:
where W is the beam particle toroidal frequency, n is the mode number, w
nWw wr
is the mode frequency, and wr is the particle radial bounce frequency.
 The beam plasma resonance is verified by 3D hybrid simulations using the HYM code [2].
The C-2U experiment offers a unique plasma environment combining a high beta field reversed configuration (FRC) embedded in a low beta magnetic mirror with high power neutral beam injection. The beams are injected tangentially into a modest magnetic field so that the orbits of the resulting fast ions encircle the entire plasma. The dominant population of large orbit fast ions sustains and stabilizes the FRC, suppresses turbulence, and makes a dramatic beneficial impact on the overall plasma performance [1]. Abundant interesting new physics phenomena are observed in this high performance FRC operation regime, including micro bursts, which are benign, periodic bursting small amplitude down chirping fluctuations seen by several diagnostics. Detailed analysis of the micro bursts measurement data, bulk plasma equilibrium profiles, and fast ion orbit characteristics show that the micro bursts might be driven by a small number of resonant fast ions [2], and can be suppressed when the number of resonant particles is reduced.
 Modeling in C-2 reveals phase and amplitude profile characteristics of rigid rotating n=2 deformation
 Bursting chirps have similar phase and amplitude profile characteristics, suggesting the n=2 mode nature
 Data from bolometer arrays with 90° physical separation show 180° phasen=2 mode nature
Dj=0
Dj=
 0 and 15 cm chordin phase
 0 and 30 cm chord180° out of
phase
 SOL plasma (45 cm)detached
 Amplitude minimum at 15 cm
Bolometer Array Signals (a.u.)
 Growing/decaying sinusoidal oscillation before/after peak with decreasing (down- chirping) frequency
dneg(ttc)cos(2(f f(tt))(tt)j)
dn{0 c r c c 0 ,t<=tc
dneb(ttc)cos(2(ff(tt))(tt)j) ,t>tc 0 cracc0
dn0 – peak amplitude tc – peak time
fc – center frequency g – growth rate
b – decay rate after tc fr – chirp rate
fra – chirp rate after tc j0 – phase at tc
 Chirplet model fits data well
tc
 Variation of the chirp center frequency (fc) at peak amplitude consistent with evolution of equilibrium plasma rotation
 Higher burst amplitude with higher growth rate (g)
 Higher burst amplitude, faster frequency down chirping when t < tc, while the linear correlation is lost in the decaying phase when t > tc
t < tc
t < tc
 Higher external DC field (B0)more frequent bursts, earlier onset
 Lower beam energy (Eb)  more frequent bursts, higher amplitude, earlier onset
 Burst peak amplitude grows in fast ion slowing- down time scale (t~3 ms)
dn(ne ne)dl
 Both shots 45886 and 45887 have the same plasma discharge settings and NBI conditions. A bad shot (45887) with poor confinement does not show micro burst activity.
 Counting the total step drops when rDF changes from 35 to 20 cm, the best FRC discharges with > 10 ms lifetime have the most micro burst activity.
 Micro bursts depend sensitively on injection beam energy, maybe peaking near 12 keV.
Best (>10 ms) FRC Good (~ 7 ms) FRC
General Characteristics
Comparing the Observation and Theory
Circular orbit of 12.5 keV proton
B djbxB
 Fast ion orbit matches micro burst mode structure, i.e., n=2
 The Lorentz force due to perturbed fast ion current, djbxB, reinforces the elliptical
deformation destabilize the n=2 mode
 Observed micro burst frequency range (50-150 kHz, shaded) matches the fast ion orbit
precession frequency rangeconsistent with the theoretical resonance condition
 During the growing phase the mode frequency is higher than diamagnetic drift frequency
 inverse Landau damping drive mechanism in the angular momentum space
 Particles with Eb<=7 keV not in resonance with micro bursts  consistent with
microburst-free operation data
 High energy (20 keV) particles have high orbit rotation frequency when the ellipticity (e) is significant, less likely to resonate with mode; at resonant frequency range the ellipticity is close to 1, i.e., more circular  High energy particles are less destabilizing micro bursts not evident in C-2
 Energy near 12 keVbest matching the resonance conditionmost unstable
 Remaining questions:
 How does down chirping occur?
 How do fast ions get lost in the bursts?  Why is the burst amplitude small?
 References:
[1] M. Binderbauer et al., Physics of Plasmas, 22, 056110 (2015). [2] E.V. Belova, Bull. of Am. Phys. Soc., 58, p. 128, GP8 54 (2013). [3] M. Tuszewski et al., Phys. Rev. Lett., 108, 255008 (2012).
[4] M. Thompson et al., Rev. Sci. Instrum., 83, 10D709 (2012).
[5] J.M. Finn and R.N. Sudan, Phys. Fluids, 22, 1148 (1979).
 Rotational n=2 instability suppressed by plasma gun edge biasing and neutral beam injection, leading to high performance FRC [3]
 Periodic micro-bursts observed with FIR interferometer and other diagnostics
 Burst amplitude scales linearly with step drop in rDF [4]
drDF dn0
 Strong frequency down-chirping FIR nedl Power spectrogram
Microburst – Free Operation
 For the same plasma discharge settings and Bext, micro bursts are not observed with 8 keV NBI.
 Smaller beam power is not the cause of microburst-free operation because (1). the plasma lifetime is about the same, and (2). The data above shows that higher beam power at 15 keV injection can lead to less micro burst activity than 12.5 keV injection.
 Theoretical analysis shows that 8 keV beam particles are not in resonance with the plasma.
Equilibrium Profile Peaking at Bursts
 Fast ion loss at burstsbulk plasma compressed to make up for the fast ion pressure lossplasma density increases after bursts, as measured by the CO2 and FIR interferometers:
C-2U Plasmas are Kinetic
58th Annual Meeting of the APS Division of Plasma Physics, October 31 – November 4, 2016 · San Jose, California
 C-2U bulk plasmas are kinetic with small S*:
S*r /d ~7 DF pi
19 3 r ~0.35mn~210m
DF i
dpi c/wpi ~0.05m


































































































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