An Interesting Poster to look at from the Tri Alpha Energy Team in California

Effects of Ionization on Beam Parallel Component and Beam-Driven Perpendicular Modes
B. Scott Nicks, A. Necas, T. Tajima, and the TAE Team
TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610
• 𝜔≈Ω𝑖
• Magnetic probes2 (left) in C2U find IB modes, including 𝑛 = 1
• Magnetic spectrogram1 (above) shows strong signal at deuteron cyclotron fundamental
1. Motivation
 Experiments1 indicate beam-driven mode in the vicinityoftheioncyclotronfrequency 𝑛=1 seen at low 𝛽—conditions typically found in C2U FRC scrape-off layer and outbound of separatrix.
 1D PIC simulations with ion beam reproduce ion cyclotron mode for parallel beam/propagation.
 Velocity-space broadening by ionization may create population of beam ions with increased parallel velocity component.
 This work explores the effect of ionization of a neutral beam on perpendicular beam-driven modes and the creation of more strongly parallel beam ions in a uniform magnetic field.
Regimes 1D PIC Beam-Driven Modes
3. 1D Verification of Ionization Model
𝑣𝜎𝑣=
𝑒 𝑒 𝜋 𝑣3 𝑒 𝑒 2𝑣 𝑒
2. Setup
Ions Electrons
Beam Ions
Beam Neutrals
Velocity Effects
• Tail of fast background ions produced from beam-driven wave interaction
• Electrons warmed from collisions during ionization
• Ionization broadens beam ion distribution in both perp. and parallel directions, mitigating micro-instability growth
4. 2D Simulation Results
Parallel: Right-handed Alfven mode dominates with peak at ion cyclotron fundamental
Perpendicular: Harmonics of beam ion-Bernstein modes and excitation of shear Alfven dominate
 Geometry reduced to 1D and neutral beam injected at edge of domain, directed along 𝑥 axis
 Periodic boundary conditions
 Same boosted ionization model as 2D setup with no
charge exchange
 Penetration of neutrals shows good agreement with
theoretical mean free path 𝜆𝑚𝑑𝑝 derived from assumption
that 𝑣𝑏 ≪ 𝑣𝑇𝑒.
𝜆𝑚𝑓𝑝 = 𝑣𝑏
𝑛 𝑣𝜎𝑣
12𝑒𝑒𝑒2 21∞ 1𝑣
𝑣3𝜎𝑣exp− 𝑒 𝑑𝑣 𝑒0 𝑇𝑒
Ionization verification
• The functional form of the cross section is taken from NIST (right), and boosted by a factor of 50.
• The simulated mean free path agrees well with the calculated value above through
𝑥 𝜆𝑚𝑓𝑝 = 5.
Field Effects
• Proton ion-Bernstein modes of beam excited, roughly consistent with 1D dispersion, and leads to ion heating.
• Low-frequency activity seen in 𝐵 , which is consistent with shear 𝑦
Alfven mode seen in 1D.
• Growth rate of mode is much slower than in 1D case, where mode
saturates at 𝑡~2𝜏𝑖, because of velocity broadening.
6. Summary and Continuing Work
• Beam-driven modes from 1D PIC simulations with Maxwellian beams motivate moving to 2D PIC geometry. Currently, only simulation of perpendicular plane is possible.
• Perpendicular modes seen in 1D are reproduced in 2D, but ionization of neutral beam introduces a significant broadening (slow- down) in beam distribution, mitigating these modes.
• Ionization also introduces population of beam ions with enhanced parallel velocity, which could possibly account for observed 𝑛 = 1 mode through a parallel-propagating fast Alfven wave.
• The next step: inject beam in similar manner into 2D C2U-like FRC.
 Implicit PIC code LSP
 Ambient magnetic field 𝐵0 ∥ 𝑧
 2D simulation domain: 𝑥, 𝑦 plane
 Conducting boundaries; impacting particles lost
 Uniform background: electrons, deuterium plasma
 Probe measures time evolution of fields in beam
ring
 Neutral hydrogen beam injected with local density
of 10% of background electron density 𝑛𝑒 Beamhas𝑣⊥ and𝑣∥;𝜌𝑏 =22cm≈10𝜌𝑖
 Charge-exchange not included; ionization 𝜎
𝐵0
Plasma Parameters
Field Probe
multiplied by 50 to approximately compensate
𝑩𝟎
𝑻𝒊,𝒆
𝑻𝒃
𝜽𝒃
𝜷
5. Experimental Results1,2
7. References
0.075 T
200 eV
0eV
𝑬𝒃
15 keV
𝒏𝒆
7E18 m−3
70∘
10%
1. R. Magee, “Collective Phenomena in the Advanced, Beam-Driven FRC”, IAEA, 2017 2. T. Roche, “Edge/SOL Plasma Parameter/Magnetic Field Profile and Fluctuation
Measurements at C2U Midplane”, poster, APS DPP 2016
Field FFT Velocity Space