An Interesting Poster to look at from the Tri Alpha Energy Team in California
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                                                                                                                        Fusion Enhancement from Bunched Ion Beams
B. Scott Nicks, A. Necas, T. Tajima, and the TAE Team
TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610
         1. Motivation
 Experiments1 indicate non-destructive ion cyclotron mode in C-2U, likely in scrape-off-layer (SOL) of FRC
 Anomalous neutron rate observed, exceeding predicted thermonuclear value by > 102
 Beam-driven ion-Bernstein mode seen theoretically, exhibits wakefield character that creates similar large fast ion tail and fusion enhancement
 If beams are seeded with density modulations at the wavelength of the dominant mode, fusion enhancement is further improved
3. Beam-Driven Ion-Bernstein Wakefield
4. Beam-Driven Ion-Bernstein Wakefield
 Ion Phase Space and Wakefield
Reactivity Scaling with Beam Velocity
            Beam-driven ion-Bernstein modes at beam cyclotron harmonics along Alfven speed, shifted by beam resonance condition: 𝜔 = 𝑘∥𝑣𝑏∥ + 𝑛Ω𝑏
 Manifests as wakefield, saturation at Tajima-
 11 10
10 10
109 108 107
Fusion Rate2
≈ 300
    Dawson field:
𝑚 𝜔𝑣 𝑣
  𝐸 = 𝑖 𝜙=𝑛𝐵 𝐴 𝑇𝐷 𝑞𝑖 0𝑐
   Wake peaks accelerate ions to phase velocity, execute cyclotron motion
 Large increase in D-D reactivity: > 𝟏𝟎𝟒 over thermonuclear
 Creates beam/ion density fluctuations
  −2 0 2 4 6 8 𝑡 (ms)
2. Scan of Ion-Cyclotron Modes
 Implicit PIC code LSP (1-2/2D)3
 Uniform 𝐵0 ∥ 𝑧Ƹ, SOL background (electrons, deuterium)
 Propagation angle 𝜃𝑘, beam injection angle 𝜃𝑏, relative to 𝐵0.  𝜽𝒌 = 𝟖𝟓∘, 𝜽𝒃 = 𝟕𝟓∘ best for fusion enhancement
𝒛ො
𝒚ෝ
𝑣Ԧ𝑏
𝜃𝑘
 Boron-11 plasma rather than deuterium
 Reduction in Alfven speed  proportional reduction in saturation
 Boosting of ion plasma frequency creates preference for continuum mode
 Low-frequency component adds secondary length scale
Ion Phase Space and Wakefield (B11)
5. Beam-Driven Boron-11 Wakefield
1.E+09
1.E+06
1.E+03
             1.E+00
4 8 16 32 64 128
No bunching
Beam density modulation (Bunching)
𝝀𝒃 = 𝟐𝝅𝒗𝑨Τ𝒏𝛀𝒊
v Τ/ v 𝒗𝒗
         2𝑛𝑏0 0
b𝒃 𝑻th𝒊i
n𝑛2=bu2nbcuhnincgh n𝑛1=bu1nbcuhnincgh C-2U
Density Fluctuations and Wakefield
𝑥/𝜆, 𝜆 = 2𝜋𝑣 /2Ω 𝐴𝑖
        Bunching at wavelength of dominant mode
 Scan over beam energies with bunching
𝟓.𝟔
    𝜆=2𝜋𝑣 ΤΩ and𝜆=2𝜋𝑣 Τ2Ω andnobunching
    𝐴𝑖𝐴𝑖
 Fusion enhancement scaling: 𝑭 ∝ 𝒗𝒃Τ𝒗𝑻𝒊
          For 𝑣𝑏Τ𝑣𝑇𝑖 < 32, enhancement improved
 For 𝑣𝑏Τ𝑣𝑇𝑖 > 32, bunching converges to non- bunched case, and dispersion relation moves
away from IB modes
 C-2U result broadly falls along power law
     ≈ 4𝜆
References
1. R. Magee, “Collective Phenomena in the Advanced, Beam- Driven FRC”, IAEA, 2017
2. R. M. Magee, TAE
3. D. R. Welch, D. V. Rose, B. V. Oliver, and R. E.
  𝒌 ∥ 𝒙ෝ
Clark, Nucl. Inst. Meth. Phys. Res. A 464, 134 (2001).
         Rate (s-1)
Fusion Enhancement
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