An Interesting Poster to look at from the Tri Alpha Energy Team in California
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                                                                                                                       Formation And Translation Experiments On The C-2W Experiment
Erik Trask1, H. Gota1, P. Yushmanov1, Y. Mok1, E. A. Baltz2, W. D. Heavlin2, and TAE/Google Team1,2
1TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610; 2Google LLC, 1600 Amphitheatre Parkway, Mountain View, CA 94043
        Abstract
Increased stored energy, improved pulsed power reliability, and dynamic control of magnetic fields have allowed creation of FRC targets with improved characteristics. Parameters achieved so far include relative velocities of over 1000 km/s, trapped flux of over 15 milliwebers, and diamagnetic energy of over 10 kilojoules. Translation characteristics have been scanned over wide ranges of magnetic fields, including passage through mirror fields of over 0.7 Tesla. A review of achieved initial conditions and experimental observations will be presented.
Goal: Create Plasma Target For Advanced Beam- Driven FRC
 Optimal targets are as close to fusion conditions as possible
 Creation of high temperature, high flux plasma requires careful
optimization of dynamic formation process
 FRCs cannot be created by beams alone
 Separation of confinement/heating region from the formation
sections complicates
 Creation and equilibrium requirements have opposite dependencies  i.e. Good translation = Straight fields = No mirror confinement
 Optimization is necessary to balance tradeoffs
Machine Upgrades Enhance Capabilities
 C-2W: Increased power and speed
 Higher voltages and increased beam
power allow increased initial conditions and greater heating inputs
 C-2W: More control points
 Individual control of charging voltages
and timings for pulsed power
 Current waveforms allow fine tailoring of magnetic field topologies
Experimental Methodology For Optimization
 Reduce dimensions by creating meta-parameters (MPs)
 MPs are low order groupings (moments) of variables that are
physically relevant
 Run experiments at appropriate precision
 Designed mapping experiments optimally fit low order polynomials
 Explore parameter space constantly by controlled randomization OptometristAlgorithm:[1] MCMCwalksthroughparameterspace
paired with human choice
 ‘Dithering’ experiments: Pair small changes in ‘unimportant’ variables with large step experiments
Dynamic Formation: Creation Of FRC
 ‘Snowplow’ formation both traps flux and accelerates plasma
 Variation of timing and voltages optimize FRC parameters
 Target must have sufficient kinetic energy to climb up mirror ‘hill’
Translation Requires Optimization
 Deformable magnetic ‘pipe’ guides plasma to the confinement vessel
 ‘Bumpy’ fields induce losses as the plasma changes size
 Target must have sufficient kinetic energy to climb up mirror ‘hill’
Merging Process Couples Competing Requirements
 Field magnitude and shape set FRC size and control merging process
 Pressure balance and FRC energy set radius
 Curvature at the midplane affects elongation and reconnection scale
Experiment: Characterize C-2W Formation Section
 Operate with ‘straight’ B fields, scan over 4 meta-parameters  Control of ramp times optimizes energy
 Meta-parameter example
 Timing of pulsed power linked by initial ‘velocity and ‘acceleration’
 Deep reversed fields maximize energy
Experiment: Find Ranges Of B For Translation
C-2W: Translation Velocity Scales As Expected
 Kinetic energy per particle is higher on C-2W
 Set by formation timings 550
450 350
250  Velocity scales with stored energy
150  Higher voltage, faster C-2U C-2W dynamics
C-2W: Larger Energy Target Achieved After Collision
               Meta-Parameters
  Voltage: Axial Average
  Voltage: Axial Gradient
  Timing: ‘Acceleration’
  Timing: ‘Velocity’
           Thermal energy can be double that of C-2U
    Scan field strength in inner divertor
 Wall contact cools and slows down FRC
 B > 0.5 kG is sufficient for translation

12 10 8 6 4 2 0
Allows broad range of initial conditions
C-2U C-2W
 C-2W is more efficient  Accounting for more
energy, more can still be delivered
        C-2W vs C-2U
Stored Energy
~ Doubled
Formation Knobs
16x
Diagnostics
8x
Magnetic Structure
Time varying
Field Supplies
8x
        Meta-Parameters
  Minimum Field
  Mirror Bumpiness
  Magnetic Field Timings
  Peak Mirror Field
     Excessive mirror fields reflect FRC
 Tradeoff between confinement and initial energy
 Good translation for B < 6 kG
C-2W: Higher Flux Shortens Steps To Ramp Up
     Reflection
No Reflection
 Poloidal flux is up to 75% higher than C-2U
 Allows broad range of initial conditions
15 10 5 0
C-2U C-2W
Summary: Improved System, Better Performance
 Higher velocity, energy, flux can be delivered
 Translation through inner divertor into high mirror ratio of confinement is possible
    Experiment: Match C-2U Machine Settings
 Cross-machine comparison by matching:
 Same Settings, Same Initial Conditions
 More efficient flux trapping
 Likely due to improved ionization system (RMF) and higher pulsed power voltages
           Equilibrium Field Profile
  Theta-pinch (MR) Voltage
  MR Energy
  MR Timing
  Gas Inventory
 Results
C-2U
Shot 43833
C-2W
Shot 104878
Poloidal flux 𝜙P
3.8 mWb
1.9 mWb
Thermal energy Eth
2.4 kJ
2.7 kJ
# of particles NP
2x1019
2.2x1019
Temperature Ttot
0.5 keV
0.5 keV
       Meta-Parameters
  Mirror Ratio
  Average Field Strength
  Field Curvature
  FRC Energy
  FRC Trapped Flux
     Experiment efficiently by ‘scripting’ shots
 Preplanned experimental runs increase efficiency
[1] E. Baltz, E. Trask, M. Binderbauer, M. Dikovsky, H. Gota, R. Mendoza, J. Platt, and P. Riley, Scientific Reports 7, 6425 (2017).
Poloidal Flux (mWb)
Energy After Collision (kJ) Initial Velocity (km/s)
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