An Interesting Poster to look at from the Tri Alpha Energy Team in California
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1,2,* 1 1 1 1
Manjit Kaur , Peter Yushmanov , Vladimir Sokolov , Kan Zhai , James Sweeney and TAE Team
1TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610, 2University of California Irvine, Irvine, CA 92697 *
In TAE Technologies’ current experimental device, C-2W (also called β€œNorman”) [1], record-breaking,
advanced beam-driven field reversed configuration (FRC) plasmas are produced. FRCs are sustained
in the central confinement vessel (CV) in the steady state utilizing variable energy neutral beams,
advanced divertors, end bias electrodes, and an active plasma control system. In this presentation, we
study the effect of end electrode bias both under steady-state and transient conditions on the e-
temperature (𝑇 ) measured using a Thomson scattering diagnostic in the mid-plane of CV. The steady- 𝑒
state analysis allows distinguishing between the effects of bias voltage versus current. Dynamic bias allows measuring 𝑇 rise/decay rates and thus makes it possible to analyze the effect of bias on e-
confinement. The effectiveness of biasing – fraction of current and voltage delivered to CV – is
analyzed using a single-sided bias where electrodes on the opposite end act as floating electrostatic
probes. A strong correlation of 𝑇 with the bias is observed, which might be an indication of e- heating
by the applied bias.
[1] H. Gota et al., Nucl. Fusion 59, 112009 (2019).
οƒ˜ A common assumption about electron heating in mirror devices with NB heating is that electrons are heated by accumulated fast ions as fast ions mostly transfer energy to electrons.
οƒ˜ We have experimentally observed a strong correlation between biasing and 𝑻𝒆, which may suggest that our understanding of electron heating by fast ions alone is incomplete.
οƒ˜ Electrode biasing is a high power source (a few MW in C-2W), which may play many roles in plasma discharges:
οƒ˜ Does biasing cause an improvement in electron confinement or heating?
οƒ˜ If it is electron heating, then is it through
οƒ˜ effect of bias on fast ions?
οƒ˜ heating by bias-induced plasma rotation? οƒ˜ direct bias heating (voltage or current)?
A. Coulomb heating from ions: Heating from fast and warm ions.
(𝑻𝒇𝒂𝒔𝒕 βˆ’π‘»π’†) 𝝉𝒇𝒂𝒔𝒕,𝒆
(𝑻 βˆ’πŸπ‘» ) 𝑻 π‘·π’Š,𝒆~ 𝒕𝒐𝒕 𝒆 ~ 𝒆
π‰π’Šπ’† 𝝉𝑬𝒆
  (𝑻 βˆ’π‘» )
π‘·π’Šπ’•π’‰,𝒆~ π’Š 𝒆 ,π‘·π’Šπ’‡π’‚π’”π’•,𝒆~ π‰π’Šπ’†
  Thermal ion heating
Fast ion heating
Total heating due to ions For details, see poster by Erik Trask, UP10.00125
B. Rotational heating:
οƒ˜ Biasing drives plasma rotation via 𝑱 Γ— 𝑩 force which is balanced by azimuthal friction. This friction may lead to plasma heating (plasma rotation is an indication of a radial electric field) – β€œperpendicular resistive heating”.
οƒ˜ Azimuthal friction between ions and electrons leads to Ohmic heating of electrons.
Can biasing directly affect electrons? C. Electrostatic heating:
Secondary electrons from electrode surface may gain high energy in the Debye sheath and equilibrate with thermal electrons.
    D. Improved electron confinement:
𝝏𝑻𝒆 𝝏𝒕
οƒ˜ Increase in 𝑽 may act as a deeper potential well for e-, π‘©π’Šπ’‚π’”
hence, better confinement.
Both above effects should be visible in 𝑻𝒆 at a fast time scale.
Which one of the above mechanisms is responsible for observed rise in 𝑻𝒆?
 𝝏𝑬𝒕𝒉,𝒆 𝝏𝒕
π‘·π‘―π’†π’‚π’•π’Šπ’π’ˆ 𝒏𝒆
𝑻𝒆 𝝉𝑬𝒆
οƒ˜ Increase in 𝑻𝒆 may be due to increase in π‘·π‘―π’†π’‚π’•π’Šπ’π’ˆ or reduction
= π‘·π‘―π’†π’‚π’•π’Šπ’π’ˆ βˆ’ 𝑷𝒍𝒐𝒔𝒔 ֜ in 𝑷𝒍𝒐𝒔𝒔 (i.e., improvement in 𝝉𝑬𝒆).
𝑇 𝑒
 A fast increase in
π‘½π‘©π’Šπ’‚π’”, βˆ†π‘· β‰ˆ πŸ‘π‘΄π‘Ύ
𝑻𝒆 increased from ~180 to ~280 eV, Heating power β‰ˆ 𝟎.πŸ’π‘΄π‘Ύ
Flat density
Flat 𝑻𝒕𝒐𝒕 No change in
Size of plasma stays same for > πŸπŸŽπ’Žπ’”
Faster rise in diamagnetic energy
  οƒ˜ Fast increase in π‘½π‘©π’Šπ’‚π’” results in a fast rise in 𝑻𝒆.
οƒ˜ Observed change in heating power is β‰ˆ 𝟏𝟎% of applied βˆ†π‘·π‘©π’Šπ’‚π’”.
οƒ˜ Direct Indication of non-ion-induced heating.
οƒ˜ Total temperature and ion rotation remain same.
οƒΌ NB-driven FRC plasmas stay in a steady-state for long time and allow a thorough study of electron heating mechanisms.
οƒΌ Core plasma 𝑻𝒆 shows a strong correlation with π‘½π‘©π’Šπ’‚π’” in the steady- states.
οƒΌ In dynamic studies, a fast ramp in π‘½π‘©π’Šπ’‚π’” is accompanied by a fast rise in γ€ˆπ‘»π’†γ€‰, whereas 𝑻𝒕𝒐𝒕 , π‘°π‘©π’Šπ’‚π’” and πŽπ’“π’π’•,π’Š remain same. This indicates that π‘½π‘©π’Šπ’‚π’” is directly affecting γ€ˆπ‘»π’†γ€‰.
οƒΌ Improvement in γ€ˆπ‘»π’†γ€‰ with π‘½π‘©π’Šπ’‚π’” may be a combined effect of additional heating and improved electron confinement.
Future Plans:
οƒ˜ Design & perform experiments to distinguish the effect of bias voltage – Heating versus Improvement in confinement?
Thomson scattering diagnostics
 In the C-2W[1] device, we generate field-reversed configuration (FRC) plasma and heat it with 8 neutral beams at two axial locations in the confinement vessel (CV). Edge biasing is applied to stabilize the highβˆ’πœ· plasma.
 The core FRC is surrounded by scrape-off-layer (SOL) & plasma edge (halo plasma).
 Open magnetic field lines allow SOL exhaust to be collected outside CV on the divertor electrodes.
 The halo plasma does not make it through mirror region and terminates on CV wall
 Thomson scattering diagnostic in the CV at 16 radial locations in the mid plane. Temporal resolution of 𝟏 π’Œπ‘―π’› for 30 pulses + 6 pulses at πŸπŸ‘ π’Œπ‘―π’›. Capable of measuringdensity:𝟏𝟎𝟏𝟐 βˆ’πŸπŸŽπŸπŸ’π’„π’Žβˆ’πŸ‘,𝑻𝒆:πŸπŸŽπ’†π‘½βˆ’πŸπ’Œπ’†π‘½.
 Thomson scattering diagnostic at 5 radial locations in the open field region (jet region). Temporal resolution of 𝟏𝟎𝟎 𝑯𝒛.
o Clear increase in γ€ˆπ‘»π’†γ€‰ in the confinement vessel (& jet region) with an increase in the edge biasing voltage (π‘½π‘©π’Šπ’‚π’”).
o Increase in electrode/biasing current (π‘°π‘©π’Šπ’‚π’”) does not lead to an increase in γ€ˆπ‘»π’†γ€‰.
o No clear change in γ€ˆπ‘»π’†γ€‰ with π‘·π‘©π’Šπ’‚π’”.
Strong correlation of γ€ˆπ‘»π’†γ€‰ with π‘½π‘©π’Šπ’‚π’” but not with π‘·π‘©π’Šπ’‚π’”. Does it indicate improvement in confinement?
οƒ˜ Determine time intervals (β‰₯ πŸ’. πŸ“ π’Žπ’”) with constant (within 𝟏𝟎%):
οƒ˜ 𝑹𝒔 (> 𝟐𝟎 π’„π’Ž)
οƒ˜ Elongation
οƒ˜ Thermal energy
οƒ˜ Determine average plasma parameters (inside 𝑹𝒔) for these time intervals.
οƒ˜ Identified ~300 steady state events, πŸ’. πŸ“ βˆ’ πŸπŸ– π’Žπ’” long