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Abstract In TAE Technologies’ current experimental device, C-2W (also called “Norman”)\[1\], record breaking, advanced beam-driven field reversed configuration (FRC) plasmas are produced and sustained in steady state utilizing variable energy neutral beams (15-40 keV, total power up to 20 MW), advanced divertors, end bias electrodes, and an active plasma control system. New data on the plasma confinement from the C-2W experiment will be presented and interpreted by an improved fidelity model, focusing on confinement variation as a function of both machine and plasma parameters. Experimental confinement times have been collected from TAE Technologies’ C-2, C-2U and C-2W FRC experiments. Previous work has identified collisionality (1Τ𝜐∗) as a strong predictor of electron heat confinement. The emerging electron energy confinement time appears to be proportional to a positive power of the electron temperature\[2\], which may ultimately enable advanced fuel fusion concepts. \[1\] H. Gota et al., Nucl. Fusion 59, 112009 (2019) \[2\] M.W. Binderbauer et al., AIP Conf. Proc. 1721, 030003 (2016) C-2W Program Goal: Minimize Electron Losses  High expansion divertors and good wall conditioning push towards convective scaling of electron losses  See Hiroshi (poster 123) for the overview and Vladimir (poster 141) for details on divertors  Systematic estimates of power flows are needed  Power flows are estimated with 0D transport code  See Ryan (126) for code details, James (136), Martin (140), and Erik (143) for various power flow terms Ensemble averaging captures trends and ranges Strong Correlation Between Electron Temperature And Confinement Time Transport Scaling Reflects Collisional Processes  The primary heating terms for the electrons are from warm ions (Pie) and fast ions (Pfe) Transport Scaling From C-2 to C-2W Field-Reversed Configuration Experiments Erik Trask, R. Clary, M. Griswold, N. Bolte and the TAE Team TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610   Broad survey of parameter space is necessary for scaling studies  C-2: 9 ensembles from over 200 shots  C-2U: 10 ensembles from over 150 shots  C-2W: ~75 shots in this ensemble Steady improvement seen during progressive experiments  Lifetime and electron temperature show the greatest improvement  Median of the dataset is used for averages 𝑛 𝑇 −𝑇 𝑛 𝑇−𝑇 𝑓 𝑓 𝑒 𝑛 𝑇 −2𝑇 𝑒 𝑡𝑜𝑡 𝑒 𝜏𝑖𝑒 𝑖 𝑖 𝑒 𝑃~ ,𝑃~ ⇒𝑃~ 𝑖𝑒 𝜏𝑖𝑒 𝑓𝑒 𝜏𝑓𝑒 𝜏𝐸,𝑒 ≡ 𝑒 ⇒𝝉𝑬,𝒆~ 𝒆 ~ 𝑖𝑛,𝑒 𝑛𝑉𝑇 𝑻𝟐𝟏 𝑃 𝑒 𝟓 ൗ 𝒏𝑻−𝟐𝑻 𝝂∗ 𝒕𝒐𝒕 𝒆 Parameters C-2 C-2U C-2W Lifetime <>: 3.4 ms <>: 8.3 ms <>: 15-30 ms Trapped PBEAM <>: 1.1 MW Max: ~2 <>: 2.8 MW Max: ~6 <>: 3.3 MW Max: ~7 𝜆𝑀𝐹𝑃 <>: 2.2 m Max: ~5 <>: 3.7 m Max: ~10 <>: 6.6 m Max: ~50 <T –T> tot e <>: 545 eV Max: ~1000 <>: 575 eV Max: ~900 <>: 835 eV Max: ~2500 <T > e <>: 80 eV Max: ~120 <>: 100 eV Max: ~200 <>: 130 eV Max: ~400 What Scaling Might We Have?  Try various scaling models\[3\] incorporating different physics assumptions   𝒑𝒒𝒓𝒔𝑻𝒕𝒖 𝑩𝝉 = 𝑭 𝒏 ,𝑻 ,𝑩 ,𝒂 , 𝒊 ,𝑬 Dimensional constraints 𝑻𝒆 ∗∗  Dimensional constraints link 𝜌 , 𝜈 , and 𝛽 exponents  \[3\] J.W. Connor, J.B. Taylor, Nucl. Fusion 17, (1977) Best fit is for collisional high-beta model Constraintis𝑠=2𝑝+1𝑞+5𝑟andexponentialmodel 24 Summary Discussion  Steady-state plasmas exist for many confinement times  Transport analysis is simplified and more robust when power flows are constant  Plasma is collisionless  Mean free paths (electron) >> characteristic lengths of ~ 1 m  Confinement scaling is limited to the electron channel, since warm / fast ion ratio is not well known  Waiting on CHERS to resolve Ti vs < Ef >  Power balance estimates match experimental values  𝜼𝒆~𝟔 − 𝟕, matching ideal ambipolar confinement ηe ~5-6,  For free-streaming electron losses ηe ~50  Electron losses are primarily convective  Contrast this with operation on C-2 and C-2U, where anomalous losses in excess of classical conduction exceeded convection by a factor of 10 \[4\] Kaye S.M. et al Nucl. Fusion 47 499 (2007) \[5\] Kaye S.M. et al Nucl. Fusion 53 063005 (2013) \[6\] Valovic M. et al Nucl. Fusion 49 075016 (2009)  Convective electron losses achieved in collisionless steady-state regime  𝜂𝐸 ~ 6 − 7 shows that flared fields reduce electron heat losses  Electron confinement times have increased by ~ x10  Peak values exceed 2 ms  Electron scaling explained by simple model of ion heating and mean free path  Hot ions determine discharge evolutions Future Work  Separate fast / warm ion power flows with CHERS diagnostic  Diagnostic neutral beam is being installed now  Include more scaling parameters  Mirror ratio, bias voltage, etc.  Extend to coupled CORE/SOL model Power Law 𝝆∗ 𝝂∗ 𝜷 Ti/Te 𝜿 R2 𝑩𝝉𝐸,𝑒 -1.4 -0.9 0.3 -0.9 0.3 0.81 ST Scaling \[4-6\] \[-3, -2\] \[-1.2, -1.1\] -0.1 - - -  Resolution of open field line effects should improve core estimates