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022503-7 Steinhauer, Berk, and TAE Team
vn approaches the classical rate, and sjj is consistent with empty-loss-cone mirror scaling, both of which are superior to traditional FRCs. If the trend toward classical and mirror- like rates can be sustained, then the temperature scaling of particle confinement is with the square of the temperature.
The uniqueness of the FRC as a magnetic confinement system presents both advantages and challenges. Among the challenges is a property of purely poloidal magnetic systems: even a tiny field perturbation “opens up” all interior mag- netic surfaces.26 This can have a major effect on processes regulated by electron physics because of their high mobility along field lines. The consequent electrical “shorting” influ- ences and may dominate interior plasma rotation.26,27 Further, field-line opening accentuates electron thermal transport across “average” magnetic surfaces hwi 1⁄4 const. Both effects greatly broaden the surface-to-surface “reach” of electron physics. On the other hand, particle diffusion (rel- ative to average surfaces) arises locally because of electron- ion friction. Weak fluctuating fields may play a role in increasing the friction, but the method used here (Sec. II) directly infers the effective resistivity. Indeed, it may be comparable to the base-level classical rate.
An advantage of the FRC system is the degree to which reduced end loss (of particles) can have a strong favorable effect on overall confinement. Evidence presented here indi- cates end-confinement times sjj within a factor of 1/3 to 1/2 of the cross-field times s?. Moreover, sjj may leverage s?, i.e., improved sjj may feed-back to improve s?. This prop- erty locates the FRC as a genuinely hybrid system, situated somewhere between traditional toroidal systems dominated by s? and open systems dominated by sjj.
An interesting question is whether improvements seen in C-2 and C-2U might apply equally well to magnetic mir- ror systems without field reversal, i.e., how important is it to actually have a field reversed core. One advantage of field reversal is that it creates a substantial core volume exceeding the volume of the peripheral plasma (outside the separatrix) by a geometric factor, separatrix radius/SOL thickness. This factor is 4 to 6 in typical experiments. Another advantage is that field reversal creates a deep mag- netic well in the neighborhood of the X-points (which are on-axis in an FRC). This may well increase the effective- ness of the end confinement.
ACKNOWLEDGMENTS
The authors thank Hiroshi Gota, Erik Trask, Peter Yushmanov, Sergey Putvinsky, and Toshi Tajima for a careful reading and incisive comments. We also thank Houyang Guo and Sean Dettrick for access to data from C-2 and C-2U. Special thanks go to John Santarius and Tom O’Neil for their repeated encouragements. We are also grateful to the TAE shareholders for their continued support.
APPENDIX: PARTICLE TRANSPORT RATE FORMATS
Recall from Eq. (4) that the particle flux is referenced to the density gradient, –v rn. v itself follows from resistive
Phys. Plasmas 25, 022503 (2018) vn 1⁄4 cdðbloc=2Þg?=l0: (A1)
Here, bloc 1⁄4 2l0p/B2 is based on the local pressure p and magnetic field B. The factor cd reflects the combined effects of gradients in density and temperatures in driving particle diffusion. Suppose that thermodynamic variables are linked in barotropic relationships, e.g., p 􏰁 nc and T 􏰁 nc–1. For C-2 and C-2U, reasonable values are c 1⁄4 3/2 and cd 1⁄4 1.4. Then, Eq. (A1) takes the form vn 􏰁 na/B2; expectation values of a are mentioned shortly. Pursuant to an analytical solution to the SOL system Eq. (7), the 1/B2 dependence is dropped. This leads shortly to the result for the eigenvalue k 1⁄4 (1 þ a/ 2)1/2‘i/Ln,s. Classical particle transport has g? 􏰁 Te–3/2. With c1⁄43/2, Te 􏰁 n1/2 so that a1⁄43=4. Bohm scaling vn 􏰁 Te/B ignores the resistivity; with B 1⁄4 const and Te 􏰁 n1/2 as before,a1⁄41=2.Ifthe1/B2factorisrestoredandBisdeter- mined by force balance (p þ B2/2l0 1⁄4 const), the solution of Eq. (7) requires a modest numerical computation. For C-2U #43,628 at t 1⁄4 3 ms, the eigenvalue is k 1⁄4 1.53‘i/Ln,s.
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nn
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