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Stellarator bootstrap current and plasma flow velocity at low collisionality

  • P. Helander (a1), F. I. Parra (a2) (a3) and S. L. Newton (a3) (a4)

The bootstrap current and flow velocity of a low-collisionality stellarator plasma are calculated. As far as possible, the analysis is carried out in a uniform way across all low-collisionality regimes in general stellarator geometry, assuming only that the confinement is good enough that the plasma is approximately in local thermodynamic equilibrium. It is found that conventional expressions for the ion flow speed and bootstrap current in the low-collisionality limit are accurate only in the $1/\unicode[STIX]{x1D708}$ -collisionality regime and need to be modified in the $\sqrt{\unicode[STIX]{x1D708}}$ -regime. The correction due to finite collisionality is also discussed and is found to scale as  $\unicode[STIX]{x1D708}^{2/5}$ .

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Beidler, C. D., Allmaier, K., Isaev, M. Y., Kasilov, S. V., Kernbichler, W., Leitold, G. O., Maassberg, H., Mikkelsen, D. R., Murakami, S., Schmidt, M. et al. 2011 Benchmarking of the mono-energetic transport coefficients-results from the International Collaboration on Neoclassical Transport in Stellarators (ICNTS). Nucl. Fusion 51 (7), 076001.
Beidler, C. D. & DHaeseleer, W. D. 1995 A general-solution of the ripple-averaged kinetic-equation (GSRAKE). Plasma Phys. Control. Fusion 37 (4), 463490.
Boozer, A. H. 1983 Transport and isomorphic equilibria. Phys. Fluids 26 (2), 496499.
Braun, S. & Helander, P. 2010 Pfirsch–Schluter impurity transport in stellarators. Phys. Plasmas 17 (7), 072514.
Calvo, I., Parra, F. I., Alonso, J. A. & Velasco, J. L. 2014 Optimizing stellarators for large flows. Plasma Phys. Control. Fusion 56 (9), 094003; 19th International Stellarator-Heliotron Workshop held Jointly with the 16th Reversed Field Pinch Workshop, Padova, Italy, 16–20 September, 2013.
Calvo, I., Parra, F. I., Velasco, J. L. & Alonso, J. A. 2013 Stellarators close to quasisymmetry. Plasma Phys. Control. Fusion 55 (12, 1–2), 125014.
Calvo, I., Parra, F. I., Velasco, J. L. & Alonso, J. A. 2015 Flow damping in stellarators close to quasisymmetry. Plasma Phys. Control. Fusion 57 (1), 014014.
Calvo, I., Parra, F. I., Velasco, J. L. & Alonso, J. A. 2017 The effect of tangential drifts on neoclassical transport in stellarators close to omnigeneity. Plasma Phys. Control. Fusion; accepted, arXiv:1610.06016 (2016).
Cary, J. R. & Shasharina, S. G. 1997 Omnigenity and quasihelicity in helical plasma confinement systems. Phys. Plasmas 4 (9), 33233333.
Helander, P. 2014 Theory of plasma confinement in non-axisymmetric magnetic fields. Rep. Prog. Phys. 77 (8), 087001.
Helander, P., Geiger, J. & Maassberg, H. 2011 On the bootstrap current in stellarators and tokamaks. Phys. Plasmas 18 (9), 092505.
Helander, P. & Nührenberg, J. 2009 Bootstrap current and neoclassical transport in quasi-isodynamic stellarators. Plasma Phys. Control. Fusion 51 (5), 055004.
Helander, P. & Sigmar, D. J. 2002 Collisional Transport in Magnetized Plasmas. Cambridge University Press.
Hinton, F. L. & Rosenbluth, M. N. 1973 Transport properties of a toroidal plasma at low-to-intermediate collision frequencies. Phys. Fluids 16 (6), 836854.
Hirshman, S. P., Shaing, K. C., van Rij, W. I., Beasley, C. O. & Crume, E. C. 1986 Plasma transport-coefficients for nonsymmetric toroidal confinement systems. Phys. Fluids 29 (9), 29512959.
Hirshman, S. P. & Sigmar, D. J. 1981 Neoclassical transport of impurities in tokamak plasmas. Nucl. Fusion 21 (9), 10791201.
Ho, D. D. M. & Kulsrud, R. M. 1987 Neoclassical transport in stellarators. Phys. Fluids 30 (2), 442461.
Kernbichler, W., Kasilov, S. V., Kapper, K., Martitsch, A. V., Nemov, V. V., Albert, C. & Heyn, M. F. 2016 Solution of the drift kinetic equation in stellarators and tokamaks with broken symmetry using the code neo-2. Plasma Phys. Control. Fusion 56 (10), 104001.
Landreman, M. & Catto, P. J. 2011 Effects of the radial electric field in a quasisymmetric stellarator. Plasma Phys. Control. Fusion 53 (1), 015004.
Landreman, M. & Catto, P. J. 2012 Omnigenity as generalized quasisymmetry. Phys. Plasmas 19 (5), 056103.
Nakajima, N., Okamoto, M., Todoroki, J., Nakamura, Y. & Wakatani, M. 1989 Optimization of the bootstrap current in a large helical system with . Nucl. Fusion 29 (4), 605616.
Parker, J. B. & Catto, P. J. 2012 Variational calculation of neoclassical ion heat flux and poloidal flow in the banana regime for axisymmetric magnetic geometry. Plasma Phys. Control. Fusion 54 (8), 085011.
Parra, F. I., Calvo, I., Helander, P. & Landreman, M. 2015 Less constrained omnigeneous stellarators. Nucl. Fusion 55 (3), 033005.
van Rij, W. I. & Hirshman, S. P. 1989 Variational bounds for transport-coefficients in 3-dimensional toroidal plasmas. Phys. Fluids B 1 (3), 563569.
Rosenbluth, M. N., Hazeltine, R. D. & Hinton, F. L. 1972 Plasma transport in toroidal confinement systems. Phys. Fluids 15 (1), 116140.
Shaing, K. C. & Callen, J. D. 1983 Neoclassical flows and transport in non-axisymmetric toroidal plasmas. Phys. Fluids 26 (11), 33153326.
Shaing, K. C., Carreras, B. A., Dominguez, N., Lynch, V. E. & Tolliver, J. S. 1989 Bootstrap current control in stellarators. Phys. Fluids B 1 (8), 16631670.
Simakov, A. N. & Helander, P. 2009 Neoclassical momentum transport in a collisional stellarator and a rippled tokamak. Phys. Plasmas 16 (4), 042503.
Taguchi, M. 1988 Ion thermal-conductivity and ion distribution function in the banana regime. Plasma Phys. Control. Fusion 30 (13), 18971904.
Weyl, H. 1916 Über die Gleichverteilung von Zahlen mod. Eins. Math. Ann. 77, 313327.
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Journal of Plasma Physics
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  • EISSN: 1469-7807
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