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Title: Radial confinement of deeply trapped particles in a non-symmetric magnetohydrodynamic equilibrium

 [1]; ORCiD logo [1]
  1. Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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Sponsoring Org.:
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Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 25; Journal Issue: 2; Related Information: CHORUS Timestamp: 2018-02-12 13:47:04; Journal ID: ISSN 1070-664X
American Institute of Physics
Country of Publication:
United States

Citation Formats

Sengupta, Wrick, and Weitzner, Harold. Radial confinement of deeply trapped particles in a non-symmetric magnetohydrodynamic equilibrium. United States: N. p., 2018. Web. doi:10.1063/1.5011760.
Sengupta, Wrick, & Weitzner, Harold. Radial confinement of deeply trapped particles in a non-symmetric magnetohydrodynamic equilibrium. United States. doi:10.1063/1.5011760.
Sengupta, Wrick, and Weitzner, Harold. 2018. "Radial confinement of deeply trapped particles in a non-symmetric magnetohydrodynamic equilibrium". United States. doi:10.1063/1.5011760.
title = {Radial confinement of deeply trapped particles in a non-symmetric magnetohydrodynamic equilibrium},
author = {Sengupta, Wrick and Weitzner, Harold},
abstractNote = {},
doi = {10.1063/1.5011760},
journal = {Physics of Plasmas},
number = 2,
volume = 25,
place = {United States},
year = 2018,
month = 2

Journal Article:
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This content will become publicly available on February 12, 2019
Publisher's Accepted Manuscript

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  • This paper studies confinement properties of 1 = 2 torsatron/heliotron configurations with number of toroidal field periods, M, in the range of 10 to 14. This involves the calculation of zero-current and flux-conserving equilibria; stability against Mercier modes and low-n ideal modes, with n denoting the toroidal mode number; and orbit confinement of deeply trapped energetic particles. Optimization of both magnetohydrodynamic (MHD) and transport properties is pursued under the condition of plasma aspect ratio A = R/a {ge} 7, with R denoting the major radius and a the average plasma radius. For configurations with M, {le} 12, an average MHDmore » beta limit of 4 to 5% is possible. The addition of a quadrupole field improves the confinement of trapped particles at zero pressure, but particle losses increase with increasing beta. This loss is less severe if the vacuum magnetic axis is shifted slightly inward. A configuration with M = 10, a coil pitch parameter p{sub c} in the range 1.25 to 1.30, and an added quadrupole field satisfies the beta and energetic particle confinement requirements for the next generation of large torsatron/heliotron devices.« less
  • Weak axial variations in B(z) or {phi}(z) in 'axisymmetric' plasma traps cause a fraction of the particles to be trapped axially, with a velocity-space separatrix between trapped and passing populations. The trapped and passing particles experience different dynamics in response to a variety of {theta}-asymmetries in the E x B rotating plasma, so a discontinuity in the velocity-space distribution f(v) tends to form at the separatrix. Collisional scatterings thus cause large fluxes as they smooth the distribution in a boundary layer near the separatrix. In essence, this separatrix dissipation damps the AC or DC longitudinal currents induced by plasma wavesmore » or confinement field asymmetries. This trapped-particlemediated damping and 'neoclassical' particle transport often dominates in cylindrical pure electron plasmas, and may be important in other nominally symmetric open systems.« less
  • Confinement of trapped fast ions in the Wendelstein-line stellarators in the presence of the radial electric field, E{sub r}, is studied. It is shown that negative electric field improves the confinement; in particular, a radially localized field can play the role of a transport barrier for the ions escaping from the plasma when E{sub r}=0. In contrast to this, the positive electric field tends to deteriorate the ion confinement, unless its magnitude is very large. Such a field accompanied by the plasma rotation with the frequency around a certain magnitude, which we refer to as the resonance rotation frequency, leadsmore » to a quick particle loss. A possibility of using the plasma rotation with the resonance frequency for the ash removal in a Helias reactor is considered. The mentioned results are obtained analytically and numerically. The analytical consideration was done on the basis of the derived bounce-averaged equations of the particle motion. The numerical calculations were carried out for Wendelstein 7-X [G. Grieger et al., J. Plasma Fusion Res. Series 1, 53 (1998)] and a Helias reactor [J. Kisslinger et al., Proceedings of the 17th International Conference, Yokohama, 1998 (1999), Vol. 4, p. 1239] by the guiding center code ORBIS (ORBits In Stellarators) developed in this work.« less
  • A low-beta tandem-mirror trapped-particle instability theory is developed for arbitrary azimuthal mode number including the effects of radial equilibrium electric fields. A stability window is seen to exist for inward-pointing electric fields even when passing electrons bounce beyond passing ions. This stability window can persist at zero radial electric field when the instability drive is sufficiently small. The theory also predicts the possibility of an additional instability when E x B rotation is present: a rotationally driven trapped-particle mode.
  • An alternative representation of an ideal magnetohydrodynamic equilibrium is developed. The representation is a variation of one given by A. Salat, Phys. Plasmas 2, 1652 (1995). The system of equations is used to study the possibility of non-symmetric equilibria in a topological torus, here an approximate rectangular parallelopiped, with periodicity in two of the three rectangular coordinates. An expansion is carried out in the deviation of pressure surfaces from planes. Resonances are manifest in the process. Nonetheless, provided the magnetic shear is small, it is shown that it is possible to select the magnetic fields and flux surfaces in suchmore » a manner that no singularities appear on resonant surfaces. One boundary surface of the parallelopiped is not arbitrary but is dependent on the equilibrium in question. A comparison of the solution sets of axisymmetric and non-axisymmetric equilibria suggests that the latter have a wider class of possible boundary shapes but more restrictive rotational transform profiles. No proof of convergence of the series is given.« less