Stellarator and Heliotron Devices

by Wakatani, Masahiro

• ISBN13: 9780195078312
• ISBN10: 0195078314
• Format: Hardcover
• Copyright: 1998-05-14
• Publisher: Oxford University Press

Summary

This monograph describes plasma physics for magnetic confinement of high temperature plasmas in nonaxisymmetric toroidal magnetic fields or stellarators. The techniques are aimed at controlling nuclear fusion for continuous energy production. While the focus is on the nonaxisymmetric toroidal field, or heliotron, developed at Kyoto University, the physics applies equally to other stellarators and axisymmetric tokamaks. The author covers all aspects of magnetic confinement, formation of magnetic surfaces, magnetohydrodynamic equilibrium and stability, single charged particle confinement, neoclassical transport and plasma heating. He also reviews recent experiments and the prospects for the next generation of devices.

Table of Contents

1 INTRODUCTION	1	(6)
2 DESIGN PRINCIPLES OF COIL SYSTEMS IN THE STELLARATOR AND HELIOTRON	7	(48)
2.1 Introduction	7	(1)
2.2 The magnetic surface and the rotational transform	8	(5)
2.3 The magnetic well and magnetic shear	13	(6)
2.4 The average magnetic surface	19	(5)
2.5 The helically symmetric magnetic field	24	(10)
2.6 The magnetic island and destruction of the magnetic surface	34	(9)
2.7 The magnetic surface by line tracing calculation	43	(12)
3 A DESCRIPTION OF MAGNETICALLY CONFINED PLASMAS	55	(46)
3.1 Introduction	55	(1)
3.2 The basic properties of high-temperature plasmas	55	(4)
3.3 The Vlasov equation for describing incompressible phase fluid and moment equations	59	(8)
3.4 Magnetohydrodynamic equations	67	(7)
3.5 MHD waves	74	(3)
3.6 The drift-kinetic equation	77	(3)
3.7 Transport equations	80	(2)
3.8 The averaged reduced MHD equations	82	(19)
4 THE MHD EQUILIBRIUM OF A TOROIDAL PLASMA IN THREE-DIMENSIONAL GEOMETRY	101	(47)
4.1 Introduction	101	(3)
4.2 The generalized Grad Shafranov equation	104	(4)
4.3 The averaged MHD equilibrium equation	108	(11)
4.4 A three-dimensional MHD equilibrium calculation based on the variational principle	119	(3)
4.5 The Solov'ev Shafranov equation	122	(13)
4.6 The Pfirsch-Schluter current, and equilibrium with rational magnetic surfaces	135	(13)
5 MHD INSTABILITIES IN HELIOTRONS	148	(81)
5.1 Introduction	148	(2)
5.2 Linear MHD stability and the energy principle	150	(16)
5.3 The ballooning mode equation	166	(11)
5.4 The Mercier criterion	177	(10)
5.5 The resistive interchange instability	187	(14)
5.6 The role of localized mode stability criteria (Suydam criterion and Mercier criterion)	201	(11)
5.7 Pfirsch-Schluter current driven magnetic islands in stellarators	212	(4)
5.8 The pressure-driven sawtooth in the Heliotron E	216	(8)
5.9 The current-driven sawtooth in the Heliotron E	224	(5)
6 THE PARTICLE ORBIT IN HELIOTRONS	229	(42)
6.1 Introduction	229	(2)
6.2 Drift equations of motion in Boozer coordinates	231	(5)
6.3 J invariance, trapping, and detrapping	236	(20)
6.4 The Characteristics of trapped particle confinement	256	(9)
6.5 The Monte Carlo method for transport phenomena	265	(6)
7 NEOCLASSICAL TRANSPORT IN THE STELLARATOR AND HELIOTRON	271	(54)
7.1 Introduction	271	(2)
7.2 Neoclassical transport in a straight stellarator	273	(11)
7.3 Neoclassical transport of a toroidal heliotron with multiplehelicity magnetic fields in the low-collisionality regime	284	(7)
7.4 Flux-friction relations	291	(4)
7.5 The geometrical factor, [G(BS)](l/v)	295	(11)
7.6 Parallel viscosity-driven fluxes and the bootstrap current	306	(9)
7.7 Energy transport equations in the presence of a radial electric field	315	(10)
8 THE HEATING AND CONFINEMENT OF STELLARATOR AND HELIOTRON PLASMAS	325	(70)
8.1 Introduction	325	(2)
8.2 Plasma heating in heliotron devices	327	(32)
8.3 The LHD scaling law of heliotron plasmas	359	(3)
8.4 The bootstrap current, and plasma rotation in heliotron devices	362	(4)
8.5 Pellet injection and the density limit in the Heliotron E	366	(10)
8.6 Pressure gradient driven turbulence	376	(6)
8.7 Mixing length theory and scale invariance	382	(13)
9 THE STEADY-STATE FUSION REACTOR	395	(36)
9.1 Introduction	395	(1)
9.2 Fusion reactions and power balance	396	(7)
9.3 The alpha particle distribution function and alpha density	403	(5)
9.4 The alpha-driven toroidal Alfven eigenmode	408	(8)
9.5 The divertor physics of the stellarator and heliotron	416	(9)
9.6 The characteristics of the steady fusion reactor	425	(6)
Index	431