Theory of Tokamak Transport: New Aspects for Nuclear Fusion Reactor Design Book

Preface     XI
Lists of physical constants, plasma parameters and frequently used symbols     XV
The quest for fusion power     1
Tokamak machines     1
Topology and ignition     1
Some early tokamaks     4
Toroidal current     5
Basic tokamak variables     6
Aspect ratio     6
Beta     7
Safety factor     8
Z-effective     9
Global confinement times     10
Energy confinement time     11
Electron-energy confinement time     12
Particle confinement time     13
Momentum confinement time     14
Heating     14
Ohmic heating     15
Neutral beam heating     16
Radio-frequency heating     17
Electron energy confinement time     18
Ohmically-heated tokamaks     18
Auxiliary heated plasmas     22
Profile shapes and energy losses     23
Disruptive instabilities     24
References     25
Tokamak magnetic fields     27
Axisymmetric toroidal equilibrium     27
Grad-Shafranov equation     28
First integral constraint     30
Second integral constraint     31
Diffusion velocity     32
Equilibrium in a circular torus     34
Shafranov geometry     34
Solution of the Grad-Shafranov equation     35
Magnetic fields and electric currents     37
Particle trapping in magnetic fields     38
Magnetic bottles     38
Fraction of trapped particles     39
Trapping in tokamak magnetic fields     40
Tokamak mirrors     40
Trapped particles     41
Bounce time in a tokamak field     42
Trapped particle resistivity     43
Diffusivity of trapped particles     45
Energy sinks at magnetic mirrors     45
Physics of diffusivity     46
Parallel diffusivity due to trapped particles     48
Thermal pumping     49
References     52
Energy transport in Tokamaks     53
Banana orbits     53
Drifts due to variations in the magnetic field     53
Gyro-averages     55
Banana width     58
Neoclassical diffusivity     60
Thermal conductivity      61
Neutral gas     61
Magnetoplasma     62
Fluid shear and transport     66
Heat flux, second-order in Knudsen number     67
Classical treatment of particle transport     68
Equilibrium currents     68
Pfirsch-Schluter current     69
Mass diffusivity     70
Neoclassical theory and its validity     71
Banana and plateau regimes     71
Testing neoclassical theory     73
Bootstrap current     74
Second-order transport     76
Electron thermal diffusivity     76
Cylindrical coordinates     78
Physical mechanism for heat flux     79
Role of turbulence     82
Knudsen number constraint     84
References     85
Energy losses from tokamaks     87
Low poloidal beta     88
Empirical profiles     88
Radial distribution of thermal diffusivity     90
Electron energy confinement time     91
Comparison of theory with observation     94
High poloidal beta     95
Oscillatory temperature profiles     95
Thermal diffusivity     97
Electron energy confinement time     98
The L- and H-modes     99
Role of boundary conditions     99
Energy confinement in the L- and H-modes     101
Thermal transport in the ion fluid     102
Thermal diffusivity     102
Ambipolar constraint     103
Comparison of experiment and theory     104
Neutral beam injection     104
Confinement times for L- and H-modes     105
Loop voltage     107
Steady state with ohmic heating     108
Internal transport barriers     110
Profile instabilities     112
Safety factor     112
Thermal instability     114
Review of electron thermal transport     115
References     117
Plasma flow and loop voltage     119
Flow of plasma across strong magnetic fields     119
Plasma particle confinement     119
Viscous stress tensor in cylindrical geometry     121
Radial diffusion velocity     122
Ambipolar flow     123
Particle transport     125
Particle diffusivity and the pinch velocity     125
Particle confinement time     127
Plasma source term     128
Observations of particle confinement     129
The toroidal current and voltage relationship     130
Loop (induced) voltage     130
Lorentz voltage     132
Loop voltage instability     133
Lorentz current     135
Determining Z[subscript eff] from current and loop voltage     137
Toroidal velocities     138
Role of second-order viscosity     138
Angular momentum diffusivity     139
Comparison of theory and observation     141
References     142
Thermal Instabilities     143
Sawtooth oscillations     144
Some observations of temperature and density sawteeth     144
Kadomtsev's model of sawtooth oscillations     145
Sawtooth ramp phase     147
Sawtooth period     149
Theory v. observation for the sawtooth period     150
Disruptions     151
Description of major disruptions     151
Precursor waves     154
Collapse phase     156
MHD instabilities     158
Ideal and resistive instabilities     158
Theory of the ballooning stability limit     159
Some observations of limiting betas     162
L [Double Right Arrow] H transition, ELMS, Snakes, PEPS, and MARFES     163
The L [Double Right Arrow] H transition     164
Edge Localized Modes     166
Snakes     168
Pellet enhanced performance mode (PEP)     171
MARFES     173
Minimum reactor size for ignition     174
Stability constraints     174
Minimum dimensions     175
References     177
Plasma Physics Notes     179
Equations of fluid motion     179
Collision intervals and Spitzer resistivity     180
Energy in the electron and ion fluids     183
Cyclotron frequencies     184
Dimensional analysis applied to energy confinement time     185
Divergence and curl in cylindrical coordinates     186
Tensorial form for Ohm's law     187
Constants of the motion of gyrating particles     188
Equilibrium velocity distribution function     190
Escape time for trapped particles     191
Motion of a fluid element     192
Kinetic equations     193
Drift kinetic equation     196
Guiding center drifts      197
Convection and diffusion     198
The decomposition of second-order tensors     199
Div and curl in local toroidal coordinates     200
Knudsen numbers and local thermodynamic equilibrium     201
Onsager's reciprocal relations in neoclassical transport     202
Putative role of turbulence in transport     204
Solution of a vector equation     205
Viscous stress tensor     206
Solution of a tensor equation     208
MHD instabilities     209
The Catherine wheel fallacy     212
Limitations of Boltzmann's kinetic equation     215
References     217
Index     219