(BQ) Part 2 book Fusion physics has contents: Plasma heating and current drive by neutral beam and alpha particles, plasma–wall interactions, helical confinement concepts, inertial fusion energy, the broader spectrum of magnetic configurations for fusion.
CHAPTER PLASMA HEATING AND CURRENT DRIVE BY NEUTRAL BEAM AND αLPHA PARTICLES M Kikuchi, Y Okumura Fusion Research and Development Directorate, Japan Atomic Energy Agency, Japan 5.1 H EATING AND CURRENT DRIVE PHYSICS BY NEUTRAL BEAM AND ALPHA PARTICLES 5.1.1 Basic processes of neutral beam injection The purpose of plasma heating is to raise the plasma temperature enough to produce a deuterium and tritium reaction (D + T → 4He + n) The required plasma temperature T is in the range of 10–30 keV Since the high temperature plasma is confined by a strong magnetic field, injection of energetic ions from outside to heat the plasma is difficult due to the Lorenz force The most efficient way to heat the plasma by energetic particles is to inject high energy “neutrals” which get ionized in the plasma Neutral beam injection (NBI) with a beam energy much above the average kinetic energy of the plasma electrons or ions is used (beam energy typically ~40 keV – MeV) This heating scheme is similar to warming up cold water by pouring in hot water There are two types of neutral beam, called P-NBI and N-NBI (P- and Nmeans “positive” and “negative”, respectively) P-NBI uses the acceleration of positively charged ions and their neutralization, while N-NBI uses the acceleration of negative ions (electrons attached to neutral atoms) and their neutralization Details are given in NBI technology Section 5.2 The first demonstration of plasma heating by P-NBI was made in ORMAK [5.1] and ATC [5.2] in 1974, while that by N-NBI was made in JT-60U [5.3] for the first time in 1996 ITER has also adopted the N-NBI system as the heating and current drive system with a beam energy of MeV Figure 5.1 shows a typical bird’s eye view of a tokamak with N-NBI and N-NBI (JT-60U) Since the magnetic confinement system is a torus and the tokamak has a toroidal plasma current, there are three injection geometries, namely co-tangential, counter-tangential and perpendicular injection, as shown schematically in Fig. 5.2 “Co-” means that beam is injected parallel to the toroidal plasma current, while “counter” means that beam is injected anti-parallel to the plasma current “Perpendicular” means that beam is injected (nearly) perpendicular to 535 KIKUCHI and OKUMURA FIG 5.1 Bird’s eye view of tokamak with P-NBI and N-NBI (JT-60U) [5.4] Reprinted from Ref [5.4] Copyright (2011), IOP Publishing Ltd the magnetic field A plasma can be heated in all injection geometries In addition to plasma heating, co-injection can also drive the plasma current (see Sections 5.1.7–5.1.9) and also drive co-toroidal rotation through its momentum input, while counter-injection can drive a counter-plasma current and counter-toroidal rotation FIG 5.2 Schematics of tokamak plasma geometry and NBI beam orientations After the injection, beam neutrals are ionized through various atomic processes such as charge exchange, ionization by ions and ionization by electrons, which will be described in detail in Sections 5.1.2 and 5.1.3 After the ionization, there is some possibility of re-neutralization and loss of fast ions due to charge exchange with residual neutrals in the plasma The main sources of neutrals in a high temperature plasma are edge warm neutrals and halo neutrals The source of edge neutrals is neutrals from the wall and divertor, while the source of halo neutrals is charge exchange processes between the neutral beam and bulk plasma ions 536 PLASMA HEATING AND CURRENT DRIVE Ionized ions are magnetically trapped in the plasma and their orbit follows the magnetic surface with only slight deviation There are two types of particle orbits, namely, passing particles and trapped particles (see Section 5.1.5) The magnetic field should be strong enough to confine these energetic ions until they transfer their energy to plasma electrons and ions The tokamak system is axisymmetric but real machines have small non-uniformities in the toroidal direction because of the finite number of toroidal field coils; this is called toroidal field ripple This ripple causes loss of fast ions The detailed physics of particle orbits in a tokamak will be described in Sections 5.1.5 and 5.1.10 The energy transfer from ionized beam fast ions to thermal ions and electrons is basically through classical Coulomb collision processes The basic processes of Coulomb collision between fast ions and a thermal plasma are slowing down and diffusion in the velocity space If the beam energy Wb is sufficiently high (Wb > 15Te,), fast ions transfer their energy mainly to electrons, while more energy is transferred to ions when W b< 14.8 for hydrogen and Wb < 19 for deuterium Details of classical beam–plasma Coulomb interactions will be given in Section 5.1.4 5.1.2 Physics of ionization of injected neutral beam Here we discuss the basic atomic processes which are important during the ionization of a neutral beam in a high temperature plasma For simplicity we consider the case of injection of a deuterium neutral beam into an electron– deuterium impurity plasma The processes are direct ionization of the ground state (1s) of the deuterium neutral beam through charge exchange (CX) with bulk ions, ionization by ion impact, ionization by impurity and ionization by electron impact Decay of the neutral beam intensity Ib(t) is governed by the processes given in Table 5.1 TABLE 5.1 BASIC ATOMIC PROCESSES DURING IONIZATION OF A NEUTRAL BEAM IN A HIGH TEMPERATURE PLASMA (The subscript ‘b’ stands for beam, and D and A for the deuterium and impurity species, respectively) Charge exchange Db0(1s) + D+ → Db+ + D0 Ionization by ions Db0(1s) + D+ → Db+ + D+ + e Ionization by impurities Db0(1s) + Az+ → Db+ + Az+ + e Impurity CX Db0(1s) + Az+ → Db+ + A(z–1)+ Ionization by electrons Db0(1s) + e → Db+ + 2e 537 KIKUCHI and OKUMURA dI b n e s v b I b dt (5.1) s (ni cx ni i n z z ) / n e e v e v b (5.2) where ne, ni, nz, s , cx , i , z , e v e and v b are the electron density, the ion density, the impurity density, the stopping cross-section, the charge exchange cross-section, the ionization cross-section by ions, the ionization and CX by impurities, the electron ionization rate coefficient and the beam speed, respectively Since the pioneering work of Riviere [5.5] on ionization of a neutral beam in a high temperature plasma, extensive efforts have been made to accumulate atomic data for fusion under the auspices of the IAEA The analytical equations for the ionization cross-sections cx and i of ground state hydrogen isotopic atoms by hydrogen isotopic ions under the condition of v th,i v b are given by Janev and Smith [5.6] (Table 5.2) Since the beam speed is dominant in the relative speed ( v r ,i v b v th,i ~ v b ), the crosssections cx and i are simply functions of energy/mass number (u = Wb/Ab) and shown for the case of a deuterium beam in Fig. 5.3 FIG 5.3 Beam energy dependence of charge exchange, ion, impurity and electron ionization cross-sections (calculated from Table 5.2) Charge exchange is the dominant process in the low energy regime (Wb/Ab < 45keV) and ionization by hydrogen ions is dominant in the high energy regime (Wb/Ab > 45 keV) A fusion plasma is always accompanied by some impurities such as carbon and helium The cross-section for ionization by impurities z 538 PLASMA HEATING AND CURRENT DRIVE includes both charge exchange and ionization and scales as z ~ Z f (Wb / Ab / Z ) (where Zf is the Z of the fast ions) as found by Olson [5.7] Janev [5.8] gave an analytical formula for z (see Table 5.2), which is consistent with various charge state impurity measurements (He, C, O, Fe) In Fig. 5.3, z for fully stripped carbon (Z = 6) is shown Although the cross-section z is much larger than cx i , its contribution to the stopping cross-section is comparable or smaller if the impurity content is small The relative speed of ionization processes by electrons is dominated by the electron speed ( v r ,e v b v th,e ~ v th,e ) So the reaction has to be averaged over the Maxwellian electrons Janev [5.9] gave an analytical formula for the electron ionization rate coefficient (see Table 5.2) This rate coefficient becomes a maximum just above 0.1 keV and decreases with Te The contribution to the stopping cross-section from this process is < e v e / v b > for the average over velocity) (where ve stands for the electron velocity and and is shown in Fig. 5.3 for Te = 1 keV and 10 keV TABLE 5.2 CROSS-SECTION AND RATE COEFFICIENT FORMULAS Charge exchange [5.6] scx[m2]=[a1ln(a2/u+a6)]/[1+a3u+a4u3.5+a5u5.4]; Ionization by ions [5.6] si[m2]=b1[exp(-b2/u)ln(1+b3u)/u+ b4exp(-b5u)/(ub6+b7ub8)]; [an]=[3.2345 × 10–20, 235.88, 0.038371, 3.8068 × 10–6, 1.1832 × 10–10, 2.3713] [bn]=[12.899 × 10–20, 61.897, 9.2731 × 103, 4.9749 × 10–4, 3.9890 × 10–2, -1.5900, 3.1834, -3.7154] Ionization by impurities [5.8] Electron ionization rate coefficient (Te [keV] > 0.002) [5.9] sz[m2]=c1Z[(1+c2u/Z)–1+c3(c4+u/Z)–1ln(1+ c5u/Z)] ; [cn]=[7.457 × 10–20, 0.08095, 2.754, 64.58, 1.27] [m3/s]=10–6exp[Sn=1,9dn(lnTe)n–1]; [dn]=[-32.714, 13.537, -5.7393, 1.5632, -0.28771, 0.034826, -2.6320 × 10–3, 1.1195 × 10–4, -2.0392 × 10–6] u=Wb/Ab[keV] The solution of Eq. (5.1) is given as I b I exp( v b t / ) , where / n e s is the called the e-folding length of the beam attenuation The electron density will be around 1020 m–3 in ITER or the DEMO reactor For a deuterium beam energy of MeV, the stopping cross-section s is ~4 × 10–21 m2 and the e-folding length 2.5 m, which is comparable with the plasma minor 539 KIKUCHI and OKUMURA radius of ITER and the DEMO reactor But the above discussion is based on the ionization from the ground state and the inclusion of multi-step ionization through excited states changes the situation This effect will be discussed in the next section 5.1.3 Multi-step ionization and Lorenz ionization In the previous section, we considered ionization only from the ground state Ionization can also occur from excited states (n = 2–6, ) In this case, we have to consider first excitation from the ground state (for example, D(1s) → D*(2s,2p)), and then ionization from an excited state (for example, D*(2s,2p) → D+) So, the ionization process becomes “multi-step” ionization (MSI) This MSI is important for high energy beams, especially those for ITER (1 MeV) and beyond [5.8, 5.10] Figure 5.4 shows a comparison of the measured neutral beam current profile and the calculated one (both with and without multi-step ionization process in the N-NBI experiment) [5.11] Good agreement is obtained only for the calculation with multi-step ionization processes So, it is important to understand these processes FIG 5.4 Experimental NBCD current profile compared with calculation with and without multi-step ionization [5.11] Here jNNB is the non-inductively driven current density by the injection of negative ion based neutral beam injection r (horizontal axis) is the plasma minor radius normalized to the plasma minor radius a 540 PLASMA HEATING AND CURRENT DRIVE Comprehensive atomic data including excitation from the ground state and ionization from excited states are compiled by the IAEA [5.6] The excitation cross-section ex from the ground state to the excited state with principal quantum number n is a decreasing function of n, while the ionization cross-section from an excited state increases with n as seen in Fig. 5.5 FIG 5.5 Ionization and CX cross-sections from excited (n = 2~6) and ground (n = 1) states (calculated from ion and cx formulas given in Sections 2.2 and 2.3 of Ref. [5.6] with obvious correction of Wn = (n/3)2 W on page 74 of Ref. [5.6]) Higher excited states are subject to ionization by the Lorenz field E L v b B The critical electric field for Lorenz ionization is given by E L,c (n) / (16n ) and an excited state n is ionized if E L E LC (n) where is the classical electric field at the first Bohr radius The highest principal quantum number of an excited hydrogen atom determined by the Lorenz field ionization limit is given by N ( / 16 E L )1/4 For MeV/amu and B = 5 T, N is calculated to be The neutral beam intensity Ib(x) at a distance x from the entry of the injection is the sum of the intensities at quantum number n as follows: I b ( x) N I n 1 n ( x) (5.3) The rate equations can be expressed by vb dI n dx Q n' n'n I n ' (5.4) 541 KIKUCHI and OKUMURA vb dI n d e K n I n K n'n I n' K nn' Ann' I n dx n ' n K n ' n e nn' I n d K n'n An'n I n' (5.5) where Kn is the rate for electron loss from state n due to ionization including d e Lorentz ionization and charge exchange K nn' and K nn' are the rates of de-excitation from n to n´ due to collisions, and the rate of excitation from n to n′, Ann′ is the radiative decay and vb is the beam speed, respectively The j v , where nj is the collisional transition rate is given as K n'n j n j n'n j density of particles j, n'n is the cross-section of hydrogen for transition from n′ to n through collision with particle j (= e, i, I) being electron, ion or impurity respectively Equations (5.4) and (5.5) can be approximately rewritten by using the beam stopping cross-section s as dI b n e s I b dx (5.6) where Ib=SIn, s / v b n e , where is the minimum eigenvalue of the transition matrix {Qn’n} The contributions of multi-step processes and ionization by the Lorentz field are given by the following enhancement factor defined by s s(0) s(0) (5.7) where s(0) is the stopping cross-section in which the multi-step processes and ionization by the Lorentz field are not taken into account For a beam energy range of 0.5–1 MeV expected in ITER, the enhancement factor can be of the order of 0.3–0.5 for an electron density ne = 1020 m–3 [5.8] The stopping cross-section s has a strong dependence on the beam energy W, the electron density ne, the electron temperature Te and the effective charge Zeff and has almost no dependence on ion temperature Ti and the magnetic field B An analytical fit of the stopping cross-section based on recent data is given in Ref. [5.12] and typical values of are shown in Fig. 5.6 An experimental measurement of the multi-step effect has been made in various tokamaks and was published in the ITER physics basis as shown in Fig. 5.6 The shine through rate (h = Ib(L)/Ib(0), where Ib(x) is the beam intensity at x) is compared with calculations with and without multi-step ionization in JT-60U showing better agreement with the multi-step process as shown in Fig. 5.6 542 PLASMA HEATING AND CURRENT DRIVE FIG 5.6 Top: Comparison of measured and calculated enhancement [5.13] Below: Comparison of measured shine through rate h with calculation with and without multi-step ionization [5.14] Here L is the plasma length along the beam path 5.1.4 Energy transfer to electrons and ions by neutral beam injection A fundamental feature of heating by a neutral beam was clarified by Stix [5.15] and can be seen in introductory textbooks such as that by Wesson [5.16] Here, we discuss the issue using the correct impurity contribution Neutral beam “heating” occurs through energy transfer by the Coulomb collision of the energetic beams with bulk Maxwellian electrons and ions (deuterium, tritium and impurities) with the electron temperature Te and ion temperature Ti, respectively The beam speed vb is usually much larger than the ion thermal speed 543 KIKUCHI and OKUMURA v th,i due to the heating objective and much less than the electron thermal speed v th,e due to the large mass ratio (for beam mass mb (mb / m e )1/2 ~ 42.8 Ab1/2 ), v th,i v b v th,e Under this condition the energy loss of the beam is given by [5.15] dWb dt se Wc3/2 1 3/2 Wb Wb (5.8) where Wb is the beam energy, and Wc and se are called the critical energy and beam electron slowing down time, respectively The formulas for Wc and se are as follows 9 m p Wc [keV] 16m e se [s] 1/3 j n j Z 2j ne A j 2/3 AbTe 14.8Z 2/3 Ab1/3Te [keV] 3(2 ) 3/2 02 mbTe3/2 0.2 AbTe [keV] 3/2 e Z b2 n e m1/2 Z b2 n e [10 20 m –3 ]ln e ln (5.9) (5.10) Here, Z n j Z 2j Ab / (n e A j ) The first term on the right hand side of Eq. (5.8) is the energy loss through beam–electron Coulomb collisions Since the electron mass is much smaller than beam ion (see Fig. 5.7a), me/mD ~ 1/3672, beam ions lose energy through the friction with bulk electrons W mb v b v (where v is the velocity of ions in the parallel direction) with negligible diffusion in velocity space in both the parallel and perpendicular directions The energy decay time by the electron channel does not depend on the beam energy and is half of the slowing down time, se /2, since the energy is proportional to the square of the speed This power 2Wb/ se is transferred from the beam to the bulk Maxwellian electrons The second term is the energy loss through beamion/impurity Coulomb collisions (see Fig. 5.7a) Since the field particles have equal or larger mass than the beam ions, the beam ions lose energy through friction with bulk ions, W mb v b v and gain less energy by the pitch angle scattering with bulk ions, W mb ( v ) / (where v is the ion velocity in the direction perpendicular to the magnetic field), while there is negligible energy diffusion in the parallel direction The energy decay time by the ion channel depends on the beam speed ( ~ v 3b ) If the beam energy Wb is higher than Wc, the energy transfer to ions is smaller than that to electrons, while the energy transfer to ions becomes dominant when Wb becomes less than Wc This is the reason why Wc is called the “critical energy” The instantaneous ion heating fraction is given by Fi(Wb/Wc) = 1/(1+(Wb/Wc)3/2) The fast ion distribution function fb(Wb) is given by the flux conservation in energy space and is shown in Fig. 5.7b as follows: 544 INDEX cyclotron frequency 63, 67, 93, 179, 304, 305, 384, 428, 474, 475, 612, 615, 617, 620, 621, 630–632, 635, 636, 638, 659, 660, 662, 716, 717, 866, 885, 894, 1013 cyclotron radius 63 D damage potential 349 Debye length 629 density control 832 density fluctuation measurements 482 density fluctuations 61, 84, 91, 93, 114, 170, 171, 178, 191, 428, 476, 479, 481, 482, 1061 density limit 343, 678, 696, 702, 867, 930 density limit disruptions 343 density scale length 59 detachment 805, 828 diagnostic neutral beams 435 diagnostics 360 diffusion coefficient 73, 762, 898, 918 dimensional parameters 124 dimensionless analysis 136 dimensionless parameters 239 dispersion interferometers 468 disruption 342 disruptive instabilities 342 dissipative trapped electron mode 101 distribution function 63 divertor operation regimes 799 drift kinetic equation 71 drift wave turbulence 109, 112, 175 drift waves 86 D–T experiments 568 1121 INDEX E edge localized modes (ELMs) 327 edge pedestal 169 electrical probes 368 electromagnetic turbulence 60 electron Bernstein waves (EBWs) 392, 612 electron cyclotron current drive (ECCD) 620, 703 electron cyclotron emission 183, 384 electron cyclotron resonance heating (ECRH) 612 electron drift instabilities 86 electron dynamics 99 electron heat transport 114, 914 electron temperature gradient instability 99 electron thermal transport 113 electron transport 113 ELMy H-mode 328, 906 energetic particle modes 311, 337 energy confinement 18, 123, 230 energy scenarios 11 energy transfer 543 ergodization 285 error analysis 133 F fast ignition 1069, 1074, 1077, 1082 fast ion diffusion coefficient 549 fast ion distribution function 551 fast particle effects 313 feedback control 489 field reversed configuration (FRC) 1000 filamentation instability 1062 first wall 756 fishbones 321 frequency spectra 187 1122 INDEX fusion power gain 17 fusion power production 42, 45 fusion reactions 20 G gas puffing 831 geodesic acoustic modes (GAMs) 192 global Alfvén eigenmodes 176, 886 global MHD modes 306 Greenwald density 143 Greenwald limit 931 H hard X rays 412 heat load 327, 831–833 heat pulse 349 heat transport 114, 909 heavy ion beam probe 181 helical system 861 helicity injection 987, 994 heliotron 855, 941 high beta 982, 1024 H-mode 120, 128, 915 H-mode confinement trends 128 H-mode pedestal 265 H-mode threshold 123 I ion Bernstein waves (IBWs) 653, 656 ion cyclotron resonance heating (ICRH, ICRF) 630 ideal MHD stability 246 ignition 19, 36, 1043 implosion physics 1051 improved confinement regimes 32, 915 1123 INDEX impurity control 758, 789, 798, 832 impurity transport 375, 378, 918 inertial confinement fusion (ICF) 27, 35, 38, 1043 instabilities 86, 95, 246, 342, 877, 984, 1012, 1058, 1068 interchange mode 246, 247, 262 interferometry 452 internal inductance 236 internal kink modes 317 internal transport barrier (ITB) 128, 163, 265, 699, 922 International Thermonuclear Experimental Reactor (ITER) 2, 360, 574, 597, 727, 730 ion source 437, 575, 584 ion temperature gradient (ITG) 85, 89, 96 ion transport 148, 175, 904 island divertor 923 K kinetic MHD 302 kinetic models 299 kink modes 317 L Langmuir probes 368 large aspect ratio approximation 234 laser fusion power plant 1095 L-H threshold scalings 140 L-H transition 140 limiter plasmas 758 linear stability of global modes 269 local transport 145 long pulse operation 836 Lorenz ionization 540 lower hybrid current drive (LHCD) 642 1124 INDEX M Mach probes 372 magnetic configuration 65, 847, 913, 958 magnetic confinement fusion 27 magnetic field ripple 78 magnetic measurements 362 magnetic reconnection 317, 967 magnetic shear 98, 104, 850 magnetized plasma 611, 1024 magnetized target 1024 MHD energy principle 248 MHD model 246, 287 MHD modes 316, 334 MHD stability 246 microturbulence 103 microwave interferometry 459 mirror machine 1008 mirrors 1105 momentum transport 116 multi-stage acceleration 581 N negative ion based NBI 595 negative ion extraction 594 negative ion production 588, 595 negative ion source 571, 587 neoclassical tearing modes (NTMs) 317, 322, 325 neoclassical theory 152 neoclassical transport 59, 64, 901, 904, 906, 919, 937 neutral beam injection (NBI) 535 neutral transport 149 non-ideal effects 313, 336 non-linear gyrokinetic simulations 114, 191 non-local effects 195 1125 INDEX O one dimensional equilibria 253 operational limits 930 P particle drifts 63, 563 particle transport 114, 810, 909 passive neutral particle analysis 394 pedestal 133, 169, 173, 192, 265, 328 pellet injection 467, 831 Peri-plasmatron 575 petawatt laser 1069, 1075 phase contrast imaging 181 plasma confinement 30, 59, 63, 124, 136, 853, 1008 plasma elongation 126, 1001 plasma equilibrium 232, 239, 870 plasma facing components (PFCs) 349, 364, 796, 797, 834, 835, 837 plasma focus 1026 plasma generator 575, 576, 582, 584 plasma heating 535, 536, 1074 plasma length 230, 1001 plasma rotation 116, 336, 440, 1003, 1005 polarimetry 452, 454 positive ion based NBI 574 power balance 17, 160 power flows 60 profile stiffness 160, 161, 163, 176 Q Q factor 17 R radial fluxes 59 radial profiles 189–191 1126 INDEX radio frequency (RF) heating 150, 658 reconnection 285 recycling 47, 759, 764, 767, 802, 803 re-deposition 794 reduced (low frequency) MHD 291 reflectometry 179, 452 resistive bolometers 380 resistive instabilities 276 resistive wall mode (RWM) 270, 278, 281, 335 reversed field pinch (RFP) 959 reversed magnetic shear 122, 164 reversed shear Alfvén eigenmodes 338 runaway electrons 353, 364, 391, 419, 757 S safety factor 65 sawtooth, sawteeth 317 scrape-off layer (SOL) 765, 932 sheared flow 61, 122 spectroscopy 182, 183, 404, 438 spherical tokamak 50, 175, 1000 spherical torus 113, 190 spheromak 990 sputtering 486, 772, 774 stability 85, 89, 225, 984, 1059, 1062 steady state operation 823, 836 steady state tokamak 324, 333 stellarator 871, 936 stochastic field 64, 82 straight tokamak model 258, 272 structural materials 40, 486 superconductor 848, 944 suprathermal electrons 390, 864, 1057 1127 INDEX T target design 1092 tearing modes 272 temperature fluctuations 191 temperature gradient 75, 85, 89, 96, 99 temperature gradient mode 85, 96 thermal quench 345 Thomson scattering 426, 429, 431 tokamak 32, 91, 225, 246, 568, 831 tokamak configuration 226, 227 tokamak dynamics 228 tokamak equilibrium 230, 232 tokamak plasma geometry 536 tokamak turbulence 91 toroidal angular momentum 59 toroidal current 27, 997 toroidal field coils 854, 855, 859 toroidal geometry 106, 306, 648, 651, 653, 825, 870 transport barriers 118, 163 trapped electrons 99, 551 trapped ion mode 100, 102, 103 trapped particle instabilities 95 triangularity 30, 138 tritium handling 1101, 1103 tritium inventory 41, 832, 835 tritium retention 780, 797, 835 turbulence measurements 176 turbulent transport 176, 784, 906, 958 two-fluid effects 300 U UV spectroscopy 375 1128 INDEX V vacuum vessel 376, 459, 465, 468, 756, 779 vertical displacement events 758 Vlasov equation 63, 92, 94, 95 volume recombination 803 vorticity 293, 297 W wall conditioning 786 wall modes in rotating plasmas 278 wall pumping 789, 833 wall stabilization 334 waste 40, 41, 47 wavenumber spectra 185, 188 X X ray radiation 400, 1077, 1086 Z zonal flow 100, 108, 192, 211 zonal flow shear 108 1129 @ No 22 Where to order IAEA publications 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12-13151 This publication is a comprehensive reference book for graduate students and an invaluable guide for more experienced researchers It provides an introduction to nuclear fusion and its status and prospects, and features specialized chapters written by leaders in the field, presenting the main research and development concepts in fusion physics It starts with an introduction to the case for the development of fusion as an energy source Magnetic and inertial confinement are addressed Dedicated chapters focus on the physics of confinement, the equilibrium and stability of tokamaks, diagnostics, heating and current drive by neutral beam and radiofrequency waves, and plasma–wall interactions While the tokamak is a leading concept for the realization of fusion, other concepts (helical confinement and, in a broader sense, other magnetic and inertial configurations) are also addressed in the book At over 1100 pages, this publication provides an unparalleled resource for fusion physicists and engineers Edited by: Mitsuru Kikuchi Karl Lackner Minh Quang Tran INTERNATIONAL ATOMIC ENERGY AGENCY VIENNA ISBN 978–92–0–130410–0 ! @ Edited by: Mitsuru Kikuchi Karl Lackner Minh Quang Tran ... -l 12 bi l11 bI l11 bb l11 0 ee -l 21 ei -l 21 eI -l 21 eb -l 21 ee l 22 ei l 22 eI l 22 ie -l 21 ii -l 21 iI -l 21 ie l 22 ii l 22 iI l 22 Ie Ii -l 21 -l 21 II -l 21 Ie l 22 Ii l 22 II l 22 be... j Z 2j ne A j 2/ 3 AbTe 14.8Z 2/ 3 Ab1/3Te [keV] 3 (2 ) 3 /2 02 mbTe3 /2 0 .2 AbTe [keV] 3 /2 e Z b2 n e m1 /2 Z b2 n e [10 20 m –3 ]ln e ln (5.9) (5.10) Here, Z n j Z 2j Ab... thermal energy Wth,i th ~ se se Wb Wth , i dWb3 /2 Wb3 /2 Wc3 /2 se ln 3 /2 Wb3 /2 Wc 3 /2 Wth3 /2 ,i W c ln((Wb / Wc ) 3 /2 1) (5. 12) and the integrated power fraction to ions as a