Showing papers in "Nuclear Fusion in 1981"
TL;DR: In this paper, a closed set of moment equations is presented for the time evolution of thermodynamic and magnetic field quantities which results from collisional transport of the plasma and two-dimensional motion of the magnetic flux surface geometry.
Abstract: Tokamak plasmas are inherently comprised of multiple ion species. This is due to wall-bred impurities and, in future reactors, will result from fusion-born alpha particles. Relatively small densities nI, of highly charged non-hydrogenic impurities can strongly influence plasma transport properties whenever . The determination of the complete neoclassical Onsager matrix for a toroidally confined multispecies plasma, which provides the linear relation between the surface averaged radial fluxes and the thermodynamic forces (i.e. gradients of density and temperature, and the parallel electric field), is reviewed. A closed set of one-dimensional moment equations is presented for the time evolution of thermodynamic and magnetic field quantities which results from collisional transport of the plasma and two-dimensional motion of the magnetic flux surface geometry. The effects of neutral-beam injection on the equilibrium and transport properties of a toroidal plasma are consistently included.
1,081 citations
TL;DR: In this article, a new type of axisymmetric magnetohydrodynamic equilibrium is presented, characterized by a region of pressure and safety factor variation with a short scale length imposed as a perturbation.
Abstract: A new type of axisymmetric magnetohydrodynamic equilibrium is presented. It is characterized by a region of pressure and safety factor variation with a short scale length imposed as a perturbation. The equilibrium consistent with these profile variations can be calculated by means of an asymptotic expansion. The flexibility obtained by generating such equilibria allows for a close examination of the mechanisms that are relevant to ballooning instabilities – ideal-MHD modes with large toroidal mode number. The so-called first and second regions of stability against these modes are seen well within the limits of validity of the asymptotic expansion. It appears that the modes must be localized in regions with small values of the local shear of the magnetic field. The second region of stability occurs where the local shear is large throughout the range where the magnetic-field-line curvature is destabilizing.
260 citations
TL;DR: In this article, the state-of-the-art in the knowledge of rate coefficients, cross-sections, transition probabilities, and ionization equilibrium calculations is reviewed, and a short discussion of X-ray plasma sources and instrumental problems is presented.
Abstract: Soft X-ray spectroscopic diagnostics of laboratory plasmas are considered. To start with, the state of the art in the knowledge of rate coefficients, cross-sections, transition probabilities, and ionization equilibrium calculations is reviewed. Next, the plasma spectral emission, i.e. continuum and line emission (including satellites), line broadening (including opacity), and total emitted radiation as an energy loss process, is considered. To conclude, a short discussion of X-ray plasma sources and instrumental problems is presented.
188 citations
TL;DR: In this paper, the particle influx is proportional to the anomalous outward diffusion coefficient, and its dependence on the main plasma parameters that has been adopted makes it possible to reproduce both the time evolution and the steady state of the density profiles observed in a relatively large variety of experiments.
Abstract: The density profiles that have been observed experimentally in magnetically confined plasmas, both in stationary and time-dependent conditions, suggest that they result from the balance of an outward particle diffusion and an inward plasma flux whose rates are higher than those predicted by the collisional transport theory. The outward particle diffusion is considered to be proportional to the effective electron thermal conductivity that has been shown in previous papers to be consistent with existing observations of the electron temperature profiles and the scaling for the electron energy confinement time. The adopted expression for the particle influx is proportional to the anomalous outward diffusion coefficient, and its dependence on the main plasma parameters that has been adopted makes it possible to reproduce both the time evolution and the steady state of the density profiles observed in a relatively large variety of experiments.
107 citations
TL;DR: In this paper, Doppler shifts of appropriate spectra lines were made from both hydrogen and deuterium beams and include data from both co-and counter-injection at several electron densities.
Abstract: Toroidal plasma rotation in the Princeton Large Torus, PLT, has been measured for various plasma and neutral-beam injection conditions. Measurements of the plasma rotational velocities were made from Doppler shifts of appropriate spectra lines and include data from both hydrogen and deuterium beams and co- and counter-injection at several electron densities. Without injection, a small but consistent toroidal rotation exists in a direction opposite to the plasma current (counter-direction) in the plasma centre but parallel to the current (co-direction) in the plasma periphery. Using these velocities measured in the absence of injection, and the plasma density and temperature gradients, radial electron fields can be determined from theory, giving Er ≈ 40 V · cm−1 in the plasma centre and Er ≈ 10 V · cm−1 near the plasma edge. Insertion of a local, 2.5% magnetic well produced no observable effect on the beam-driven rotation. Modelling of the time evolution and radial distribution of the rotation allows one to deduce an effective momentum diffusivity of the order of (1–5) × 104 cm2 · s−1.
105 citations
TL;DR: In this article, the critical β for stability against ideal hydromagnetic internal ballooning modes as a function of the toroidal mode number, n, is calculated for two different equilibrium sequences by use of a finite-element technique (n 20), and a WKB formalism (n 5).
Abstract: The critical β for stability against ideal hydromagnetic internal ballooning modes as a function of the toroidal mode number, n, is calculated for two different equilibrium sequences by use of a finite-element technique (n 20), and a WKB formalism (n 5). The agreement between the two methods is good in the overlap region 5 n 20. The WKB formula reduces to the '1/n correction' at very high n, but is much more accurate at moderate n. The critical-β-versus-n curves exhibit oscillatory structure at low n, but in both sequences the lower bound on βc is set by n = ∞ modes at about βc ~ 5%.
88 citations
TL;DR: In this paper, a transport model for the toroidal wall of a tokamak was analyzed, where convective flow of the plasma from the boundary layer to the first wall permits elevated particle densities in the boundary layers and leads to very high particle and energy transport.
Abstract: In a tokamak configuration, superposition of the magnetic field of resonant helical windings which surround the toroidal plasma current outside the first wall destroys the magnetic surfaces in the boundary layer (ergodization). A transport model is analysed, where convective flow of the plasma from the boundary layer to the first wall permits elevated particle densities in the boundary layer and leads to very high particle and energy transport. The convective flow is driven by the pressure gradient along the field lines which intersect the toroidal wall at an oblique small angle . The required thickness ? of the boundary layer is around 1015 n?1?cm?2. As a result, the plasma temperature there can be reduced towards the threshold of critical plasma-wall-interaction processes, the plasma core can be shielded against impurities from the wall and, at the same time, a very short life-time of all particles in the boundary layer can be achieved (use of pumpholes and/or scrape-off-limiters for removing ash). Thus, this model also improves the concepts of edge radiation cooling. An estimate is given of the parameters of INTOR using only a weak helical perturbation field which conserves the magnetic surfaces in the plasma core: one can reach wall temperatures Tw between 20 and 30 eV in the presence of wall densities nw approaching 1014cm?3.
86 citations
TL;DR: In this article, a fusion neutron emission of 1.5 × 1014 neutrons s−1 and 2 × 1013 neutrons/pulse has been observed for PLT deuterium discharges with up to 2.5 MW of neutral-beam injection.
Abstract: Fusion neutron emission of 1.5 × 1014 neutrons s−1 and 2 × 1013 neutrons/pulse has been observed for PLT deuterium discharges with up to 2.5 MW of deuterium neutral-beam injection. The neutron time evolution and magnitude are consistent with theoretical calculations of the fusion reactions caused by energetic injected ions which are confined and slow down classically. The factor-of-two accuracy in the absolute neutron calibration is the major uncertainty in the comparison with theory. Neutron sawtooth oscillations ( 3%) are observed which can also be explained classically.
80 citations
TL;DR: In this paper, the magnetic and electrostatic spectra of a Macrotor were compared in the frequency range above the usual low-frequency Mirnov oscillations, and no local cross-correlation between and has been detected.
Abstract: Probe measurements of magnetic and electrostatic fluctuations in Macrotor are compared. Attention is concentrated on small-scale fluctuations which lie in the frequency range above the usual low-frequency Mirnov oscillations. In this range, 20 kHz 125 kHz, the spectra of and are similar; the radial profile of /n is, however, peaked toward the outside while that of r is peaked toward the centre, and no local cross-correlation between and has been detected. The radial correlation length of is smaller than that for r (both being much smaller than the minor radius), but the poloidal correlation lengths of p and are similar. Both and fluctuations rotate in the electron diamagnetic drift direction. The spectra are roughly invariant to an increase in density; however, the magnitude of /n decreases with density while that of r remains unchanged. No connection between these fluctuations and anomalous transport has been established.
80 citations
TL;DR: In this article, a pre-ionization experiment was performed on a tokamak by injecting about 80 kW of microwave power at 35 GHz for up to 15 ms and the observed parameters were shown to be consistent with a theory which employs classical models of energy and particle balance.
Abstract: Pre-ionization experiments have been performed on a tokamak by injecting about 80 kW of microwave power at 35 GHz for up to 15 ms. Microwave absorption occurs at the electron cyclotron and upper hybrid resonance frequencies as predicted by theory. Pre-ionization causes substantial (40%) reductions in loop voltage during the initial phase of the tokamak shot. Flux (volt-second) savings with pre-ionization are about 30% in the first 2 ms or about 2% of the total flux expenditure in a tokamak shot. The plasma current begins 200 μs earlier and rises 1.4 times more rapidly in the pre-ionized case. Electron densities of 5 × 1012 cm−3 can be sustained throughout the microwave pulse with only a toroidal magnetic field during microwave injection. The bulk electron temperature in the pre-ionized plasma is about 10 eV although there are indications of higher electron temperatures (50 eV) in the upper hybrid resonance layer. Although questions exist concerning the quiescent behaviour of the pre-ionized plasma, the observed parameters are shown to be consistent with a theory which employs classical models of energy and particle balance. During the early stages of Ohmic heating, the pre-ionization is effective in decreasing the peak of the radiated power.
74 citations
TL;DR: In this paper, the preferential heating of ions travelling in one direction but with no net momentum injected into the system was proposed to generate electric currents in a two-ion-species plasma.
Abstract: It is proposed that electric currents be generated from the preferential heating of ions travelling in one direction but with no net momentum injected into the system. This can be accomplished with, for example, travelling waves in a two-ion-species plasma. The current can be generated efficiently enough for the scheme to be of interest in maintaining steady-state toroidal currents in a reactor.
TL;DR: In this article, the effect of impurity radiation from the low-temperature boundary region of a confined plasma exceeds the power transported from the central region, and the temperature profile will collapse.
Abstract: If the power lost by impurity radiation from the low-temperature boundary region of a confined plasma exceeds the power transported from the central region then temperature equilibrium is impossible and the temperature profile will collapse. This situation is studied on the assumption of coronal equilibrium and the results are used to predict the permissible impurity concentration at the edge of a tokamak reactor. The effect of neoclassical impurity transport is studied analytically and a 1D tokamak diffusion code is used to illustrate the detailed collapse of the temperature profile when the plasma density in a radiation-cooled tokamak is increased. Finally, the results are used to predict the limiting density of a radiation-cooled tokamak; this predicted density limit is compared with the density limits observed in current tokamak experiments.
TL;DR: In this paper, a numerical solution of the Fokker-Planck equation is used to verify the theory of Fisch and Boozer and to extend their results into the non-linear regime.
Abstract: Certain aspects of the generation of steady-state currents by electron cyclotron waves are explored. A numerical solution of the Fokker-Planck equation is used to verify the theory of Fisch and Boozer and to extend their results into the non-linear regime. Relativistic effects on the current generated are discussed. Applications to steady-state tokamak reactors are considered.
TL;DR: In this article, the outermost flux surfaces in tokamaks are expanded to provide a large volume for radiative cooling, and the resulting edge cooling and reduced heat load on the limiter may significantly retard impurity generation.
Abstract: It is proposed to expand the outermost flux surfaces in tokamaks to divert the heat flux emerging from the plasma core The expanded flux surfaces provide a large volume for radiative cooling The radiative power at the boundary is enhanced by the effects of plasma flow as well as by a volumetric factor, and the resultant edge cooling and reduced heat load on the limiter may significantly retard impurity generation Furthermore, it seems to be compatible with reactor engineering requirements
TL;DR: In this paper, neutral-beam injection of up to 25 MW into plasmas in the ISX-B tokamak (R0 = 093 m, a = 027 m, BT = 09-15 T, Ip = 70-210 kA, e = 25-10×1013 cm−3) has created plasmas with volume-averaged beta of up-to ~ 25, peak beta values of upto ~ 9%, and root-mean-square beta values up to ~ 35% energy confinement time is observed to decrease
Abstract: Neutral-beam injection of up to 25 MW into plasmas in the ISX-B tokamak (R0 = 093 m, a = 027 m, BT = 09–15 T, Ip = 70–210 kA, e = 25–10×1013 cm−3) has created plasmas with volume-averaged beta of up to ~ 25%, peak beta values of up to ~ 9%, and root-mean-square beta values of up to ~ 35% Energy confinement time is observed to decrease by about a factor of two as beam power goes from 0 to 25 MW; the decrease is caused predominantly by the electron confinement time falling below the predictions of 'Alcator scaling' by a factor of 3–4 at high beam power An empirical relationship of the form fits our measurements over a wide range of plasma parameters The function f(Pb), where Pb is the beam power, is linear for Pb ≤ 12 MW but tends to saturate for 12 MW ≤ Pb ≤ 25 MW Although the equilibria attained in ISX-B are predicted to be above the threshold for the ideal magnetohydrodynamic (MHD) ballooning instability, no evidence of these modes is observed
TL;DR: In this paper, the results and interpretation of the modest-power (~90 kW) lower-hybrid-heating experiment on Alcator A are presented, and the possible effects of parametric instabilities, scattering from density fluctuations, and imperfect energetic ion confinement are addressed.
Abstract: The results and interpretation of the modest-power (~90 kW) lower-hybrid-heating experiment on Alcator A are presented. The expected results from linear waveguide-plasma coupling theory are outlined, and the possible effects of parametric instabilities, scattering from density fluctuations, and imperfect energetic ion confinement are addressed. It is found experimentally that good coupling and the absence of RF breakdown are achieved with a double waveguide array at available RF power densities PRF ≤ 4.5 kW.cm·−2, the waveguide vacuum windows being outside the toroidal field magnets; a waveguide array having vacuum windows near the waveguide mouth so that the ω = ωce layer can be pressurized shows no breakdown at PRP > 8 kW/cm2 when a single waveguide is energized. Energetic ion production and a factor-of-50 increase in the fusion neutron rate are observed to take place at well defined values of central plasma density; below these densities electron heating occurs. The ion tail production is found to be independent of the relative phase of the double waveguide array employed. This ion heating occurs at a lower density than theoretically expected; together with the electron heating this indicates waves having n|| ~5 being absorbed near the plasma centre. Probes at the plasma edge observe a frequency-down-shifted and broadened RF pump signal that is strongly attenuated as the plasma density increases through the neutron production band. These anomalous heating results and probe signals can be explained by a parametric decay of the pump wave into higher n|| lower hybrid waves near the plasma edge. An alternate qualitative explanation would be the poloidal scattering of the lower hybrid waves at the plasma periphery due to density fluctuations; the n|| of the scattered lower hybrid waves would then increase as they propagated inward because of magnetic shear. The neutron rate decay times imply that the RF creates ion tails having a substantial fraction of their energy above 50 keV. The neutron decay times and rates strongly depend on plasma current and indicate the expected influence of ion confinement on RF heating efficiencies. Finally, the RF heating efficiencies are assessed.
TL;DR: In this article, two features of the ablation structure in the presence of hot electrons are clarified by simulation and theoretical analysis, one feature is the possibility of steady deflagration wave being formed by collisional energy deposition of hot particles in the high-density region of laser targets, the other one is the creation of a steep density profile near the critical point, associated with hot-electron trapping and coldelectron heating.
Abstract: Two features of the ablation structure in the presence of hot electrons are clarified by simulation and theoretical analysis. One feature is the possibility of steady deflagration wave being formed by collisional energy deposition of hot electrons in the high-density region of laser targets, the other one is the creation of a steep density profile near the critical point, associated with hot-electron trapping and coldelectron heating due to a high electric field enhanced by anomalous resistivity to the return current. It should be noted that, in this anomalous region, a significant fraction of hot-electron energy is transferred to thermal electrons above 5 × 1015Wcm−2. A theoretical analysis is given which qualitatively agrees well with the simulation results. Possible applications of the theory to recent experiments are proposed.
TL;DR: In this paper, a simple impedance-matching argument was used to show that coupling is optimum for an edge density, n 0, determined by, where nc = ω2me/4πe2 and n|| is the parallel index of refraction of the lower hybrid wave.
Abstract: The usual predictions of linear coupling theory for lower hybrid waves are altered by including an overdense edge plasma (ω < ωpe) in the plasma model. Coupling is found to depend strongly on the value of the edge density, as well as the density gradient. The regimes, where one or the other of these parameters is important, are investigated. Typically, only the first few millimetres of the edge plasma are important in determining coupling. The major implications of the problem of coupling to an overdense plasma can be derived from a simple impedance-matching argument. In general, coupling is optimum for an edge density, n0, determined by , where nc = ω2me/4πe2 and n|| is the parallel index of refraction of the lower hybrid wave.
TL;DR: In this article, the effect of finite-ion-Larmor-radius averaging and ion Landau damping on ballooning modes is investigated for a large-aspect-ratio circular-cross-section tokamak equilibrium.
Abstract: The effect of finite-ion-Larmor-radius averaging and of ion Landau damping on ballooning modes is investigated for a large-aspect-ratio circular-cross-section tokamak equilibrium. – Finite-Larmorradius (FLR) effects are found to be weakly de-stabilizing for small values of the FLR parameter kai, but become strongly stabilizing for kai ~ 0.5. A residual instability driven by inverse ion Landau damping persists, however, at shorter wavelengths (kai > 0.5).
TL;DR: In this paper, a class of high-gain ICF targets driven by electrons or light ions is discussed, characterized by a low-beam-intensity requirement and large size, and the addition of a cryogenic fuel layer increases the gain without requiring significantly increased beam power and intensity.
Abstract: A class of high-gain ICF targets driven by electrons or light ions is discussed. The targets are characterized by a low-beam-intensity requirement and large size. A magnetic field provides thermal insulation of pre-heated, low-density fuel. The addition of a cryogenic fuel layer increases the gain without requiring significantly increased beam power and intensity. The higher fuel adiabat and reduced fuel losses produce ignition and burn for lower implosion velocities and at lower power and intensity than conventional ablative designs. Gains of 20 to 40 are expected for intensities of 80 TWcm−2, initial magnetic fields of 30–60 kG, an initial fuel radius of 0.2–0.4 cm, and irradiation uniformities of 6–7%. Driver requirements are 45 TWcm−2 if the initial magnetic field is 300–600 kG, sufficient for alpha trapping in the compressed low-density fuel. Voltage shaping increases fuel burn-up and target ρr and lowers power and intensity levels by an additional factor of about 0.6.
TL;DR: In this paper, the ideal MHD stability properties of a class of hollow oblate spheromaks are studied numerically with a spectral code, and an internal kink instability is found whenever the safety factor on axis, qo, rises above one.
Abstract: The ideal-MHD stability properties of a class of hollow oblate spheromaks are studied numerically with a spectral code. An internal kink instability is found whenever the safety factor on axis, qo, rises above one. Its growth rate is only a weak function of the pressure. By shaping the current profile such that, simultaneously, q0 = 1 and the Mercier criterion is satisfied, full stability against internal perturbations is obtained up to a maximum value of β, this value increasing with the aspect ratio. For a configuration without a central hole, the maximum β is 1.5% and for an aspect ratio of 2.34, which is the largest that has been studied, it reaches 40%. Without a conducting shell, all equilibria are unstable to free-boundary modes, the fastest-growing mode being that associated with a global tilting motion. These modes, in contrast to the internal modes, are stabilized as the aspect ratio decreases. In the limiting case of no hole, the force-free equilibrium is only unstable with respect to n = 1 displacement which can be stabilized by a conducting shell located at a distance from the plasma boundary of 30% of the plasma minor radius.
TL;DR: In this article, a model of the plasma scrape-off is presented which explains pattern and extent of the damage, which is consistent with a radially outward drift velocity of 2 × 104 mms−1.
Abstract: PLT limiters used during Ohmic and neutral-beam heated discharges were melted and eroded. For the steel limiters, the pattern of large (20 cm2) melted areas was 0.1–1.0-mm ripples in a regular array. The various types of damage can be explained by the power and momentum fluxes of bulk plasma and beam ions and by disruptions. The plasma scrape-off distance inferred from the extent of the damage ranges from 5 to 30 mm and is consistent with a radially outward drift velocity of 2 × 104 mms−1. A new model of the plasma scrape-off is presented which explains pattern and extent of the damage.
TL;DR: In this paper, the stabilizing influence of finite-ion-gyroradius effects on magnetohydrodynamic ballooning modes for a simple model toroidal equilibrium is demonstrated.
Abstract: The stabilizing influence of finite-ion-gyroradius effects on magnetohydrodynamic ballooning modes for a simple model toroidal equilibrium is demonstrated
TL;DR: In this paper, the feasibility of heating tandem-mirror devices with microwaves near the electron cyclotron frequency or its harmonic is examined, and the optimal angle of wave launching for maximal absorption is found.
Abstract: The feasibility of heating tandem-mirror devices with microwaves near the electron cyclotron frequency or its harmonic is examined. Ray-tracing calculations are performed to find the optimal angle of wave launching for maximal absorption. It is found that the mirror plugs of present-day tandem-mirror devices can be heated effectively via the extraordinary mode, and that in the next generation of devices both the ordinary and the extraordinary mode of propagation can be used. Presently available gyrotrons can be used as sources of microwave energy in these experiments.
TL;DR: In this article, the authors construct an analytic reactor model in which neutral-beam input balances ion heat loss and show that the effect of anomalous resistivity is incorporated heuristically by assuming an anomalous resistance which is enhanced by a factor A over classical resistivity.
Abstract: Classical transport of particles and heat in field-reversed mirrors is discussed. The X-points (field nulls on axis) are shown to have no deleterious effect on transport; this conclusion is true for any transport model. For an elongated Hill's vortex equilibrium the classical diffusion coefficient is calculated analytically and used to construct an analytic solution to the transport equation for particles or energy ; this yields exact results for particle and energy confinement times. These life-times are roughly 3 to 6 times shorter than previous heuristic estimates. Experimentally determined life-times are within a factor of 3 to 4 of our estimates. To assess the impact of these results on reactor designs, the authors construct an analytic reactor model in which neutral-beam input balances ion heat loss. Energy loss due to synchrotron radiation is calculated analytically and shown to be negligible, even with no wall reflection. Formulas are presented which give the reactor parameters in terms of plasma temperature, energy multiplication factor Q, and allowed neutron wall loading. The effect of anomalous resistivity is incorporated heuristically by assuming an anomalous resistivity which is enhanced by a factor A over classical resistivity. For large A the minimum power of a reactor scales as A11/6. A = 50 gives a reactor design which still seems reasonable, but A = 200 leads to extremely large, high-power reactors.
TL;DR: In this paper, a horizontal polarization from the outside midplane at an angle nearly perpendicular to the 10-kG toroidal field of the JFT-2 tokamak was reported.
Abstract: Radio-frequency power of up to 110 kW for 14 ms at 28 GHz is launched in a horizontal polarization from the outside midplane at an angle nearly perpendicular to the 10-kG toroidal field of the JFT-2 tokamak. With initial Ohmic power comparable to the RF power, the central electron temperature increases from 600 to 1000 eV in 10 ms. Details of the electron heating are reported.
TL;DR: In this article, the effects of the cross-sectional shape, aspect ratio, and the location of a conducting wall on the stability of spheromak plasmas are investigated, and a circular cross-section configuration with a flux hole δ = 0.5 (aspect ratio R/a = 2) will will be stabilized by an ellipsoidal wall of mean separation of 1.3 minor radii from the plasma.
Abstract: In the absence of a conducting wall, typical spheromak plasmas are unstable to tilting and/or shifting modes. The effects of the cross-sectional shape, aspect ratio, and the location of a conducting wall on the stability of these modes are investigated. A circular cross-section (b/a ~ 1) configuration with a flux hole δ = 0.5 (aspect ratio R/a = 2) will will be stabilized by an ellipsoidal wall of mean separation of 1.3 minor radii from the plasma.
TL;DR: In this paper, the velocity-space loss region is determined from the condition whether the drift surfaces cross a limiter radius or not, and the transition probability between localized particles and blocked particles is assumed to be unity.
Abstract: Velocity-space loss regions are studied systematically on the basis of the adiabatic invariants J and in a large-aspect-ratio toroidal helical system with an l = 2 helical winding. The adiabatic invariant J is related to bounce motions in a helical ripple and used to study drift surfaces of localized particles, while the adiabatic invariant is related to bounce motions in a toroidal ripple and used to find drift surfaces of blocked particles or transit particles. The velocity-space loss region is determined from the condition whether the drift surfaces cross a limiter radius or not. The transition probability between localized particles and blocked particles is assumed to be unity. – For a configuration with large rotational transform and high shear, or a helical system with a short-pitch helical winding such as Heliotron E, localized particles trapped in helical ripples and with small parallel velocities, v|| 0, are confined in a plasma column by a drift motion due to a strong magnetic-field inhomogeneity. Velocity-space loss regions appear for both v|| > 0 and v|| < 0. On the other hand, for a configuration with weak shear such as the W VII A stellarator, localized particles are lost from the confinement region completely. Then the velocity-space loss region appears in the neighbourhood of v|| 0. – Velocity-space los is strongly dependent on the type of helical system.
TL;DR: In this article, the root-mean-square emittance and focal-spot size of a heavy-ion beam propagating through a vacuum reactor vessel were investigated. And the resulting constraints on heavy ion fusion-system design were discussed, together with possible means of relaxing these constraints.
Abstract: A heavy-ion beam propagating through a vacuum reactor vessel suffers phase-space distortion caused by anharmonic self-forces. If the distortion remains uncorrected, an enlarged focal spot results. Analytic predictions of an increase in root-mean-square emittance and focal-spot size are presented and shown to agree with computer simulation. The resulting constraints on heavy-ion fusion-system design are discussed, together with possible means of relaxing these constraints.
TL;DR: In this article, the Fokker-Planck equation is bounce-averaged over the large banana-width orbits after the variables have been transformed to the constants-of-motion space.
Abstract: Fusion-product thermalization and heating are calculated on the assumption of collisional slowing-down. The present analytical model describes fast-ion orbits and their distribution function in realistic, high-beta, non-circular tokamak equilibria. The Fokker-Planck equation is bounce-averaged over the large banana-width orbits after the variables have been transformed to the constants-of-motion space. First-orbit losses, trapping effects, and slowing-down drifts are fully treated. By solving a 3-D (+ time) partial differential equation, it is possible to obtain an invariant of the slowing-down process, μ/E = (magnetic moment)/energy = constant, and explicit expressions for the slowing-down drifts. Large banana-width effects give rise to a net co-going alpha-particle current. The large banana-width orbits smear the energy deposition over large regions of the plasma. This causes the in-situ heating rates to be 20–25% above theflux-surface-averagedrates on axis but enhances the edge heating 10-fold over in-situ deposition. While this result implies reduced alpha 'ash' accumulation on axis, the reduced heating rate makes start-up and maintenance of ignition more difficult.