[Show abstract][Hide abstract] ABSTRACT: A similarity technique is described in which the temperature and density profiles and fusion performance of ITER and DEMO are determined from the D–T and D–D discharges completed on JET. The limitations and errors associated with this technique are also briefly described.
[Show abstract][Hide abstract] ABSTRACT: The large increase in radiation during neutral injection in DITE is identified as being primarily due to the charge-exchange recombination of the impurities on the fast neutrals. The time dependence of the increase in line eion and its dependence on injection power and plasma density is shown to fit the theory. – The line emission and the total radiated power are found to be toroidally asymmetric, being larger in the region of beam deposition. A theoretical explanation for this asymmetry is given. The recombination of impurities by thermal neutrals is found to be important in low-density Ohmic discharges, and the implications of this are discussed.
[Show abstract][Hide abstract] ABSTRACT: Auxiliary heating by neutral beam injection (NBI) or ion cyclotron resonance heating (ICRH) can broaden or steepen the plasma current density profile. A measure of changes to the current density profile J is established by a combination of current moments which yields the profile broadening parameter ζ. JET experiments are demonstrated to increase ζ (broaden J) when NBI is applied to discharges which exhibit either L-mode or H-mode confinement; pellet injection and ICRH or current decay are demonstrated to decrease ζ (peak J). The time evolution of the parameter ζ is shown to correlate with the changes to the Dα emission seen in H-mode discharges with and without edge localized modes. The broadening of J by NBI, especially for H-mode pulses, smarts in the edge region and it is identified with the non-inductive bootstrap current component as a consequence of steep density profiles. Associated with current profile broadening is an increase in the edge pressure and the total stored plasma energy W. An analysis of global confinement (variations of W with power P) is made by splitting W into three parts: the fast ion energy, Wf, the edge energy, W1, which is empirically shown to be proportional to the current profile broadening parameter ζ, and the bulk plasma thermal energy, Wp. It is shown that the scaling for Wp in the L- and H-mode confinement regimes is similar.
[Show abstract][Hide abstract] ABSTRACT: A subset of the ITER L-mode and H-mode confinement data is tested against the constraints imposed by various theoretical models for thermal plasma transport. Matrix algebra is used to facilitate such tests. A new result obtained is that the fundamental constraint imposed by the high-β collisional Fokker-Planck equation (Kadomtsev) is satisfied by the data. An additional constraint on the characteristic scale length associated with thermal diffusion can also be satisfied by the data. Dimensionally correct empirical scaling laws embodying theoretical constraints can thus be derived.
[Show abstract][Hide abstract] ABSTRACT: It is shown that a high-energy tail may form on the background-ion distribution during neutral-injection heating. The temperature of this tail is found to depend critically upon the velocity dependence of the particle and energy loss mechanisms. – The Fokker-Planck equation for the equilibrium thermal-ion distribution is solved both numerically for all v and analytically for large v. Results from the numerical solution are presented for various cases of particle or energy loss including particle loss by charge exchange or diffusion and energy loss by thermal conduction. An analytic expression for the ratio of tail to actual temperature is derived for the case of good high-energy containment and for energy-independent particle loss (e.g. charge exchange). The expression derived for the latter case is shown to be in good agreement with the numerical results.
[Show abstract][Hide abstract] ABSTRACT: The steady-state collisional distribution function of a mirror-confined plasma which is known from Fokker-Planck calculations, implies a unique relationship between the plasma pressure and the magnetic field strength at any point within the plasma. Using this relationship it is possible to deduce the maximum β consistent with macroscopic stability in a mirror machine with given mirror ratio. This β limitation is found to impose a rather mild restriction upon reactor designs. For fields which satisfy this β limitation, the profile of the magnetic field along its axis is restricted but not fully determined, by the minimum-B requirement, and the remaining freedom can be used to optimize the magnet design by maximizing the ratio of the thermonuclear power produced to the cost of the magnetic field windings. It is found that even when the profile has been optimized in this way, the plasma density and pressure profiles are rather peaked towards the centre of the reactor, and the ratio of the thermonuclear power produced in such an optimized minimum-B reactor to the power which would be produced in a reactor of the same dimensions but with a square well profile (if it were stable) is approximately 1/4.
[Show abstract][Hide abstract] ABSTRACT: The total heat flux q arising in steady state from Ohmic and neutral beam heating is calculated for a series of power scan experiments on JET. A radial resolution of q at selected radii is made to examine the dependence of q upon local plasma parameters such as density ne, temperature Te, current I and their gradients. Non-linear regression analysis techniques are applied to fit the data on q to empirical expressions qfit, involving the local plasma parameters. The most plausible fit emerging from the analysis is qfit = − (C/I)ne ∇Te− qpinch, in which C is a constant, I the current enclosed by a plasma surface and qpinch a constant so-called heat pinch. The net heat diffusivity inferred from this relationship agrees with estimates from heat pulse propagation measurements and it leads to a scaling law for the incremental energy confinement time which agrees with the one determined experimentally. There is a substantial amount of scatter in the data due to approximations made in the analysis and due to uncertainties in the experimental measurements.
[Show abstract][Hide abstract] ABSTRACT: A Fokker-Planck treatment of the current induced by a beam of fast ions circulating in a toroidal plasma is developed. The electron Fokker-Planck equation is first reduced to an integro-differential equation which is then solved analytically in the limiting cases of: (a) a large plasma Z and (b) a large ratio of the electron thermal velocity ve to the fast ion velocity vb. In addition, a numerical solution was obtained for the complete range of values of ve/vb and for several values of Z. It is found that the resulting net plasma current has a very different functional dependence upon electron temperature than that given by the conventional theoretical treatment in which the electrons are assumed to be Maxwellian. In particular, for ve > vb and Z = 1, which is the limit appropriate to many present tokamak experiments, the net current is found to be in the opposite direction to the fast-ion current. The theory is compared with recent measurements of this current which were made by using the Culham Levitron, and agreement is found between theory and experiment.
[Show abstract][Hide abstract] ABSTRACT: On the basis of an analysis of the ITER L-mode energy confinement database, two new scaling expressions for tokamak L-mode energy confinement are proposed, namely a power law scaling and an offset-linear scaling. The analysis indicates that the present multiplicity of scaling expressions for the energy confinement time τE in tokamaks (Goldston, Kaye, Odajima-Shimomura, Rebut-Lallia, etc.) is due both to the lack of variation of a key parameter combination in the database, fs = 0.32 R a−0.75 k0.5 ~ A a0.25k0.5, and to variations in the dependence of τE on the physical parameters among the different tokamaks in the database. By combining multiples of fs and another factor, fq = 1.56 a2 kB/RIp = qeng/3.2, which partially reflects the tokamak to tokamak variation of the dependence of τE on q and therefore implicitly the dependence of τE on Ip and ne, the two proposed confinement scaling expressions can be transformed to forms very close to most of the common scaling expressions. To reduce the multiplicity of the scalings for energy confinement, the database must be improved by adding new data with significant variations in fs, and the physical reasons for the tokamak to tokamak variation of some of the dependences of the energy confinement time on tokamak parameters must be clarified.
[Show abstract][Hide abstract] ABSTRACT: Neutral beam heated H-mode DIII-D and JET expanded boundary divertor discharges were examined to study the parametric dependence of the thermal energy confinement on the plasma current, plasma size and neutral beam power. Single-null discharges in both machines were examined during the ELM-free phase (ELM stands for edge localized mode) to extract information about the intrinsic H-mode thermal energy confinement time τth. A power law dependence of ELM-free thermal energy confinement was assumed, with the result that for Bτ ≈ 2.2 T and κ = 1.8, τth = C Ip1.03±0.07 PL−0.46±0.06 L1.48±0.09. The size dependence of τth is described by the linear dimension L since the determination of the individual dependences on the minor and major radii is precluded by the similar aspect ratio of the two machines. For this representation of τth (units of s, MA, MW and m), when L is the plasma major radius, C = 0.106 ± 0.011, and when L is the plasma minor radius, C = 0.441 ± 0.044. A dimensionally correct version of the scaling, consistent with the constraints of a collisional high beta model, is τth∝ Ip1.06 PL−0.45 L1.40 ne0.07 Bτ0.06. These results indicate that, within the experimental error, the empirical scaling and the dimensionally correct scaling are the same.
[Show abstract][Hide abstract] ABSTRACT: A powerful beam of neutral hydrogen is injected tangentially into the plasma produced in the Cleo-Tokamak apparatus. The effect on the macroscopic parameters of the plasma and on the equilibrium are found to be small. The energy spectrum of the resulting fast ions contained in the plasma is deduced from measurements of tangentially emitted charge-exchange neutrals. The results for injection parallel and anti-parallel to the plasma current are compared with a classical theoretical model, and good agreement is obtained. Measurements of the perpendicular energy spectrum of 'plasma ions' show that the bulk of the ions are heated by about 10%, and that the low-energy ion distribution has a 'tail', which is consistent with the spectrum of decelerated injected ions.
[Show abstract][Hide abstract] ABSTRACT: Calculations of Q including the effects of velocity diffusion, finite ion temperature, electric fields and charge exchange are presented. It is found that if all charge-exchange fast ions are lost then Q is severely reduced for a neutral fraction, nn/ne7 × 10−6. These losses are reduced by re-ionization of the charge-exchanged fast ions. Calculations for the case of a two-component tokamak show that the effective charge-exchange rate is typically reduced by 2.5−4 times owing to re-ionization. With allowance for this, it is found that, in a stationary system, the plasma loss rate nτp must be greater than 1012 cm−3 to achieve a Q greater than unity.
[Show abstract][Hide abstract] ABSTRACT: Neutral beam heating data from JET have been analysed in detail to determine what proportion of the current is driven non-inductively. It is found that in low density limiter discharges, currents of the order of 0.5 MA are driven, while in H-mode plasmas currents of the order of 0.7 MA are measured. These measured currents are found to be in reasonable agreement with theoretical predictions based on neoclassical models. In low density plasmas the beam driven current is large while the neoclassical bootstrap current dominates H-mode plasmas.
[Show abstract][Hide abstract] ABSTRACT: The temperature profiles produced by various heating profiles are calculated from local heat transport models. The models take the heat flux to be the sum of heat diffusion and a non-diffusive heat flow, consistent with local measurements of heat transport. Two models are developed analytically in detail: (i) a heat pinch or excess temperature gradient model with constant coefficients; and (ii) a non-linear heat diffusion coefficient (χ) model. Both models predict weak (20%) temperature profile responses to physically relevant changes in the heat deposition profile – primarily because the temperature profile is a double integral of the heating profile. The model predictions are shown to agree with JET data for a variety of heating profiles ranging from peaked on-axis through approximately flat (NBI at high density) to localized off-axis (ICRH). The modest temperature profile responses that result from the models clarify why temperature profiles in many tokamaks are often characterized as exhibiting a high degree of 'profile consistency'. Global transport scaling laws are also derived from the two models. The non-linear model with χ ∝ dT/dr produces a non-linear energy confinement time (L-mode) scaling with input power, . The constant heat pinch or excess temperature gradient model leads to the offset linear law for the total stored energy W with Pin, W = τinc Pin + W(0), which describes JET auxiliary heating data quite well. It also provides definitions for the incremental energy confinement time , the heating effectiveness η, and the energy offset W(0). Considering both the temperature profile responses and the global transport scaling, the constant heat pinch or excess temperature gradient model is found to best characterize the present JET data. Finally, new methods are proposed for interpreting auxiliary heating data in terms of these local transport models.
[Show abstract][Hide abstract] ABSTRACT: The energy confinement properties of low density, high ion temperature L- and H-mode plasmas are investigated. For L-mode plasmas it is shown that, although the global confinement is independent of density, the energy confinement in the central region is significantly better at low densities than at higher densities. The improved confinement appears to be associated with the steepness of the density gradient. For the H-mode phase, although the confinement at the edge is dramatically improved, which is once again associated with the steep density gradient in the edge region, the central confinement properties are essentially the same as for the standard L-mode. The results are compared in a qualitative manner with the predictions of the ion temperature gradient instability theory and appear to be in disagreement with some aspects of this theory.
[Show abstract][Hide abstract] ABSTRACT: Effects of neutral beam injection upon the equilibrium of a toroidal plasma are considered. The distribution function of energetic ions produced by the beam in the plasma is calculated for injection both parallel and perpendicular to the magnetic field taking account of effects due to the toroidal geometry. The effect of trapped particles on the current induced in the plasma by such a beam is calculated, together with the associated cross-field diffusion. Loss mechanisms for the momentum deposited in the plasma by the neutral beam are considered. Ripples in the toroidal magnetic field strength are particularly efficient at destroying toroidal momentum and lead to flow velocities much less than the sound speed for typical injection parameters.
[Show abstract][Hide abstract] ABSTRACT: A model is presented which permits selfconsistent calculation of the power deposition and velocity distribution of cyclotron resonance heated ions. The model is applied to minority heating of 3He in deuterium plasmas in the JET experiment. Good agreement is found between calculated and measured values of fusion yield and energy content of 3He ions. The results indicate that the power deposition is adequately described and that the fast ions slow down on electrons by Coulomb collisions. Measurements of the electron heating after the sawtooth crash show that about 50% of the energy content of the fast ions is retained in the centre after a sawtooth crash.
[Show abstract][Hide abstract] ABSTRACT: An anisotropic high-β equilibrium is derived for the counterstreaming-beam tokamak (CBT). The critical β of the CBT is found to be of comparable magnitude to that occurring in a similar model of a scalar-pressure tokamak. It is shown that the toroidal current which is essential for equilibrium can be maintained by the counterstreaming ions. Finally, a brief discussion of the stability of the device is given.
[Show abstract][Hide abstract] ABSTRACT: The particle distribution in phase space near the loss cone of a stable mirror machine is determined by an asymptotic analysis based on the smallness of λ, the ratio of transit time between mirrors to mean collision time. Away from the loss cone, the solution is obtained by averaging over a bounce motion. Near the loss Cone, i.e., within a distance scaling as λ1/2, the governing equations are converted into a Wiener-Hopf equation along a boundary line in phase space whose solution yields the desired distribution. It is found that the ratio of plasma density in the mirror throat to central density scales as λ3/4 while the ratio of external density to central density scales as λ. For typical reactor conditions, these ratios correspond to densities of 1011 cm−3 and 108, respectively. Since the distance over which this drop occurs scales as λ1/2 times the local magnetic scale length, it is necessary to re-examine the reflection of unstable plasma waves in the neighbourhood of the mirrors.
[Show abstract][Hide abstract] ABSTRACT: From the equations which describe local transport in a turbulent plasma the scaling of the local diffusivity with the plasma parameters can be established. It is shown that, by appropriate choices of time and length scales for the turbulence, the scaling of the global energy confinement can be cast in two limiting forms: a short and a long wavelength scaling. The scaling laws consist of a leading term and a function F whose arguments are the dimensionless normalized plasma collisionality and beta. The scaling of the leading term in the short wavelength expression for global confinement is shown to fit both L-mode and H-mode confinement data from JET. The function F which describes the precise physical mechanism of the turbulence is found to increase with collisionality, but its dependence on the plasma beta remains uncertain. Several theoretical models are found to be a reasonable fit to the JET confinement data; others, however, such as that for the dissipative trapped electron mode, can be discarded. The short wavelength confinement scaling is shown to unify a multiplicity of existing theoretical/empirical scaling laws by suitable choices of the function F. These scaling laws all exhibit a similar dependence of F upon collisionality but have different dependences upon the plasma beta. It is shown that for the JET data it is very difficult to determine the beta dependence and this explains why so many apparently different scaling laws produce reasonable fits to the data. Using the leading term of the scaling, the fusion product can be extrapolated to reactor conditions (ITER) with an uncertainty factor of four. This uncertainty can be reduced to ±30% by the use of a similarity technique in which F is determined directly from the JET data.