Showing papers in "Nuclear Fusion in 1974"

Collisional losses of electrons from an adiabatic trap in a plasma with a positive potential

Abstract: The author obtains analytical expressions for the collisional losses of electrons and their energy from an adiabatic trap when the plasma has a high positive potential. The expressions are derived on the basis of an approximate solution of the Fokker-Planck equation, which yields more reliable results than those obtained with the estimative formulas used in a number of other works. In addition, an expression is obtained for the mean energy of the electrons escaping from the trap.

A powerful injector of neutrals with a surface-plasma source of negative ions

Abstract: The operation of surface plasma sources for negative ion beams is described. A diagram shows the dependence of the H/sup -/ current density inside the emission slit on the discharge current under optimized conditions with a plasma layer thickness of 0.5 mm. Various parameters of the source are discussed. (MOW)

Powerful relativistic electron beams in a plasma and in a vacuum (theory)

Abstract: The possibility of using intense relativistic electron beams (REBs) for heating plasmas in open systems is discussed. Within this context the following three sets of problems are discussed: REB transport in a vacuum with a strong magnetic field; beam equilibrium, stability and critical currents in a vacuum. Beam transport in a plasma; charge and current neutralization of the beam; reverse-current heating of the plasma, and macroscopic REB instabilities in the plasma. The theory of collective relaxation of REBs in a plasma, including quasi-linear and non-linear relaxation models; the role of plasma non-uniformity, and macroscopic effects during REB relaxation.

Theory of homogeneous isentropic compression and its application to laser fusion

Abstract: The hydrodynamic theory and properties of spherical homogeneous isentropic compression are discussed. Computer results are described showing that a close approximation to compressions of this type may be accomplished by light-induced pellet ablation if the light absorbed by the pellet is properly programmed with time, and is spatially uniform over the pellet surface. Pellet compressions in excess of ten thousand-fold are computed.

Electron beam focusing and application to pulsed fusion

Abstract: This paper reviews recent work on the focusing of high-power relativistic electron beams in diodes and discusses concepts for pulsed fusion based on this technology. The physics of high-current relativistic electron beam focusing using plasmas in high-current diodes is studied experimentally and with computer simulation. The physics of the beam interaction with dense targets and the requirements for break-even are briefly discussed.

Neutral-beam injection into a tokamak, part I: fast-ion spatial distribution for tangential injection

Abstract: The production processes and spatial distribution of fast ions resulting from tangential injection of a diffuse neutral beam into a tokamak are discussed. The spatial distribution of fast ions for various injection trajectories and absorption mean free paths are calculated and discussed in detail. Maximum beam absorption for a parabolic density profile is shown to occur for injection roughly halfway between the inner wall of the torus and the magnetic axis; however, since this maximum is near unity and only weakly dependent on the injection trajectory, this is not the most important possible optimization. Since the drift orbit surface area over which the fast ions are distributed is roughly proportional to the distance from the magnetic axis, the fast ion density is found to be strongly peaked at the magnetic axis for present experiments where the absorption mean free path λ is comparable to the plasma radius a. This geometric peaking effect is strong enough to overcome the exponential beam attenuation and cause the fast-ion density and consequent beam energy deposition to be peaked at the plasma centre as long as λ0 a/4. Charge exchange of the fast ions with neutrals in the plasma can deplete the fast-ion population, particularly near the plasma edge. When charge exchange is an important loss mechanism, beam injection nearly tangent to the magnetic axis is found to maximize the beam effectiveness in heating.

Effects of neutral injection heating upon toroidal equilibria

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.

Role of impurities in current tokamak experiments

Abstract: The authors discuss the possible consequences of the presence of multiply charged impurities in a tokamak plasma. The first such consequence is cooling of the plasma column periphery due to line radiation, which may lead to a sharpening of the electrical conductivity profile σ(r) and hence of the current density profile j(r), as is observed at high values of ne. Concentration of highly ionized impurities towards the plasma column axis is a possible competing process, leading to flattening of σ(r) and j(r) or even to a skin effect. From the results of soft (3–10 keV) X-radiation measurements the authors derive conclusions about the behaviour of impurities at the centre of the plasma. They find that the concentration of impurities can be interrupted by the development of plasma instabilities – especially kink and "disruptive" instabilities. With increasing ne, Te and discharge duration, the role of impurities in the shaping of j(r) necessarily increases. At some level, this may cause an additional deterioration in the thermal insulation and stability of the plasma column.

Laser compression of matter: optical power and energy requirements

Abstract: The optical power PL required to achieve a given measure of inertial confinement ρR of a laser-compressed DT pellet is found to be approximately proportional to (ρR)2. This result is based on a model of self-regulating pellet ablation by hot electrons of the pellet corona that is relatively insensitive to the details of the pellet ablation process. To achieve values of ρR believed necessary in the application of laser fusion to commercial power production, 3 × 1015 W of optical power is found to be required, implying a total laser output aperture of 30 m2. (The same power requirement would appear to apply to pellet compression by charged-particle beams.) An estimate of the required laser-pulse energy WL, assuming corona-core decoupling to be the controlling limitation, is also given. In the application to commercial power production the required pulse energy is found to range from 70 kJ at 0.265 μm to 3 MJ at 10.6 μm.

Theory of second-harmonic generation in an inhomogeneous hot plasma

Abstract: The authors have developed a consistent theory concerning the generation of a second harmonic when an electromagnetic wave is incident on a weakly inhomogeneous isotropic plasma, and have studied the dependence of the effect on plasma temperature. They point out the qualitative difference between the mechanisms of second harmonic generation in cases involving low and high temperatures and indicate the oscillatory nature of the intensity of second-harmonic emission. Attention is drawn to the strong enhancement of the effect when the density profile has inflection or extremum points. The influence of changes in density profile due to the high-frequency pressure of the incident wave on the generation of the second harmonic is discussed. The significance of second-harmonic generation in the laser-power heating problem is also discussed.

Impurity transport in tokamaks in the banana-plateau regime

Abstract: Transport coefficients, relating ion and impurity fluxes, and their fluxes of energy, to the density and temperature gradients, are derived from neoclassical theory. The ions are assumed to have mean free paths much longer than the torus connection length. The banana-plateau transition is shown to depend upon additional parameters which are not present in the electron-ion problem. Only two different ion masses are considered, but the heavier ions may have an arbitrary number of different possible ionization states. The mass ratio is arbitrary; the small mass-ratio limit is considered in detail, however. In that limit, the critical value of the collisionality parameter υ1*, for the transition from banana regime to plateau regime for the fluxes due to ion-impurity collisions, is shown to be ~(n1/ni)(m1/mi)1/2, where i denotes light ions and I denotes impurities. The plateau regime values of the corresponding transport coefficients are proportional to this parameter, which may be much smaller than unity, in typical cases. The modification of electron transport properties due to impurities is also discussed.

Absolute parametric instabilities in inhomogeneous plasmas

Abstract: The excitation of absolute instabilities in three-wave parametric couplin g processes in inhomogeneous plasmas has been studied analytically . A detailed examination of the full fourth-order set of differential equations describing such processes in infinite media confirms the WKB-criterion that absolute instabilities arise only if . A model calculation using the WKB-approximation has also been carried out to study the effects of finite plasma extent and pump depletion; conditions for the excitation of absolute instabilities in this case have also been obtained.

Servo-control of plasma position in Cleo-Tokamak

Abstract: A system for servo-control of the plasma position in a tokamak discharge is described. Measurements of the stability boundary of the servo-loop in the Cleo-Tokamak apparatus are presented and compared with a theoretical model. They show reasonable agreement. Using servo-control, the discharge time was extended from 110 ms to nearly 200 ms, and the plasma remained within ±10 mm of the centre of the vacuum vessel for up to 140 ms. The instability caused by a deliberately applied vertical field with positive gradient was stabilized.

MHD instabilities as an initial boundary-value problem

Abstract: The gross MHD instabilities of straight cylindrical plasmas with elongated cross-section are investigated by solving the linearized MHD equations as an initial boundary-value problem on the computer. The linearized equations are Fourier-analysed along the ignorable co-ordinate of the equilibrium in order to reduce the computation to two dimensions. The method is applied to find the fixed-boundary instabilities of an equilibrium with rectangular walls. Starting with an arbitrary initial perturbation and following it for many Alfven transit times, we find that the dominant instability overwhelms all stable oscillations after several e-folding times. We determine the growth rates of the fastest growing instabilities as a function of the equilibrium parameters. Then we examine the spatial structure of the physical variables (1, 1, p1). We find that the cross-section of the velocity field displays a distinctive convection pattern. This structure becomes spatially concentrated around the point of maximum rotational transform as the equilibrium current is decreased to the marginal point, and concentrates near the wall as the current is increased. Given the equilibrium p'(ψ) = Jzc ψ/ψc, ψ (wall) = 0, we find that the marginal current density Jzc for each mode increases as the cross-section is elongated. But the growth rates of the higher azimuthal m-modes increase with elongation and their intervals of instability overlap with the lower m-modes.

Vertical stability of elongated tokamaks

Abstract: The vertical stability of an elongated tokamak plasma with infinite conductivity is numerically investigated under simple assumptions, in toroidal co-ordinates The rectangular configuration is stable for an elongation ratio of less than 3 ~ 4, depending upon the current profile It is shown that the stabilization at high elongation ratio is related to the rotational-transform constraint

Stability of a finite-β inhomogeneous plasma in a sheared magnetic field

Abstract: In a plasma immersed in a sheared magnetic field of shear length Ls and having a density gradient of scale length Ln, finite s (plasma pressure/magnetic pressure) results in an additional stabilizing influence over and above that due to magnetic shear. Employing a full electromagnetic treatment, these finite-s corrections are evaluated for , where ai is the ion gyration radius and k is the wave vector perpendicular to both the direction of the density gradient and the unsheared component of the magnetic field. For the parameter ranges least stabilized by shear, the dominant finite-s- stabilization effect occurs within the region about the rational surface where the phase velocity is larger than the Alfven speed. As s increases toward or (kaim/M)2/3 [In (MLn/m|Ls|)]4/3 this finite-s correction must be retained, where m/M = electron mass/ion mass.

The nuclear performance of vanadium as a structural material infusion reactor blankets

Abstract: The nuclear performance of vanadium as a structural material in a deuterium-tritium fusion reactor is discussed. For comparison, calculations are also presented for niobium. The areas considered include: (1) tritium breeding; (2) nuclear heating; (3) radiation effects relating to material damage; and (4) neutron-induced activity. It is concluded that: (1) the tritium breeding characteristics of vanadium are somewhat superior to those of niobium; (2) nuclear heating in the first wall of the blanket will be substantially lower with vanadium than with niobium; (3) helium and hydrogen production in the first wall will be significantly greater with vanadium than with niobium; and (4) vanadium will exhibit an afterheat and biological hazard several orders of magnitude lower than that of niobium for times-after-shutdown of ~ 100 days and greater.

Two-dimensional calculation of tokamak stability

Abstract: A numerical procedure for determining the hydromagnetic stability of axisymmetric systems is described. The growth rates and eigenfunctions are determined by means of a modified initial value method. A number of tokamak configurations have been studied and stability boundaries and growth rates are given. With a conducting wall on the plasma the fundamental toroidal mode is stable and the m = 1 mode is stable for q 1/2.

Free-boundary MHD-equilibria in axisymmetric tori

Abstract: A method of numerical computation is presented in order to obtain equilibrium configurations in axisymmetric tori with ideally conductive shells of arbitrary cross-sections and/or with control-field coils. In this method, an artificial function S(ψ) is introduced, which makes it possible to combine the equilibrium equations in the plasma and the equation for the vacuum into one equation. The alternating-direction implicit method coupled with the Marder-Weitzner iteration scheme is used to solve the combined equilibrium equation under the boundary condition given on the shell. The continuity conditions at the plasma-vacuum interface are automatically satisfied in the solutions obtained. Some results of the computation are illustrated for cases where the shell shapes are of circular, square, rectangular and finger-ring type, respectively, and for a case with a ring coil placed inside the square shell.

Confinement of charged particles in adiabatic traps in the presence of monochromatic cyclotron oscillations

Abstract: The author formulates the conditions under which cyclotron oscillations randomize the motion of charged particles in an adiabatic trap. When the amplitude of the cyclotron wave is considerable, the randomization is due to the resonance of the longitudinal oscillations between the magnetic mirrors with transverse oscillations in the cyclotron wave field. If the amplitude is moderate, then the effect is due to phase shift at the resonance point. It is demonstrated that in the latter case the loss of particles from the trap may be insignificant, provided the oscillations have a short wave-length and the plasma is collisionless.

Particle drifts and the transition to containment in the LT-3 Tokamak

Abstract: The Canberra Tokamak LT-3 exhibits a delay between the application of the toroidal electric field and the main rise in gas current indicating bulk ionization of the gas. During this "prebreakdown" phase the electric field is high and the current is dominated by runaway electrons. The rotational transform is very low, however, and the condition for compensation of transverse particle drifts is not satisfied. A theoretical model is considered which includes only the curvature drift of the runaways. This provides estimates of the maximum energy an electron achieves before it is lost to the walls and a critical condition on the current when the transition to particle containment and total gas breakdown should occur. Measurements of runaway electron energies and gas currents in LT-3 are in agreement, within experimental and theoretical accuracy, with the predictions of the model. The effect of a compensating perpendicular magnetic field also confirms the model. The mechanisms governing the duration of the delay to breakdown remain obscure. In view of the short particle lifetime a means of re-introducing electrons, such as secondary emission, seems indicated. The prebreakdown phase may be avoided by pre-ionization to densities above a critical value. The particle drifts are then compensated and no delay occurs before the onset of exponential ionization increase.

Runaway electrons in the ormak device

Abstract: Runaway electron currents of up to 140 kA with energies in the MeV-range and lasting for a tenth of a second have been observed in ORMAK. A theory which predicts the production and acceleration of these electrons is presented and compared with recent experimental results. Agreement between the two appears to be good.

Guiding-centre diffuse pinch and local instability

Abstract: The stability problem of a linear diffuse pinch is studied by a normal-mode analysis using guiding-centre theory. The general normal-mode equation capable of determining the growth rate is obtained. The guiding-centre Suydam instability and the associated eigenvalue (growth rate) are examined.

Plasma equilibrium and stability in the Scyllac toroidal sector experiments

Abstract: Experiments are reported on helical plasma equilibrium and stability in the Scyllac toroidal θ-pinch sectors (120°) which have major radii of 2.375 and 4.0 m with coil arc lengths of 5.0 and 8.4 m, respectively. In these experiments the outward toroidal drift force was compensated by a combination of l = 1 helical and l = 0 bumpy fields which are generated by shaping the inner surface of the compression coil or by driven l = 1 windings. Time-resolved measurements were made of the gross plasma-column motion, the plasma radius, the magnetic flux excluded by the plasma, the external magnetic field, the plasma density, the electron and ion temperatures, and the plasma β at axial locations of minimum and maximum plasma radius. These data are used to study the approach to the theoretically predicted toroidal equilibrium (including axial pressure equilibrium). The plasma column remained in stable equilibrium for 7 – 10 μs in the 8-m sector compared with 4 – 7 μs in the 5-m experiment, at which times the onset of a terminating m = 1, k ≈ 0 sideways motion occurred. The results show that the plasma achieved axial pressure equilibrium (nkT = const) in 4 – 6 μs, while maintaining equilibrium in the toroidal plane for 10 μs or longer. The measurements of the plasma radius, β and magnetic field in the various experiments have confirmed in detail the stable toroidal equilibrium observed in the streak photographs during the first 4-10 μs of the discharge. The observed toroidal equilibria of the high-β, θ-pinch plasma are in quantitative agreement with MHD sharp-boundary theory and confirm the theoretical scaling of the equilibrium field between the 5-m and the 8-m sector experiments.

Stability of diffuse high-beta helical systems

Abstract: The stability of m = 1 long-wavelength kink modes in diffuse high-β l = 0 and l = 1 systems has been investigated. For l = 0 it is found that new modes exist with potentially dangerous growth rates and mode structure but which degenerate into zero growth-rate modes in the sharp boundary limit. The existence of such modes provides an explanation to an apparent paradox in the literature concerning l = 0 wall stabilization. For l = 1, it is found that the sharp boundary wall stabilization of the gross m = 1 mode remains essentially unchanged for diffuse profiles. This is favourable for the Scyllac programme.