A two-year study of recirculating induction heavy ion accelerators as low-cost driver for inertial-fusion energy applications was recently completed. The projected cost of a 4 MJ accelerator was estimated to be about $500 M (million) and the efficiency was estimated to be 35%. The principal technology issues include energy recovery of the ramped dipole magnets, which is achieved through use of ringing inductive/capacitive circuits, and high repetition rates of the induction cell pulsers, which is accomplished through arrays of field effect transistor (FET) switches. Principal physics issues identified include minimization of particle loss from interactions with the background gas, and more demanding emittance growth and centroid control requirements associated with the propagation of space-charge-dominated beams around bends and over large path lengths. In addition, instabilities such as the longitudinal resistive instability, beam-breakup instability and betatron-orbit instability were found to be controllable with careful design.
A simple formula for tracking the cutoffs of waves in the electron cyclotron range of frequencies is presented for plasmas with electron temperatures similar to those of existing large tokamaks (∼10 keV) and conditions of negligible wave absorption.
Experiments have been performed in the Tokamak Fusion Test Reactor [D. M. Meade et al. in Plasma Physics Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 9] with neutral beam injection of up to 4 sec. duration, which is comparable to the time scale for resistive redistribution of the plasma current profile. These plasmas were created using a rapid decrease of the plasma current which initially created a plasma with enhanced stability and confinement. As the current profile evolved, a significantly reduced beta limit was observed. The high εβp plasmas had up to 90% of the current driven noninductively which significantly broadened the current profile during the long pulse lengths. These experiments demonstrated that high βN plasmas could not be sustained for times longer than the resistive relaxation of the outer current region which at early times after the current ramp-down carried negative current. At later times in lower βN discharges, beta collapses were sometimes observed as the current profile broadened at βN∼1.5. The appearance of disruptions was consistent with the predictions of ideal magnetohydrodynamics (MHD) stability analyses.
A two-year study of recirculating induction heavy-ion accelerators (recirculators) as low-cost drivers for inertial-fusion energy power plants has recently been completed. A summary of that study and other recent work on recirculators is presented.
The role of plasma in advanced accelerators is reviewed with emphasis on three significant areas of research: plasma guiding of beams in accelerators, plasma focusing of beams in high-energy linear colliders, and plasma acceleration of beams.
A class of two-dimensional force-free equilibria are shown to be subject to an ideal linear instability. This instability is similar to the coalescence instability for chains of magnetic islands. Semianalytic methods are used to find second magnetic equilibrium which is accessible from the first and has lower magnetic energy. This equilibrium has a discontinuous magnetic field and current sheets at these discontinuities. Numerical simulations indicate that the nonlinear evolution of the instability allows the plasma to relax to this discontinuous equilibrium.
The equilibration of spin temperature Tspin with kinetic temperature T is examined in a weakly correlated pure electron plasma in the strongly magnetized limit, where the distance of closest approach is large compared to the Larmor radius. In this limit, the spin precession frequency Ωp=gΩc/2 is large so the component of spin along the magnetic field is an adiabatic invariant that is broken only by resonant magnetic fluctuations of frequency Ωp. (Here Ωc is the electron cyclotron frequency and g≂2.002.) In this case, the most important spin flip mechanism stems from electron–electron collisions in a spatially inhomogeneous magnetic field. Such collisions cause an exchange of spin and cyclotron quanta, and consequently the conventional many-electron adiabatic invariant (i.e., the total number of cyclotron quanta) is broken and is replaced by a new adiabatic invariant, equal to the sum of the spin and cyclotron actions. A quantum Boltzmann equation is derived to describe the equilibration of Tspin toward T.
The Shafranov equilibrium formulas for tokamaks relate volume-averaged thermal pressure and magnetic pressure to integrals of the measurable poloidal magnetic field energy at the plasma surface. Similar integral relations are derived that are valid for a general, three-dimensional plasma confinement geometry.
Three‐wave, nonlinear, tearing mode coupling has been measured in the Madison Symmetric Torus (MST) reversed‐field pinch (RFP) [Fusion Technol. 19, 131 (1991)] using bispectral analysis of edge magnetic fluctuations resolved in ‘‘k‐space.’’ The strength of nonlinear three‐wave interactions satisfying the sum rules m1+m2=m3 and n1+n2=n3 is measured by the bicoherency. In the RFP, m=1, n∼2R/a (6 for MST) internally resonant modes are linearly unstable and grow to large amplitude. Large values of bicoherency occur for two m=1 modes coupled to an m=2 mode and the coupling of intermediate toroidal modes, e.g., n=6 and 7 coupled to n=13. These experimental bispectral features agree with predicted bispectral features derived from magnetohydrodynamic (MHD) computation. However, in the experiment, enhanced coupling occurs in the ‘‘crash’’ phase of a sawtooth oscillation concomitant with a broadened mode spectrum suggesting the onset of a nonlinear cascade.
A comment on effects of neutral beam injection on poloidal rotation and energy transport in tokamaks plasma is presented. The enhanced neoclassical effects such as poloidal mass flow, viscous heating and the convective flow of main plasma ions which is inward for coinjection should be taken into account in the interpretation of experimental data. (AIP)
Comparisons of the accuracy of liquid sodium structure calculations are given. The accuracy required for calculations of thermodynamic properties and for meaningful validation of computational techniques is discussed.
an algebraic error is found in Equation (1) of the paper by Mizuno et al.1 Their measured threshold is analyzed following the corrected from of Equation (1). (AIP)
Pure electron plasmas are routinely confined within cylindrically symmetric Penning traps. In this paper the static and dynamic properties of plasmas confined in traps with applied electric field asymmetries are investigated. Simple analytical theories are derived and used to predict the shapes of the stable noncircular plasma equilibria observed in experiments. Both analytical and experimental results agree with those of a vortex-in-cell simulation. For an ℓ=1 diocotron mode in a cylindrically symmetric trap, the plasma rotates as a rigid column in a circular orbit. In contrast, plasmas in systems with electric field asymmetries are shown to have an analog to the ℓ=1 mode in which the shape of the plasma changes as it rotates in a noncircular orbit. These bulk plasma features are studied with a Hamiltonian model. It is seen that, for a small plasma, the area enclosed by the orbit of the center of charge is an invariant when electric field perturbations are applied adiabatically. This invariant has been observed experimentally. The breaking of the invariant is also studied. The dynamic Hamiltonian model is also used to predict the shape and frequency of the large amplitude ℓ=1 and ℓ=2 diocotron modes in symmetric traps.
A theory of the space-charge limiting current is developed for a relativistic electron beam propagating through a grounded conducting cylinder. The beam electron density is assumed to be uniform. It is found that the propagating current depends very sensitively on the current density profile. Moreover, the self-consistently evaluated limiting current is considerably larger than the conventionally estimated value.
Several points concerning the section ‘‘Comparison with the Swedish stability and transport analysis’’ in the paper by Horton et al. are discussed and clarified. In particular it is pointed out that the Swedish model gives about the right ratio of χe/χi for the Tokamak Fusion Test Reactor (TFTR) [Phys. Rev. Lett. 63, 520 (1989)] density modification experiment.
Magnetic islands play an important role in determining plasma transport in toroidal magnetic confinement systems. The magnetic error fields and the associated islands can be theoretically described by a Hamiltonian approach. Experiments have been conducted on the Compact Auburn Torsatron [Fusion Technol. 18, 281 (1990)] to test the applicability and limits of the first-order Hamiltonian theory to magnetic islands. A novel set of helical trim coils with the same spatial periodicity as an ι– = 1/2 magnetic island were used to create a perturbation field of variable magnitude and phase. Extensive experimental parametric studies of the magnetic island were conducted and compared with theory. It was found that the first-order Hamiltonian theory is applicable for the complete range of experimental error fields.
A nonlinear analysis of the wave–particle interaction in the output cavity of a frequency-doubling magnicon amplifier is presented. The cavity is immersed in an axial magnetic field, wherein electrons interact with a rotating TM210 mode via a gyroresonant mechanism. The electron equations of motion and the wave equation for the radio-frequency (rf) field are derived and expressed in terms of scaled variables in order to study the general scaling of the output cavity. Single-electron, time-dependent simulation of the interaction in the cavity is performed to assess the accessibility and stability of high-efficiency states for an X-band magnicon. Results from multielectron, steady-state simulation are presented to show the effect of spreads in electron-beam radius, energy, and transverse momentum on the efficiency.
