V. E. Moiseenko

Radio-frequency heating of sloshing ions in a straight field line mirror

A scenario to sustain a sloshing ion population with radio-frequency heating in a newly proposed mirror device, the straight field line mirror, is examined. The possibilities of ion cyclotron heating in two-ion species plasma have been analyzed and a scheme with longitudinal wave conversion and fundamental harmonic heating of deuterium ions in tritium plasma has been investigated. This scheme provides efficient ion heating for high deuterium “minority” concentration without substantial conversion to slow waves and heating of the electrons. Numerical calculations carried out for a reactor-scale device show that conversion of the fast magnetosonic wave to the fast Alfven wave occurs. For reasons of strong cyclotron absorption of the fast Alfven wave, only a small portion of the wave energy transits through the cyclotron layer and penetrates to the central part of the trap. The power deposition is peaked at the plasma core. The amount of deposited power does not depend sensitively on the parameters of the di...

Second harmonic ion cyclotron heating of sloshing ions in a straight field line mirror

A qualitative analysis of second harmonic heating is carried out, in which a fast magnetosonic wave is launched from a location near the magnetic mirror (where the magnetic field is stronger than the second harmonic resonance field) and directed to the midplane of the open trap. The analysis shows that there is no “magnetic beach” heating in contrast to the case with minority heating on the fundamental harmonic. Conversion to the ion Bernstein wave would distort the heating pattern, and the condition for this conversion is estimated. The scenario of second harmonic heavy ion heating is examined numerically. In the scenario chosen, the regime of global resonance overlapping is achieved that provides good heating performance. The computations show that the power deposition is core, the amount of deposited power does not depend sensitively on the parameters of the discharge, and the range of plasma beta at which the heating is efficient is not narrow. The estimated antenna Q is noticeably low and, therefore, the antenna performance is high.A qualitative analysis of second harmonic heating is carried out, in which a fast magnetosonic wave is launched from a location near the magnetic mirror (where the magnetic field is stronger than the second harmonic resonance field) and directed to the midplane of the open trap. The analysis shows that there is no “magnetic beach” heating in contrast to the case with minority heating on the fundamental harmonic. Conversion to the ion Bernstein wave would distort the heating pattern, and the condition for this conversion is estimated. The scenario of second harmonic heavy ion heating is examined numerically. In the scenario chosen, the regime of global resonance overlapping is achieved that provides good heating performance. The computations show that the power deposition is core, the amount of deposited power does not depend sensitively on the parameters of the discharge, and the range of plasma beta at which the heating is efficient is not narrow. The estimated antenna Q is noticeably low and, therefore,...

Four motional invariants in axisymmetric tori equilibria

In addition to the standard set (e,μ,pφ) of three invariants in axisymmetric tori, there exists a fourth independent radial drift invariant Ir. For confined particles, the net radial drift has to be zero, whereby the drift orbit average Ir=⟨r¯0⟩ of the gyro center radial Clebsch coordinate is constant. To lowest order in the banana width, the radial invariant is the gyro center radial coordinate r¯0(x,v), and to this order the gyro center moves on a magnetic flux surface. The gyro center orbit projected on the (r,z) plane determines the radial invariant and first order banana width corrections to Ir are calculated. The radial drift invariant exists for trapped as well as passing particles. The new invariant is applied to construct Vlasov equilibria, where the magnetic field satisfies a generalized Grad-Shafranov equation with a poloidal plasma current and a bridge to ideal magnetohydrodynamic equilibria is found. For equilibria with sufficiently small banana widths and radial drift excursions, the approxi...

Gyro center invariant and associated diamagnetic current

The gyro center radial Clebsch coordinate r¯0 is an exact invariant in confining fields where the gyro center is restricted to move on a magnetic flux surface, and r¯0 could also be expected to be a useful approximating invariant in other confining magnetic fields. A radial drift invariant Ir generalizes the invariance of r¯0 if there are oscillatory gyro center radial displacements off the magnetic surface. Expressions for r¯0(x,v) and Ir(x,v) are obtained for gyrating particles in the drift ordering. An exact energy integral is proven to exist for the first-order drift motion of the gyro center. The gyro center parallel motion is periodic with respect to a certain curve parameter τ¯‖ (the “proper time” for the parallel motion) that deviates slightly, due to the slow perpendicular drift, from the ordinary time. A modification of the parallel invariant J‖ is derived which leads to an exact (not only adiabatic) invariant to first order. By using r¯0 in solutions of the Vlasov equation, it is demonstrated t...

Stellarator-Mirror Hybrid with Neutral Beam Injection

A stellarator-mirror fusion-fission hybrid has recently been proposed. Neutral beam injection (NBI) is here studied numerically for this hybrid using a two-dimensional kinetic code, KNBIM. The code accounts for Coulomb collisions between the hot ions and the background plasma. The geometry of the confining magnetic field is arbitrary for the code and is accounted for via a numerical bounce averaging procedure. Along with the kinetic calculations the neutron production intensity is computed. The calculated hot ion distribution function from NBI is used in power balance estimates for the whole system. The requirement that the fast neutrals should be efficiently captured in the plasma is imposed to restrict the range of plasma parameters. The results obtained balance calculations are close to results obtained previously with a bi-Maxwellian ion distribution function. The calculated parameters for a power producing stellarator mirror device and within modern top technical capabilities. The parameters of plasma and NBI characteristics seem also attainable. The calculated fusion Q is within a range with potential for energy production in a hybrid reactor.

Research on stellarator–mirror fission–fusion hybrid

The development of a stellarator–mirror fission–fusion hybrid concept is reviewed. The hybrid comprises of a fusion neutron source and a powerful sub-critical fast fission reactor core. The aim is the transmutation of spent nuclear fuel and safe fission energy production. In its fusion part, neutrons are generated in deuterium–tritium (D–T) plasma, confined magnetically in a stellarator-type system with an embedded magnetic mirror. Based on kinetic calculations, the energy balance for such a system is analyzed. Neutron calculations have been performed with the MCNPX code, and the principal design of the reactor part is developed. Neutron outflux at different outer parts of the reactor is calculated. Numerical simulations have been performed on the structure of a magnetic field in a model of the stellarator–mirror device, and that is achieved by switching off one or two coils of toroidal field in the Uragan-2M torsatron. The calculations predict the existence of closed magnetic surfaces under certain conditions. The confinement of fast particles in such a magnetic trap is analyzed.

Magnetic field of a combined plasma trap

This paper presents numerical simulations performed on the structure of a magnetic field created by the magnetic system of a combined plasma trap. The magnetic system includes the stellarator-type magnetic system and one of the mirror-type. For the stellarator type magnetic system the numeric model contains a magnetic system of an l=2 torsatron with the coils of an additional toroidal magnetic field. The mirror-type magnetic system element is considered as being single current-carrying turn enveloping the region of existence of closed magnetic surfaces of the torsatron. The calculations indicate the existence of a vast area of the values of the additional magnetic field magnitude and magnetic field of the single turn where, in principle, the implementation of the closed magnetic surface configuration is quite feasible.

Plasma heating and hot ion sustaining in mirror based hybrids

Possibilities of plasma heating and sloshing ion sustaining in mirror based hybrids are briefly reviewed. Sloshing ions, i.e. energetic ions with a velocity distribution concentrated to a certain pitch-angle, play an important role in plasma confinement and generation of fusion neutrons in mirror machines. Neutral beam injection (NBI) is first discussed as a method to generate sloshing ions. Numerical results of NBI modeling for a stellarator-mirror hybrid are analyzed. The sloshing ions could alternatively be sustained by RF heating. Fast wave heating schemes, i.e. magnetic beach, minority and second harmonic heating, are addressed and their similarities and differences are described. Characteristic features of wave propagation in mirror hybrid devices including both fundamental harmonic minority and second harmonic heating are examined. Minority heating is efficient for a wide range of minority concentration and plasma densities; it allows one to place the antenna aside from the hot ion location. A simp...

Fusion neutron generation computations in a stellarator-mirror hybrid with neutral beam injection

In the paper [Moiseenko V.E., Noack K., Agren O. “Stellarator-mirror based fusion driven fission reactor“ J Fusion Energy 29 (2010) 65.], a version of a fusion driven system (FDS), i.e. a sub-critical fast fission assembly with a fusion plasma neutron source, is proposed. The plasma part of the reactor is based on a stellarator with a small mirror part. Hot ions with high perpendicular energy are assumed to be trapped in the magnetic mirror part. The stellarator part which connects to the mirror part and provides confinement for the bulk (deuterium) plasma. In the magnetic well of the mirror part, fusion reactions occur from collisions between a of hot ion component (tritium) with cold background plasma ions. RF heating is one option to heat the tritium. A more conventional method to sustain the hot ions is neutral beam injection (NBI), which is here studied numerically for the above-mentioned hybrid scheme. For these studies, a new kinetic code, KNBIM, has been developed. The code takes into account Coul...

The hybrid reactor project based on the straight field line mirror concept

The straight field line mirror (SFLM) concept is aiming towards a steady-state compact fusion neutron source. Besides the possibility for steady state operation for a year or more, the geometry is ...