Straight Field Line Mirror Research Articles

COIL DESIGN FOR THE STRAIGHT FIELD LINE MIRROR

This paper briefly describes numerical design of 3D super-conduction coils aimed to mimic analytically derived magnetic field for the Straight Field Line Mirror (SFLM) concept. The paper is based on a manuscript for a previous IAEA report, i.e. IAEA-TECDOC-1998.

Magnetic shaping for a minimum B trap

• A minimum B field provides MHD stability, but a threat is the flux tube ellipticity, which is optimized in the study. • The magnetic shaping minimizes the flux tube ellipticity and neoclassical effects with MHD stability preserved. · • A controlled weak radial electric field restricts the guiding center motion to the immediate vicinity of a flux surface. · • Superconducting 3D coils have been computed which reproduce the derived magnetic field. · • In a minimum B vacuum field, a finite plasma beta may increase the mirror ratio to values exceeding 10. A mirror machine with a minimum B field for MHD stability is an option for a steady-state compact fusion neutron source design. A previous calculation of an idealized quadrupolar mirror field in Ref Ågren and Moiseenko (2017) is extended to a magnetic field which smoothly evolves to expander regions beyond the mirror throats. In a minimum B field, the projection of a flux surface on planes perpendicular to the magnetic axis evolves from a circular shape at the mid-plane to a highly elliptical shape as the mirror ratio is increased. Magnetic shaping is made to find the minimal ellipticity. The ellipticity depends sensitively on the gyro center magnetic drift in the confinement region, and the optimal result approaches a state where the magnetic drift is made as small as possible, which corresponds to the SFLM (Straight Field Line Mirror) field. In such a magnetic field, in combination with a weak radial electric field, each guiding center is forced to move close to its mean magnetic surface, thereby suppressing neoclassical transport effects. Biased end plates, placed at the end tank outside the confinement region, is a tool to control the radial electric field. The biased end plates could also assist to more precisely determine the positioning of drift surfaces in the confinement region. The reproduction of the optimized magnetic field with superconducting coils is a challenge due to the strong gradients in B . This is solved by a special arrangement with compact 3D superconducting coils, and the reproduction of the magnetic field is demonstrated with a mirror ratio of 4. Mirror ratios exceeding 10 may be reachable with finite β effects included. Analytical expressions in closed form are derived.

Hybrid Reactor Studies Based on the Straight Field Line Mirror

The straight field line mirror (SFLM) hybrid reactor studies aim to identify a concept where the safety of fission power production could be enhanced. A fusion neutron source could become a mean to achieve this. The SFLM studies address critical issues such as reactor safety, natural circulation of coolants, steady state operation for a year or more and means to avoid too strong material loads by a proper geometrical arrangement of the reactor components. A key result is that power production may be possible with a fusion Q factor as low as 0.15. This possibility arises from the high power amplification by fission, which within reactor safety margins may exceed a factor of 100. The requirements on electron temperature are dramatically lower for a fusion hybrid compared to a stand-alone fusion reactor. This and several other factors are important for our choice to select a mirror machine for the fusion hybrid reactor studies.

Hybrid Reactor Studies Based on the Straight Field Line Mirror

Hybrid Reactor Studies Based on the Straight Field Line Mirror

A Compact Non-Planar Coil Design for the SFLM Hybrid

A non-planar single layer semiconductor coil set for a version of the Straight Field Line Mirror Hybrid concept with reduced magnetic field has been computed. The coil set consists of 30 coils that are somewhat similar to baseball coils with skewed sides. The coil set has been modeled with filamentary current distributions and basic scaling assumptions have been made regarding the coil widths. This coil set is expected to be considerably cheaper than a previous computed coil set. The coils can probably be produced with technologies known today.

Fusion-Fission Hybrid Reactor Studies for the Straight Field Line Mirror

A comparatively small mirror fusion hybrid device may be developed for industrial transmutation and energy production from spent nuclear waste. This opportunity ensues from the large fission to fusion energy multiplication ratio, Qr = Pfis/Pfus ≤ 150, in a subcritical fusion device surrounded by a fission mantle with the neutron multiplicity keff ≈ 0.97. The geometry of mirror machines is almost perfectly suited for a hybrid reactor application, and the requirements for plasma confinement can be dramatically relaxed in correspondence with a high value of Qr. Steady state power production in a mirror hybrid seems possible if the electron temperature reaches 500 eV. A moderately low fusion Q factor, the ratio of fusion power to the power necessary to sustain the plasma, could be sufficient, i.e. Q ≈ 0.15. Theoretical predictions for the straight field line mirror (SFLM) concept are presented, including results from radio frequency heating, neutron Monte Carlo and magnetic coil computations. Means to achieve an electron temperature of 500 eV are briefly discussed. The basic study considers a 25 m long confinement region with 40 cm plasma radius with 10 MW fusion power and a power production of 1.5 GW thermal.

Radio-Frequency Heating in Straight Field Line Mirror Neutron Source

There is a need in a practical scenario for ion heating up to high temperatures in a mirror based neutron source. Such a scenario could be developed with the ion cyclotron heating. Fundamental harmonic ion cyclotron heating of deuterium and second harmonic heating for tritium are studied numerically from the point of view of antenna coupling and heating efficiency. The behavior of the antenna loading resistance and radio-frequency power shine-through the cyclotron zone with the heating frequency, plasma density and temperature and the antenna position is analyzed.

Studies of a Straight Field Line Mirror with Emphasis on Fusion-Fission Hybrids

The straight field line mirror (SFLM) field with magnetic expanders beyond the confinement region is proposed as a compact device for transmutation of nuclear waste and power production. A design with reactor safety and a large fission-to-fusion energy multiplication is analyzed. Power production is predicted with a fusion Q = 0.15 and an electron temperature of ~500 eV. A fusion power of 10 MW may be amplified to 1.5 GW of fission power in a compact hybrid mirror machine. In the SFLM proposal, quadrupolar coils provide stabilization of the interchange mode, radio-frequency heating is aimed to produce a hot sloshing ion plasma, and magnetic coils are computed with an emphasis on minimizing holes in the fission blanket through which fusion neutrons could escape. Neutron calculations for the fission mantle show that nearly all fusion neutrons penetrate into the fission mantle. A scenario to increase the electron temperature with a strong ambipolar potential suggests that an electron temperature exceeding 1 keV could be reached with a modest density depletion by two orders in the expander. Such a density depletion is consistent with stabilization of the drift cyclotron loss cone mode.

Studies of a Straight Field Line Mirror with Emphasis on Fusion-Fission Hybrids

Studies of a Straight Field Line Mirror with Emphasis on Fusion-Fission Hybrids

On Possibilities for Transmutation of Nuclear Waste and Energy Production with a “Straight Field Line Mirror” Neutron Source

A pure fusion mirror device suffers from the predicted low values of the Q factor (energy gain factor). A much higher energy production may be achieved in a fusion-fission reactor, where the fusion plasma neutron source is surrounded by a fission mantle. The fusion neutrons are capable of initiating energy producing fission reactions in the surrounding mantle. A mirror machine can probably be designed to provide sufficient space for a 1.1 m wide fission mantle inside the current coils, and the power production from the fission reactions can in such a case exceed the fusion power by more than two orders of magnitude (Pfis/Pfus ≈ 150), suggesting a realistic reactor regime for a mirror based fusion-fission device. An energy producing device may operate with an electron temperature around 1 keV. Transmutation of long-lived radio active isotopes (minor actinides) from spent nuclear fuel from fission reactors can reduce geological storage from 100 000 years to only 300 years. Since the energy of D-T fusion neutrons are above the threshold for the most important transmutation reactions desired for treatment of nuclear waste, there may be an interest for a mirror transmutation device even if no net energy is produced. Recent theoretical simulations have considered the possibility to use the Gas Dynamic Trap (GDT) at Novosibirsk as a subcritical burner for transmutation by fusion neutrons. In the present work, possibilities for mirror based fusion-fission machines are discussed. Means to achieve sufficient end confinement for a straight field line mirror fusion-fission system with a thermal barrier are briefly analyzed. End leakage can alternatively be avoided by connecting the ends of a magnetic mirror with a stellerator tube, while the fusion neutrons are produced in the mirror part where a high energy sloshing ion component is confined. A zero dimensional model for such a mirror-stellarator system has been developed. The computed results indicate some possible parameter regimes for industrial transmutation and power production.

Coil Design for the Straight Field Line Mirror

Coil systems for producing the Straight Field Line Mirror field using axisymmetric and quadrupolar coils are calculated. Two applications are intended, a fusion-fission nuclear waste transmutation device and a small plasma deposition device. Position, size and current for the axisymmetric coils are optimized as well as radial profile and current for the quadrupolar coils for the two applications. Calculations show that such a coil system can produce the Straight Field Line Mirror field for long-thin mirrors with moderate mirror ratio, but some other coil configuration needs to be found for mirrors where the coils cannot reside close to the plasma edge. In this work, the material science experiment mirror can be produced with about 1% error but the fusion-fission device field has not at this moment been reproduced with acceptable errors.

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.

On MHD Stability, Ellipticity, Omnigenuity, Constants of Motions and a Modified Thermal Barrier of a Straight Field Line Mirror

The straight field line mirror field is the unique field which gives the lowest ellipticity of the flux tube of an MHD stable minimum B mirror field. In this particular vacuum field, each gyro center bounces back and forth on a single magnetic field line, and a pair of two new constants of motion is associated with this property. Using these invariants in the Vlasov equation, it can be shown that the radial gyro center magnetic drift is absent to first order in the plasma beta, and the equilibrium is omnigenous. The neoclassical increase of the radial transport may thus be avoided without an axisymmetrization of this single cell mirror.A scheme to improve end confinement of ions, and simultaneously create an electric potential barrier for the electrons and a sloshing ion component, has been proposed. The end plugging transforms ions under way to escape into the loss cone into sloshing ions by ion cyclotron resonance heating. Numerical studies on sloshing ion production by RF heating demonstrate strong absorption of the RF field near the fundamental gyro frequency resonance of the minority deuterium ions as well as near the tritium second harmonic gyro frequency resonance. The scenario indicates a possibility to achieve a high energy gain factor in this kind of single cell mirror with the proposed modified thermal barrier.

Second Harmonic Cyclotron Heating of Sloshing Ions in a Straight Field Line Mirror

The second harmonic heating in mirrors is explicated. A new coordinate-independent form of the second harmonic term in the plasma dielectric response is derived. The second harmonic heating in the WKB limit is addressed and compared with minority heating. A newly developed three-dimensional model for the time-harmonic boundary problem for Maxwell’s equations is used for second harmonic heating modeling in the reactor-scale straight field line mirror device. Computations show that the antenna Q is low and the regime of global resonance overlapping is in effect. 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.

Finite β correction to the magnetic flux tube ellipticity of the straight field line mirror

A marginal minimum B mirror magnetic field has been proposed as an external plasma confining magnetic field for a single cell open magnetic mirror trap. An analytical expression for the flux tube ellipticity of this magnetic field has in a previous study been derived with a zero plasma β approximation. This mirror field, which consists of straight nonparallel field lines in the confinement region, has a particular interest since it is likely to correspond to the smallest possible ellipticity for a magnetohydrodynamic stable mirror confinement. The plasma current is in this paper taken into account to the first order in β and the influence of the plasma magnetic field on the magnetic flux surface geometry is studied.

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 Alfvén wave occurs. For reasons of strong cyclotron absorption of the fast Alfvén 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 discharge. The study uses numerical three-dimensional calculations for the time-harmonic boundary problem for Maxwell’s equations. For radio-frequency heating in this scheme, a simple efficient strap antenna is proposed. It has low Q antenna and operates in the regime of global resonance overlapping.