Axisymmetric Mirror Research Articles

Recent Experiments on Stability and Heating in the Hiei Tandem Mirror

MHD stability and ion cyclotron heating are investigated in the axisymmetric tandem mirror HIEI, which is a three-cell device with a typical magnetic field strength of 0.05-0.3-0.1-0.3 T, from central cell midplane to outer throat of plug cells. A magnetic divertor configuration introduced in the central cell provides magnetic nulls and stabilizes MHD activities by shorting-out the charge separation in the azimuthal direction. The density fluctuation of m = 1 flute mode is observed to decrease significantly by using the divertor. The stabilization effect of the divertor is stronger as the nulls are located at inner radius. It is observed from the cross correlation measurement that the electrons exhibit E × B motion in unstable plasmas, while they tend to follow the Boltzmann relation in the divertor-stabilized plasmas. The second harmonic ion cyclotron heating is also investigated. In the divertor configuration where the magnetic field strength varies significantly in radial direction, the ICRF waves have a large transverse gradient in amplitudes to enhance the finite Larmor radius effect. The wave propagation and damping are investigated theoretically and experimentally.

Experiments with Dense Plasma in the Central Solenoid of Ambal-M

At present the axisymmetric ambipolar mirror trap AMBAL-M consists of a central solenoid which is attached to a plugging and MHD stabilizing end system and is filled from the other end by a plasma stream generated by a gas-discharge source. In the first experiments we obtained the plasma in the solenoid with ~0.4 m diameter, density ~6·1012cm−3, electron temperature ~50 eV, and ion energy ~250 eV. In order to enhance the plasma flow from the source into the solenoid, the distance between the entrance throat of the solenoid and the plasma source was gradually decreased, and the plasma density was increased to ~2·1013 cm−3. Installation of a second source from the opposite end of the machine allowed us to increase the plasma density up to ~2.5·1013 cm−3 in the solenoid and up to ~1.5·1013 cm−3 in the mirror trap of the end system. For better propagation of the plasma stream from the second source into the trap the coil of the MHD-stabilizer semicusp was switched in the same direction as all other coils, thus the magnetic configuration consisted of a series of simple mirrors. However, the plasma remained MHD stable owing to its line-tying to conducting ends. When this line-tying broke during the fast cut-off of the source current, the density profile in the solenoid abruptly rearranged pointing to possible MHD activity, and independently of the initial shape it became almost flat up to the limiter.Further enhancement of the plasma density was achieved using hydrogen puffing into the solenoid plasma while only the first source was functioning. Two methods of gas puffing were used – through a ceramic tube to the solenoid axis and into a gas-box surrounding the plasma. Optimization of the hydrogen puffing rate led to the density increase up to ~ 6·1013 cm−3 without noticeable degradation of the ion temperature which remained at a high level of ~200 eV (the ratio of the plasma pressure to the magnetic field pressure β~0.1), which is provided by stochastic ion heating from electrostatic oscillations when the source is working. The obtained solenoid plasma density is the highest one achieved in ambipolar mirror traps.

The Kinetic Stabilizer: Further Calculations and Options

The Kinetic Stabilizer, employing injected and mirror-reflected ion beams, represents a method for stabilizing axisymmetric mirror and tandem mirror systems. Building on earlier work, this paper presents further calculations on the concept and explores some new options that promise to enhance its capabilities

The kinetic stabilizer: Issues and opportunities

Five decades of fusion research have resulted in a solid base of understanding of the physics of plasma confinement by magnetic fields, including documentation of the role of the topology of the magnetic fields, i.e., “open” or “closed” field lines, in determining the confinement. Without known exception, closed systems, such as tokamaks, stellarators, or reversed-field pinches, have confinement times that are dominated by turbulence. As a result, to produce net fusion power, closed systems must be so large in size as to raise questions as to their practicality. By contrast, there are examples of open (mirror-based) systems where turbulence, if present at all, was at such low levels as to have a negligible influence on the confinement. Specifically, members of a subset of open systems, those with axisymmetric fields, have demonstrated cross-field transport rates that agree with classical predictions, opening up the possibility of fusion power systems that would be much smaller than their closed-field counterparts. Standing in the way of implementing axisymmetric mirror-based fusion systems is the MHD-unstable nature of their equilibria. The kinetic stabilizer represents a proposed way to overcome this difficulty, one based on theory that has been confirmed in the gas dynamic trap (GDT) axisymmetric mirror experiment in Novosibirsk, Russia. MHD-stabilization in the GDT arises from the presence of a sufficient density of effluent plasma on the outwardly expanding field lines outside the mirrors. However, in those mirror-based fusion systems, such as tandem-mirrors, that would operate at lower plasma collisionalities than the GDT, the effluent plasma density would be too low for this stabilization method to be effective. The kinetic stabilizer overcomes this difficulty by using ion beams injected from ion sources located far out on the expanding field lines beyond the outer mirror. These ion beams, aimed at small angles to the field lines, are compressed, stagnated, and reflected by the inwardly converging field, forming a localized plasma that accomplishes the stabilization. In previous papers, theory was developed and examples were given of mirror and tandem-mirror systems using kinetic stabilizers to achieve fusion-relevant plasma regimes. In this paper, some of the special issues that must be faced in pursuing the kinetic-stabilizer approach to fusion power will be discussed, together with some perceived opportunities for optimizing such systems.

MHD stability of a plasma in an axisymmetric open divertor configuration

For a plasma with Open image in new window confined in a system of two simple axisymmetric mirror cells separated by a divertor cell, a radial plasma pressure profile is obtained that is stable against convective modes and drops off to zero at the separatrix. The shape of the marginally stable pressure profile depends on the geometric parameters (such as mirror ratios and the localization of the divertor cell), the ratio of the pressure in the mirrors cells to the pressure in the divertor cell, and the degree of pressure anisotropy.

The EPSILON experimental pseudo-symmetric trap

Within the framework of the Adaptive Plasma Experiment (APEX) conceptual project, a trap with closed magnetic field lines, the Experimental Pseudo-Symmetric Closed Trap (EPSILON), is examined. The APEX project is aimed at theoretical and experimental development of the physical foundations for a steady state thermonuclear reactor designed on the basis of an alternative magnetic trap with tokamak-like large β plasma confinement. A discussion is given of thefundamental principle of pseudo-symmetry, which a magnetic configuration with tokamak-like plasma confinement should satisfy. Examples are given of calculations in the paraxial approximation of pseudo-symmetric curvilinear elements with a poloidal modulus B isoline. The EPSILON trap, consisting of two direct axisymmetric mirrors linked by two curvilinear pseudo-symmetric elements, is considered. To increase the equilibrium β, the plasma currents are short-circuited within curvilinear equilibrium elements. An untraditional scheme of MHD stabilization for a trap with closed field lines by use of axisymmetric mirrors with a divertor is analysed. The experimental installation EPSILON-One Mirror Element (OME), which is under construction for experimental investigation of stabilization by divertor, is discussed. The opportunity for applying the ECR method of plasma production in EPSILON-OME in conditions of high density and low magnetic field is examined.

New Linked Mirrors

The conceptual project APEX (Adapted Plasma Experiment) is discussed. The APEX objective is the development of a physical foundations for the CW fusion reactor, created on a base of an alternative type of magnetic trap, which could provide a “tokamak scale” confinement time at much higher β. Linked mirrors are the prototypes of this heading. The main idea of DRACON trap – the short circuit secondary plasma currents inside the curve elements (CE) – is kept. The new principle of poloidal pseudosymmetry and the non-traditional scheme of MHD plasma stabilization by “magnetic hump” give a possibility of a new approach to reduce plasma losses.The APEX concept provides for the Experimental Pseudo SYmmetric Linked trap (EPSYLON) design. The whole installation will be have two axisymmetric mirror parts (OME) closed with two CEs. Each OME contains the diverter. CE should have a strongly rippled magnetic field. As far as each OME and each CE is a trap with mirror confinement it is possible to start an investigation of the system from separate experiments with different parts of the whole system. The EPSYLON construction will be adapted to the experimental results. The experiment with OME is chosen now as the first step of the program. The main objective of this first experiment is the investigation of the “magnetic hump” MHD stabilization produced by divertor. EPSILON-OME installation is discussed. The closed system calculations are going in parallel.

Formation of multi-charged ions and plasma stability at quasigasdynamic plasma confinement in a mirror magnetic trap

It is known that an increase in plasma density in sources of multicharged ions leads to a substantial increase of ion current and slightly improves the ion distribution over charge states. The validity of this statement was verified in experiments with plasma densities not exceeding several units of 1012 cm−3. In the present work it is demonstrated experimentally that, for the electron densities exceeding 1013 cm−3, the regime of plasma confinement in a trap changes significantly and the quasigasdynamic regime of plasma confinement is realized. Comparison of numerical simulations and experimental data showed the essential influence of the anisotropy of electron velocity distribution in a plasma on the ion charge state distribution. This allows looking for the optimal conditions for the creation of highly charged ions in plasma. In this article we also address problems of plasma stability in an axisymmetric mirror trap under powerful microwave pumping. First experiments on ion extraction from a dense plasma pumped by millimeter wave radiation are described.

Possibility of demonstrating a self-sustained fusion reaction in an ambipolar trap

A brief description is given of an axisymmetric mirror trap to demonstrate ignition of a D-T plasma confined by ambipolar barriers. Key problems for this demonstration are ion pumping and suppression of instabilities in the thermal barriers. It is suggested that the fusion-fuel ions can be pumped away from the thermal barriers by exciting trapped-ion bounce oscillations at parametric resonances.

ICRF Plasma Heating in Axisymmetric Mirrors

The problems of Alfven and ion cyclotron heating in axicymmetrical mirrors are addressed.For the Alfven resonance heating scheme, the properties of continuum waves and kinetic (modified) Alfven waves are considered. The numerical modeling and experimental results for Alfven resonance heating with triple loop antenna are discussed.The specific features of magnetic beach ion cyclotron heating scenario in axisymmetric mirror are considered from the point of view of propagation condition and accessibility of the fast Alfven wave for excitation with external currents. The magnetic beach for continuum Alfven wave is analyzed. Using ray tracing calculations, the significant cyclotron damping of kinetic Alfven wave is predicted for the magnetic beach case.For fast magnetosonic wave cyclotron heating, the mechanisms of wave energy damping are described. The structure of global resonances is discussed. Heating scenarios with single global resonance and resonance overlapping are compared.The applicability of the scenarios mentioned for mirror based neutron source is addressed.

Plasma confinement studies in open systems

Studies in open systems in the world are reviewed from viewpoints of the potential confinement and magnetohydrodynamic (MHD) stability. The tandem mirror GAMMA 10 has shown the potential confinement of a high-ion-temperature plasma from an analysis of the time evolution of end-loss ion current and end-loss ion energy distributions. The central cell density was increased by 50% by the potential confinement. In the HIEI tandem mirror H-mode-like phenomena were observed with an increase in density and diamagnetic signal in a limiter biasing experiment. Potential formation phenomena in plasmas are studied by -like Upgrade under different magnetic field configurations and plasma conditions. The fully axisymmetric tandem mirror AMBAL-M is under construction and its end mirror system has been assembled. Heating experiments of a plasma gun produced plasma by neutral beam injection and ICRF heating are in progress. The gas dynamic trap (GDT) experiment has successfully produced an MHD-stable high-temperature, high-density plasma. In GOL-3-II, a high-density plasma with several 100 eV temperature is created by powerful relativistic electron beam injection. Construction of HANBIT has been completed and experiments on plasma production and ICRF heating have begun.

MHD Stability in Axisymmetric Multiple Mirror Geometry

The marginal stability of MHD modes is discussed in application for high beta multiple mirror experiments planned at Budker Institute of Nuclear Physics. Flute modes arc dangerous in axisymmetric systems with β < 1. In the case of “wall confined” plasmas, (β ≫ 1), pressure slightly varies along the radius providing less radial gradient and more stability against MHD modes. Effect of ion-ion viscosity becomes important in corrugated magnetic field. It results in the reduction of the growth rate by a factor β1/2. In the process of start up and plasma heating β < 1. If flute modes are stabilized during this period by the line-tying mechanizm ballooning modes are still unstable when β > βcr. A very low ballooning margin is predicted in multiple mirror with the large number of cells: βcr < π2 /N2. For the number of cells N ≃ 10: βcr ≃ 5%. Results of the calculations are discussed in the context of old and new multiple mirror experiments.

Measurements on rotating ion cyclotron range of frequencies induced particle fluxes in axisymmetric mirror plasmas

A comparison of phenomenological features of plasmas is made with a special emphasis on radio-frequency induced transport, which are maintained when a set of two closely spaced dual half-turn antennas in a central cell of the Phaedrus-B axisymmetric tandem mirror [J. J. Browning et al., Phys. Fluids B 1, 1692 (1989)] is phased to excite electromagnetic fields in the ion cyclotron range of frequencies (ICRF) with m=−1 (rotating with ions) and m=+1 (rotating with electrons) azimuthal modes. Positive and negative electric currents are measured to flow axially to the end walls in the cases of m=−1 and m=+1 excitations, respectively. These parallel nonambipolar ion and electron fluxes are observed to be accompanied by azimuthal ion flows in the same directions as the antenna-excitation modes m. The phenomena are argued in terms of radial particle fluxes due to a nonambipolar transport mechanism [Hojo and Hatori, J. Phys. Soc. Jpn. 60, 2510 (1991); Hatakeyama et al., J. Phys. Soc. Jpn. 60, 2815 (1991), and Phys. Rev. E 52, 6664 (1995)], which are induced when azimuthally traveling ICRF waves are absorbed in the magnetized plasma column.

Dielectric permeability of a mirror-trapped plasma

Analytical expressions for the wave permeability tensor are derived for a two-dimensional plasma model of a straight axisymmetric mirror trap. The dielectric tensor components are found through a solution of the Vlasov equation, using the theory of Jacobian elliptic functions. The bounce-resonance effect of trapped particles on wave dissipation is analysed. It is shown that collisionless wave dissipation in the plasma with a mirror-trap configuration of a magnetic field can differ essentially from Landau damping in a plasma with straight uniform magnetic field lines. This dielectric tensor can be used in numerical calculations of Alfvén and ion cyclotron heating of mirror-trap plasmas.

Magnetohydrodynamic stability of an axisymmetric mirror device with ‘‘massive’’ end-sections

Magnetohydrodynamic (MHD) stability of an axisymmetric mirror device with long end-sections filled with a collisional plasma is studied. It is shown that unstable perturbations in such a system, if they exist, are localized at a distance ∼vA/Γ near the central cell (vA is the Alfvén velocity and Γ is the growth rate). Perturbations of the magnetic field do not penetrate into regions where plasma beta is greater than unity. Therefore, regions of weak magnetic field has a stabilizing effect on MHD-perturbations.

Contribution of trapped particles to the dielectric tensor of magnetospheric plasmas

Analytical expressions for the components of the dielectric permeability operator tensor of plasmas confined in planetary dipolar magnetospheres are derived. The kinetic Vlasov's equation of a two‐dimensional plasma model, confined by an axisymmetric mirror trap, with circular magnetic field lines has been used. The conditions for single‐particle resonances of trapped particles are discussed, taking into account the bounce resonances. It is shown that the collisionless Cherenkov damping of the Alfvén and magnetosonic waves differs substantially from the Cherenkov damping of these modes in the straight confining magnetic field case; this is true due to the presence of the trapped particles. Estimations of the damping coefficients for Langmuir and kinetic Alfvén waves are made, and some observational consequences of this study are discussed.

Measurements of plasma equilibrium response to external multipole magnetic fields in an axisymmetric mirror

The paper is devoted to the experimental investigation of the plasma equilibrium response to externally applied non-axisymmetric disturbances of the magnetic field in an axisymmetric open trap. The results are presented for dipole and quadrupole disturbances which were applied inside the expander end cell. Comparison of the experimental data with the estimates made on the basis of the magnetohydrodynamic (MHD) theory is given.

Attractive Characteristics of Mirrors

A summary of the attractive characteristics of mirror devices is presented. Recent progress in development of axisymmetric mirror devices is described. Potentialities of mirrors as a basis for D{sup 3}He fusion power generators and high flux neutron sources for fusion material tests are discussed. 16 refs., 2 figs.

Ponderomotive stabilization of interchange modes at ICRF heating

The ponderomotive stabilization of plasma in an axisymmetric mirror device is considered. It is assumed that (i) the RF field is excited by a full-turn-loop antenna and (ii) its frequency is below the eigenfrequency spectrum of the plasma column. It is shown that the dissipation of the RF power drives an instability that originates from a resonant-particle interaction. This instability is weak except for the case when the minority ion scheme of ICRF heating is used. However, even in the latter case, the resonant-particle instability can be suppressed by quasilinear diffusion of the minority ions in the velocity space at a sufficiently high level of RF power. With the instability suppressed, a simple criterion for the ponderomotive force to stabilize flute perturbations in mirror plasmas is obtained.

EXPERIMENTS ON INSTABILITY AND POTENTIAL CON- FINEMENT CONFIGURATION IN MM-4U TANDEM MIRROR

Experimental results on plasma instability and potential confinement configuration in MM-4U tandem mirror are presented. The measured axial potential profile shows that the axisymmetric negative plasma potential tandem mirror confinement configuration has been established; the obtained plasma density profile is similar to the potential profile. The relationships between the plasma parameters and the eng-neering parameters have also been studied prelimilarily. The low frequency instability was observed at low plasma density in the central cell. By means of the linear spectral analysis techniques, the instability mode has been determined. It is suggested that the instability is excited in the low density plasma when the electron beam drift velocities exceed the ion acoustic speed.