Axisymmetric Magnetic Mirror Research Articles

Experimental studies of cusp stabilization in Keda Mirror with AXisymmetricity (KMAX)

Stabilization of the axisymmetric magnetic mirror relies on the pressure-weighted magnetic field curvature. We report a new experiment by configuring a magnetic cusp structure to stabilize m = 1 interchange mode in the KMAX tandem mirror. The cusp configuration is formed by reversing currents in the two side cell coils, and a stronger cusp can lead to a more stable plasma once the null point of the cusp is less than 35–40 cm away from the device axis. The density fluctuations measured by four axial Langmuir probes are mitigated by 70%–80%. The stabilization effect is consistent with the prediction of a theoretical calculation.

Stable confinement of high-electron-temperature plasmas in the GDT experiment

Having the ability to control the operation of advanced plasma heating methods is essential for the achievement of fusion-relevant plasmas in open traps. We describe a technique to deal with the increased transport brought about by the electron cyclotron heating in axisymmetric magnetic mirror device. The technique is based on shaping of the plasma potential by means of a set of specifically biased electrodes facing plasma at both open ends of a trap. In the experiments with combined microwave and neutral beam plasma heating performed in the gas-dynamic trap (GDT) facility at the Budker Institute, we show that a value of on-axis electron temperature up to 450 eV at plasma density m−3 can be supported steadily for 1.5 ms limited by the available heating and magnetic confinement systems. Stable high-temperature discharge, no longer degraded by low-frequency instabilities, offered a unique opportunity to confirm quantitatively the gas-dynamic plasma confinement model in a new range of parameters.

Sheath and presheath in a collisionless plasma containing negative ions with an open magnetic field

The effects of an axisymmetric magnetic mirror field with diverging field lines on the plasma presheath and sheath are numerically investigated by solving the plasma–sheath equation for a collision...

Electron Escaping in the Magnetically Confined Electron Cloud

The morphology of magnetic equipotential lines in axisymmetric magnetic mirror field was analyzed. Based on the magnetic fluid theory of electrons, an electron cloud model formed by magnetic mirror field confined electrons was built in this paper. And twodimension differential potential equations were solved by using Runge-Kutta method. The calculation gave the Boltzmann distribution and potential distribution of electron density. The principle of both electron escape and confinement were analyzed in magnetic mirror field environment, the runaway electron current situation of the electronic cloud boundary was analyzed. Based on the leakage current of electron boundary, the balance of ionization electrons and escape electrons was used to deprive the confined region leakage current factor relationship equation in magnetic mirror environment. The relationship between the runaway electron current and the runaway factor, the effects electron temperature, electron velocity, and magnetic field lines on runaway factor were given. Furthermore, the minimum confined magnetic field needed to build electron cloud in magnetic mirror field was also given in this paper.

Control of the Radial Energy Deposition Profile in an Open Magnetic Trap During Electron Cyclotron Plasma Heating

We propose a method for controlling the radial profile of electron cyclotron plasma heating in an axisymmetric magnetic mirror by using minor perturbations of the magnetic field of the mirror. The method is based on the analysis of the ray trajectories behavior near the surface of the electron cyclotron resonance. A way to produce such perturbations by supplementing the system with an additional “quadrupole” pair of magnetic coils is also proposed. The possibility to improve the coupling of radiation with the plasma in an open trap is demonstrated, as well as the possibility to control the energy deposition profile by means of small variations of the current in the additional coils for two basic scenarios of electron cyclotron plasma heating, specifically, longitudinal launching of microwave radiation to the magnetic mirror region and trapping of obliquely launched radiation by the inhomogeneous magnetized-plasma column.

Nonstationary model of an axisymmetric mirror trap with nonequilibrium plasma

The DOL nonstationary model intended to describe plasma processes in axisymmetric magnetic mirror traps is considered. The model uses averaging over the bounce period in order to take into account the dependence of plasma parameters on the coordinate along the facility axis. Examples of calculations of trap parameters by means of the DOL code based on this model are presented. Among the features of the DOL model, one can single out two points: first, the capability of calculating the terms of the collision integral with the use of a non-Maxwellian scattering function while evaluating the distribution function of fast ions and, second, concerning the background plasma, the capability of calculating the longitudinal particle and energy fluxes in confinement modes with the particle mean free path being on the order of the trap length. The influence of the scattering function approximation used to calculate the collision integral on the solution to the kinetic equation is analyzed. The dependences of plasma parameters on the power of heating injectors and the length of the fast-ion turning zone are presented as calculation examples. The longitudinal profile of the fusion reaction rate in the case of a trap with a long fast-ion turning zone is shown to depend strongly on the input parameters of the model.

Influence of the shear flow on electron cyclotron resonance plasma confinement in an axisymmetric magnetic mirror trap of the electron cyclotron resonance ion source

Influence of shear flows of the dense plasma created under conditions of the electron cyclotron resonance (ECR) gas breakdown on the plasma confinement in the axisymmetric mirror trap ("vortex" confinement) was studied experimentally and theoretically. A limiter with bias potential was set inside the mirror trap for plasma rotation. The limiter construction and the optimal value of the potential were chosen according to the results of the preliminary theoretical analysis. This method of "vortex" confinement realization in an axisymmetric mirror trap for non-equilibrium heavy-ion plasmas seems to be promising for creation of ECR multicharged ion sources with high magnetic fields, more than 1 T.

High Beta Experiments in the GDT Axisymmetric Magnetic Mirror

This paper reports recent results from the Gas Dynamic Trap magnetic mirror device. Achieving plasma betas up to 60% provides a basis for extrapolating this concept to a fusion relevant 14 MeV neutron source for testing and validating materials applicable to fusion systems.

Development and Applications of Axisymmetric Magnetic Mirror Concepts

Recent results from Russia and Japan have sparked renewed interest in magnetic mirror concepts. The Russian Gas Dynamic Trap experiment achieved 60% beta in an axisymmetric magnetic mirror. The Japanese Gamma-10 experiment demonstrated the suppression of radial transport due to drift-wave turbulence. This paper describes the evolution of magnetic mirrors, identifies a number of methods to stabilize axisymmetric mirrors, and suggests areas of needed research. The simple axisymmetric configuration has applications ranging from a source for material testing with plasma and neutrons to a driver for fusion-fission hybrid to the possibility of a fusion power plant.

Development and Applications of Axisymmetric Magnetic Mirror Concepts

Development and Applications of Axisymmetric Magnetic Mirror Concepts

Influence of the radial profile of the electric potential on the confinement of a high-β two-component plasma in a gas-dynamic trap

One of the most important problems to be studied in the gas-dynamic trap (GDT) facility is the investigation of MHD stability and cross-field transport in a plasma with a relatively high value of β = πp/B2. Recent experiments demonstrated that the radial electric field produced in the plasma by using radial limiters and coaxial end plasma collectors improves plasma stability in axisymmetric magnetic mirror systems without applying special MHD stabilizers. The experimental data presented in this work show that stable plasma confinement can be achieved by producing a radial potential drop across a narrow region near the plasma boundary. Creating radial electric fields of strength 15–40 V/cm causes a shear plasma flow, thereby substantially increasing the plasma confinement time. When all the radial electrodes were grounded, the confinement was unstable and the plasma confinement time was much shorter than the characteristic time of plasma outflow through the magnetic mirrors. Measurements of cross-field plasma fluxes with the use of a specially designed combined probe show that, in confinement modes with differential plasma rotation, transverse particle losses are negligibly small as compared to longitudinal ones and thus can be ignored. It is also shown that, when the GDT plasma is in electric contact with the radial limiters and end collectors, the growth rate of interchange instability decreases considerably; such a contact, however, does not ensure complete MHD stability when the electrodes are at the same potential.

Wall stabilized high beta mirror plasma in a rippled magnetic field

A simple axisymmetric magnetic mirror may be MHD stable, provided that (1) a certain length of magnetic field has a series of ripples in it, (2) with isotropic pressure the plasma beta value is higher than 50%, and (3) the conducting wall is very close to the plasma surface. The theory and its physical picture are discussed, and a Sturm-Liouville form is presented as well as numerical results that illuminate the requirements of field structure and anisotropy.

Experimental observation of stabilization of an axisymmetric mirror at high beta with a nearby wall

A high β plasma is injected into an axisymmetric magnetic mirror. The β is varied principally by varying the midplane value of the magnetic field. The plasma fills most of the space inside of a conducting vacuum chamber. It is observed for a radially averaged 〈β〉>35% that the plasma is initially stable, while for 〈β〉<25% the plasma is initially unstable. The values of β required for stability are lower than those predicted from magnetohydrodynamic (MHD) theory.

X-Ray Measurements during Whistler-Mode Electron Cyclotron Resonance Plasma Startup and Heating in an Axisymmetric Magnetic Mirror

New measurements and analyses of whistler-mode electron cyclotron resonant heating (ECRH) startup and heating in an axisymmetric magnetic mirror are presented. Experimental studies of startup are presented which include the effects of initial neutral gas pressure on density and energy buildup rates, the effects of electron-beam-generated seed plasma on startup times, and a possible density threshold for the absolute whistler instability. Results of two types of analyses are presented. The first is a Fokker-Planck finite-element simulation the principal result of which is the prediction of the creation of a sloshing electron velocity distribution in the first 10 ?s after microwave power is applied. The second simulation uses rate equations to predict buildup, with rate coefficients based on a model sloshing-electron distribution function. Both results are consistent with experimental observations. Measurements of X-ray emission provided information about plasma transport, the sloshing electron spatial distribution, and the hot-electron average energy. The foil ratio technique gave average energies of 1-3 keV during whistler-mode ECRH, in agreement with afterglow measurements of hot electron decay. Possible applications of whistler-mode ECRH plasma production and heating are for plasma soft X-ray sources and plasma potential modification in tandem mirror machines.

Motion of charged particles in an axisymmetric magnetic mirror.

The basic features of the notion of charged particles in an axisymmetric mirror, when the magnetic field varies sinusoidally along lines of force, is examined and the diffusion rate for the magnetic moment near the loss cone is obtained.

Compatibility of Alfvén ion-cyclotron and magnetohydrodynamic stability criteria for an axisymmetric magnetic mirror

The stability of an axisymmetric magnetic-mirror cell surrounded by a conducting wall is studied using the sharp-boundary model. Depending on the ion pressure model p(B), magnetohydrodynamic (MHD) stability can be achieved in certain ranges at either high or low β. Suppression of the Alfvén ion-cyclotron microinstability requires the mirror cell to be short (length≲20 ion Larmor radii). Adiabaticity of ion orbits is then found to be a constraint that is difficult to satisfy. Within the approximations used in this paper, satisfaction of all constraints is achieved in only a small region of parameter space.

Efficient heating and confinement of ions in an axisymmetric magnetic mirror supplemented with DC electric field

Strong heating and improved confinement of ions have been observed in an axisymmetric magnetic mirror field supplemented with an electrostatic DC field across and along the magnetic field lines. The increased life time of ions is understood as trapping of ions in the electrostatic potential well in the magnetic mirror field. The efficient heating of ions results from thermalization through weak collisions and/or finite correlation time of the strong E*B type instabilities excited by the radial current flowing into the outer electrode. The ion temperature increases in proportion to VH2, the square of the applied DC voltage for heating.

Experiments on whistler mode electron-cyclotron resonance plasma startup and heating in an axisymmetric magnetic mirror

Whistler mode electron-cyclotron resonance heating (ECRH) has been performed simultaneously with whistler mode electron-cyclotron emission measurements on an axisymmetric magnetic mirror plasma. Results presented include a study of the early plasma startup phase and two instability phases, one believed to be caused by a whistler instability and another by magnetohydrodynamic (MHD) flute instability. Enhanced microwave emission at frequencies below the midplane electron-cyclotron frequency has been correlated with enhanced electron endloss during the whistler instability. Cyclotron emission spectra during the startup phase match predictions for a ‘‘sloshing electron’’ type distribution based on numerical modeling. This distribution also agrees with anisotropic distributions resulting from electron-cyclotron heating as predicted by Fokker–Planck computer simulations. Experimentally measured heating rates show good agreement with simplified analytical models based on stochastic heating.

Stability of an elongated axisymmetric mirror with an energetic axis-encircling ion component

The equilibrium and stability of a long–thin axisymmetric magnetic mirror with a nearly axis-encircling energetic ion component is presented. A local sufficient condition valid for arbitrary azimuthal mode number (m) is derived and numerically evaluated. The results indicate that the ion beam component is highly stabilizing in regions where the beam density is increasing outwards and destabilizing where it is decreasing outwards. The results also show the existence of a persistent coupling of the beam particles to the magnetohydrodynamic interchange mode for large m. This result disagrees with previous work which showid a decoupling of orbits and mode perturbations for large m. This disagreement is attributable to the special periodic nature of the nearly axis-encircling orbits in long and thin configurations and indicates that aperiodic or stochastic orbits whose gyrocentres have a minimum spread would be more effective in providing stabilization.

Interchange stability of an axisymmetric, average minimum-B magnetic mirror

An axisymmetric magnetic mirror with large diameter and easily variable mirror ratio is described. The magnetic field configuration is a simple mirror with an average minimum-B field region on the outer surface. Experimental results are given which demonstrate that the surface field region ensures interchange stability. Stability can be maintained with both positive and negative radial plasma pressure gradients provided that the product of the pressure gradient and specific flux volume gradient is positive.