Magnetic Mirror Machine Research Articles

Development of a new magnetic mirror device at the Korea Advanced Institute of Science and Technology

A new magnetic mirror machine named KAIMIR (KAIST mirror) has been designed and constructed at the Korea Advanced Institute of Science and Technology (KAIST) to study mirror plasma physics and simulate the boundary regions of magnetic fusion plasmas such as in a tokamak. The purpose of this paper is to introduce the characteristics and initial experimental results of KAIMIR. The cylindrical vacuum chamber has a length of 2.48 m and a diameter of 0.5 m and consists of three sub-chambers, namely the source, centre and expander chambers. A magnetic mirror configuration is achieved by electromagnetic coils with a maximum magnetic field strength of 0.4 T at the mirror nozzles and 0.1 T at the centre. The source plasma is generated by a plasma washer gun installed in the source chamber with a pulse forming network system. The typical discharge time is ~12 ms with a ~6 ms (1–7 ms) steady period. Initial results show that the on-axis electron density at the centre is 1019–20 m−3 and the electron temperature is 4–7 eV. Two parameters were varied in this initial phase, the source power and the mirror ratio, which is the ratio of highest to lowest magnetic field strength in the mirror-confined region. We observed that the increase of the electron density was mitigated for a source power above 0.2 MW. It was also found that the electron density increases almost linearly with the mirror ratio. Accordingly, the stored electron energy was also linearly proportional to the mirror ratio, similar to the scaling of the gas dynamic trap.

A magnetic velocity Verlet method

We discuss an extension of the velocity Verlet method that accurately approximates the kinetic-energy-conserving charged particle motion that comes from magnetic forcing. For a uniform magnetic field, the method is shown to conserve both particle kinetic energy and magnetic dipole moment better than midpoint Runge–Kutta. We then use the magnetic velocity Verlet method to generate trapped particle trajectories, both in a cylindrical magnetic mirror machine setup and for dipolar fields like the earth's magnetic field. Finally, the method is used to compute an example of (single) mirror motion in the presence of a magnetic monopole field, where the trajectory can be described in closed form.

Stabilization of magnetic mirror machine using rotating magnetic field

An increase in symmetry is observed for a low density non-collisional plasma, in a simple magnetic mirror machine, due to the application of external oscillating magnetic fields of 1.5 MHz frequency. The increase in symmetry is attributed to an increase in stability of the flute mode and is dependent on the field’s polarization and trap magnetic field strength.

Overview of ECR plasma heating experiment in the GDT magnetic mirror

This paper summarizes the results of experiments on electron cyclotron resonance heating (ECRH) of plasma obtained at the axially symmetric magnetic mirror device gas dynamic trap (GDT) (Budker Institute, Novosibirsk). The main achievement is the demonstration of plasma discharges with extremely high temperatures of bulk electrons. According to the Thomson scattering measurements, the on-axis electron temperature averaged over several sequential shots is 660 ± 50 eV with peak values exceeding 900 eV in a few shots. This corresponds to an at least threefold increase as compared to previous experiments both at the GDT and at other comparable machines, thus demonstrating the maximum quasi-stationary (∼0.6 ms) electron temperature achieved in open traps. The breakthrough is made possible with the successful implementation of a sophisticated ECRH scheme in addition to standard heating by neutral beams (NBs). Another important result is the demonstration of the significantly increased lifetime of NB-driven fast particles with the application of ECRH, leading to a 30% higher plasma energy content at the end of the discharge. All available data including the previously demonstrated possibility of plasma confinement with β as high as 60%, allows us to consider fusion applications of axially symmetric magnetic mirror machines on a realistic basis.

Experiments in the Hanbit Mirror Device with the Kinetic Stabilizer

The Hanbit device is a magnetic mirror machine which has a central cell, one anchor cell and one plug cell. The Hanbit device has been involved in a series of experiments on stabilization of the MHD flute type mode including stability experiments with a divertor. We have undertaken investigations to see if the Kinetic Stabilizer (KS) of R. F. Post can stabilize the MHD instability. According to the theory, by locating a stabilizing plasma pressure on the field lines at a region with a strong second derivative and large radius in the expanding field region outside the mirrors, the main plasma in the mirror central cell in regions with unfavorable field line curvature can be stabilized. The Hanbit KS uses microwave produced plasmas on field lines in the cusp tank region. Two coils on the cusp tank are configured to produce expanding field lines with a large positive radius of curvature. A 5-kW 2.45 GHz magnetron is used to produce the stabilizing electron cyclotron resonant heated (ECRH) plasma pressure in this region. Details of the experimental arrangement and stabilizing plasma parameters were previously reported. For normally terminating plasmas, a reduction in the instability duration has been observed and the range of density where the instability occurs has decreased. However, for higher density plasmas which disrupt due to an m=-1 instability, a prevalent m=+1 instability is removed while the duration of the m=-1 instability is increased.

Alpha Channeling in Mirror Machines

The injection of radio frequency waves can cool charged particles trapped in a magnetic mirror. This cooling effect relies upon waves with azimuthal and axial phase velocities resonating with ions in different axial locations. The ions are then forced to diffuse along highly constrained orbits, such that they can only exit the magnetic trap at low energy. This cooling effect may have application to magnetic fusion mirror machines, where the free energy of the fusion by-products, the alpha particles, might be channeled into the waves that effect the cooling, thereby both extracting the fusion ash quickly and making that energy available in a convenient form for more useful purposes.

The Measurements of Ion Currents and Ion Energy Distributions in the Hanbit Mirror Plasma Heated by ICRF

Ion cyclotron resonant heating (ICRH) experiments have been carried out on the central cell of the HANBIT magnetic mirror. In these experiments were tested startup, heating, electrostatic ion confinement and electric potential modification which makes use of the electron cyclotron resonant heating (ECRH).The ions heated by the wave are generally either reflected near magnetic field or are eventually disappeared into the loss cone. The small Faraday cup is used to measure the ions heated by the RF wave. End loss analyzers, types of electrostatic potential multi-grid Faraday cup have been used to measure the current and the axial energy distribution of ions escaping along magnetic field lines in the magnetic mirror machine. The change of the end loss ion current was shown to be consistent with the measured changes in the plasma potential when the ECRH occurred at the Plug region.

Design of a bolometer for Hanbit magnetic mirror device

We designed and constructed a metal-resistor bolometer to measure the total radiation of the plasma in the Hanbit device, a magnetic mirror machine at the Korea Basic Science Institute. The target parameters for the plasma, the duration of which was 100–500 ms, at the central cell were the ion energy of 1 keV, the electron temperature of 200 eV, and the electron density of 5×1012 cm−3. A preliminary test showed that the cooling time constant and the absolute sensitivity of the homemade bolometer were 12 ms and 0.031 V/mW, respectively; the sensitivity was calibrated using an Ar ion laser. A test run of the homemade bolometer in the Hanbit device produced a signal of ∼25 mW/cm2, which was equivalent to the total power loss of about 40 kW, for the input rf power of 200 kW.

X-ray imaging characteristics from a large spherically bent mica crystal (abstract)

A high vacuum x-ray crystal spectrometer was fabricated utilizing a large spherically bent mica crystal (2 cm×7 cm) and a x-ray sensitive charge coupled device camera to observe heliumlike neon spectra in the wavelength range from 13.4474 to 13.6980 A and heliumlike spectra of other low-Z elements, such as Mg and Al. The spectrometer was specifically designed for use at a low x-ray intensity magnetic mirror machine. The x-ray imaging characteristics of the large spherically bent mica crystal have been tested in the laboratory with an x-ray source, using the bremsstrahlung continuum. The results of these calibration measurements will be presented.

ECR ion source using slow wave structures

In this ECR ion source, the possibility of maintaining the plasma by slow wave structures (SWS), helical coil, and slotted line antennas, in the region where wce, wpe ≫ wrf (wce, wpe, and wrf are electron cyclotron, plasma, and microwave frequencies, respectively) is exploited. The plasma parameters, plasma density, and electron temperature are maximized by coupling microwave (frequency: 2.45 GHz; power: 650 W) at two places in a magnetic mirror machine (mirror ratio Rm ≂ 1.45) to obtain higher beam current. Initially, the plasma is produced by coupling microwave to SWS at the mirror throat. The microwave is coupled by exciting the dominant slow wave field component of SWS, using an E-plane horn antenna. Then the plasma is brought to the region wce, wpe ≫ wrf at the mirror throat by increasing the magnetic field. Simultaneously, the ECR region is shifted from mirror throat to the center where second microwave coupling is done at the resonant region using another horn antenna. The characterization of plasma parameters are presented for both helical coil and slotted line antennas. Enhancement of plasma parameters are observed in the present scheme. Also, the SLA is found to produce better plasmas (ne ∼ 7 × 1012 cm−3 and Te ∼ 12 eV) than the helical coil and hence the SLA is chosen for the ion beam characterization. The extracted ion beam current density in the present scheme is ∼25 mA/cm2 at 2-kV extraction voltage.

Characteristics of Hot Electron Ring in a Simple Magnetic Mirror Field

Characteristics of a hot electron ring are studied in a simple magnetic mirror machine. Hot electron rings (n≈1010 cm-3, T≈100 keV) are most effectively generated under two conditions, when the magnetic field on the axis of the midplane is set near the fundamental, or the second harmonic electron cyclotron resonance to the applied microwave frequency (6.4 GHz). The density profile of the hot electrons is observed to take a so-called ring shape. The radial-cut view of the ring, however, indicates an M-shape density profile, and the density of hot electrons on the axis at the center and is about one-half of the peak ring density encircling the axis. The hot electron ring is susceptible to a few instabilities which can be artificially triggered. With the instability generated, the hot electron ring is observed to transform into a filled cylinder in a few microseconds and then disappears.

Simulating Field-Reversed Magnetic-Mirror Fusion Devices

Array processing techniques are allowing physicists to program in FORTRAN and generate fast machine code. The simulations show close agreement with theoretically predicted results. Nuclear energy research at Lawrence Livermore National Laboratory indicates that field-reversed magnetic mirror machines may offer greater efficiency and higher electrical yields than current reactor designs. Since theoretical analysis of the FRM is difficult, they are modelling the ion kinetics and electron physics of a fusion plasma to analyze the buildup and decay processes that might be characteristic of an actual machine. They have developed a simulation that accurately models the developing current distribution and use an array processor to obtain faster run times. 13 references.

Control of Plasma/Wall Interactions in Tandem Mirrors

Data from the Tandem Mirror Experiment (TMX) and other recent research show how to control plasma/wall interactions in tandem mirrors (TMs). Based on current knowledge, plasma/wall interactions will not limit the performance of TM reactors-either at the end walls or the radial walls. Magnetic field expansion and gas pumping can be used to regulate the plasma conditions at the end wall. Specifically, in TMX the plasma density at the end wall was found to be approx. =2 x 10/sup 9/ cm/sup -3/, whereas the end-plug density was approx. =2 x 10/sup 13/ cm/sup -3/; also, the sheath potential at the wall (8 V) was <10% of the end-plug electron temperature. The ''natural divertor'' effect-by which positively charged plasmas in magnetic mirror machines exhaust particles and energy to the end wallcan be used to both control the plasma conditions at the radial walls and divert impurities to the end wall. These techniques, the data that support them, and needed areas of further research are discussed.

Open traps

Traps in which the plasma confinement regionis bounded along the lines of force of the magneticfield are customarily called open traps. The bestknownand most common type of open trap is theso-called 'magnetic-mirror machine' or 'mirror trap',suggested in the early fifties independently byG.I. Budker in the USSR and R.F. Post in the USA.Plasma confinement in the mirror trap is dueto the reflection of particles from the regions ofstrong magnetic field ('mirrors') at the ends of thedevice. These reflect only particles with sufficientlylarge magnetic moment. Particles with small magneticmoment freely fly out of the device so that a conical'hole' without particles, the loss cone, is formed inthe phase space.

Normal form for mirror machine Hamiltonians

A systematic algorithm is developed for performing canonical transformations on Hamiltonians which govern particle motion in magnetic mirror machines. These transformations are performed in such a way that the new Hamiltonian has a particularly simple normal form. From this form it is possible to compute analytic expressions for gyro and bounce frequencies. In addition, it is possible to obtain arbitrarily high order terms in the adiabatic magnetic moment expansion. The algorithm makes use of Lie series, is an extension of Birkhoff’s normal form method, and has been explicitly implemented by a digital computer programmed to perform the required algebraic manipulations. Application is made to particle motion in a magnetic dipole field and to a simple mirror system. Bounce frequencies and locations of periodic orbits are obtained and compared with numerical computations. Both mirror systems are shown to be insoluble, i.e., trajectories are not confined to analytic hypersurfaces, there is no analytic third integral of motion, and the adiabatic magnetic moment expansion is divergent. It is expected also that the normal form procedure will prove useful in the study of island structure and separatrices associated with periodic orbits, and should facilitate studies of breakdown of adiabaticity and the onset of ’’stochastic’’ behavior.

Electron and ion escape over a potential barrier in a mirror field

The problem of calculating the electron loss rate and the corresponding energy loss rate from a magnetic mirror machine having a positive potential has been examined and solved to a reasonable approximation by Pastukhov (1974). This approximation is followed to produce particle and energy confinement times for ions which can be readily utilized in the study of plasma confinement in tandem mirrors. It is shown that a single additional parameter, labeled C, can be incorporated into the appropriate equations to make them equally applicable to electrons and ions; C=1 for electrons and C= square root 2 for ions.

Current Expectations for Fusion Power from Toroidal Machines

The rapidly increasing effort to solve the problems of the controlled release of nuclear fusion energy has been stimulated by recent maturation of the science of plasma physics, especially in one area -- the confinement of plasma in closed magnetic fields. At the same time, significant experimental progress has been achieved with magnetic mirror machines, and a large toroidal theta pinch is under construction at Los Alamos. Enthusiasm is running high in groups working on laser-ignited fusion. Perhaps all of these approaches will lead to viable power systems. It seems to be generally accepted, however, that toroidal magnetic machines have the greatest probabilit-y of being first if not the only approach to succeed, and this paper restricts its attention to that category. Current theories correspond to experimental results in the laboratory, and predictions of these theories imply the possibility of successful thermonuclear reactors. At the same time increasingly more realistic studies of hypothetical fusion power stations carried out by laboratory, university, utility, and manufacturing personnel make them appear to be potentially of great economic interest. Serious problems still remain, but increasing government support leads many to expect a scientific feasibility experiment and a demonstration of thermonuclear burning of deuterium-tritium fuel before 1980.

Ion Cyclotron Instabilities in Short Mirror Machine Plasmas

An appropriate finite geometry theoretical model of a magnetic mirror machine is examined for ion cyclotron instabilities. The normal modes of the finite model are shown to be unstable even in the presence of large magnetic field gradients. The effect upon the ion cyclotron instability of particle mirroring is discussed. Electron Landau damping is shown to be stabilizing for these modes, but low mirror ratio machines will require high electron temperatures to stabilize instabilities at frequencies near the high harmonics of ωci.

Charged-Particle Containment in rf-Supplemented Magnetic Mirror Machines

We study the containment of particles in the loss cone of a magnetic-mirror machine by means of rf fields whose frequency slightly exceeds the maximum value of the ion cyclotron frequency within the plasma. We report computations which verify the adiabatic theory of this confinement system.

Experiments on Nonadiabatic Trapping of High Energy Hydrogen Ions in a Magnetic Mirror Machine

Ion cyclotron resonance heating and nonadiabatic trapping of the hydrogen ions are investigated using a magnetic mirror machine with a mirror ratio of 2. A high energy (150–450 eV) and low intensity (500 µA) hydrogen ion beam is injected along the magnetic lines of force and subjected to ion cyclotron resonance heating by a constant frequency (4.5 Mc/s) r.f. electric field at the midplane of the magnetic mirrors. Nonadiabatic trapping of the atomic and the molecular ions is observed distinctly. More than fifty percent of the injected atomic and molecular ions is reflected by the mirror field, the reflected ions having energies of 300–900 eV.