Mirror Machine Research Articles

Plasma modeling of MFTF-B and the sensitivity to vacuum conditions

The tandem mirror machine, MFTF-B, is scheduled to begin operation early in 1987. We have developed a time-dependent plasma-modeling code to examine the expected operating parameters. Using this code, we studied the effect of vacuum conditions on the plasma in each region of the machine. In particular, this study specified the vacuum requirements to which the machine is being designed. We will present the details of our study together with the current design of the vacuum system.

Edge diagnostics for tandem mirror machines (invited)

The edge plasma in a tandem mirror machine shields the plasma core from cold neutral gas and impurities. A variety of diagnostics are used to measure the fueling, shielding, and confinement of the edge plasma in both the end plug and central-cell regions. Fast ion gauges and residual gas analyzers measure the gas pressure and composition outside of the plasma. An array of Langmuir probes is used to measure the electron density and temperature. Extreme ultraviolet (EUV) and visible spectroscopy are used to measure both the impurity and deuterium densities and to estimate the shielding factor for the core plasma. The linear geometry of a tandem mirror also allows direct measurements of the edge plasma by sampling the ions and electrons lost out of the ends of the machine. Representative data obtained by these diagnostics during operation of the Tandem Mirror Experiment (TMX) and Tandem Mirror Experiment-Upgrade (TMX-U) experiments are presented. Diagnostics that are currently being developed to diagnose the edge plasma are also discussed.

Instabilities excited by an energetic ion beam and electron temperature anisotropy in tandem mirrors

The theory of cross-field ion streaming instabilities is applied to the parameter regime of the end cells of the upgraded Tandem Mirror Experiment with neutral beam injection. The cross-field ion drift as well as the electron thermal anisotropy Te⊥>Te∥ provides the free-energy that drives various instabilities. Three instabilities, a nearly perpendicular propagating modified two-stream instability, an obliquely propagating ion–ion streaming instability, and an obliquely propagating electromagnetic lower-hybrid instability, have been identified. The first two waves are electrostatic and have the largest growth rate. For the actual operation conditions of the tandem mirror machines, it is found that the ion–ion streaming instability has the largest growth rate. When more energetic neutral beams become available, the two-stream instability may play the dominant role in the stability of these devices.

Observation of enhanced particle removal rates in pump limiter simulation experiments

The performance of particle removal schemes for density and impurity control in tokamaks and mirror machines depends strongly on the plasma parameters and local recycling near the plasma neutralizer plates and gas pumping ducts. The relationship between plasma density, electron temperature, ion energy and gas flow and particle removal rate through a pumping duct located near a plasma neutralizer plate has been experimentally investigated in the steady state plasma device PISCES. Results indicate that initially the particle removal by pumps at the end of the duct is proportional to the plasma flux to the plate. A nonlinear increase in the pumping rate occurs when the ionization mean free path for neutrals from the plate becomes less than the plasma radius. The transition from a transparent to an opaque plasma due to local ionization of the neutrals produced at the netralizer plate greatly enhances the particle removal rate by recycling of the neutral gas as it flows away from the neutralizer plate or out of the pumping ducts. Parameters were varied to determine the importance of “ballistic scattering” of higher energy ions from the plate, but no effects were found in these experiments.

New tandem mirror machine starts operation at MIT

New tandem mirror machine starts operation at MIT

Parametric instabilities near the ion-cyclotron frequency in an inhomogeneous plasma

A kinetic theory for the parametric instabilities of ion-cyclotron, drift-cyclotron, and drift-cyclotron-loss-cone modes of finite wavenumber in an inhomogeneous plasma is developed. The Vlasov equation is solved in guiding center coordinates for two types of equilibria, viz., Maxwellian and loss-cone velocity distributions. For flute modes (k∥=0) or modes with long parallel wavelengths (k∥vi∥<ω) the coupling coefficients are greatly simplified. Ion-cyclotron waves are seen to decay efficiently into low-frequency drift waves in tokamaks. In a mirror machine a high-amplitude drift-cyclotron-loss-cone mode of negative energy decays into low-frequency positive-energy modes, giving rise to explosive instability.

Evolution of the mirror machine

The history of the magnetic-mirror approach to a fusion reactor is primarily the history of our understanding and control of several crucial physics issues, coupled with progress in the technology of heating and confining a reacting plasma. The basic requirement of an MHD-stable plasma equilibrium was achieved following the early introduction of minimum B multipolar magnetic fields. In refined form, the same magnetic-well principle carries over to our present experiments and to reactor designs. The higher frequency microinstabilities, arising from the non-Maxwellian particle distributions inherent in mirror machines, have gradually come under control as theoretical prescriptions for distribution functions have been applied in the experiments. Even with stability, the classical plasma leakage through the mirror posed a serious question for reactor viability until the principle of electrostatic axial stoppering was applied in the tandem mirror configuration. Experiments to test this principle successfully demonstrated the substantial improvement in confinement predicted. Concurrent with advances in mirror plasma physics, development of both high-power neutral beam injectors and high-speed vacuum pumping techniques has played a crucial role in ongoing experiments. Together with superconducting magnets, cryogenic pumping, and high-power radio frequency heating, these technologies have evolved to a level that extrapolates readily to meet the requirements of a tandem mirror fusion reactor.

Effect of electron beam injection on DCLC instabilities in mirror machines

A model for the effect of an electron beam on the drift cyclotron loss cone (DCLC) instabilities in mirror machines is presented. It is shown that because of the ponderomotive force of the beamgenerated plasmons, the growth rates of the DCLC instability are modified substantially. The model explains some of the observations on the Constance mirror machine where the DCLC instability was found to be quenched by the injection of an electron beam.

Simulation Study on Sloshing Ion Formation and Sustainment of Associated Potential Dip in a Plug Cell of GAMMA 6

A Monte Carlo simulation on sloshing ion formation and the associated potential dip is described. It is shown in the GAMMA 6 tandem mirror machine that the sloshing ion distribution can be sustained for about 500 µs. The warm passing ions have a density depression in the region of the sloshing-ion density dip because of the acceleration due to the potential. This effect is included in the evaluation of the potential dip self-consistently. The potential dip is sustained for the duration of sloshing ion formation because the trapped cold ions obtain energy from the passing ions and escape from the potential dip.

ECRH in Tandem Mirror Machines

Electron cyclotron resonance heating (ECRH) is important in tandem mirror devices which incorporate thermal barriers to enhance plasma confinement. ECRH in the end cells generates hot mirror-confined electrons to form the thermal barrier and creates the plugging potential to reduce ion end loss from the central cell. Important considerations for heating include a) the proper choice of wave polarization and harmonic number for wave penetration and efficient absorption, b) the possibility for control of hot electron energy and anisotropy by spatially limited heating, and c) the particle feed for hot electrons due to RF trapping processes. Fokker-Planck and Monte Carlo computer codes are useful for understanding these effects. The Tandem Mirror Experiment Upgrade (TMX-U) was constructed to investigate plasma confinement for the thermal barrier mode of operation. We carried out experiments to generate the hot electrons that are required for the thermal barrier. Heating efficiencies as large as 30 percent were observed. By combining the hot electron population with neutral-beam-injected hot ions and ECRH at the location of the desired potential peak, we strongly reduced the end loss of ions and measured plugging potentials up to 700 V. These results are consistent with the thermal barrier model.

Driven Current Tokamak (DCT) Scoping Study

The present Department of Energy (DOE) plan calls for the construction of an Engineering Test Reactor (ETR) that is to be the last major experimental fusion device prior to the commercialization of fusion power. The plasma driver of the ETR is to be either a long-pulse tokamak or a tandem mirror machine. The possibility of using the Tokamak Fusion Test Reactor (TFTR) facility to consolidate the physics and technology database for the tokamak version of the ETR has been considered. This paper addresses two of the options being considered: (1) a superconducting toroidal field (TF) coil-hydrogen plasma alternative, and (2) a superconducting or hybrid TF coil-high Q alternative. Both options assume essentially steady-state operation through the application of rf current drive. The options are evaluated on the basis of performance and cost determined by application of the Fusion Engineering Design Center (FEDC) Tokamak System Code.

Quasilinear theory of suprathermal ions in mirror machines in the presence of radio-frequency fluctuations

A theory of fast-ion generation in the 2XIIB mirror experiment due to a single resonant electrostatic ion-cyclotron mode is presented. Assuming weak radial gradients of the magnetic induction, which appear to be consistent with experimental data, it is shown that ions with small parallel excursions can be accelerated into the 40 keV region. Allowance for a periodic temporal variation of the amplitude of the mode results in stochastic motion of those ions whose range of parallel excursions form a limited but significant fraction of the plasma length. The diffusion coefficients of this class of ions are computed in the quasilinear approximation. The corresponding diffusion times are in reasonable accord with those from the experiment.

Stabilization of ion cyclotron turbulence in mirror machines

The saturation level of ion cyclotron turbulence in mirror machines is examined by using the perturbed-orbit formalism. The non-linear effects give rise to the perturbation of the orbits and are represented by a turbulent diffusion that leads to the saturation of the unstable modes. For 2XIIB, the calculated saturation level agrees well with the observed values.

Emission, absorption, and tunneling of whistler waves in an inhomogeneous magnetic field

Measurements of electron cyclotron emission parallel to a magnetic field in the regime where finite density effects are important and measurements of electron cyclotron wave tunneling parallel to a magnetic field are reported. The experiments were conducted in a low-temperature (Te ∼2 eV) moderate-density (ne =3×109–3×1012 cm−3) gas discharge plasma in a magnetic mirror geometry. Experimental results are compared with two models, both of which employ Kirchoff’s law to relate emission and absorption. In one model, absorption from hot-plasma theory is calculated and in the other a cold-plasma Budden tunneling type analysis is employed. Both models are in reasonable agreement, with the data generally bracketing the experimental results, and the experiment could not resolve which model is superior. The utility of whistler mode cyclotron emission as an electron temperature diagnostic measurement on mirror machines is confirmed.

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.

Surface magnetic confinement in toroidal and linear mirror systems

Plasma confinement by surface magnetic (SURMAC) fields is presented for toroidal multipole and linear magnetic mirror systems. The toroidal system is the Dodecapole Surmac device where stable confinement of high temperature ( T i∼500 eV), high density ( n∼10 13 cm −3), and high β (∼8%) plasma is demonstrated. No ballooning mode exists even at β=8% and the plasma is stable. Guarding of internal hoop supports is investigated and the main loss area is around the field null, with a width of ∼2p ci. The loss through a guarded support is estimated to be 2.5% of an unguarded one. The Large Axisymmetric Mirror Experiment (LAMEX) employs surface magnetic field to stabilize a simple mirror while axisymmetry is maintained. This allows the mirror ratio to vary from conventional to rather high values (∼37) so that it is suitable for studying fundamental mirror physics. The main experimental findings are: 1. (1) Stabilization of interchange by surface fields in a mirror machine is demonstrated. 2. (2) Wavelengths of DCLC modes at harmonics of ω ci have been measured in the axial, azimuthal and radial directions. Their amplitudes depend on density (dielectric constant) and the free energy sources: pressure gradient and ion loss cone (determined by mirror ratio). The instability peaks at the location of the maximum density gradient and its frequency corresponds to the ion cyclotron frequency of the B field at a location where the magnetic field gradient is zero and resonant wave-particle interaction is optimal. 3. (3) The multiple DCLC burst at , ω ci are observed to have increasing azimuthal wavenumbers as the zeroth order pressure gradient relaxes and the pressure gradient drift decreases. 4. (4) In the strongly collisional regime where the mean free path is less than one tenth of the length of the device, axial confinement time is proportional to the mirror ratio.

Current Status in, and Future Trends of, Ultraprecision Machining and Ultrafine Materials Processing

The historical progress of machining accuracy is plotted and its probable further development is shown by extrapolation, both in the micro-technology and nano-technology regions. Single point “mirror machining” of soft metals and the ultraprecision polishing of hard and brittle materials are discussed. The concept of “atomic-bit” chip removal first by elastic emission machining, etc. is introduced. Photolithography for LSI wafer processing and electron beam processing/lithography for IC photo masks are then described. Ion beam sputtering, a promising atomic-bit machining process for the near future, is also described. Finally, analysis is made of the problems to be addressed and solved in achieving true accuracies of 0.1 μm - 0.05 μm for electronic, optical and mechanical workpieces; measuring resolution and random errors in the required ultra-precision processing machines will have to be no worse than 0.01 μm (10 nm).

A Preshaping Transition Coil for a Small Minimum-B Magnetic Mirror

An additional coil between the plasma source and the mirror cell prefans incoming plasma to map it directly into the well-known twisted bow-tie shape and thus avoids reshaping drifts generated in conventional min-B mirror machines. This reduces vacuum chamber size requirements and eliminates any drift reshaping delay. Wound in series with the standard quadrupole loffe bar set, this dual-coil system features end connections which contribute no field on axis.

A Beam Waveguide Launcher for High Power ECRH Heating in Large Tandem Mirror Machines

We explore the possibility of applying a quasi-optical beam waveguide of the Cassegrain type as a launching system for RF heating of a fusion plasma. The plane wave required for proper operation of the Cassegrain antenna can be obtained from the azimuthally polarized TE0n gyroton output by means of, e. g., a horn reflector with a stepped-twist reflector mounted in its throat. Our launcher has the potential to keep the loss level extremely low, continue the outputs of a number of gyrotrons, and direct the radiation on the plasma in specific directions and polarization states.