Tandem Mirror Experiment Upgrade Research Articles

X-ray diagnostic for measurement of hot-electron power loss

A significant fraction of the power lost from a confined plasma can be carried by energetic electrons. When such electrons are incident on a probe or limiting surface, they produce thick-target x rays. It is shown that a properly filtered measurement of this x-ray flux is proportional to the electron-power loss, with little dependence on the electron loss mechanism and velocity-space distribution. The diagnostic was successfully implemented to study the radial loss of hot electrons in the Tandem Mirror Experiment-Upgrade. The method provides a very fast measurement of electron loss processes, and could therefore be useful in other areas of plasma research such as magnetic confinement in tokamaks, and inertial-confinement fusion.

Ion temperature measurements on TMX-U using a gridless electrostatic analyzer

A small retarding-potential analyzer was used on the Tandem Mirror Experiment-Upgrade (TMX-U) to investigate the radial profiles of ion temperature, density, and plasma potential during ion cyclotron resonance heating (ICRH). The analyzer uses the magnetic field of TMX-U, rather than biased grids, to prevent electrons from reaching the biased ion collector. The probe, the Radial Energy Analyzer (REA), has been inserted into the central-cell plasma at temperatures of 200 eV and densities of 3×1012 cm−3 without damage to the probe or major degradation of the plasma. This analyzer measured an increase in ion temperature from 20 to 150 eV with 60 kW of ICRH. The REA measurements agree with other diagnostics on TMX-U. A one-dimensional code was written to investigate the effect of space charge on the flow of ions inside the probe tip. The effect was found to be minimal, in agreement with experimental data.

Experimental beta limit in an average minimum-B tandem mirror

High density (non-thermal-barrier) operation in the Tandem Mirror Experiment Upgrade (TMX-U) is found to be restricted by a stability limit. This limit is observed in the ratio of the neutral beam sustained central cell beta βc to the hot ion beta βih in the minimum-B anchor cells at both ends of the central cell, qualitatively consistent with a flute interchange stability limit. The ratio is βc/βih = 5, over the range of 0.03 ≤ βc ≤ 0.22, with no apparent reduction due to ballooning at high βc. This is a factor of six below the standard magnetohydrodynamic (MHD) m = 1 stability theory prediction of βc/βih = 33 at βc ≤ 0.1, where ballooning corrections to flute modes are small. The discrepancy could be due to approximations in the theory; however, experimental data indicate that the stability limit is due to drift wave turbulence or to large-m MHD flute or ballooning modes. The experimental beta limit is nearly independent of the hot electron beta in the anchor cells, which is compatible with theoretical predictions that the hot electron beta will decouple from MHD activity.

Stable operation of an effectively axisymmetric neutral beam driven tandem mirror

A quiescent plasma is sustained for 80 energy confinement times by only gas fuelling and neutral beam heating in an axisymmetric region of the Tandem Mirror Experiment Upgrade (TMX-U). This plasma should be unstable because of the bad magnetic curvature and the absence of ion cyclotron heating which previously provided ponderomotive stabilization to sustain plasmas in bad-curvature regions of other axisymmetric mirror experiments. The TMX-U data are consistent with stabilization by a symbiosis between two mechanisms – line tying, which reduces the growth rate, and finite Larmor radius edge stabilization, which can result in quiescent operation.

Low-frequency stability analysis of the Tandem Mirror Experiment-Upgrade (TMX-U)

The paper presents an MHD stability analysis for low frequency modes observed in the Tandem Mirror Experiment-Upgrade (TMX-U). This MHD flute mode analysis emphasizes two key points concerning TMX-U: (1) the central cell E⃗ × B⃗ rotation, with appropriate radial boundary conditions, is a significant instability drive for the m = 1 mode, and (2) the anchor hot electrons decouple from the MHD dynamics. It is found that the stability predictions and the oscillation frequencies are consistent with the selected TMX-U mode of operation that has been analysed. The principal stabilizing effect of hot electrons is to introduce a negative charge uncovering and to increase the effective curvature of the anchor region so that the sloshing ions can have a stabilizing influence. Instability can occur when ion charge uncovering caused by the finite Larmor radius cancels the negative effects of the hot electron charge uncovering.

Scaling of plasma potentials in TMX-U with the end walls grounded

The scaling of the axial potential profile measured in the Tandem Mirror Experiment-Upgrade (TMX-U) is reported. These measurements were done with the end walls at ground potential. As predicted theoretically, the results suggest that a deep thermal barrier is achieved when the mirror confined electron fraction in the end cells exceeds 90% of the total density and when there is sufficient pumping of cold, potentially confined ions. In operation with shallow thermal barriers, a potential maximum near the inner turning point of the sloshing ions is frequently observed. The central cell confining potential associated with this local maximum is large enough to have a significant effect on the ion axial confinement time. Measurements of the total ion confining potential were difficult. There is evidence of classical scaling of the parallel particle confinement with the magnitude of the ion confining potential. However, in some cases, long axial confinement times are accompanied by enhanced ambipolar radial losses. These losses are interpreted as occurring in the population of passing ions. Finally, it is observed that the overall machine potential is determined by the plasma densities, the thermal barrier depth and the electron cyclotron heating power, consistent with theoretical predictions based only on collisional and radiofrequency diffusion of the electrons.

Simulation of ion confinement during ion cyclotron heating in the TMX-U tandem mirror

Particle and energy confinement of ions during ion cyclotron heating (ICH) in the centre cell of a tandem mirror is simulated by a Monte Carlo code. The interaction of the ion cyclotron wave with the ions is calculated using reduced equations of motion, and Coulomb collisions are modelled using a Monte Carlo algorithm. An axial electrostatic potential profile is generated by an iteration procedure, assuming Maxwellian electrons. The axial profile of neutral gas which fuels the ions from a localized gas box is determined from a neutral particle Monte Carlo code. Steady state calculations are reported for the Tandem Mirror Experiment Upgrade (TMX-U). The calculated energy confinement time τE is about twice that measured for off-midplane fuelling. The calculated τE can be decreased to the experimental value by either introducing extra gas at the ICH antenna to model the effect of ions striking the antenna or assuming anomalous radial loss. However, the enhanced radial loss also increases the end loss current well above that measured. Experimental and calculated τE agree more closely for midplane fuelling with heating from one antenna.

Detailed shape analysis of tandem-mirror end-loss-ion energy spectra

Equations have been derived for relating the shape of measured end-loss-ion energy spectra in tandem-mirror magnetic-fusion experiments to key plasma parameters. The authors assume a collisional central-cell ion distribution. Equation parameters include the end-cell peak potential, the potential at the end-cell inner mirror peak, the magnetic field at the peak-potential position, and the central-cell ion temperature. These equations have been used to obtain good fits to end-loss-ion energy spectra from the Tandem Mirror Experiment-Upgrade (TMX-U). An especially interesting application of this analysis is to TMX-U operating conditions where strong deuteron and proton end losses occur simultaneously. Independent fits to these two quite different spectra, using the spectra-shape equations, give the same value of peak potential. Such consistency gives credibility to the usefulness of this type of analysis.

Analysis of Langmuir probe measurements from the Tandem Mirror Experiment Upgrade (TMX-U)

A nonlinear least-squares curve-fitting routine has been used to analyze single-tip Langmuir probe measurements from the Tandem Mirror Experiment Upgrade during high-density (≊1×1012 cm−3) operation. This procedure provided estimates of uncertainties (variances) in the electron temperature and plasma density due to noise in the probe current. The electron temperature and plasma potential inferred from the fit were found to increase with the upper cutoff voltage used above a certain voltage. This effect appears to be due to a departure of the electron current from an exponentially increasing function for probe positions inside the limiter radius only. The fitted values for electron temperature and plasma density are consistent with previous measurements obtained with a double-tipped probe and the fitted values of space potential indicate a linear relationship with electron temperature.

Relationships between external neutral gas and radial plasma transport in mirror confined plasmas

Neutral molecular densities were measured just outside the plasma edge at 14 axial locations in the Tandem Mirror Experiment Upgrade (TMX-U). Bayard-Alpert gauges can be operated routinely as calibrated pressure gauges in magnetic fields between 0.3 and 0.7 T. The pressures at the outer turning point and at the midplane of the plug are moderately low, 1 × 10−6 torr, but during plasma operation the inner turning point pressure is as high as 2 × 10−5 torr. This high pressure is consistent with a wall reflux coefficient of approximately 14, assuming that local anomalous radial loss is the cause. Fokker-Planck modelling of the plasma densities with molecular and energetic atomic fuelling shows that this high inner turning point pressure does not account for the measured plasma densities. However, an as yet undetermined additional radial transport of sloshing ions with a 1 ms rate does produce agreement. Both measurements and modelling show that the charge exchange rate at the exposed sloshing ion turning points is high (0.5 ms), but the plasma is self-shielding for most of the remaining axial distance, and the bounce averaged, charge exchange radial loss time constant is 5 ms.

Axial potential profile measurements in TMX-U

The diagnostics used to determine the axial potential profiles in the Tandem Mirror Experiment-Upgrade (TMX-U) are described, together with the initial results of these measurements. The application of electron cyclotron resonance heating (ECRH) in the anchors is found to create high central-cell potentials. When the end walls are grounded, deep thermal barriers are created by the application of second harmonic ECRH. Rapid decay of these barriers suggests that they are formed by the presence of low temperature, magnetically confined electrons. Axial confinement of the central-cell ions is sometimes poor, even in the presence of a deep thermal barrier. Frequently, a potential maximum is observed near the inner turning point of the anchor sloshing ions. This potential is sometimes large enough to explain the reduced axial current from the central cell.

Franck–Condon energy spread in diagnostic neutral-particle-beam probes

Plasma potentials can be measured in open-ended magnetic-fusion experiments with neutral beams injected at angles within the loss cone. Beam atoms that are ionized by the plasma follow magnetic-field lines and leave the machine with energy equal to their original beam energy plus the potential through which they have dropped. These diagnostic neutral beams often are composed of hydrogen or deuterium, and they can have components with energy less than the full beam energy because of the breakup of diatomic and triatomic molecules. The Franck–Condon energy released in this breakup can create a considerable energy spread in these lower-energy components. Here experimental results for this spread are summarized, obtained while using neutral beams for plasma-potential measurements in the Tandem Mirror Experiment-Upgrade (TMX-U). These energy-spread results agree with theoretical estimates. This inherent energy spread is emphasized because it can be important in interpreting plasma-potential data obtained with neutral-particle-beam probes and because its existence is not always anticipated.

TMX-U thermal-barrier experiments

Thermal-barrier experiments in the Tandem Mirror Experiment Upgrade (TMX-U) are reported, along with progress made at the Lawrence Livermore National Laboratory in plasma confinement and central-cell heating. Thermal barriers in TMX-U improved axial confinement by two orders of magnitude over a limited range of densities, compared with confinement in single-cell mirrors at the same ion temperature. It is shown that central-cell radial nonambipolar confinement scales as neoclassical theory and can be eliminated by floating the end walls. Radial ambipolar losses can also be measured and reduced. The electron energy balance is improved in tandem mirrors to near classical, resulting in T/sub e/ up to 0.28 keV. Electron cyclotron heating (ECH) efficiencies up to 42%, with low levels of electron microinstability, were achieved when hot electrons in the thermal barrier were heated to average betas as large as 15%. The hot-electron distribution was measured from X-rays and is modeled by a Fokker-Planck code that includes heating from cavity radio-frequency (RF) fields. >

Determination of ambipolar radial transport from the particle balance in the TMX-U tandem mirror

Ambipolar radial transport (equal ion and electron flux) is not directly measured in tandem mirror experiments because the particle flow does not produce a net electrical current. The first absolute measurements of the ionization source in the Tandem Mirror Experiment Upgrade (TMX-U) plasma have been obtained. These have permitted the determination of the magnitude of ambipolar radial transport from the particle balance. Furthermore, comparisons of the source measurements with a Monte Carlo neutral transport code have shown reasonable agreement. Measurements of the particle balance under several operating conditions are presented. For some of these cases, the ambipolar radial transport is smaller than the other measured losses.

Ion microinstability at the outer sloshing-ion turning point of the tandem mirror experiment upgrade (TMX-U).

Since the start of TMX-U operations we have observed weak oscillations with a frequency approximately twice the ion-cyclotron frequency at the end-cell midplane. Recent results show that this instability is driven at the sloshing-ion outer turning point. We find that the sloshing-ion lifetime scales inversely with the instability amplitude. The sensitivity of this instability to the cold-ion density shows that this is a loss-cone instability. These results have important implications for mirror fusion experiments as well as solar and space plasmas.

Improved system for perpendicular electron-cyclotron emission measurements on TMX-U

Perpendicular electron-cyclotron emission (PECE) is used on Tandem Mirror Experiment-Upgrade (TMX-U) to diagnose thermal-barrier hot electrons (TH∼100–400 keV, yielding the time history of the temperature of these relativistic electrons. We describe an improved quasioptical viewing system for these measurements that uses high-sensitivity superheterodyne receivers at fixed frequencies of 60, 98, 130, and 196 GHz. The improved viewing and transport system consists of an off-axis ellipsoidal mirror that images the plasma onto a V-band conical collection horn, an overmoded circular waveguide ( 7/8 in. diam) that transports the radiation outside the vacuum vessel where the polarization is selected, and a high-absorptivity Macor beam dump to prevent internal wall reflections from entering the viewing system. A relativistic code is used to calculate optically thin PECE signals from relativistic electrons for various energy and pitch angle distributions.

Database tools for enhanced analysis of TMX-U data

A commercial database software package has been used to create several databases and tools that assist and enhance the ability of experimental physicists to analyze data from the Tandem Mirror Experiment-Upgrade (TMX-U) experiment. This software runs on a DEC-20 computer in M-Divisions’s User Service Center at Lawrence Livermore National Laboratory (LLNL), where data can be analyzed off line from the main TMX-U acquisition computers. When combined with interactive data analysis programs, these tools provide the capability to do batch-style processing or interactive data analysis on the computers in the USC or the supercomputers of the National Magnetic Fusion Energy Computer Center (NMFECC) in addition to the normal processing done by the TMX-U acquisition system. One database tool provides highly reduced data for searching and correlation analysis of several diagnostic signals within a single shot or over many shots. A second database tool provides retrieval and storage of unreduced data for use in detailed analysis of one or more diagnostic signals. We will show how these database tools form the core of an evolving off-line data analysis environment on the USC computers.

Optically thin perpendicular electron-cyclotron emission from hot electrons in TMX-U

Perpendicular electron-cyclotron emission (PECE) from relativistic (TH∼100–400 keV) hot electrons within the thermal-barrier region of Tandem Mirror Experiment-Upgrade (TMX-U) is detected at 35, 60, 94, and 98 GHz. For the operating regime of TMX-U, these signals are optically thin (τ≪1) and thus proportional to the radial hot-electron line density. A relativistic code is used to calculate the theoretical temperature dependence of the perpendicular emission coefficient, j⊥(ω, TH), for each of the detected frequencies. This dependence has been verified experimentally by x-ray measurements of the hot electron temperature, TH. The observed qualitative agreement demonstrates that optically thin PECE signals can be used to determine the temporal evolution of TH. An inability to absolutely calibrate the present PECE waveguide system has prevented quantitative agreement.

Neutral-particle densities outside the TMX-U plasma edge

Neutral molecular densities just outside the plasma edge are measured at 11 axial locations in tandem mirror experiment-upgrade (TMX-U). These densities are time dependent and vary greatly with different modes of TMX-U plasma operation. The densities are low in the ion-cyclotron resonance heated central cell because of plasma pumping. The density is high in the plug near the sloshing-ion turning point. These densities are measured with a combination of new retractable, and fixed, magnetically unshielded Bayard–Alpert gauges that can be oriented to provide calibrated operation in the high (7 kG) TMX-U magnetic fields. The role of the neutral density in simultaneously fueling and charge exchanging away the plug density is modeled using smoke, a Fokke–Planck code.

Diagnostic system for measurement of particle balance in TMX-U

Several diagnostics measure the particle sources and losses in the Tandem Mirror Experiment-Upgrade (TMX-U) plasma. An absolutely calibrated high-speed (0.5 ms per frame) filtered (6561 Å) video camera measures the total ionization source as a function of radius. An axial view of the plasma automatically integrates the axial variations within the depth of field of the system. Another camera, viewing the plasma radially, measures the axial source variations near the deuterium fueling source. Axial ion losses are measured by an array of Faraday cups that are equipped with grids for repelling electrons and are mounted at each end of the experiment. Unequal ion and electron (nonambipolar) radial losses are inferred from net current measurements on an array of grounded plates at each end. Any differences between the measured particle losses and sources may be attributed to ambipolar radial losses and/or azimuthal asymmetries in the particle-loss profiles. Methods of system calibration, along with details of computer data acquisition and processing of this relatively large set of data, are also presented.