Axisymmetric Mirror Research Articles

Influence of the shape of a conducting chamber on the stability of rigid ballooning modes in a mirror trap

MHD stabilization of flute and ballooning modes in an axisymmetric mirror trap is studied under the assumption of strong finite Larmor radius effect that suppresses all perturbations with azimuthal numbers m⩾2 and makes the m = 1 mode ‘rigid’. The rigid mode can be effectively suppressed using perfectly conducting lateral wall without any additional means of stabilization or in combination with end MHD anchors. Numerical calculations were carried out for an anisotropic plasma produced in the course of neutral beam injection into the minimum of the magnetic field at the right angle to the trap axis. The stabilizing effect of the conducting shell made of a straightened cylinder is compared with a proportional chamber, which, on an enlarged scale, repeats the shape of the plasma column. It is confirmed that for convincing wall stabilization of the rigid modes, the plasma beta (β, the ratio of the plasma pressure to the magnetic field pressure) must exceed some critical value βcr2 . When conducting lateral wall is combined with conducting end plates imitating MHD end anchors, there are two critical betas and, respectively, two stability zones β<βcr1 and β>βcr2 that can merge, making the entire range 0<β<1 of betas allowable for stable plasma confinement. The dependence of the critical betas on the plasma anisotropy, mirror ratio, width of the vacuum gap between the plasma column and the lateral wall, radial pressure profile and the axial magnetic field profile is examined.

Soft X-ray wavefront sensing at an ellipsoidal mirror shell

A reliable `in situ' method for wavefront sensing in the soft X-ray domain is reported, developed for the characterization of rotationally symmetric optical elements, like an ellipsoidal mirror shell. In a laboratory setup, the mirror sample is irradiated by an electron-excited (4.4 keV), micrometre-sized (∼2 µm) fluorescence source (carbon K α, 277 eV). Substantially, the three-dimensional intensity distribution I(r) is recorded by a CCD camera (2048 × 512 pixels of 13.5 µm) at two positions along the optical axis, symmetrically displaced by ±21–25% from the focus. The transport-of-intensity equation is interpreted in a geometrical sense from plane to plane and implemented as a ray tracing code, to retrieve the phase Φ(r) from the radial intensity gradient on a sub-pixel scale. For reasons of statistical reliability, five intra-/extra-focal CCD image pairs are evaluated and averaged to an annular two-dimensional map of the wavefront error {\cal W}. In units of the test wavelength (C K α), an r.m.s. value \sigma_{\cal{W}} = ±10.9λ0 and a peak-to-valley amplitude of ±31.3λ0 are obtained. By means of the wavefront, the focus is first reconstructed with a result for its diameter of 38.4 µm, close to the direct experimental observation of 39.4 µm (FWHM). Secondly, figure and slope errors of the ellipsoid are characterized with an average of ±1.14 µm and ±8.8 arcsec (r.m.s.), respectively, the latter in reasonable agreement with the measured focal intensity distribution. The findings enable, amongst others, the precise alignment of axisymmetric X-ray mirrors or the design of a wavefront corrector for high-resolution X-ray science.

MCTrans++: a 0-D model for centrifugal mirrors

The centrifugal mirror confinement scheme incorporates supersonic rotation of a plasma into a magnetic mirror device. This concept has been shown experimentally to drastically decrease parallel losses and increase plasma stability as compared with prior axisymmetric mirrors. MCTrans++ is a dimensionless (0-D) scoping tool which rapidly models experimental operating points in the Centrifugal Mirror Fusion Experiment (CMFX) at the University of Maryland. In the low-collisionality regime, parallel losses can be modelled analytically. A confining potential is set up that is partially ambipolar and partially centrifugal. Due to the stabilizing effects of flow shear, the perpendicular losses can be modelled as classical. Radiation losses such as bremsstrahlung and cyclotron emission are taken into account. A neutrals model is included, and, in some circumstances, charge-exchange losses are found to exceed all other loss mechanisms. We use the SUNDIALS ARKODE library to solve the underlying equations of this model; the resulting software is suitable for scanning large parameter spaces, and can also be used to model time-dependent phenomena such as a capacitive discharge. MCTrans++ has been used to verify results from prior centrifugal mirrors, create an experimental plan for CMFX and find configurations for future reactor-scale fusion devices.

Effects observed in numerical simulation of high-beta plasma with hot ions in an axisymmetric mirror machine

We present the results of numerical simulation by two-dimensional hybrid particle-in-cell code of high-beta plasma with hot ions in an axisymmetric mirror machine. Two particular effects are discussed: the self-rotating of plasma with Maxwellian ions in regime of diamagnetic confinement and the excitation of axisymmetric magnetosonic waves in a high-beta plasma with sloshing ions.

Prospects for a high-field, compact break-even axisymmetric mirror (BEAM) and applications

This paper explores the feasibility of a break-even-class mirror referred to as BEAM (break-even axisymmetric mirror): a neutral-beam-heated simple mirror capable of thermonuclear-grade parameters and $Q\sim 1$ conditions. Compared with earlier mirror experiments in the 1980s, BEAM would have: higher-energy neutral beams, a larger and denser plasma at higher magnetic field, both an edge and a core and capabilities to address both magnetohydrodynamic and kinetic stability of the simple mirror in higher-temperature plasmas. Axisymmetry and high-field magnets make this possible at a modest scale enabling a short development time and lower capital cost. Such a $Q\sim 1$ configuration will be useful as a fusion technology development platform, in which tritium handling, materials and blankets can be tested in a real fusion environment, and as a base for development of higher- $Q$ mirrors.

Physics basis for the Wisconsin HTS Axisymmetric Mirror (WHAM)

The Wisconsin high-temperature superconductor axisymmetric mirror experiment (WHAM) will be a high-field platform for prototyping technologies, validating interchange stabilization techniques and benchmarking numerical code performance, enabling the next step up to reactor parameters. A detailed overview of the experimental apparatus and its various subsystems is presented. WHAM will use electron cyclotron heating to ionize and build a dense target plasma for neutral beam injection of fast ions, stabilized by edge-biased sheared flow. At 25 keV injection energies, charge exchange dominates over impact ionization and limits the effectiveness of neutral beam injection fuelling. This paper outlines an iterative technique for self-consistently predicting the neutral beam driven anisotropic ion distribution and its role in the finite beta equilibrium. Beginning with recent work by Egedalet al.(Nucl. Fusion, vol. 62, no. 12, 2022, p. 126053) on the WHAM geometry, we detail how the FIDASIM code is used to model the charge exchange sources and sinks in the distribution function, and both are combined with an anisotropic magnetohydrodynamic equilibrium solver method to self-consistently reach an equilibrium. We compare this with recent results using the CQL3D code adapted for the mirror geometry, which includes the high-harmonic fast wave heating of fast ions.

Wall stabilization of high-beta anisotropic plasmas in an axisymmetric mirror trap

The stabilization of the ‘rigid’ flute and ballooning modes both with and without the effect of additional MHD anchors in an axisymmetric mirror trap, with the help of a perfectly conducting lateral wall, is studied using a model pressure distribution of a plasma with a steep-angle neutral beam injection at the magnetic field minimum. The calculations were performed for an anisotropic plasma in a model that simulates the pressure distribution during the injection of beams of fast neutral atoms into the magnetic field minimum. It is assumed that the lateral wall is an axisymmetric shell surrounding the plasma that follows the shape of the magnetic field line and is placed at a certain distance to the plasma border. It has been found that for the effective stabilization of the modes by the lateral wall only the parameter beta (β, ratio of plasma pressure to the magnetic field pressure) must exceed some critical value β crit. When combined with the conducting end plates imitating the MHD end stabilizers, there are two critical beta values and two stability zones and that can merge, making the entire range of allowable beta values stable. The dependence of the critical betas on the degree of plasma anisotropy, the mirror ratio, and the width of the vacuum gap between the plasma and the lateral wall is studied. In contrast to the previous studies focusing on a plasma model with a sharp boundary, we calculated the stability zones for a number of diffuse radial pressure profiles and several axial magnetic field profiles.

An axisymmetric mirror device for studying confinement and instability.

We describe a magnetic mirror device, namely, the Keda Mirror with AXisymmetricity (KMAX), which aims to study new approaches to confine and stabilize the mirror plasma as well as basic plasma research. KMAX consists of one central cell, two side cells, and two end chambers at two ends of the device. For the central cell, the mirror-to-mirror distance is 5.2m, while the central cylinder is 2.5m in length and 1.2m in diameter. The plasmas are generated by two washer guns located in the end chambers, which subsequently flow into the central cell and merge there. The density in the central cell is usually adjusted by changing the magnetic field strength inside the side cell, and it ranges from 1017 to 1019m-3, depending on the experimental requirement. Ion cyclotron frequency heating with two 100 kW transmitters is routinely used to heat up the ions. Plasma controls mainly rely on configuring the magnetic geometry and rotating magnetic fields to improve the confinement and suppress instability. Routine diagnostics, such as probes, interferometers, spectrometers, diamagnetic loops, and bolometers, are also reported in this paper.

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.

Abrasive slurry jet machining system using polyurethane@silica core-shell particles for internal surfaces of axisymmetric x-ray mirrors.

Abrasive machining has been used for inner surface processing of various hollow components. In this study, we applied an in-air fluid jet as a precision machining method for the inner surface of an axisymmetric x-ray mirror whose inner diameter was less than 10mm. We employed an abrasive with a polyurethane@silica core-shell structure, which has a low density of about 1.2 g/cm3 and a relatively large particle size of about 15 µm. By using this abrasive, a practical removal rate and a smooth machined surface were simultaneously obtained. We performed figure corrections for an axisymmetric mirror and improved the circumferential figure accuracy to a sub-10nm root mean square level. To evaluate the machining performance in the longitudinal direction of the ellipsoidal surface, we also performed periodic figure fabrication on the inner surface of a 114 mm-long nickel ellipsoidal mirror. X-ray ptychography, an optical phase retrieval method, was also employed as a three-dimensional figure measurement technique of the mirror. The wavefield of the x-ray beam focused by the processed ellipsoidal mirror was observed with the ptychographic system at SPring-8, a synchrotron radiation facility. The retrieval calculations for the wavefront error confirmed that a sinusoidal waveform with a period of 12mm was fabricated on the mirror surface. These experimental results suggest that a nanoscale figure fabrication cycle for the inner surface consisting of jet machining and wavefront measurement has been successfully constructed. We expect this technique to be utilized in the fabrication of error-free optical mirrors and various parts having hollow shapes.

Fusion by beam ions in a low collisionality, high mirror ratio magnetic mirror

The classical problem of neutral beam ions slowing down in a magnetic mirror geometry is revisited to provide predictive capability for the new Wisconsin HTS Axisymmetric Mirror under development at the University of Wisconsin. A Fokker–Planck model named fast beam ion solver (FBIS) is developed to include the spatial non-uniformity of a physical mirror geometry. The mathematical framework allows for efficient orbit averaging of the pitch-angle scattering operator, and permits a determination of the axial profile of the ambipolar potential confining the electrons. The numerical results from FBIS are consistent with earlier work, but further show how mirror-ratio and a near square magnetic well optimizes the fusion gain. The numerical results are also applied to inform the conceptual design of WHAM++, a low capital-cost breakeven-class magnetic mirror device.

Investigation of the confinement of high energy non-neutral proton beam in a bent magnetic mirror

By using the particle-in-cell (PIC) simulation method, we studied how the proton beam is confined in a bent magnetic mirror. It is found that the loss rate of the charged particles in a bent mirror is less than that in the axi-symmetric mirror. For a special bent mirror with the deflection angle of the coils α = 45°, it is found that the loss rate reaches maximum value at certain ion number density where the ion electrostatic oscillation frequency is equal to the ion cyclotron frequency. In addition, the loss rate is irrelevant to the direction of the proton beam. Our results may be helpful to devise a mirror. In order to obtain the least loss rate, we may choose an appropriate deflection angle, and have to avoid a certain ion number density at which the ion electrostatic oscillation frequency is equal to the ion cyclotron frequency.

High-precision profile measurement method for axisymmetric aspheric mirror (invited)

High-precision profile measurement method for axisymmetric aspheric mirror (invited)

On the stability of small-scale ballooning modes in axisymmetric mirror traps

It is shown that a steepening of the radial plasma pressure profile leads to a decrease in the critical value of beta, above which, small-scale balloon-type perturbations in a mirror trap become unstable. This may mean that small-scale ballooning instability leads to a smoothing of the radial plasma profile. The critical beta values for the real magnetic field of the gas-dynamic trap and various plasma pressure radial profiles was also calculated. For a plasma with a parabolic profile critical beta is evaluated at the level of 0.72. A previous theoretical prediction for this trap was almost two times lower than maximal beta 0.6 achieved experimentally.

Теория и расчет электростатических электронных зеркал с учетом релятивистских эффектов

Using the central particle method, the equations of the trajectory of charged particles in an axisymmetric electrostatic mirror are obtained with an accuracy of the third order of smallness inclusive with account for relativistic effects. The conditions for spatial focusing and the coefficients of spatial aberrations in the Gaussian plane of the mirror image are determined with account for relativism. By means of numerical calculations, conditions for simultaneous elimination of spherical and axial chromatic aberrations are determined, taking into account relativistic effects, in an axisymmetric electrostatic mirror when the object plane of the mirror is aligned with its focal plane. It is shown that account for high particle velocities leads both to a shift in the position of the Gaussian image plane and a change in the focusing quality.

Design of Neutron Microscopes Equipped with Wolter Mirror Condenser and Objective Optics for High-Fidelity Imaging and Beam Transport.

We present and compare the designs of three types of neutron microscopes for high-resolution neutron imaging. Like optical microscopes, and unlike standard neutron imaging instruments, these microscopes have both condenser and image-forming objective optics. The optics are glancing-incidence axisymmetric mirrors and therefore suitable for polychromatic neutron beams. The mirrors are designed to provide a magnification of 10 to achieve a spatial resolution of better than 10 m. The resolution of the microscopes is determined by the mirrors rather than by the L/Dratio as in conventional pinhole imaging, leading to possible dramatic improvements in the signal rate. We predict the increase in the signal rate by at least two orders of magnitude for very high-resolution imaging, which is always flux limited. Furthermore, in contrast to pinhole imaging, in the microscope, the samples are placed far from the detector to allow for a bulky sample environment without sacrificing spatial resolution.

Fabrication and testing of high-performance all-metal neutron guides and axisymmetric mirrors by electrochemical replication

ABSTRACTNeutron scattering is one of the most useful methods of studying the structure of matter, with applications to biomedical, structural, magnetic and energy-related materials. Neutron-scattering instruments are installed around research reactors or accelerator-based neutron sources, and neutron guides are critical components of these facilities. They are neutron-transport optical devices consisting of state-of-the-art mirrors often tens of meters long. Here we demonstrate a novel fabrication method of all-metallic neutron guides and axisymmetric mirrors by electroplating from precision mandrels. The process allows for the fabrication of single-piece all-metal guides of prismatic and axisymmetric shapes. We also demonstrate supermirror guides and axisymmetric focusing supermirrors produced with the same technology. We present the fabrication and tests of the multilayer-coated replicated guides and optic and show that the mandrel is reproduced with high fidelity and reliability. Such supermirror optics will provide game-changing improvements in neutron techniques.

Analytical Potentials for the Efficient Simulation of Planar and Axisymmetric Ion Mirrors

In this paper, we obtained analytical equations for electrostatic fields of two-dimensional planar and axially symmetric mirrors with piecewise-constant and piecewise-linear potentials on electrode surfaces located symmetrically in parallel planes or on a cylindrical surface, in particular, in the presence of an additional end electrode. The results can be used for the efficient optimization of aberration properties of time-of-flight mass analyzers and electrostatiс ion traps with gridless ion mirrors based on both standard planar or ring-type electrodes with finite gaps between them and PCB plates.

Spontaneous multi-keV electron generation in a low-RF-power axisymmetric mirror machine

X-ray emission shows the existence of multikilo-electron-volt electrons in low-temperature, low-power, capacitively coupled RF-heated magnetic-mirror plasmas that also contain a warm (300 eV) minority electron population. Though these warm electrons are initially passing particles, we suggest that collisionless scattering—μ nonconservation in the static vacuum field—is responsible for a minority of them to persist in the mirror cell for thousands of transits during which time a fraction is energized to a characteristic temperature of 3 keV, with some electrons reaching energies above 30 keV. A heuristic model of the heating by a Fermi-accelerationlike mechanism is presented, with μ nonconservation in the static vacuum field as an essential feature.

Multidiagnostics investigation of the role of the magnetic field profile in a simple mirror trap

The impact of the magnetic field profile on the operations of plasma-based Electron Cyclotron Resonance Ion Sources (ECRIS) has been debated and investigated for a long time, and a summary is given by the collection of the so-called ``magnetic scaling laws'', i.e., some rules-of-thumb providing the optimal configuration of the axial and radial confining magnetic fields. Anyway, the optimal configurations have been found just looking at the output beam currents and charge states. Only recently, more advanced experiments have shown that the optimal performances are related to some ``islands in the parameters space leading to a dense, energetic but stable plasma. A general, systematic characterization of plasma density and temperature as a function of the magnetic scaling, and for different energy domains (i.e., for cold, warm, and hot electrons) is not yet available. This paper presents a multidiagnostics characterization of a hydrogen plasma heated by microwaves at around 6.8 GHz via Electron Cyclotron Resonance, and confined in an axisymmetric simple mirror magnetic trap. Investigation of plasma response to solely the axial field profile gives the unique opportunity to decouple the effect of simple mirror field from the radial components that are, usually, provided by a hexapole. Optical emission spectroscopy, Langmuir probe, and an x-ray silicon drift detector were simultaneously used to evaluate the plasma density and temperature in different energy domains, thus exploring the electron energy distribution function from a few eV to hundreds of keV. Plasma parameters have been measured as a function of the magnetic field profile (in particular by varying the ratio ${B}_{\mathrm{min}}/{B}_{\mathrm{ECR}}$), of the microwave power and of the neutral pressure. Furthermore, for the same scaling, the relative abundances of $H$ atoms and ${H}_{2}$ have been estimated. Data show smooth trends of electron density and temperatures versus microwave power and neutral pressure, but strong and even nonlinear responses as a function of the magnetic field profile variation, allowing us to connect semiempirical scaling laws to changes in plasma parameters.